I’m happy to publish this essay because it is filled with insights about how the Universe might work. Physicist Mark John Fernee spent his career thinking about and doing experiments to work out some answers that ring true, at least to me. I learned about him on Quora.
Since humans first grasped the idea that stars are not tiny holes in a tarp that shades Earth from Heaven, scientists have made progress toward resolution of questions both fundamental and mysterious which can finally be defended with logic and evidence.
Think about it.
Is a creator necessarily constrained by laws of physics to initiate the cosmos people see? Is a first cause necessary to start any Universe? What underlying reality hidden from science permits God to evade any concept of law to become the essential, fundamental, irreducible first cause of all that has ever been or ever will be?
People, a few of them, continue to believe that stars are pin-holes; Earth is flat, disease is demon-caused, and on and so on. These speculations are obviously false to anyone who tests them against dispassionate observation, which is the process called science.
Is the Universe deterministic? The answer to this question—should anyone know—might help answer whether anyone is truly free to decide. Can people make decisions unconnected to events that go back to some conjectured beginning or are they instead prisoners of delusions of freewill peculiar to all conscious life-forms like us?
What follows is an answer, first posted on Quora. I let it percolate on the site for months to absorb whatever reaction it might garner from interested folks. I wrote not only to learn from others but to make the idea of determinism comprehensible to the curious who can read.
Of course, I’m a Pontificator, not a credentialed scientist nor theologian nor philosopher. What I’ve learned—what I write—remains unvalidated by any expert or guild.
Added at the end of the essay is a link to one of many posts on Quora by Mark John Fernee about some of the science of determinism.
For the interested, click the link at the end of my essay to review some of Fernee’s thoughts on the physics of determinism. After reading, login to Quora to access readers’ comments and Fernee’s responses.
(Note: It will be necessary to visit several spaces on Quora to find every comment.)
Unusual insights hide in plain sight like Easter eggs.
Here goes my essay:
It might be difficult for intelligent, science-indoctrinated people to accept but the universe at all scales is most likely not deterministic and never has been.
Before folks who “know better” wander off to search for something more confirmational of their biases, I hope to convince a few of the more open-minded to reflect on a couple of stomach-churning examples.
After all, simple statistics suggest that some preordained percentage of readers will read on; a well-defined subset of those readers are certain to agree with my arguments, which might take any arbitrary form at all—depending on the vagaries of my imagination and what I ate for dinner, perhaps.
Sounds deterministic, doesn’t it?
Not really.
The truth is I have no idea what I will write before I write it. I’ve staked a position, which I intend to defend until I convince myself of its truth. Some predictable number will read and be likewise convinced.
Let me admit right now that I have no idea whether the universe is deterministic. I don’t know if my will is my own or someone else’s.
I don’t know who I am, where I am, what I am, or why I am. I don’t know what time it is. I don’t know where I’m going. I can’t remember where I’ve been. I have no clue what 99% of me looks like because it’s inside a place I can’t see. It’s never been photographed. I’ve seen no reflection or picture of almost all of me.
I don’t know how my brain works or why I’m conscious. I haven’t seen my brain. Doctors tell me I have one. They gave me some films from an MRI and told me the grey smears were it. I took their word. It’s puzzling because the universe inside my head seems larger—infinitely more vast than plate smudge.
I have ideas but 99% of them are likely to be mostly wrong. Why? Because my ideas come from somewhere else, and I alter them. I channel ideas but if you ask where they come from, I can’t say. I don’t know why I think and say and write the things I do.
Well, most of the time I think I know. It’s called being well-grounded. Yeah, that’s me. I’m grounded to a reality that makes no sense during those times when I think deeply about what reality might be.
Take blue for instance—the color. It’s a hallucination, right? It tells me nothing about the wavelength of light that triggers blue in my brain. I’ve never seen a photon, have you? When stripped of color, what might a photon be? I have no idea. Some say it’s an electromagnetic corpuscle with wave-like properties.
What the hell is that?
Who knows that galaxies are fragile? So are orbits of planets and moons. As are universes.
The Higgs field is unstable, right? It can undergo phase transitions. Scientists say it’s true. It’s like flushing a toilet. One moment the toilet is a stinky mess; phase transition is the sound of swirling water—a whirlpool that dumps all into the abyss. What returns is blue water and clean porcelain.
What will all that went before mean? Trillions of lifeforms found comfort in the mess. What kind of determination pushed the handle to upend the destinies of trillions of tiny creatures no human will meet or see?
Why do humanoids feel free to make arbitrary decisions if it isn’t true that they make them? Does it mean that everything they believe is a lie?
Has the Universe made us its fools?
I will tell you this: the thought has occurred to me that the Universe might be my fool. Without me to tell its stories it’s nothing but a dead thing with no past and no future.
Apart from conscious-life—in particular, my life—the Universe is simply impossible.
I don’t believe the consciousness we experience dies. It’s something foundational that everyone plugs into when they live. Somehow, we all live inside each other, and conscious life lives inside us. When we die our bodies abandon consciousness and decay away, but conscious life lives on into the past and future as it always has and always will.
Our bodies count for nothing. It’s why none have seen themselves. A quick, confirmational glimpse of this or that part of us is all we can hope for—then it’s gone.
A few months ago, I published 25 Answers to questions readers of Quora.com took time to ask me, because they trusted I knew what I was writing about. Yes, the world is easily fooled by pontificators posing as experts. I confess, I am one of them.
I am a bona-fide pontificator and intend to continue pontificating until I can no longer remember my name. For me, it’s art. My promise is truth, accuracy, and to fix screw-ups when someone points them out.
The response to my blog-bag of answers was underwhelming to the point where I wondered whether I should ever inflict another anthology of eclectic curiosities on any group of readers anywhere in the world.
Yes! I decided. Of course, I will. I love to read what I write!
When I forget what I once knew, I read the posts and remember how smart I was when I could remember stuff. It’s a good feeling. Someday I hope my grandchildren will understand why I don’t remember their names or how old they are. Someday I hope they will get what I’m talking about.
Brain-dead and happy is a wonderful combination, and I have it. Yes, I do. It is wonderful. I feel happy and content most of the time.
My mother had Alzheimer’s for years. It was a peculiar variation where she could remember twenty-five quips and jokes, which she repeated to anyone who would listen. Sometimes she wondered what was wrong with her. She asked about it, sometimes.
She always forgot the answer, but to the end she never forgot her repertoire of sure-fire laugh lines. Mom delighted us to the very end of her life, God bless her.
Anyway, I know stuff, and I’m no longer afraid to share. I would say I am becoming fearless.
This essay is a collection of 25 more questions that people from around the world have asked, and I have dared answer. My last Quora compilation was mostly math and physics. Not this time. Here answers focus more on politics, philosophy, religion, and other esotery.
Oh, I might slip a science or math question in here or there for nerds I know are out there who read my stuff and cling to every word.
Here goes.
1 – How is it “just” for jails to be privately owned in the U.S.?
Allowing private citizens to own the means-of-incarceration is as insane as it is unjust and undemocratic.
Since 1984, America has allowed people to sequester as much wealth as they can manage. The looting, cheating, and chicanery that followed has turned America into one of the most corrupt, cruel, and unfair countries the world has ever known.
The result is that now we have an associate of a powerful Russian cartel serving as our president. Are we really going to allow his friends to own our prisons?
Are we out of our minds?
The situation is far worse than you can imagine.
Billionaires run the media. You aren’t going to hear about ways of organizing our country that are in opposition to their consensus about how things should be done. What passes as “dissent” on shows like Rachel Maddow, for example, has the backing of some billionaire somewhere.
We don’t know the names of the people who run our country. They don’t run for office. They do buy the services of office holders on both sides of the aisle — GOP and Democrat. It’s disturbing, especially when people finally realize that they are at bottom mere slaves with no real power. If voting made a difference, would billionaires allow it? Would you, if you were rich? I don’t think so.
Even now, confidence in our electoral system is being undermined. Reality Winner, the NSA contractor who exposed Russian tampering with our election results, rots in jail; she can’t obtain bail. The media doesn’t cover her. They want us to forget all about her.
Keeping Reality incarcerated undermines confidence, because it makes it seem like the government has something to hide about our election process.
Elon believes (correctly) that the risk of a future human extinction event approaches certainty over a very short period of time that can be estimated to be in the hundreds of years or less.
Elon believes we are in a race against catastrophe; humans are special and must be protected; one way to reduce extinction probabilities for humans is to establish populations on other planets and moons.
There are 165 or so rocky (solid) bodies in the solar system with enough gravity that humans can walk on them. Places where large populations can survive are fewer than five and could be as few as absolute zero.
Mars has special problems for human survival which must be solved. It has no protection from high energy radiation and cosmic rays. It lacks a magnetosphere and the atmospheric gases like nitrogen and oxygen that are opaque to harmful rays and particles. Elon believes these problems will be solved and that risk of extinction can be reduced if we establish vigorous colonies there.
He has hope where most informed people do not. My hope is that we can avoid extinction on Earth, but volatile climate and frequent ice ages are difficult to overcome.
We also have new and unusual risks associated with our technologies —biological, nuclear, AI, totalitarianism, resource depletion, and runaway climate change.
Natural risks include asteroid strikes, super nova irradiation, and volcanism. These natural risks are likely to be the same (or larger) on other bodies in the solar system as they are on Earth.
Two human-like species are known to have gone extinct in the geological record. (Some anthropologists say it’s three.) Human populations experienced a near extinction event 70,000 years ago when the total population collapsed to less than 4,000.
I do not know what Elon Musk thinks about organized religion.
I see religion as a brake on the tendency of humans to kill each other, which history teaches has sometimes been effective and at other times not. Sometimes, strongly held religious beliefs lead to war.
On one thing humans agree: they love to fight.
3 – What is the greatest achievement in human history?
Blaise Pascal said that civilization advanced when people finally understood that being the son of a Queen did not qualify someone to be a King.
Nepotism kills civilizations and impedes human progress. An example is the president bringing in his family to manage the United States, presumably because loyalty trumps ability.
The cascading catastrophe that is enveloping us will soon teach anyone who is teachable that placing loyalty to a “king” above the ability to serve our country is one of the many roads that leads nations to ruin.
4 – Why is there a lot of woo-woo surrounding the double slit experiment?
If you shot a BB gun once every five minutes for two weeks at a steel plate that had cut into it two quarter-inch slits, you wouldn’t expect to find 25 or so tidy columns of holes in the wall behind when you were done. People who have done this experiment with atomic scale particles always say “woo” after, because the phenomenon makes no sense.
The mathematics to describe the phenomenon is the same as that used to explain wave-behavior. The problem is this: even if you shoot one wave packet at a time (using photons) instead of solid BB-like particles (like Buckyballs), no one expects that over a few weeks tidy columns will form on the back wall that look like wave interference. The reason for the pattern is a total mystery.
5 – What is the origin of geometric shapes (triangle, circle, cube, etc.)? If the universe was governed by different laws, would it be possible that these concepts would also be different?
People speculate about the origins of idealized shapes that don’t occur in nature (except approximately). People seem to crave symmetry. They don’t like cognitive dissonance, uncertainty, or ambiguity.
People who are dissonant-intolerant are easy to manipulate. Politicians prey on people’s discomfort by offering simple solutions in return for votes. The result is always disillusionment, because nothing involving people is simple.
Nothing in nature is simple, either.
Triangles, circles, and cubes seem simple because of their symmetries. They appeal to the simple-minded among us — which is 99% of the population, right? It might be 100% if mathematics and language are insufficient to understand ultimate reality.
Einstein had this theory that only mass and energy exist. They are equivalent; they are two sides of the same coin. Space and time are a consequence, not a cause.
Space-time was described by tensor-metrics, and the metrics show that space-time does not have to be flat.
Lines can be thought of as geodesics, which are “straight” only when the metrics of space-time are “flat”. When the metrics “curve” space-time (as they do near massive objects) parallel lines might be parallel in one place only, as lines of longitude on Earth are parallel in one place only — at the equator.
The laws of physics seem unlikely, because twenty or so constants in nature have been discovered that can’t be derived and seem to make no sense. All these constants have been revealed by experiments and seem to be irrational. One example is the constant “α” (alpha), which is discussed in the first link that follows this answer.
Stephen Hawking says that the odds of a universe configured like ours are 1E500 against, which is close to an infinity. But Stephen Wolfram says that at the heart of the universe is a simple algorithm. In his view the algorithm, should anyone ever discover it, will prove that our universe is the only configuration possible.
6 – What salary in the United States puts you in the top 10%, top 5%, top 2%, and top 1% in terms of salary?
All anyone needs to know about train-wreck America is that half of all black families live on less than $40K per year; half of all non-black families live on less than $75K per year. It’s hard to imagine that families can survive, let alone prevail, on so little income.
The USA is segregated by income and race. Poor people have no idea how easy life is for the wealthy; the wealthy don’t believe America has poverty.
I have five sons and one daughter. Only two of the six are in the top 1%. The most talented one, an assistant professor of kinetic art at a major university, is in the bottom half. His brothers give him money so he can get by.
7 – Modern humans appeared 200,000; civilization 10,000; and advanced technology 500 years ago. Why no advancement for something like 190,000 years?
Technology advances when survival demands it. Wars involving large populations did not become possible until about 3,000 years ago, because human populations were small.
Technology (to wage war) began to advance when population size increased; war technology percolated into the general population during peacetime.
70,000 years ago the human population collapsed to what some anthropologists believe was fewer than 4,000 individuals. The climb back took a long time because the world was in an ice age until 15,000 years ago or so. It has taken time to reach seven billion individuals.
The good news is that advances in technology and science are no longer driven by war, but by the preparation for war. Entertainment, comfort, convenience, and other factors drive inventors to bring clever technologies to peacetime populations.
Avoidance of war should become the highest priority of humankind from here on out, or we might suffer a catastrophic population collapse that would most certainly set back human development for hundreds of thousands of years.
