Infinities and singularities are equivalent when mass is absent and entropy (that is, randomness) is maximum, because in both states the ability of the universe to scale itself is lost.
It is called conformal equivalence. It means that the shape of everything in two systems is the same; the scale is indeterminate or irrelevant. Size can’t be measured.
Warning to the faint of heart: this essay will reveal ideas that might change the way some readers think about the universe. Keep an open mind.
What is the fate of the cosmos? Almost everyone agrees that it will expand exponentially, possibly forever. As it does, all matter will be sucked into black holes like water into bathtub drains where — perhaps over trillions of years — it will evaporate by a mechanism believed to produce Hawking radiation; mass converts into massless photons and radiates outward until every black hole evaporates and disappears.
Sir Roger Penrose, the brilliant mathematical physicist, has said that new satellite data might support his theory of Eons, which asserts among other things that the universe expands while black holes collect and evaporate away all matter; entropy (or randomness) increases to maximum.
At the termination of the Eon the universe cannot tell whether it is at its beginning or its end because it doesn’t know what size it is; all its metrics become equivalent to those found in the singularity that many speculate preceded the emergence of the Universe humans find themselves in today.
In the unimaginable heat of a singularity, the concept of mass also disappears; it becomes irrelevant. Energy dwarfs mass to overwhelm it; runaway entropy (randomness) goes to maximum.
With no mass the concept of scale disappears. Without mass all the gravitational degrees of freedom vanish. The universe doesn’t know what size it is or if it is any size at all.
Entropy (or randomness) of “the singularity” initiates the Big Bang in the same way as a maximally expanded and evaporated universe; the two states — infinity and singularity — are equivalent. They are not distinguishable; one is like the other and emerges from the other.
Both the singularity and the infinitely expanded universe are unable to determine how big they are because both lose the ability to scale themselves when matter is no longer present; both states have maximum entropy; the distribution of energy becomes infinitely random.
The result is that the expansion of a maximally expanded universe starts anew as if it were a singularity. A new “eon” begins at the end of each expansion; the universe expands in stages with the beginning of each stage indistinguishable from a singularity.
The universe seems to chug along like a smoking choo-choo train — almost like a perpetual motion machine that generates a brand new universe on the fading gasp of its last puff.
A contraction of mass into a singularity is a popular idea, but it never happens — not in this theory — except in black holes where all matter evaporates over time into the pure energy of Hawking radiation. In Penrose’s theory, only an infinite series of expansions following one upon the other from singularities indistinguishable by their metrics from maximally-expanded-universes will emerge.
It’s like a woman who gives birth to a daughter. The process repeats forever in the history of humans. Daughter buds from mother. Mother doesn’t contract to the size of a baby who then grows to become a new mother.
No, the process is continuous — one mother gives birth to a baby who grows to become a mother who births a new baby and on and on into an infinity of mothers that progress in a line of succession to the end of a time that has no end.
The universe expands until it becomes a singularity that expands into a new universe. The process never ends. There is no beginning and no end.
Roger Penrose at a conference. Photo by Biswarup Ganguly.
Does this idea by Roger Penrose resonate with the ring of truth to anyone? Roger has said that his idea is having some trouble catching on with bona-fide cosmologists.
For me, Roger Penrose’s idea feels like truth. His truth sets me free; everything falls into place; a weight is lifted from my shoulders when I think about what it means and why things might be the way they are.
Roger says that he is retired; the mathematics of his theory are worked out by his acolytes; they make predictions that are testable. One thing they predict are “Hawking points” or spots.
Hawking points are places where massive black holes have evaporated away every bit of the matter of the galaxies that fell into them. This radiation is concentrated; it will emerge to imprint the cosmic background of the universe that follows. The points or regions will spread to cover a circle in the sky that is four degrees across — close to eight times that of the Moon. Hawking points, if verified, will emit an energy that is ten to fifteen times more intense than the cosmic background radiation.
Hawking “spots” should be findable by humans. The radiation they represent bled into our universe from the universe that preceded and spawned them. Identifying Hawking spots will lend credence to the idea that a universe preceded ours and that another will follow in the far distant future — perhaps trillions of years from now.
Perhaps thirty candidates have been identified by recent satellite observations. The WMAP (Wilkinson Microwave Anisotropy Probe) satellite — illustrated above — and the newer Planck satellite have identified in the microwave background radiation (CMB) areas in space where the predictions of the Eon theory seem likely to be confirmed.
Roger claims that — absent mass — big and cold is equivalent to small and hot. The laws of thermodynamics hold in both worlds and are conformally equivalent. The mathematics are the same.
Roger Penrose has won 17 major awards in science; he has made major contributions in at least 30 areas of science and mathematics. The implications of his theory of conformal cyclic cosmology (CCC), if accepted by mainstream science, are worthy of a Nobel Prize.
I hope he lives long enough to receive it.
The video above, at 23:23, explains a consequence of the theory that dark matter (called erebons by Penrose) is required to make it work. Erebons are hugely massive compared to other atomic particles; they possess the mass equivalent of the eyeball of a flea. Sir Roger predicts that they decay and leave behind signals that will be confirmed by a focused analysis of data collected by the Laser Interferometer Gravitational-Wave Observatory LIGO.
Another interesting and rather strange consequence of the theory addresses the Fermi Paradox. From Wikipedia is the following reference:
”In 2015 Gurzadyan and Penrose discussed the Fermi paradox, the apparent contradiction between the lack of evidence but high probability estimates for the existence of extraterrestrial civilizations. Within conformal cyclic cosmology, the cosmic microwave background provides the possibility of information transfer from one Eon to another, including of intelligent signals within the information panspermiaconcept.”
NOTE: The members of the EDITORIAL BOARD are aware that many readers may not have studied physics or astronomy. They might be under the false impression that an article like the one that follows is going to be incomprehensible.
Nothing could be farther from the truth. Yes, those who have studied Maxwell’s Equations and Einstein’s theories will find his essay a kind of cakewalk. No doubt, eggheads will have issues with some assertions. Submit objections in comments — your head does not have to look like an egg.
WE, THE EDITORS wish to reassure readers — especially those who have yet to study math and science — that they have intelligence and imagination enuf to understand Billy Lee’s basic arguments.
We know Billy Lee. We work with him every day. He talks and tweets a lot but what does he really know?
Billy Lee likes to share notions with folks who can read. He claims it does no harm. For those who get “high” on science, Billy Lee included videos to make rabbit-hole hopping fun. Don’t be afraid to watch some.
THE EDITORIAL BOARD
UPDATE BY THE EDITORIAL BOARD:May 15, 2019; Victor T. Toth, the Hungarian software developer, author, and Quora guru of quantum physics wrote, “a photon has no rest mass, but it carries plenty of energy, and