Extinction is another possibility. At least two intelligent hominid species are known to have gone extinct during the past 200,000 years. There may be others.
Sorry for the short answer. The list of technologies and natural catastrophes that can annihilate homo sapiens is long. Click the following link to read about most of them.
8 – Should the USA build a competing Status-6 Oceanic Multipurpose System (Doomsday) Nuclear warhead?
Enough Pu239 has already been produced in weapons and processed from nuclear fuel rods to sterilize planet Earth of all life.
One country, Japan, has isolated 47 tons of Pu239 from fuel rods, is adding 8 tons per year, and has complained on NHK television that they don’t know what to do with it. Ten pounds is enough to make one atomic bomb.
Plutonium 239 is bomb making material. Japan has 94,000 pounds. It is producing 16,000 pounds per year. Twelve pounds makes one high-yield bomb.
The level of toxicity of Pu239 dust has recently become controversial. My understanding is the traditional one: the speck of brown dust that kills you, you will never see.
The half-life of Pu239 is 24,000 years. Risk studies (which include about a dozen hazards not related to plutonium) have shown that the chance that homo sapiens will survive a catastrophic population collapse during the next 24,000 years is less than one-in-a-million.
Humans cannot baby-sit all the plutonium that exists in facilities on every continent and keep life on earth safe from annihilation by contamination. The warheads and storage facilities are going to rot over time, and the earth will soak up the poisons left behind like vinegar in a sponge.
Doomsday is not a question of whether-or-not but of fast-or-slow. There is no upper limit to the size of a hydrogen bomb, so fast is doable. A rogue group with enough resources could construct a bomb powerful enough to obliterate Earth.
No one can undo the poisons that now exist, so slow is inevitable.
9 – What is the evolutionary reason that human beings are superficial and attracted to external appearances more than towards intrinsic qualities such as intelligence, character, integrity, honesty and virtuosity?
My reading and life experience tell me that humans are attracted to symmetry.
There could be any number of reasons, but it is easy to argue that symmetry seems to create less stress in those who encounter it, which may make them more receptive (and less reluctant) to mate with those who have it.
Reduction of cognitive dissonance is a major driver of conscious-life; symmetry seems to reduce dissonance in sentient beings like humans.
Interest by humans in mathematics and art seems to confirm, at least to my mind, that folks are driven to imbibe “harmonies” and “patterns” in nature; these symmetries provide them with reassurance that the world is not hostile and that happiness and reduction of stress is possible in the face of accidents, disease, and predators.
Intelligence, character, integrity, honesty and virtuosity are qualities that are not easily perceived and can even be illusory. People are good at feigning all these qualities to manipulate others to satisfy their needs — especially their sexual appetites and their desire for power over others.
Symmetry is not easily disguised (or the lack of it, even with good grooming) and can be an indicator of good mental and physical health, because symmetrical (attractive) people tend to have higher status and are in general less traumatized by mistreatment (on average) than people who do not have this physical quality.
People may mate with high symmetry individuals and later discover than the intangible moral qualities that they value in a life-partner are missing. Such a discovery can lead to separation, but meanwhile offspring have been spawned who have high levels of symmetry, and the process of selection for this quality continues unabated into future generations.
Yes, I have no evidence that this conjecture is correct; it’s not my field, but it seems to be a factor in the world I find myself.
10 – How does Russia stay on par with the USA in many high-tech military systems when their GDP and military budget is so small by comparison? Shouldn’t we be light-years ahead of them by now?
USA military spending is deceptive and classified.
The United States has 800 bases inside 70 countries. It is at war with every country that doesn’t do what it’s told.
Since the end of WW2, the USA has attacked one-fourth of the 195 countries on the earth. Depending on who counts, the USA has killed between 10 and 65 million people, most of them civilians. Injured people are uncountable.
The high casualty rates are due to the way it fights. The USA bombs the enemy to rubble, then moves in a few troops supported by large numbers of indigenous mercenaries to deny the rubble to the enemy.
Take two countries the size of the USA and put them side by side. The land area is less than Russia. Russia is huge. Its entire population is technically literate.
In the USA, only elites are educated. The vast majority of Americans are poorly trained, because public education is underfunded and neglected. Under the American system, education doesn’t generate profits for the wealthy, so they won’t support it.
Because America is segregated by race and income, it is difficult for visitors to get a sense of how poor the general population is. Wealthy Americans are in complete denial of the simple truth that their country is a train wreck for 75% of the people who live in it.
People with the money to travel don’t explore urban ghettos or rural wastelands. They don’t know things, nor do they want to know.
The USA has the world’s biggest and cruelest prison system for a reason.
Think about it.
Every country in the world, including Russia, is trying to avoid the wrath of the United States. They say nice things to us, so we won’t hurt them. They build as much deterrence as they can to avoid being attacked or embargoed.
11 – Has anyone considered leaving the USA because of the gun laws?
Anyone who has to carry a gun to feel safe is living in the wrong place. My recommendation is to move to safety ASAP.
The guns that many civilians own today inflict shattering injuries that no one who is shot can recover from. The slugs are high velocity and tumble. They are designed in non-conformance with the Geneva accords and are diabolical workarounds.
I would rather die myself than fire one of these weapons at another human being, no matter what they’ve done.
We have police and soldiers who are trained to inflict mayhem when necessary to protect civilians from human predation. Why not let them do their jobs while we civilians throw our war guns away?
Carrying a high-powered weapon into a wild area that is rife with people-eating predators might be a good idea under some circumstances. I don’t have a problem with defense-by-gun against wild animals who might be trying to kill for food or fun.
My recommendation is to travel in wild areas in a way that doesn’t unnecessarily encourage attack by dumb and innocent animals — because, can we face facts? — they don’t know any better.
Animals have a right to live in a natural way and not be provoked. People are smart enough to travel in the wild and avoid unnecessary contacts with carnivores.
12- What would happen to Hitler if he was captured today?
Well, I believe he would be released and featured in the next GOP presidential debates, win the Republican nomination, lose the popular vote by millions in the general election but win the electoral college, and become president.
As a lunatic with delusions of grandeur, he might do very well indeed.
I don’t think he would kill nearly a hundred million people like he did the last time around. It is more likely closer to two billion. But hey, that leaves five billion humans to abase themselves before him, so it would be worth it, right?
13 –Would you consider the USA a noble superpower when compared to other superpowers like Russia and China?
The billionaires who run the USA believe that private ownership is noble and that public ownership is ignoble. They are in a war against any form of socialism or collectivism.
Since the end of WW2, the wealthy have used the military power of the United States to attack one-fourth of the 195 countries on the earth to prevent a cascade of civilizations into communism. This war has, with a few exceptions, been enormously successful.
Today, they are fighting to consolidate their power. The billionaires of Russia, China, Israel, and the USA are dividing up the world like the New York City crime families of a few generations ago (watch the Godfather Trilogy or read the book by Mario Puzo).
Private ownership (called Capitalism) is a permutation of slavery that can be corrupting to democratic governance — as is obvious to any observer of U.S. history.
14 – How do you interpret human consciousness? Are you the center of the universe?
Consciousness is the fundamental and foundational principle of the universe. Conscious life plugs into this foundational consciousness in a way analogous to televisions plugging into a cable outlet. A television can be unplugged and replaced. But the cable programming continues. It is eternal. Consciousness is at the center of the universe. Conscious life is at the periphery.
15 – How would slavery have evolved in society if it was not seen as morally wrong?
“Capitalism” is the modern term for slavery. Owners of plantations, factories, and other businesses accrue the benefits of the plantation owners of former times.
Instead of providing slave quarters and food to their slaves, they pay a tiny stipend (called a minimum wage) to their laborers, which frees owners from the additional responsibility of caring for and protecting workers.
Putting the burden of housing, food, health care, and transportation on the backs of low-paid workers is called “freedom.”
The legal system disciplines unruly workers, while the state unemployment system helps dissatisfied owners replace those workers they believe are unfit.
For a small percentage of Americans, it’s a beautiful system.
Because the USA segregates workers both by race and income, most poor people don’t interact with the wealthy. This lack of contact between rich and poor reduces conflict and promotes peaceful living.
17 – Which among these countries is the best to live? Canada, USA or Australia? Why?
My question is, which country is the best place to live if you are poor? Most people are born poor.
If people go on living by being born again after they die, the odds that they will be born impoverished is high regardless of how well they lived in their prior life. That’s why its important to make the world a good place to live for impoverished people.
Does anyone seriously believe that they only live once? Consciousness continues somewhere, and it’s all there is, right? Absent conscious-life the universe can have no meaning.
I believe Cuba is the best place to live if you are poor, because it has a good climate and the government tries to provide services to ordinary people that are available only to the well-to-do in places like Canada, Australia, and the USA.
People might want to go to Cuba to find out how the poor live on that island. Then come back and observe how the poor live in their own countries.
The United States is segregated by income and wealth, so it’s hard to find poor people if you are rich, and if you are poor it is impossible to meet rich people.
18 – Trump wants to develop a lot of smaller, “tactical” nukes. Should the US use these against North Korea?
The USA bombed North Korea back to the Stone Age during the Korean War.
It killed an estimated two million civilians. The bombing was led by General Curtis LeMay of the Strategic Air Command who later partnered with George Wallace when he ran for president back in the 1960s and carried several states including Michigan (if I remember it right).
Wallace was a white supremacist. The Air Force’s own official historians have called LeMay’s bombing of North Korea the cruelest use of military power in world history.
This is the same General who destroyed 67 Japanese cities and burned their populations alive with napalm (fire-jelly) during WW2.
North Korea has done nothing to justify a military strike against its territory.
Nuclear weapons of any size or type should never be used in war, especially when there is nothing to be gained but the reputation for being a monster.
What does Korea have that we could possibly want? The answer is, nothing.
We have a choice to make: are we good or evil? Our destiny depends on how we answer that question.
19 – I am terrified of single-payer systems as implemented in socialist countries. Can this happen in the US? Was Obama trying to give everyone healthcare all along?
The USA is based on a slave system (now referred to as capitalism or free-market) where the owners of the plantations have doctors, which they share with their favorite house slaves. The field hands get nothing. The plantation owners are terrified that they might have to share their doctors with “unworthy” people should a slave revolt occur, so they have built the world’s most massive prison system to isolate slaves who might dare challenge the status quo.
In other words, people have to work for the right company and have the right job to get access to free health care. Very few do.
The system is so simple, a child can understand it.
Obama threw a wrench into the system by making it possible for people who work for the wrong companies (or who don’t work at all, for whatever reason) to buy access to health care for a reduced fee. Care is still expensive, but it’s not totally out of reach anymore for about three-quarters of the population.
In Cuba (for example) every neighborhood and apartment complex has a doctor assigned to it. What could be more effective than walking down the hall or across the street to be evaluated? If necessary folks are referred for further treatment to a hospital. Otherwise they get the meds they need, and that’s as complicated and inconvenient as it gets.
I grew up in a Navy family. We had free health care. If you got sick, you just drove to the base hospital and the doctors evaluated you. No paper work, no fees. It was a “single-payer” socialized system of medicine. It was better than what we have today as civilians except that protocols, equipment, and medicines are more effective today than they were sixty years ago when I was in that Navy system.
It’s hard for me to believe that this is a serious question by a serious person, but clueless people in the USA are subject to sophisticated behavioral modification protocols due to the immense amount of money that is involved in medicine and drugs, as well as guns, entertainment, food, and transportation.
So it isn’t surprising that people fear a lot of things that aren’t dangerous and are oblivious to dangers that are serious. It’s all about helping a relatively few families and cartels sequester the lion’s share of our nation’s resources.
Someday, maybe things will become more fair than they are now. I hope so.
20 – Why is it assumed that America invented slavery when slavery has been around for much of human history?
America practiced one of the cruelest forms of slavery. It is the only country in the western hemisphere where slave revolts were successfully suppressed.
Today, slavery has been renamed; it is called capitalism. In the USA, slaves are called workers and are free to live outside the gated communities of the wealthy. Workers are segregated by income to minimize the possibility of unrest.
The USA continues to prevent a successful slave revolt by maintaining the largest prison system by far that the world has ever known.
Two-thirds of white people came to America as slaves, called indentured servants. This practice started 150 years before the country became a constitutional republic and continued for many decades after. Indentured servitude was a seven year term of slavery that ended in freedom.
For Africans slavery was permanent. 100% of Africans came to America as slaves for life. There were notable exceptions. Billy Lee, George Washington’s slave and best friend, was set free when George Washington died; Billy Lee continued to live on GW’s Mount Vernon estate as a free man until his death.
22 – Is it true that until humans become one nation, we will never go further than Mars?
Organizing a human mission to Mars is expensive and dangerous. A coalition of nations might be able to manage the expense and risk.
Elon Musk’s company, SpaceX, is planning a Mars mission. I haven’t heard how the company plans to finance it.
Mars has an iron-nickel core like the earth, but it froze solid many millions of years ago. The magnetic field collapsed, which permitted the solar wind to blow away most of the planet’s atmosphere.
Any biological life forms on or near its surface will have to withstand the stress of continuous, high-energy radiation and the bombardment by cosmic particles with the energy of baseballs.
Travel to planets or moons as far as Jupiter and beyond will take many years.
Unless humans are heavily sedated, it is doubtful that they will be able to endure a journey of several years in a cramped space vehicle. They will lose muscle mass and possibly their sanity — certainly their perspectives that help them maintain a sense of normalcy.
Successful functioning by humans on an alien moon or planet after a journey of several years might not be possible no matter who organizes the trip or what precautions are taken.
23 – To Christians: Which scientific claims are incompatible with your faith, and why?
Science confirms my faith, because it seems to be saying that reality is mind-boggling; the odds against a universe constructed like ours with its unusual forces and constants seems to be infinite.
Jesus came to save the ignorant and the despised of the world, which is pretty much everyone. He avoided the subject of science altogether, for good reason.
No reasonable person can believe that the universe started with the big bang of a singularity that then inflated rapidly to create the conditions for conscious life with enough intelligence to understand its origins. That’s cray-cray, but it’s how some astronomers explain the universe.
Even with all we know, the underlying reality of existence remains a complete mystery. If Jesus came to Earth today, would he talk science to humanity?
I seriously doubt it. I don’t believe humans are hard-wired to understand how the universe works or what reality is. We evolved in an unusually safe place and time in the universe and carry with us all the peculiarities and idiosyncrasies that accompany our unlikely presence.
The Bible says plainly that one day people who have ridiculed God will be asked why they didn’t look up at the night sky and wonder why it is that they are so small and dark while the night sky is so large and bright.
How could serious people have missed such an important clue? How could anyone misunderstand their predicament and not concede the possibility that one day they might realize their hopes and dreams through the love of God who created, cares for, and protects them?
24 – Keeping the knowledge you have today, would you rather travel a thousand years into the future, or a thousand years into the past?
The risks to survival that faced individuals a thousand years ago far exceed the risks that people will face a thousand years from now—if humans survive another thousand years.
The counter-intuitive statistical reality is that the odds against species survival are actually higher than odds against survival of any individual human, should individual humans achieve viability during the next thousand years.
Most analysts of risk are suggesting that homo sapiens do not have much time left before extinction overwhelms them.
The geological record shows that at least two human-like species have already gone extinct. The particular species that thrives today (us) faces risks brought on by its technological expertise, which is certain to destroy it eventually.
I would choose to go forward in time, but I would do so with a great deal of fear knowing the old adage that curiosity kills the cat.
If everything turns out all right, the big question would be, how do uneducated, stupid people do in this new world?
Because uneducated and stupid is exactly what anyone will become who dares travel into a future one-thousand years more advanced than today.
25 – What are ways one can approach a complex idea that we don’t understand?
Complex ideas are of two kinds: ideas that one or more people understand but others don’t; and ideas which no one understands.
In the case where certain humans exist who understand a complex idea, the objective should be to learn what they know either by talking to them or reading what they have published. By this process, maybe folks can gather enough clues to guide them to further inquiries, which will lead eventually to understanding.
Many complex ideas require skills in certain subsets of knowledge like mathematics, languages, logic, philosophy, and the technical arts (such as metallurgy or whatnot) to make progress.
In the case where a complex idea can be demonstrated and stated but no one understands it (an example is “entanglement” in quantum physics), the approach is different. In these cases, it may not be possible to create a model of any kind in anyone’s mind to reduce the annoying dissonance that comes from not understanding.
People waste a lot of time — some go mad — trying to understand ideas no one understands or will ever understand. Most people seem to believe (in error, it seems to me) that everything can be understood if smart people work hard and are clever.
The idea, which I believe, is that complete understanding is not possible; it is a complex idea that no one understands, including me.
BONUS QUESTION 1 – In history, humans have fought and killed each other for every piece of land on the Earth. Why has the massive continent of Antarctica always been out of that conflict?
This absence of conflict may be coming to an end. A National Geographic reporter has been reporting on alarming developments in Antarctica over the past several years that the fake news has all but ignored.
BONUS QUESTION 2 – Why did mankind invent religion?
As far as I can tell, no records of an ancient civilization without religion have been discovered. I think that it is very scary to be suddenly aware that you exist and not know why — especially at night when wild animals roam freely, and the sky is full of lights that should not be there.
Editorial Board Recommendation: We are encouraging readers to visit Quora.com to read responses by Billy Lee (and others) to hundreds of questions asked by curious people from around the globe.
Two months ago, I discovered QUORA. It’s been around since 2009.
Since 2010, Quora has enabled people to ask experts questions about topics they like; even to answer questions on subjects they claim to know something about.
Quora is a site for geeks and nerds, and so far I like it. The people who hang out in the areas I hang out tend to be polite, kind, and smart. If they like someone, they follow them and are notified when they post. So far, ten people have signed on to follow me. It’s a start. I think most are from India.
During the first six weeks, 150 or so of my answers were viewed 35,000 times; I got nearly 175 “upvotes”, which enabled many of the answers to move to the head of the line. I wrote most answers in the wee hours between 2 AM and 7 AM when I couldn’t sleep. Insomnia inspired me.
What follows are 25 of the most popular answers I posted to the first 150 or so questions that caught my interest. They are sequenced by popularity — the most read first .
Why not read a few? How many questions can anyone answer? Not many, I’m thinking.
Who knows what you might learn?
What?
Someone thinks they know better than a pontificator with no bonafides?
I don’t think so.
No way! 😉
1) What are some of the most popular “mathematically impossible questions“?
Freeman Dyson — one of the longest-lived and most influential physicists and mathematicians of all time — argued that it is impossible to find a whole (or exact) number that is a power of two where someone can reverse its digits to create a whole number that becomes a power of 5.
In other words, , right? Reversing the digits to make 8402 does not result in an exact number that is a power of 5.
In this case, plus a lot more decimals. It’s not a whole (or exact) number. Not only that, no matter how many decimal places anyone rounds-off 6.09363… , the rounded number raised to the power of 5 will never return 8402 exactly.
Dyson claimed that this conjecture must be true, but there is nothing in mathematics that enables anyone to write a proof. He claimed that there must be an infinite number of similar statements—-each one true, none provable.
The Snowplow Problem is another “impossible” problem. My differential equations professor assigned it with the promise that anyone who solved it would receive a 4.0 grade, regardless of their performance on tests. I was the only student he ever taught who actually managed it.
The problem goes like this: It is snowing at a constant rate. A snowplow starts plowing snow at noon. By one o’clock the plow has traveled one mile. By two o’clock the plow travels an additional half mile. At what time did it start snowing?
It took me 3 days and two pages of calculations, but I got my 4.0.
Note from the Editorial Board: Over 50 people on Quora submitted answers to Billy Lee’s Snow Plow problem. One person had the right answer, but would not produce his proof. He did point out an unusual feature of the solution that Billy Lee had not noticed before. Billy Lee characterized the feature as ”very surprising.” When pressed Billy Lee refused to reveal the secret.
2) How much force is one Newton?
A newton is the force that an average sized apple makes on your hand when you hold it. No matter where in the universe you are; no matter on what planet you stand or how strong the gravitational field, a newton of force always feels the same.
A newton is one kilogram of mass that is accelerating at one meter per second per second. Gravity on Earth accelerates everything at nearly 10 meters per second per second. A kilogram of mass feels like 2.2 pounds on earth. One tenth of 2.2 pounds is 0.22 pounds or 3.5 ounces, which is the weight of a typical apple. The weight is the force that you feel against your hand. It is one newton.
On the moon, an object with the mass of a large brick would feel as light as an apple on earth due to the moon’s lower gravity. The force of the brick in your hand would feel like one newton.
3) . and .. What are x and y?
The simplest way to solve is to make y = (4-x) and create an equation in terms of x.
An easy version to create and solve is
You can solve it by hand using iteration or throw it into an app like Wolfram Alpha and let them solve it in a few seconds.
Either way, one value for x is .606098…. The other is 3.393901… , which you can assign to y. The two numbers add to 4.000… and when substituted into both initial equations return the right results.
4)If I had 1,000,000,000,000,000 times 1,000,000,000,000,000 hamsters floating in space in close proximity, would gravity turn them into a hamster planet?
Assuming the question is serious, it deserves a serious answer.
A typically fat hamster weighs around one ounce, which is about 0.03 kilograms of mass. The number of hamsters in your question is 10E30.
Multiplying the mass of a single hamster by this large number gives the result of 3E28 kilograms.
To compare, the mass of planet Earth is 6E24 kilograms. The mass of the proposed population of hamsters is 5,000 times the mass of the earth.
The sun contains 67 times more mass than the hamster population. If the hamsters are close enough together to hold paws, a hamster planet is almost certain. I haven’t worked out how long the process to congeal would take, but I can estimate that the hamsters would probably die of starvation before the inexorable forces of gravity completed their work.
The hamster planet would be formed mostly from three elements: hydrogen (64%), oxygen (33%), and carbon (10%). 3% would be trace elements like calcium and maybe lithium.
The most likely outcome, given enough time, is a planet-like object. The hamsters have only one-fifth of the mass to make the smallest of the smallest suns — red dwarfs, which populate 67 to 80 percent of the Milky Way Galaxy.
There are way too many hamsters to make a reasonably sized moon.
Their mass (3E28 kg) happens to fall on the border between the range of masses that are required to form celestial objects known as brown dwarfs and the less massive sub-brown dwarfs — sometimes referred to as free-floating planets.
Brown dwarfs don’t have enough mass to ignite like a star, but they do produce heat and can accept small orbiting planets. The chemistry of brown dwarfs is not well-understood and is a bit controversial.
It’s a toss-up, but my vote goes to the notion that the hamsters will eventually form a very large but ordinary planet — a free-floating planet — which I referred to earlier as a sub-brown dwarf. This hamster planet might wander through space for millions (or even billions) of years before being captured by a massive-enough star to begin to orbit.
Because the elements of hydrogen and oxygen are likely to become the constituents of frozen moisture (or water ice), there is the risk that the ice might melt into oceans and perhaps boil away if the hamster planet approaches too close to a star (or sun). In the case where the planet loses its water, a carbon planet with 50 times the mass of earth would form.
Otherwise, should the planet find itself in a far-distant future orbiting in the “goldilocks” zone around a sufficiently massive star, the water would not evaporate. Life could arise in the planet’s oceans. It’s possible.
Life-forms might very well crawl up out of the water and onto land someday where — over the eons and under ideal conditions — they will evolve into hamsters.
5) Why is evolution a valid scientific theory despite the fact that it can’t be conclusively proven due to the impossibility of simulating the millions-of-years processes that it entails?
Evolution is a fact that is thoroughly established by observations made in many disciplines of science. Changes in species happen fast or slow; in the lab and in the field.
The mystery is how one-celled life got established so quickly — it was solidly established within one billion years of earth’s formation. It’s taken 3.5 billion years to go from one-celled life to what we have now.
Why so fast to get life started; why so slow to get to human intelligence and civilization?
People have a lot of ideas, but no one is sure. Some life forms have orders of magnitude more DNA than humans. Only 2% of human DNA is used to make the proteins that shape us.
6) Why do cosmologists think a multiverse might exist?
Many high-level, theoretical physicists have written about the obvious problem our universe seems to have, which is that it has too many arbitrary constants that are too tightly constrained to be explained by any theory so far. No natural cause has been found for so many constants, so it’s fertile ground for theorists.
Stephen Hawking, among others, has said that the odds of one universe having the physics that ours has is 1E500 against. He is joking in his English way, because such a large number is essentially an infinity. It’s not possible to constrain a universe like ours by chance unless there are an infinity of choices, and we happen to be in the one that supports intelligent, conscious life.
Two ways of getting to infinity are the concepts of multi-verse and the new one proposed by Paul J. Steinhardt of Princeton University in 2013, which is based on data supplied by the Planck Satellite launched in 2003. Paul is the Einstein Professor of Science at Princeton, so his opinion holds a lot of weight.
Steinhardt has proposed that the universe is ekpyrotic, or cyclic. He has asserted that the universe beats like a heart, expanding and contracting in cycles, with each cycle lasting perhaps a trillion years and repeating, on and on, forever. Each cycle produces conditions — some which are ideal for life. This heart has been beating forever and will continue to do so, forever.
7) How will we visit distant galaxies if we cannot travel faster than light?
We will never visit distant galaxies, because they are too far away; most are moving away from us faster than our current technologies can overtake. At huge distances space itself is expanding, which adds to our problems.
The expansion of space is gradually accelerating. Any increase in performance by space vehicles over the next few thousand years is certain to be overwhelmed by the accelerating expansion of the universe.
As time goes on the amount of objects that are reachable (or even viewable) by earthlings will shrink.
On the happy side, our own solar system has at least 165 interesting places to visit that should keep folks fascinated for many thousands of years. A huge cavern has been discovered on Mars, for example, that might make a safe habitat against some forms of radiation dangers; it seems to be a place where a colony of humans might be able to live, work, and survive — perhaps even flourish.
Elon Musk is planning a mission to Mars soon.
8) What is the mathematical proof for a+a = 2a ?
Some things that are true can’t be proved. All math systems are based on axioms, which are statements believed to be true but which, in themselves, are not provable.
9) Can you explain renormalization in physics in simple words?
There is a problem in physics that has to do with the huge variation in scales between the very large and the very small. This problem of scales involves not only the size and mass of things, but also forces and interactions.
Philosopher Robert Pirsig believed that the number of possible explanations that scientists could invent for phenomenon were, in actual fact, unlimited.
Despite all the math and all the convolutions of math, Pirsig believed that something mysterious and intangible like quality or morality guided our explanations of the world. It drove him insane, at least in the years before he wrote his classic book, Zen and the Art of Motorcycle Maintenance.
Anyway, the newest generation of scientists aren’t embarrassed by anomalies. They have taught themselves to “shut up and calculate.” The digital somersaults they must perform to validate their work are impossible for average people to understand, much less perform. Researchers determine scales, introduce “cut-offs“, and extract the appropriate physics to make suitable matches to their experimental results.
The tricks used by physicists to zero in on pieces of a problem where sensible answers can be found have many names, but renormalization is one of the best known.
When physicists renormalize an equation, they cut away infinities and other annoying problems (like dividing by zero). They focus the range of their attention to smaller spaces where the vast differences in scales and forces don’t blow up their formulas and disrupt putative pairings of their carefully crafted mathematics to the world of actual observations.
It’s possible that the brains of humans, which use language and mathematics to ponder and explain the world, are insufficiently structured to model the complexities of the universe. We aren’t hard wired with enough power to create the algorithms for ultimate understanding.
10) If a propeller rotates at the speed of light at half of its length, what happens to the outer parts?
Only the ends of the propeller can rotate at near light speed (in theory). At half lengths the speed of the propellers will be half the speed of their ends, because the circumference of a circle is 2πr. (There is no squared term.)
So the question is: will the propellers deform according to the rules of the Lorentz transformation along their lengths due to the difference in velocity along their lengths?
The answer is, yes.
As you move outward along the propeller, it will become thinner in the direction of rotation, and it will get more massive. A watch will tick more slowly at the end than at the middle.
I am not sure how it would look to an outside observer. Maybe such a propeller would resemble in some ways the spiral galaxies, which don’t rotate the way we think they should. Dark matter and energy are the usual postulates for their anomalous rotations. Maybe their shape and motion is related to relativity in some way. I really don’t know.
In reality, no propeller can be constructed that would survive the experiment you describe. But in theory (and ignoring the physical limitations of materials) there would be consequences.
However, no part of the propeller will move at light speed or higher. Such speeds for objects with mass are impossible.
11) What is the fundamental concept behind logarithms?
The first thing that anyone might try to understand is that the word logarithm means exponent.
Example 1:
log 100 = 2 . What does this expression say? It says that the exponent that makes 100 is 2. What confuses people is this: exponent acting on what number?
The exponent acts on a number called the base. Unfortunately, the base is not written down in the two most common logarithm systems, which are log and ln.
The base for the log system is 10. In the example above, the exponent 2 acts on the base 10, which is not shown. In other words, , right? The exponent that makes 100 from the base 10 (not shown) is (equals) 2.
Example 2:
ln 10 = 2.302585… . What does this expression say? It says that the exponent that makes 10 is 2.302585… . Again, exponent acting on what number?
The base used in the ln system is 2.7182818… ,which is an irrational number that has an infinite number of decimal places. It happens to be a useful number in all branches of science and math including statistics, so mathematicians have decided to represent this difficult-to-write-down number with the letter “e”, which is known as Euler’s number.
The base for the ln system is e . In the example above, the exponent 2.302585… acts on the base e , which is not shown.
In other words, , right?
The exponent on e ( which is 2.7182818… and not shown in the original equation above) that makes 10 is (equals) 2.302585… .
All other logarithmic systems express the base as a subscript to the right of the word log.
Example 3:
This expression says: The exponent on seven that makes 49 equals 2.
12) Why do so many spiritual types have mental blocks about science and mathematics?
Everyone has mental blocks about science and math including scientists and mathematicians. Like the lyrics to the old song — people hear what they want to hear and disregard the rest — Einstein, to cite just one example, never accepted most of quantum physics even after it was well established and no longer controversial.
People don’t like the feeling of “cognitive dissonance”. The tension between strongly held beliefs and objective facts can bring unbearable psychological pain to most people. Someone once said that genius is the ability to hold contradictory ideas inside the mind. Most people don’t do that well; they don’t like contradictions.
Here is a link to an essay called Truth that some will find interesting:
Einstein said that time and space (i.e. space-time) depends on mass and energy, which are equivalent. In the absence of mass and energy, space and time are meaningless.
The most recent experiments by NASA have found no evidence that time is anything but continuous. However, the shortest time possible is the length of time it takes light to move the shortest distance possible, which is called Planck time. It is thought to be 5.39E-44 seconds.
Time can be divided into as many smaller increments as anyone wants, but nothing can happen in fewer than the number of intervals that add to 5.39E-44 seconds. Time is a variable that isn’t fundamental. It expands and shrinks in the presence of mass and energy.
Some physicists of the past suggested that the “chronon” might be the shortest interval of time. It is the time light travels past the radius of a classical (at rest) electron — an interval of 6.27E-24 seconds. Its calculation depends only on mass and charge, which can change if a particle other than an “at rest” electron is measured.
It seems to me that time is probably best thought of as being continuous. That said, it doesn’t mean that mass-energy interplay isn’t pixelated — much like a digital camera image. Pixelation is critical to a conjecture concerning the preponderance of matter over anti-matter — a conjecture described in the essay CONSCIOUS LIFE.
14) Which is bigger: or ?
Think of fractions as pies, which are all the same size. The bottom number is the total number of pieces into which each pie is cut. The first pie was cut into 5 pieces, which are all the same size. The second pie was cut into 9 pieces, which again are all the same size.
The second pie is cut into smaller pieces than the first pie, because there are more pieces. Right?
Mice come along and eat pieces from both pies. The top number is the number of pieces they left behind; the top number is the number of pieces the mice didn’t eat.
So which pie plate has more pie on it? Is it the 5 piece pie that has 3 pieces left or the 9 piece pie that has 1 piece left?
If you think hard you will figure out that it must be the first plate that has the most pie on it. Right?
15) Why is a third of 30 equal to 10 and not 9.999999999, as a third of 10 is 3.33333333?
You can make three piles of ten objects in each pile. When you count the total, it adds to exactly 30 objects. So the answer of “10” is demonstrably true, right? Three piles of ten adds to thirty.
There is no way to make three piles of any identical objects that adds to 10. Three piles of three adds to nine. Four piles of three objects adds to twelve.
We are required to make three piles of three objects and then add a piece of a fourth object to each pile that is smaller than a whole piece.
It turns out that the fourth object is 1/3 of a whole object. When these three piles of three objects plus 1/3 of an object are added up they equal exactly ten.
The problem in understanding comes from trying to grasp that 1/3 — when written as a decimal — is what mathematicians call a repeating decimal. The rules of arithmetic say that the decimal form of 1/3 is calculated by dividing “1” by “3”.
Following the rules of arithmetic when doing the division forces an answer to the problem that results in a repeating decimal — in this case, 0.333333… .
There is no way around these rules that keeps math working right, consistent, and accurate.
Sorry.
16) Will we be able to have life extension through cloning?
Cloning not only doesn’t work, it can’t work.
That said, the idea of cloning is to make a genetic replicant of an existing life-form. Extending life-span would require changes to the genome through other means involving changes to structures called telomeres, probably, which straddle the ends of chromosomes in eukaryotic cells.
A short discussion of cloning is included in the essay at this link: NO CODE
NO CODE is long (11,000 words), but explains in words, pics, graphics, videos, and links some of the complexities, misunderstandings, and dangers of current genetic-engineering at an undergraduate level. It explains basic cell biology, protein production, and much more.
17) Why does time slow down when we are on a massive planet or star like Jupiter?
Gravity is equivalent to acceleration. Accelerating clocks tick slower, according to General Relativity, which has been confirmed by experiments. It has to do with the concept of space-time and the fact that all objects travel through space-time at the same rate.
To understand, it helps to read up on space-time, special relativity, and general relativity. The concepts aren’t easy. The universe is an odd place, but it can be described to a somewhat fair degree by mathematics.
Some of the underlying reasons for why things are the way they are seem to be unknowable.
18) If the ancients had focused on science instead of religion, could we have become immortal by now?
Immortality is not possible due to the odds of accidental death, which at the current rate makes death by age 25,000 a virtual certainty for individuals.
Worse: the odds for extinction of the human species as a whole are much higher — it’s a near statistical certainty for annihilation within the next 10,000 years according to experts. It seems counterintuitive, but it’s true.
19) How do I solve, if the temperature is given by f(x,y,z) = and you are located at and want to get as cool as possible, in which direction should you set out?
You want to establish what the gradient is, establish its direction, then head in the opposite direction, right?
By partial differentiation the gradient is (6x – 10y + 4z), right? You don’t have to take another partial derivative and set it equal to zero to establish a maximum, because all the second derivatives of the variables are equal to one, right? You can drop the variables out and treat them as unit vectors like i, j, & k, correct?
The resulting vector points in the direction of increasing temperature, right?
Changing the signs makes a vector that points in the opposite direction toward cooler temperatures. That vector is (-6, 10, -4).
The polar angle (θ) is 71.068° and the azimuth angle (Φ) is 120.964°. The length (or magnitude) is 12.3288. Right? (We won’t use this information to solve the problem, but I wanted to write it down should I need to refer to it to respond to any comments or to help check my work graphically.)
These directions are from the origin, and you aren’t located at the origin. To determine the direction to travel to get to (-6, 10, -4), you need to subtract your current position. Again, for reference your location is .6333 from the origin at θ = 37.8636° and Φ = 30.9638°. Right?
After subtracting your position vector from the gradient vector, the resulting vector is (-6.333, 9.8, -4.5). Agree?
This vector tells you to travel 12.506 at a polar angle (θ) of 68.9105° and an azimuth angle (Φ) of 122.873° to intersect the gradient vector. At the intersection you must change direction to follow the gradient vector’s direction to move toward cooler temperatures at the fastest rate.
I haven’t graphed out the solution to double-check its accuracy. You might want to do this and let me know if you agree or not.
20) What is equal to?
The answer is zero, of course.
But not really. It only seems that way. Each number has three roots.
Depending on which roots are chosen the result can be one of six different sums (as well as zero if both roots are the same). We have to start somewhere so:
What is ?
i = . Right?
Therefore, a third root of i is . Right? It’s not the only root.
It’s the principal root. There are three third roots, which are equally spaced around the unit circle. Right?
It’s clear by inspection that to be equally distributed around the unit circle the other two roots must be and -i. Right?
Convert the three roots to rectangular coordinates and do the subtractions.
Here are the roots in rectangular form: (.86603 + .50000 i) , (-.86603 + .50000 i) , and (0.00000 -i).
Here are the six answers (in bold type) to the original question with the subtractions shown to the right:
These rectangular coordinates can be converted back to the Euler-form ( ). It’s easy for anyone who knows how to work with complex variables. In Euler-form the angle in radians sits next to i. The angle directs you to where the result lies on a unit circle. Right?
In fact, the six values lie 60 degrees apart on the circumference of a circle whose radius is the square root of 3. I don’t know what to make of it except to say that the result seems unusual and intriguing, at least to me.
As mentioned earlier, if both roots are chosen to be the same, then in that particular case the result is zero.
21) What is tensor analysis and how is it used in physics?
Understanding tensors is crucial to understanding Einstein’s General Theory of Relativity.
This question seems to assume that everyone knows what tensors are and how they are represented symbolically. It’s a good bet that some folks reading this question might want some basics to better understand the explanations of how tensors are used for analysis in physics.
If so, here are links to two videos that together will help with the basics:
22) What is the velocity of an electron?
Electrons can move at any speed less than light depending on the strength of the electro-magnetic field that is acting on them. Inside atoms electrons seem to move around at about one-tenth of the speed of light. You might want to check me on this number. The situation is as complicated as your mind is capable of grasping.
When interacting with photons of light electrons inside atoms seem to jump into higher or lower shells or orbits instantaneously. That said, it is impossible to directly observe electrons inside atoms.
On an electrical conductor like a wire, electrons move very slowly, but they bump into one another like billiard balls or dominoes. The speed of falling dominoes can be very high compared to the speed of an individual domino, right?
So, the answer is: it all depends…
23) What exactly is space-time? Is it something we can touch? How does it bend and interact with mass?
Spacetime, according to Einstein, depends on mass and energy for its existence. In the absence of mass and energy (which are equivalent), space-time disappears.
The energy of things like bosons of light — which seem to have no internal (or intrinsic) mass, right? — is proportional to their electric and magnetic fields. Smallest packets of electromagnetic oscillations are called photons.
Many kinds of oscillating fields, like electromagnetic light, permeate (or fill) the universe. In this sense, there is no such thing as nothing anywhere at any scale.
Instruments and tools of science (including mathematics) can give a misleading impression that at very small scales massive particles exist.
According to the late John Wheeler, mass at small scales is an illusion created by interactions with measuring devices and sensors.
Mass is a macroscopic statistical process created by accumulations of whatever it is that exists near the rock bottom of reality where humans have yet to gain access. These accumulations, some of them, are visible to humans; they seem to span 46 billion light years in all directions from the vantage-point of Earth and are displayed for the most part in as many as two-trillion galaxies according to recent satellite data by NASA.
Mass is thought to interact with everything that can be measured (including everything in the Standard Model) by changing its acceleration (that is, its velocity and/or direction), which is equivalent to changing its momentum.
It is in this sense that mass and energy are equivalent. Spacetime depends on mass and energy. Spacetime does not act on mass and energy; it is its result, its consequence.
Spacetime is a concept (or model) that for Einstein helped to quantify how mass and energy behave on large scales. It helped explain why his idea that the universe looks and behaves differently to observers in different reference frames might be the way the universe on large scales works.
His mathematical description of spacetime helped him build a geometric explanation for gravity that can be described for any observer by using tensor style matrices; many find his approach compelling but difficult computationally.
24) Hypothetically speaking, if one could travel faster than light, would that mean you would always live in the dark?
The space in which objects in the universe swim does expand faster than light when the expansion is measured over very large distances that are measured in light-years. A light year is six trillion miles.
At distances of billions of light years, the expansion of space between objects becomes dramatic enough that light begins to stretch itself out. This stretching lengthens the distance between the peaks and valleys of the electric and magnetic waves that light is made from, so its frequency appears to drop.
The wave lengths of white light can stretch so dramatically that the light begins to appear red. It’s called red shift.
Measuring the red shift of light is a way to tell how far away an object like a star is. As light stretches over farther distances the ability to see it is lost.
The wavelengths of light stretch toward the longer infra-red lengths (called heat waves) and then at even farther distances stretch to very long waves called radio-waves. Special telescopes must be placed into outer space to see these waves of light, because heat and radio waves radiating from the earth will interfere with instruments placed at the surface.
Eventually the distances across space become so great that the amplitudes (or heights) of the waves flat line. They flat-line because space is expanding faster than light can keep up. Light loses its structure. At this distance the galaxies and stars drop out of the sight of our eyes, sensors, and instruments. It’s a horizon beyond which the universe is not observable.
No one knows how big the universe is, because no one can see to its end. The expansion of space — tiny over short distances — starts to get huge at distances over 10 billion light years or so. The simple, uncomplicated answer is that the lights go out at about 14.3 billion light years.
Because there is no upper limit to how fast the universe can expand, and because the objects we see at 14.3 billion light-years have moved away during the time it has taken for their light to reach Earth, astronomers know that the edge of the universe is at least 46 billion light years away in all directions. Common sense suggests the universe might be much larger. No one has proved it, but it seems likely.
Over the next few billion years the universe that can be seen will get smaller, because the expansion of space is accelerating. The sphere of viewable objects is going to shrink. The expansion of space is speeding up.
The problem will be that the nearby stars that should always be viewable (because they are close) are going to burn out over time, so the night sky is going to get darker.
Most (4 out of 5) stars in the galaxy are red dwarfs that will live pretty much forever, but no one can see them now, so no one will see them billions of years from now, either. Red dwarfs radiate in the infra-red, which can only be seen with special instruments from a vantage point above the atmosphere.
Stars like our sun will live another 4 or 5 billion years and then die. The not-too-distant future of the ageless (it seems) universe is going to fall dark to any species that might survive long enough to witness it.
25) What does “e” mean in a calculator?
There are two “e”s on a calculator: little “e” and big “E”.
Little “e” is a number. The number has a lot of decimals places (it has an infinite number of them), so the number is called “e” to make it quick to write down.
The number is 2.71828… . The number is used a lot in mathematics and in every field of science and statistics. One reason it is useful is because derivatives and integrals of functions formed from its powers are easy to compute.
Big “E” is not a number. It stands for the word “exponent”, but it is used to specify how many places to the right to move the decimal point of the number that comes before it.
5E6 is the number 5,000,000, for example. The way to say the number is, “five times ten raised to the sixth power”. It’s basically a form of shorthand that means 5 multiplied by .
Sometimes the number after E can be negative. 5E-6 would then specify how many places to the left to move the decimal point. In this case the number is 0.000005, which is 5 multiplied by .
Bonus Question 1 – What difficulties lie in finding particles smaller than quarks, and in theory, what are possible solutions?
The Standard Model is complete as far as it goes. Unfortunately, it covers only 5% of the matter and energy believed to exist in the universe.
And humans can only see 10% of the 5% that’s out there. We are blind to 99.5% of the universe. We can’t see energy, and we can’t see most stars, because they radiate in the infra-red, which is invisible to us.
The Standard Model doesn’t explain why anti-matter is missing. It doesn’t explain dark matter and energy, which make up the majority of the material and energy in the universe. It doesn’t explain the accelerating expansion of the universe.
Probing matter smaller than quarks may require CERN-like facilities the size of our solar system, or if we’re unlucky, larger still.
We are approaching the edge of what we can explore experimentally at the limits of the very small. Some theorists hope that mathematics will somehow lead to knowledge that can be confirmed by theory alone, without experimental confirmation.
I’m not so sure.
The link below will direct readers to an essay about the problem of the very small.
Bonus Question 2 – What if science and wisdom reached a point of absolute knowledge of everything in the universe, how would this affect humanity?
Humanity has reached a tipping point where more knowledge increases dramatically the odds against species survival. Absolute knowledge will result in absolute assurance of self-destruction.
Astronomers have not yet detected advanced civilizations. The chances are excellent that they never will.
Humans are fast approaching an asymptotic limit to knowledge, which when reached will bring catastrophe — as it apparently has to all life that has gone before in other parts of the universe.
Everywhere we look in the universe the tell-tale signatures of advanced civilizations are missing.
We hope readers enjoyed the answers to these questions. Follow Billy Lee on Quora where you will find answers to thousands of unusual and interesting questions. The Editorial Board
To readers who cling to religious beliefs and ancient scriptures to keep themselves sane and inoculated against despair, I caution — please avoid this essay, if anyone can; if faith is fragile and belief not deeply rooted, why not watch a YouTube video or play a computer game?
What sense is there in exploring ways of thinking (and being) that might push the personality to unravel; that might introduce dissonance into the deepest recesses of the mind; that might, for example, induce lunatics — like suicidal lemmings — to throw themselves off cliffs of certainty into the swarming froth of oceans that want only to swallow them whole, to drown them in unfamiliar worlds of sea monsters and dark, incomprehensible dangers; to flood their lungs with the knowledge that every true thing they’ve ever learned is a lie?
Some of the smartest folks who have ever lived believe that we cannot die. No one dies; everyone lives — forever.
Some of these people would say that every person reading this essay right now is living in an afterlife; it’s an afterlife that began a very long time ago and will continue, in one form or another, forever.
OK. I warned you. Let’s get on with it.
First, some caveats. Paragraphs of caveats. The evidence seems overwhelming: all scripture in all religions was written long ago by savants who lacked — by today’s standards — education.
Scripture writers knew almost nothing about almost everything, except for those experiences unique to their personal histories, which they sometimes wrote about. Old texts written by ignorant (but smart) men are the parchment scrolls that religions always use as the foundational pillars of their creeds, doctrines, and world views.
It turns out that almost all religions promote the belief in an afterlife; the problem is that their ideas about afterlife make no sense; they don’t stand up under the scrutiny of a dispassionate examination by scholars using the methodology of science.
The Jesus of Christianity said He was God — imagine that. He was born to save the world, not judge it (as so many haters hoped he would), and to demonstrate to all the earth the sacred truth of the Bible, which says plainly that God is love.
The problem is, Jesus didn’t write anything down. A few of his male friends quoted what he said in short tracts they wrote, which were gathered together decades later into a collection that is now referred to as the Four Gospels of the New Testament.
We have to take their word. They were ordinary people; working people. They lacked credentials. Their little books, from a scholar’s perspective, are primitive and clumsily written. Their stylistic errors give their writing authenticity to a modern eye, but their understanding of theology seems confused, child-like, and kind of messy.
The value of the Gospels comes from the effort of the authors to quote from memory the amazing things Jesus said. Given the ignorance of the writers, their quotations have a miraculous lucidity, which adds weight to what they left to history.
The person who saved the New Testament for the scholar’s ear is the apostle Paul, a contemporary of Jesus whose letters make up the largest part of the volume of the New Testament; they delivered the credibility demanded by the cynical eyes of intellectuals and sceptics of all eras.
Paul was a bonafide biblical scholar — he trained under Gamaliel — and was arguably the greatest theologian who ever lived. He met Christ only once — on the road to Damascus. It was a few years after the resurrection. Paul was — along with many others at the time — on a mission from Rome to identify Christians; to arrest and turn them over to authorities for execution.
Paul’s encounter with Jesus left him blind. When his eyesight returned, he spent several years preparing. He then turned his learning and skills to the spread and growth of the new religion, which at the time was called THE WAY. Under Paul’s guidance, Christianity became a spectacular success during his lifetime. Today it is the world’s largest religion.
Since for me, Jesus is God, I don’t take any other religions seriously, though the non-Christian scriptures I’ve read are interesting — much of the writing is admittedly intelligent and enlightened.
Paul wrote many of the foundational documents of the new religion — considered by scholars today to be the most sophisticated Scriptural literature ever written. According to Paul (and other writers), what was unique about Jesus was that he claimed to have a personal knowledge of the afterlife, which he backed up by demonstrating an ability to heal people of intractable ailments and by bringing folks presumed to be dead back to life. The afterlife was real, at least for Him.
What is also puzzling — Jesus’s friends and family didn’t seem to grasp fully what He was talking about, most of the time. His closest friends (the Bible calls them disciples) followed their shepherd around like a flock of sheep, by most accounts, because feats of magic mesmerized them. His explanations were incomprehensible — right through to his crucifixion and resurrection.
Even after His resurrection, friends remained mystified. During meetings they expressed a joyful disbelief. After all, no one could survive crucifixion. Once the process started, it was a one way journey into Hell.
Survival was something that didn’t happen. Jesus’s friends couldn’t understand. Modern folks can’t help but garble what they think they know about what His friends thought they heard and saw.
If those closest to Jesus couldn’t grasp His Truth, why should modern people expect to do any better? Isn’t it a bit unrealistic to expect a modern person to have more insight than Jesus’s closest confidantes — his family and friends — who lived with him for many years and knew Him best?
Anyway, this essay is about the afterlife; it’s about what some discerning people think about it, how it might work, how people may want to plan for it, and how to protect ourselves from any consequences of not understanding it properly; of not taking it seriously.
This essay is going to unnerve some readers; especially Christians who are under the mistaken impression that they have everything figured out, because they once read and memorized John 3:16, for example, and they pray everyday.
I am probably going to take a few readers into an unfamiliar landscape — one that Jesus could not have described to primitive people. I don’t want to alarm anybody. Some readers might experience fear; a few may wobble off-balance as they feel the ground shake beneath their feet.
My intent is to strengthen the resolve of believers to make whatever changes are necessary to secure the future of humanity. Jesus said that he came to save the world, not judge it. He suffered on the cross so that those who belong to Him won’t burn in Hell, which is our destiny apart from the love of a friend who has the desire and courage to rescue us.
Jesus said that God is love, and that all people are evil. Humans — everyone of us — are haters, whether we are able to admit it or not. Wherever it is that God lives, it is no place for ordinary people; it’s off-limits to haters. People can’t live where God lives, unless they are born again into a new life that reshapes who they are at their core.
People, many of them, hate the very idea of God. They have no fear of the consequences of God’s love for the orphan and widow, the oppressed and downtrodden, the crippled and the malformed, the prisoner and the tortured, the blind and the deaf, the possessed and the mentally tormented.
They have no fear of hell — though the reality of hell lies on every side, they don’t see it. It doesn’t exist. It’s not something they feel compelled to fix. In modern minds — most minds, probably — the idea of hell is an absurdity; it can’t exist.
To be literally true, what Jesus is quoted by his friends to have said must make sense and be aligned with the reality we observe when people look up into a night sky full of stars or gaze into a drop of pond water teaming with microscopic life.
It can’t be any other way.
His words will always align with the facts we know to be true, which we discover sometimes by doing science; by living life; by suffering; by knowing people. If they don’t, then we’re missing something — I would argue that it’s always something important.
Jesus spoke truth to people who thought stars were the light of Heaven shining through pin holes in a tarp that covered the night sky; to them, mental illness was demon possession; ailments were caused by sin. Jesus cured the anguished; healed the broken; he spoke gently, with compassion and loving sorrow in his heart; but it was frustrating, possibly exasperating; it wore him down sometimes.
In AD 30, truth sounded like lunacy to most people because everyone was ignorant and worse; people were evil — every single one. No one knew what was real and what was pretend. Everyone was crazy, by modern standards. Rulers executed people for speaking truth, and today some still do. Every thinking person knows it’s true.
OK. Enough caveats, already. I want now to move away from the religion of two-thousand years ago and move boldly toward the understanding of reality that the disciplines of the sciences provide. I want to explain what very smart people (some of whom do not think of themselves as religious) imagine is the afterlife, how it might work, why it’s important, and how culture and society might be better fashioned to give every person the best chance to live free of despair and suffering.
Although this part of the essay will abandon religion and embrace science, the intent is not to cause believers to stumble; it is to wake believers from a slumber that threatens to make them impotent before the challenges to faith that are devouring America and many other parts of the modern world.
I want readers to think about how these ideas resonate with the words of Jesus — with His Truth — which is at odds as often as not with the religions of today, which by their works alone war with God’s love for human beings; war with Earth where all people live; war with the plants and animals that God gave people to comfort and protect with enlightened stewardship.
This essay offers a speculative view of science that aligns with the words of Jesus as quoted by the people who knew him best. It is very possibly dead wrong.
How could it not be? The smartest people not only don’t know what exactly is true, but truth itself, some humans have argued, might be unknowable. To his friends Jesus said, no, that’s not quite right — you will know the truth;andthe truth will set you free.
Set us free from what? Well, maybe religion, for one thing — and, hopefully, the fear of death, for another.
Speculation about truth by a pontificator? Well, readers can believe it or not. If faith is fragile, my advice is to stop right here. Hasn’t everyone read enough? Does anyone really want to learn anything new?
Who would ever endeavor to move out of their comfort zone? Does anyone believe that fate is certain; that the future of humankind might depend on how people behave, how they organize themselves, how they treat the most miserable among them, how they lift up the lowest rung of people, who Christ loves?
Some of the smartest psychologists, philosophers, and scientists — Nobel Prize winner Erwin Schrödinger who discovered the quantum wave equation was among the first — agree that it’s possible that consciousness might be a fundamental and foundational property of the universe. The smartest human ever, John von Neumann, wrote technical papers about it. Taking this view helped him to resolve many of the most aggravating paradoxes of quantum theory. Follow-on research by other brilliant scientists revealed that the problems of understanding consciousness seemed to become less daunting, as well.
I have written several essays about conscious-life and the sciences, which take readers on wild rides into the weeds of contemporary knowledge. These essays, some of them, are mind-blowing masterpieces that rummage through the garbage bins of modern science.
Click links at the end of this essay to take in more background and deeper understanding. Trust me. It will be fun.
This essay will gloss past the technical details of the science of life (because they can be found in related essays on this site). But I can begin by reminding readers that Schrödinger (and now others) believed conscious-life was something people plugged into, much like folks today plug their televisions into a cable box or connect their computers into a wireless modem for internet access.
People who think like Schrödinger are convinced that consciousness is imbibed by life forms; it’s something life-forms drink like living water; it isn’t located inside brains, although it is most likely processed there, possibly by dedicated but as yet not understood structures like the claustrum — or in tiny, sub-cellular structures called microtubules. No one knows.
When a computer breaks down and is dumped in the recycle bin, the internet doesn’t stop broadcasting. Cable news doesn’t stop when a television breaks down either. People buy a new computer, a new television; they keep watching; they keep playing.
Consciousness doesn’t stop when a human body dies. It keeps broadcasting — from its source. When a baby is born, it is thought by some to be hooked into this foundational consciousness that the universe itself depends on to exist and continue; like a child connected to her mother by placenta and umbilical cord, life continues uninterrupted; conscious life continues; life goes on.
Another way to think about it: imagine that people are swimmers in an ocean of consciousness — the ocean doesn’t depend on them. Swimmers who submit to the waves and the undertow and the currents — which together are too overwhelming to be controlled by anyone — find themselves floating along; sometimes they are tossed by the waves; sometimes the current pulls them in a direction they don’t want to go; sometimes the undertow sucks them under. Those who don’t fight the ocean do its will — automatically.
Whether they are living or dying, joy-riding or hanging-on terrified, the drowning swimmer rides the ocean and does its bidding. Those who fight — who depend on their own strength and will — exhaust themselves against the surf and drown in a frantic fit of futility, washed up on a random sandbar like rotting seaweed, separated from the sea and baking into dust under a blazing sun.
What happens when we die? Jesus said that our bodies count for nothing. If I’m understanding Him and properly applying the views of Schrödinger (and others), then our bodies have no value except as temporary storage devices for a piece of consciousness that is not, it turns out, entangled at birth with the foundational consciousness of the universe.
When the umbilical cord is cut, the newborn gets disconnected somehow. The mother expels the placenta, and the baby cries. Getting re-entangled might be a physical process that can preserve our lives and tie our destiny to that part of reality that is eternal and foundational. The Apostle Paul called entanglement reconciliation in his second letter to the Corinthians.
People who aren’t accustomed to thinking this way, might find it unnatural and unusual. Take a few on-line courses in quantum mechanics to absolve these notions, anyone who is experiencing them. Read some of the related essays in the list at the end of this post.
When Jesus said to people more primitive than us that he was the way, the truth, and the life — that no one can come to God except through Him — maybe he might better have described a concept like entanglement to a modern audience. Who really knows? Even modern people don’t understand physics; not most of them anyway.
Jesus did say: Because I live, you also will live. Someday you will realize that I am in my Father, and you are in me, and I am in you.
I know this: If consciousness is foundational to the physical reality of our universe; if — as Neumann argued in a technical paper — process operators he named I, II, & III are required to bring forth the universe we observe, then the consciousness that makes us feel alive must be entangled (or reconciled, as Paul put it) with one of these operators to enable anyone to survive and persist past the death of their body.
Can anyone imagine a scenario where tiny bubbles of conscious-life that were never able to successfully entangle themselves to God might be regurgitated at death into new persons, as some eastern religions profess? It would be a better fate than going to Hell, right? Maybe not.
In a world where most people live in deprivation and physical suffering, it is almost certain that a bubble of conscious-life that once occupied the body of a billionaire, for example, would by chance alone come to rest more often than not in a body debilitated by malnutrition, parasites, and disease.
If people thought that they were going to be born again physically into circumstances dictated by the statistics of a random distribution, they might not be so enamored by the privilege and prerogatives of power and wealth. Laissez-faire systems, capitalism and oligarchy, might be feared like the ancients feared Hell.
Maybe people — if they knew that they were going to be regurgitated into the world they expended their lives to build — would take more time to think seriously about what to do with orphans and widows, the oppressed and downtrodden, the crippled and the malformed, the prisoner and the tortured, the blind and the deaf, the possessed and the mentally tormented, because after all, in that universe — in that place where there is no Christ — it’s who they will be someday, chances are, in the afterlife.
Many smart physicists wonder about it; some obsess over it; a few have gone mad. Physicists like the late Richard Feynman said that it’s not something any human can or will ever understand; it’s a rabbit-hole that quantum physicists must stand beside and peer into to do their work; but for heaven’s sake don’t rappel into its depths. No one who does has ever returned and talked sense about it.
I’m a Pontificator, not a scientist. I hope I don’t start to regret writing this essay. I hope I don’t make an ass of myself as I dare to go where angels fear to tread.
My plan is to explain a mystery of existence that can’t be explained — even to people who have math skills, which I am certain most of my readers don’t. Lack of skills should not trouble anyone, because if anyone has them, they won’t understand my explanation anyway.
My destiny is failure. I don’t care. My promise, as always, is accuracy. If people point out errors, I fix them. I write to understand; to discover and learn.
My recommendation to readers is to take a dose of whatever medicine calms their nerves; to swallow whatever stimulant might ignite electrical fires in their brains; to inhale, if necessary, doctor-prescribed drugs to amplify conscious experience and broaden their view of the cosmos. Take a trip with me; let me guide you. When we’re done, you will know nothing about the fine-structure constant except its value and a few ways curious people think about it.
Oh yes, we’re going to rappel into the depths of the rabbit-hole, I most certainly assure you, but we’ll descend into the abyss together. When we get lost (and we most certainly will) — should we fall into despair and abandon our will to fight our way back — we’ll have a good laugh; we’ll cry; we’ll fall to our knees; we’ll become hysterics; we’ll roll on the soft grass we can feel but not see; we will weep the loud belly-laugh sobs of the hopelessly confused and completely insane — always together, whenever necessary.
We will get lost together. This rabbit-hole is the Krubera Cave of Abkhazia land. It is the deepest cave in the world. Notice the tiny humans, for scale.
Isn’t getting lost with a friend what makes life worth living? Everyone gets lost eventually; it’s better when we get lost together. Getting lost with someone who doesn’t give a care; who won’t even pretend to understand the simplest things about the deep, dark places that lie miles beyond our grasp; that lie beneath our feet; that lie, in some cases, just behind our eyeballs; it’s what living large is all about.
Isn’t it?
Well, for those who fear getting lost, what follows is a map to important rooms in the rather elaborate labyrinth of this essay. Click on subheadings to wander about in the caverns of knowledge wherever you will. Don’t blame me if you miss amazing stuff. Amazing is what hides within and between the rooms for anyone to discover who has the serenity to take their time, follow the spelunking Sherpa (me), and trust that he (me) will extricate them eventually — sane and unharmed.
Anyway, relax. Don’t be nervous. The fine-structure constant is simply a number — a pure number. It has no meaning. It stands for nothing — not inches or feet or speed or weight; not anything. What can be more harmless than a number that has no meaning?
Well, most physicists think it reveals, somehow, something fundamental and complicated going on in the inner workings of atoms — dynamics that will never be observed or confirmed, because they can’t be. The world inside an atom is impossibly small; no advance in technology will ever open that world to direct observation by humans.
What physicists can observe is the frequencies of light that enormous collections of atoms emit. They use prisms and spectrographs. What they see is structure in the light where none should be. They see gaps — very small gaps inside a single band of color, for example. They call it fine structure.
The Greek letter alpha (α) is the shortcut folks use for the fine-structure constant, so they don’t have to say a lot of words. The number is the square of another number that can have (and almost always does have) two or more parts — a complex number. Complex numbers have real and imaginary parts; math people say that complex numbers are usually two dimensional; they must be drawn on a sheet of two dimensional graph paper — not on a number line, like counting numbers always are.
Don’t let me turn this essay into a math lesson; please, …no. We can’t have readers projectile vomiting or rocking to the catatonic rhythms of a panic attack. We took our medicines, didn’t we? We’re going to be fine.
I beg readers to trust; to bear with me for a few sentences more. It will do no harm. It might do good. Besides, we can get through this, together.
Like me, you, dear reader, are going to experience power and euphoria, because when people summon courage; when they trust; when they lean on one another; when — like countless others — you put your full weight on me; I will carry you. You are about to experience truth, maybe for the first time in your life. Truth, the Ancient-of-Days once said, is that golden key that unlocks our prison of fears and sets us free.
Reality is going to change; minds will change; up is going to become down; first will become last and last first. Fear will turn into exhilaration; exhilaration into joy; joy into serenity; and serenity into power. But first, we must inner-tube our way down the foamy rapids of the next ten paragraphs. Thankfully, they are short paragraphs, yes….the journey is do-able, peeps. I will guide you.
The number (3 + 4i) is a complex number. It’s two dimensional. Pick a point in the middle of a piece of graph paper and call it zero (0 + 0i). Find a pencil — hopefully one with a sharp point. Move the point 3 spaces to the right of zero; then move it up 4 spaces. Make a mark. That mark is the number (3 + 4i). Mathematicians say that the “i” next to the “4” means “imaginary.” Don’t believe it.
They didn’t know what they were talking about, when first they worked out the protocols of two-dimensional numbers. The little “i” means “up and down.” That’s all. When the little “i” isn’t there, it means side to side. What could be more simple?
Draw a line from zero (0 + 0i) to the point (3 + 4i). The point is three squares to the right and 4 squares up. Put an arrow head on the point. The line is now an arrow, which is called a vector. This particular vector measures 5 squares long (get out a ruler and measure, anyone who doesn’t believe).
The vector (arrow) makes an angle of 53° from the horizontal. Find a protractor in your child’s pencil-box and measure it, anyone who doubts. So the number can be written as (5∠53), which simply means it is a vector that is five squares long and 53° counter-clockwise from horizontal. It is the same number as (3 + 4i), which is 3 squares over and 4 squares up.
The vectors used in quantum mechanics are smaller; they are less than one unit long, because physicists draw them to compute probabilities. A probability of one is 100%; it is certainty. Nothing is certain in quantum physics; the chances of anything at all are always less than certainty; always less than one; always less than 100%.
To multiply the vectors Z and W, add their angles and multiply their lengths. The vector ZW is the result; its overall length is called its amplitude. When both vectors Z and W are shorter than the side of one square in length, the vector ZW will become the shortest vector, not the longest (as it is in this example), because multiplying fractions together always results in a fraction that is less than the fractions that were multiplied. Right? To calculate what is called the probability density, simply multiply the length of the amplitude vector by itself, which will shrink it further, because its length (called its magnitude) is always a fraction that is less than one in quantum probability problems. This operation is called ‘’the Born Rule” where the magnitude of an amplitude is squared; it reduces a two-dimensional complex number to a one-dimensional unit-less number, which is — as said before — a probability. Experiments with electrons and photons must be performed to reveal interaction amplitude values; when these numbers are squared, the fine structure constant is the result. The probability density is a constant. That by itself is amazing.
Using simple rules, a vector that is less than one unit long can be used in the mathematics of quantum probabilities to shrink and rotate a second vector, which can shrink and rotate a third, and a fourth, and so on until the process of steps that make up a quantum event are completed. Lengths are multiplied; angles are added. The rules are that simple. The overall length of the resulting vector is called its amplitude.
Yes, other operations can be performed with complex numbers; with vectors. They have interesting properties. Multiplying and dividing by the “imaginary” i rotates vectors by 90°, for example. Click on links to learn more. Or visit the Khan Academy web-site to watch short videos. It’s not necessary to know how everything works to stumble through this article.
The likelihood that an electron will emit or absorb a photon cannot be derived from the mathematics of quantum mechanics. Neither can the force of the interaction. Both must be determined by experiment, which has revealed that the magnitude of these amplitudes is close to ten percent (.085424543… to be more exact), which is about eight-and-a-half percent.
What is surprising about this result is that when physicists multiply the amplitudes with themselves (that is, when they “square the amplitudes“) they get a one-dimensional number (called a probability density), which, in the case of photons and electrons, is equal to alpha (α), the fine-structure constant, which is .007297352… or 1 divided by 137.036… .
Get out the calculator and multiply .08524542 by itself, anyone who doesn’t believe. Divide the number “1” by 137.036 to confirm.
From the knowledge of the value of alpha (α) and other constants, the probabilities of the quantum world can be calculated; when combined with the knowledge of the vector angles, the position and momentum of electrons and photons, for example, can be described with magical accuracy — consistent with the well-known principle of uncertainty, of course, which readers can look up on Wikipedia, should they choose to get sidetracked, distracted, and hopelessly lost.
“Magical” is a good word, because these vectors aren’t real. They are made up — invented, really — designed to mimic mathematically the behavior of elementary particles studied by physicists in quantum experiments. No one knows why complex vector-math matches the experimental results so well, or even what the physical relationship of the vector-math might be (if any), which enables scientists to track and measure tiny bits of energy.
To be brutally honest, no one knows what the “tiny bits of energy” are, either. Tiny things like photons and electrons interact with measuring devices in the same ways the vector-math says they should. No one knows much more than that.
What is known is that the strong force of QCD is 137 times stronger than the electromagnetic force of QED — inside the center of atoms. Multiply the strong force by (α) to get the EM force. No one knows why.
There used to be hundreds of tiny little things that behaved inexplicably during experiments. It wasn’t only tiny pieces of electricity and light. Physicists started running out of names to call them all. They decided that the mess was too complicated; they discovered that they could simplify the chaos by inventing some new rules; by imagining new particles that, according to the new rules, might never be observed; they named them quarks.
By assigning crazy attributes (like color-coded strong forces) to these quarks, they found a way to reduce the number of elementary particles to seventeen; these are the stuff that makes up the so-called Standard Model. The model contains a collection of neutrons and muons; and quarks and gluons; and thirteen other things — researchers made the list of subatomic particles shorter and a lot easier to organize and think about.
Some particles are heavy, some are not; some are force carriers; one — the Higgs — imparts mass to the rest. The irony is this: none are particles; they only seem to be because of the way we look at and measure whatever they really are. And the math is simpler when we treat the ethereal mist like a collection of particles instead of tiny bundles of vibrating momentum within an infinite continuum of no one knows what.
Feynman diagrams help physicists think about what’s going on without getting bogged down in the mathematical details of subatomic particle interactions. View video below for more details. Diagram protocols start at 12:36 into the video.
Physicists have developed protocols to describe them all; to predict their behavior. One thing they want to know is how forcefully and in which direction these fundamental particles move when they interact, because collisions between subatomic particles can reveal clues about their nature; about their personalities, if anyone wants to think about them that way.
The force and direction of these collisions can be quantified by using complex (often three-dimensional) numbers to work out between particles a measure during experiments of their interaction probabilities and forces, which help theorists to derive numbers to balance their equations. These balancing numbers are called coupling constants.
The fine-structure constant is one of a few such coupling constants. It is used to make predictions about what will happen when electrons and photons interact, among other things. Other coupling constants are associated with other unique particles, which have their own array of energies and interaction peculiarities; their own amplitudes and probability densities; their own values. One other example I will mention is the gravitational coupling constant.
To remove anthropological bias, physicists often set certain constants such as the speed of light (c), the reduced Planck constant (ℏ) , the fundamental force constant (e), and the Coulomb force constant (4πε)equal to “one”. Sometimes the removal of human bias in the values of the constants can help to reveal relationships that might otherwise go unnoticed.
The coupling constants for gravity and fine-structure are two examples.
for gravity;
for fine-structure.
These relationships pop-out of the math when extraneous constants are simplified to unity.
Despite their differences, one thing turns out to be true for all coupling constants — and it’s kind of surprising. None can be derived or worked out using either the theory or the mathematics of quantum mechanics. All of them, including the fine-structure constant, must be discovered by painstaking experiments. Experiments are the only way to discover their values.
Here’s the mind-blowing part: once a coupling constant — like the fine-structure alpha (α) — is determined, everything else starts falling into place like the pieces of a puzzle.
The fine-structure constant, like most other coupling constants, is a number that makes no sense. It can’t be derived — not from theory, at least. It appears to be the magnitude of the square of an amplitude (which is a complex, multi-dimensional number), but the fine-structure constant is itself one-dimensional; it’s a unit-less number that seems to be irrational, like the number π.
For readers who don’t quite understand, let’s just say that irrational numbers are untidy; they are unwieldy; they don’t round-off; they seem to lack the precision we’ve come to expect from numbers like the gravity constant — which astronomers round off to four or five decimal places and apply to massive objects like planets with no discernible loss in accuracy. It’s amazing to grasp that no constant in nature, not even the gravity constant, seems to be a whole number or a fraction.
Based on what scientists think they know right now, every constant in nature is irrational. It has to be this way.
Musicians know that it is impossible to accurately tune a piano using whole numbers and fractions to set the frequencies of their strings. Setting minor thirds, major thirds, fourths, fifths, and octaves based on idealized, whole-number ratios like 3:2 (musicians call this interval a fifth) makes scales sound terrible the farther one goes from middle C up or down the keyboard.
Jimi Hendrix, a veteran of the US Army’s 101st Airborne Division, rose to mega-stardom in Europe several years before 1968 when it became the American public’s turn to embrace him after he released his landmark album, Electric Ladyland. Some critics today say that Jimi remains the best instrumentalist who has ever lived. Mr. Hendrix achieved his unique sound by using non-intuitive techniques to tune and manipulate string frequencies. Some of these methods are described in the previous link. It is well worth the read.
No, in a properly tuned instrument the frequencies between adjacent notes differ by the twelfth root of 2, which is 1.059463094…. . It’s an irrational number like “π” — it never ends; it can’t be written like a fraction; it isn’t a ratio of two whole numbers.
In an interval of a major fifth, for example, the G note vibrates 1.5 times faster than the C note that lies 7 half-steps (called semitones) below it. To calculate its value, take the 12th root of two and raise it to the seventh power. It’s not exactly 1.5. It just isn’t.
Get out the calculator and try it, anyone who doesn’t believe.
[Note from the Editorial Board: a musical fifthis often written as 3:2, which implies the fraction 3/2, which equals 1.5. Twelve half-notes make an octave; the starting note plus 7 half-steps make 8. Dividing these numbers by four makes 12:8 the same proportion as 3:2, right? The fraction 3/2 is a comparison of the vibrational frequencies (also of the nodes) of the strings themselves, not the number of half-tones in the interval.
However, when the first note is counted as one and flats and sharps are ignored, the five notes that remain starting with C and ending with G, for example, become the interval known as a perfectfifth. It kind of makes sense, until musicians go deeper; it gets a lot more complicated. It’s best to never let musicians do math or mathematicians do music. Anyone who does will create a mess of confusion, eight times out of twelve, if not more.]
An octave of 12 notes exactly doubles the vibrational frequency of a note like middle C, but every note in between middle C and the next higher octave is either a little flat or a little sharp. It doesn’t seem to bother anyone, and it makes playing in large groups with different instruments possible; it makes changing keys without everybody having to re-tune their instruments seem natural — it wasn’t as easy centuries ago when Mozart got his start.
The point is this:
Music sounds better when everyone plays every note a little out of tune. It’s how the universe seems to work too.
As for gravity, it works in part because space-time seems to curve and weave in the presence of super-heavy objects. No particle has ever been found that doesn’t follow the curved space-time paths that surround massive objects like our Sun.
Notice the speed of the hands of the clocks and how they vary in space-time. Clocks slow down when they are accelerated or when they are immersed in the gravity of a massive object, like the star at the center of this GIF. Click on it for a better view.
Even particles like photons of light, which in the vacuum of space have no mass (or electric charge, for that matter) follow these curves; they bend their trajectories as they pass by heavy objects, even though they lack the mass and charge that some folks might assume they should to conduct an interaction.
Massless, charge-less photons do two things: first, they stay in their lanes — that is they follow the curved currents of space-time that exist near massive objects like a star; they fall across the gravity gradient toward these massive objects at exactly the same rate as every other particle or object in the universe would if they found themselves in the same gravitational field.
Second, light refracts in the dielectric of a field of gravity in the same way it refracts in any dialectric—like glass, for example. The deeper light falls into a gravity field, the stronger is the field’s refractive index, and the more light bends.
Measurements of star-position shifts near the edge of our own sun helped prove that space and time are curved like Einstein said and that Isaac Newton‘s gravity equation gives accurate results only for slow moving, massive objects.
Massless photons traveling from distant stars at the speed of light deflect near our sun at twice the angle of slow-moving massive objects. The deflection of light can be accounted for by calculating the curvature of space-time near our sun and adding to it the deflection forced by the refractive index of the gravity field where the passing starlight is observed.
In the exhilaration of observations by Eddington during the eclipse of 1919 which confirmed Einstein’s general theory, Einstein told a science reporter that space and time cannot exist in a universe devoid of matter and its flip-side equivalent, energy. People were stunned, some of them, into disbelief. Today, all physicists agree.
The coupling constants of subatomic particles don’t work the same way as gravity. No one knows why they work or where the constants come from. One thing scientists like Freeman Dyson have said: these constants don’t seem to be changing over time.
Evidence shows that these unusual constants are solid and foundational bedrocks that undergird our reality. The numbers don’t evolve. They don’t change.
Confidence comes not only from data carefully collected from ancient rocks and meteorites and analyzed by folks like Denys Wilkinson, but also from evidence uncovered by French scientists who examined the fossil-fission-reactors located at the Oklo uranium mine in Gabon in equatorial Africa. The by-products of these natural nuclear reactors of yesteryear have provided incontrovertible evidence that the value of the fine-structure constant has not changed in the last two-billion years. Click on the links to learn more.
Since this essay is supposed to describe the fine-structure constant named alpha (α), now might be a good time to ask: What is it, exactly? Does it have other unusual properties beside the coupling forces it helps define during interactions between electrons and photons? Why do smart people obsess over it?
I am going to answer these questions, and after I’ve answered them we will wrap our arms around each other and tip forward, until we lose our balance and fall into the rabbit hole. Is it possible that someone might not make it back? I suppose it is. Who is ready?
Alpha (α) (the fine-structure constant) is simply a number that is derived from a rotating vector (arrow) called an amplitude that can be thought of as having begun its rotation pointing in a negative (minus or leftward direction) from zero and having a length of .08524542…. . When the length of this vector is squared, the fine-structure constant emerges.
It’s a simple number — .007297352… or 1 / 137.036…. It has no physical significance. The number has no units (like mass, velocity, or charge) associated with it. It’s a unit-less number of one dimension derived from an experimentally discovered, multi-dimensional (complex) number called an amplitude.
We could imagine the amplitude having a third dimension that drops through the surface of the graph paper. No matter how the amplitude is oriented in space; regardless of how space itself is constructed mathematically, only the absolute length of the amplitude squared determines the value of alpha (α).
Amplitudes — and probability densities calculated from them, like alpha (α) — are abstract. The fine-structure constant alpha (α) has no physical or spatial reality whatsoever. It’s a number that makes interaction equations balance no matter what systems of units are used.
Imagine that the amplitude of an electron or photon rotates like the hand of a clock at the frequency of the photon or electron associated with it. Amplitude is a rotating, multi-dimensional number. It can’t be derived. To derive the fine structure constant alpha (α), amplitudes are measured during experiments that involve interactions between subatomic particles; always between light and electricity; that is, between photons and electrons.
I said earlier that alpha (α) can be written as the fraction “1 / 137.036…”. Once upon a time, when measurements were less precise, some thought the number was exactly 1 / 137.
The number 137 is the 33rd prime number after zero; the ancients believed that both numbers, 33 and 137, played important roles in magic and in deciphering secret messages in the Bible. The number 33 was Christ’s age at his crucifixion. It was proof, to ancient numerologists, of his divinity.
The number 137 is the value of the Hebrew word, קַבָּלָה (Kabbala), which means to receive wisdom.
In the centuries before quantum physics — during the Middle Ages — non-scientists published a lot of speculative nonsense about these numbers. When the numbers showed up in quantum mechanics during the twentieth century, mystics raised their eyebrows. Some convinced themselves that they saw a scientific signature, a kind of proof of authenticity, written by the hand of God.
That 137 is the 33rd prime number may seem mysterious by itself. But it doesn’t begin to explain the mysterious properties of the number 33 to the mathematicians who study the theory of numbers. The following video is included for those readers who want to travel a little deeper into the abyss.
Numerology is a rabbit-hole in and of itself, at least for me. It’s a good thing that no one seems to be looking at the numbers on the right side of the decimal point of alpha (α) — .036 might unglue the too curious by half.
Read right to left (as Hebrew is), the number becomes 63 — the number of the abyss.
I’m going to leave it there. Far be it for me to reveal more, which might drive innocents and the uninitiated into forests filled with feral lunatics.
Folks are always trying to find relationships between α and other constants like π and e. One that I find interesting is the following:
=
Do the math. It’s mysterious, no?
Well, it might be until someone subtracts
which brings the result even closer to the experimentally determined value of α. Somehow, mystery diminishes with added complexity, correct? Numerology can lead to peculiar thinking e times out of π. Right?
People’s fascination with the fine-structure constant has led to many unusual insights, such as this one, found during an image search on the web. The hypotenuse is 137.036015… .
The view today is that, yes, alpha (α) is annoyingly irrational; yet many other quantum numbers and equations depend upon it. The best known is:
These constants (and others) show up everywhere in quantum physics. They can’t be derived from first principles or pure thought. They must be measured.
As technology improves, scientists make better measurements; the values of the constants become more precise. These constants appear in equations that are so beautiful and mysterious that they sometimes raise the hair on the back of a physicist’s head.
The equations of quantum physics tell the story about how small things that can’t be seen relate to one another; how they interact to make the world we live in possible. The values of these constants are not arbitrary. Change their values even a little, and the universe itself will pop like a bubble; it will vanish in a cosmic blip.
How can a chaotic, quantum house-of-cards depend on numbers that can’t be derived; numbers that appear to be arbitrary and divorced from any clever mathematical precision or derivation?
The inability to solve the riddles of these constants while thinking deeply about them has driven some of the most clever people on Earth to near madness — the fine-structure constant (α) is the most famous nut-cracker, because its reciprocal (137.036…) is so very close to the numerology of ancient alchemy and the kabbalistic mysteries of the Bible.
What is the number alpha (α) for? Why is it necessary? What is the big deal that has garnered the attention of the world’s smartest thinkers? Why is the number 1 / 137 so dang important during the modern age, when the mysticism of the ancient bards has been largely put aside?
Well, two reasons come immediately to mind. Physicists are adamant; if α was less than 1 / 143 or more than 1 / 131, the production of carbon inside stars would be impossible. All life we know is carbon-based. The life we know could not arise.
The second reason? If alpha (α) was less than 1 / 151 or more than 1 / 124, stars could not form. With no stars, the universe becomes a dark empty place.
These are the values of some of the fundamental constants mentioned in this essay. Plug them into formulas to confirm they work, any reader who enjoys playing with their calculator. It’s clear that these numbers make no precisional sense; their values don’t correspond to anything one might find on any list of rational numbers. It’s possible that they make no geometric sense, either. If so, then God is not a mathematician.
Without mathematics, humans have no hope of understanding the universe.
Yet, here we are wrestling against all the evidence; against all the odds that the mysteries of existence will forever elude us. We cling to hope like a drowning sailor at sea, praying that the hour of rescue will soon come; we will blow our last breath in triumph; humans can understand. Everything is going to fall into place just as we always knew it would.
It might surprise some readers to learn that the number alpha (α) has a dozen explanations; a dozen interpretations; a dozen main-stream applications in quantum mechanics.
The simplest hand-wave of an explanation I’ve seen in print is that depending on ones point of view, “α” quantifies either the coupling strength of electromagnetism or the magnitude of the electron charge. I can say that it’s more than these, much more.
One explanation that seems reasonable on its face is that the magnetic-dipole spin of an electron must be interacting with the magnetic field that it generates as it rushes about its atom’s nucleus. This interaction produces energies which — when added to the photon energies emitted by the electrons as they hop between energy states — disrupt the electron-emitted photon frequencies slightly.
This jiggling (or hopping) of frequencies causes the fine structure in the colors seen on the screens and readouts of spectrographs — and in the bands of light which flow through the prisms that make some species of spectrographs work.
OK… it might be true. It’s possible. Nearly all physicists accept some version of this explanation.
Beyond this idea and others, there are many unexplained oddities — peculiar equations that can be written, which seem to have no relation to physics, but are mathematically beautiful.
For example: Euler’s number, “e” (not the electron charge we referred to earlier), when multiplied by the cosine of (1/α), equals 1 — or very nearly. (Make sure your calculator is set to radians, not degrees.) Why? What does it mean? No one knows.
What we do know is that Euler’s number shows up everywhere in statistics, physics, finance, and pure mathematics. For those who know math, no explanation is necessary; for those who don’t, consider clicking this link to Khan Academy, which will take you to videos that explain Euler’s number.
What about other strange appearances of alpha (α) in physics? Take a look at the following list of truths that physicists have noticed and written about; they don’t explain why, of course; indeed, they can’t; many folks wonder and yearn for deeper understanding:
1 — One amazing property about alpha (α) is this: every electron generates a magnetic field that seems to suggest that it is rotating about its own axis like a little star. If its rotational speed is limited to the speed of light (which Einstein said was the cosmic speed limit), then the electron, if it is to generate the charge we know it has, must spin with a diameter that is 137 times larger than what we know is the diameter of a stationary electron — an electron that is at rest and not spinning like a top. Digest that. It should give pause to anyone who has ever wondered about the uncertainty principle. Physicists don’t believe that electrons spin. They don’t know where their electric charge comes from.
2 — The energy of an electron that moves through one radian of its wave process is equivalent to its mass. Multiplying this number (called the reduced Compton wavelength of the electron) by alpha (α) gives the classical (non-quantum) electron radius, which, by the way, is about 3.2 times that of a proton. The current consensus among quantum physicists is that electrons are point particles — they have no spatial dimensions that can be measured. Click on the links to learn more.
3 — The physics that lies behind the value of alpha (α) requires that the maximum number of protons that can coexist inside an atom’s nucleus must be less than 137.
Think about why.
Protons have the same (but opposite) charge as electrons. Protons attract electrons, but repel each other. The quarks, from which protons are made, hold themselves together in protons by means of the strong force, which seems to leak out of the protons over tiny distances to pull the protons together to make the atom’s nucleus.
The strong force is more powerful than the electromagnetic force of protons; the strong force enables protons to stick together to make an atom’s nucleus despite their electromagnetic repulsive force, which tries to push them apart.
An EM force from 137 protons inside a nucleus is enough to overwhelm the strong forces that bind the protons to blow them apart.
Another reason for the instability of large nuclei in atoms might be — in the Bohr model of the atom, anyway — the speed that an electron hops about is approximately equal to the atomic number of the element times the fine-structure constant (alpha) times the speed of light.
When an electron approaches velocities near the speed of light, the Lorentz transformations of Special Relativity kick in. The atom becomes less stable while the electrons take on more mass; more momentum. It makes the largest numbered elements in the periodic table unstable; they are all radioactive.
The velocity equation is V = n * α * c . Element 118 — oganesson — presumably has some electrons that move along at 86% of the speed of light. [ 118 * (1/137) * (3E8) ] 86% of light-speed means that relativistic properties of electrons transform to twice their rest states.
Uranium is the largest naturally occurring element; it has 92 protons. Physicists have created another 26 elements in the lab, which takes them to 118, which is oganesson.
When 137 is reached (most likely before), it will be impossible to create larger atoms. My gut says that physicists will never get to element 124 — let alone to 137 — because the Lorentz transform of the faster moving electrons grows by then to a factor of 2.3. Intuition says, it is too large. Intuition, of course, is not always the best guide to knowledge in quantum mechanics.
Plutonium, by the way — the most poisonous element known — has 94 protons; it is man-made; one isotope (the one used in bombs) has a half-life of 24,000 years. Percolating plutonium from rotting nuclear missiles will destroy all life on Earth someday; it is only a matter of time. It is impossible to stop the process, which has already started with bombs lost at sea and damage to power plants like the ones at Chernobyl and at Fukushima, Japan. (Just thought I’d mention it since we’re on the subject of electron emissions, i.e beta-radiation.)
4 — When sodium light (from certain kinds of streetlamps, for example) passes through a prism, its pure yellow-light seems to split. The dark band is difficult to see with the unaided eye; it is best observed under magnification.
The split can be measured to confirm the value of the fine-structure constant. The measurement is exact. It is this “fine-structure” that Arnold Sommerfeld noticed in 1916, which led to his nomination for the Nobel Prize; in fact Sommerfeld received eighty-four nominations for various discoveries. For some reason, he never won.
5 — The optical properties of graphene — a form of carbon used in solid-state electrical engineering — can be explained in terms of the fine-structure constant alone. No other variables or constants are needed.
6 — The gravitational force (the force of attraction) that exists between two electrons that are imagined to have masses equal to the Planck-mass is 137.036 times greater than the electrical force that tries to push the electrons apart at every distance. I thought the relationship should be the opposite until I did the math.
It turns out that the Planck-mass is huge — 2.176646 E-8 kilograms (the mass of the egg of a flea, according to a source on Wikipedia). Compared to neutrons, atoms, and molecules, flea eggs are heavy. The ratio of 137 to 1 (G force vs. e force) is hard to explain, but it seems to suggest a way to form micro-sized black holes at subatomic scales. Once black holes get started their appetites can become voracious.
The good thing is that no machine so far has the muscle to make Planck-mass morsels. Alpha (α) has slipped into the mathematics in a non-intuitive way, perhaps to warn folks that, should anyone develop and build an accelerator with the power to produce Planck-mass particles, they will have — perhaps inadvertently — designed a doomsday seed that could very well grow-up to devour Earth, if not the solar system and beyond.
8 — The Standard Model of particle physics contains 20 or so parameters that cannot be derived; they must be experimentally discovered. One is the fine-structure constant (α), which is one of four constants that help to quantify interactions between electrons and photons.
9 — The speed of light is 137 times greater than the speed of “orbiting” electrons in hydrogen atoms. The electrons don’t actually “orbit.” They do move around in the sense of a probability distribution, though, and alpha (α) describes the ratio of their velocities to the cosmic speed limit of light. (See number 3 in this list for a description of element 118 — oganesson — and the velocity of some of its electrons.)
10 — The energy of a single photon is precisely related to the energy of repulsion between two electrons by the fine-structure constant alpha (α). Yes, it’s weird. How weird? Set the distance between two electrons equal to the wavelength of any photon. The energy of the photon will measure 137.036 times more than the repulsive force between the electrons. Here’s the problem. Everyone thinks they know that electron repulsion falls off exponentially with distance, while photon energy falls off linearly with wavelength. In these experimental snapshots, photon energy and electron repulsive energy are locked. Photons misbehave depending on how they are measured, right? The anomaly seems to have everything to do with the geometric shape of the two energy fields and how they are measured. Regardless, why “α”?
11 — The charge of an electron divided by the Planck charge — the electron charge defined by natural units, where constants like the speed of light and the gravitational constant are set equal to one — is equal to . This strange relationship is another indicator that something fundamental is going on at a very deep level, which no one has yet grasped.
12 — Some readers who haven’t toked too hard on their hash-pipes might remember from earlier paragraphs that the “strong force” is what holds quarks together to make protons and neutrons. It is also the force that drives protons to compactify into a solid atomic nucleus.
The strong force acts over short distances not much greater than the diameter of the atom’s nucleus itself, which is measured in femtometers. At this scale the strong force is 137 times stronger than the electromagnetic force, which is why protons are unable to push themselves apart; it is one reason why quarks are almost impossible to isolate. Why 137? No one has a clue.
Now, dear reader, I’m thinking that right now might be a good time to share some special knowledge — a reward for your courage and curiosity. We’ve spelunked together for quite a while, it seems. Some might think we are lost, but no one has yet complained.
Here is a warning and a promise. We are about to descend into the deepest, darkest part of the quantum cave. Will you stay with me for the final leg of the journey? I know the way. Do you believe it? Do you trust me to bring you back alive and sane?
In the Wikipedia article about α, the author writes, In natural units, commonly used in high energy physics, where ε0 = c = h/2π = 1, the value of the fine-structure constant is:
Every quantum physicist knows the formula. In natural units e = .302822….
Remember that the units collapse to make “α” a dimensionless number. Dimensional units don’t go away just because the values used to calculate the final result are set equal to “1”, right? Note that the value above is calculated a little differently than that of the Planck system — where 4πε is set equal to “1”.
As I mentioned, the value for “α” doesn’t change. It remains equal to .0073…, which is 1 / 137.036…. What puzzles physicists is, why?
What is the number 4π about? Why, when 4π is stripped away, does there remain only “α” — the mysterious number that seems to quantify a relationship of some kind between two electrons?
Well… electrons are fermions. Like protons and neutrons they have increments of 1/2 spin. What does 1/2 spin even mean?
It means that under certain experimental conditions when electrons are fired through a polarized disc they project a visible interference pattern on a viewing screen. When the polarizing disc is rotated, the interference pattern on the screen changes. The pattern doesn’t return to its original configuration until the disc is rotated twice — that is, through an angle of 720°, which is 4π radians.
Since the polarizer must be spun twice, physicists reason that the electron must have 1/2 spin (intrinsically) to spin once for every two spins of the polarizer. Yes, it makes no sense. It’s crazy — until it isn’t.
What is more insane is that an irrational, dimensionless number that cannot be derived by logic or math is all that is left. We enter the abyss when we realize that this number describes the interaction of one electron and one photon of light, which is an oscillating bundle of no one knows what (electricity and magnetism, ostensibly) that has no mass and no charge.
All photons have a spin of one, which reassures folks (because it seems to make sense) until they realize that all of a photon’s energy comes from its so-called frequency, not its mass, because light has no mass in the vacuum of space. Of course, photons on Earth don’t live in the vacuum of space. When photons pass through materials like glass or the atmosphere, they disturb electrons in their wake. The electrons emit polaritons, which physicists believe add mass to photons and slow them down.
The number of electrons in materials and their oscillatory behavior in the presence of photons of many different frequencies determine the production intensity of polaritons. It seems to me that the relationship cannot be linear, which simply means that intuition cannot guide predictions about photon behavior and their accumulation of mass in materials like glass and the earth’s atmosphere. Everything must be determined by experiment.
Theories that enable verifiable predictions about photon mass and behavior might exist or be on the horizon, but I am not connected enough to know. So check it out.
Anyway… frequency is the part of Einstein’s energy equation that is always left out because, presumably, teachers feel that if they unveil the whole equation they won’t be believed — if they are believed, their students’ heads might explode. Click the link and read down a few paragraphs to explore the equation.
In the meantime, here’s the equation:
When mass is zero, energy equals the Planck constant times the frequency. It’s the energy of photons. It’s the energy of light.
Photons can and do have any frequency at all. A narrow band of their frequencies is capable of lighting up our brains, which have a strange ability to make sense of the hallucinations that flow through them.
Click on the links to get a more detailed description of these mysteries.
What do physicists think they know for sure?
When an electron hops between its quantum energy states it can emit and absorb photons of light. When a photon is detected, the measured probability amplitude associated with its emission, its direction of travel, its energy, and its position are related to the magnitude of the square of a multi-dimensional number. The scalar (α) is the probability density of a measured vector quantity called an amplitude.
When multi-dimensional amplitudes are manipulated by mathematics, terms emerge from these complex numbers, which can’t be ignored. They can be used to calculate the interference patterns in double-slit experiments, for one thing, performed by every student in freshman physics.
The square root of the fine-structure constant matches the experimentally measured magnitude of the amplitude of electron/photon interactions — a number close to .085. It means that the vector that represents the dynamic of the interaction between an electron and a photon gets “shrunk” during an interaction by almost ten percent, as Feynman liked to describe it.
Because amplitude is a complex (multi-dimensional) number with an associated phase angle or direction, it can be used to help describe the bounce of particles in directions that can be predicted within the limitations of the theory of quantum probabilities.
Square the amplitude, and a number (α) emerges — the one-dimensional, unit-less number that appears in so many important quantum equations: the fine-structure constant.
Why? It’s a mystery. It seems that few physical models that go beyond a seemingly nonsensical vision of rotating hands on a traveling clock can be conjured forth by the brightest imaginations in science to explain the why or how.
The fine-structure constant, alpha (α) — like so many other phenomenon on quantum scales — describes interactions between subatomic particles — interactions that seem to make no intuitive sense. It’s a number that is required to make the equations balance. It just does what it does. The way it is — for now, at least — is the way it is. All else is imagination and guesswork backed by some very odd math and unusual constants.
By the way (I almost forgot to mention it): α is very close to 30 times the ratio of the square of the charge of an at-rest electron divided by Planck’s reduced constant.
Anyone is welcome to confirm the calculation of what seems to be a fairly precise ratio of electron charge to Planck’s constant if they want. But what does it mean?
What does it mean?
Looking for an answer will bury the unwary forever in the rabbit hole.
I’m thinking that right now might be a good time to leave the abyss and get on with our lives. Anyone bring a flashlight?
, right? Reversing the digits to make 8402 does not result in an exact number that is a power of 5.
plus a lot more decimals. It’s not a whole (or exact) number. Not only that, no matter how many decimal places anyone rounds-off 6.09363… , the rounded number raised to the power of 5 will never return 8402 exactly.
. and . 
. What are x and y?
, right? The exponent that makes 100 from the base 10 (not shown) is (equals) 2.
, right?
or 
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and you are located at 
and want to get as cool as possible, in which direction should you set out?![\sqrt[3]{i} - \sqrt[3]{i}](https://www.thebillyleepontificator.com/wp-content/ql-cache/quicklatex.com-1d1f75d0d026c7150eebe5ec9e034c9c_l3.png "Rendered by QuickLaTeX.com")
equal to?
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. Right?
. Right? It’s not the only root.
and -i. Right?
). It’s easy for anyone who knows how to work with complex variables. In Euler-form the angle in radians sits next to i. The angle directs you to where the result lies on a unit circle. Right?
.
.
for gravity;
for fine-structure.
= 
.
. This strange relationship is another indicator that something fundamental is going on at a very deep level, which no one has yet grasped.
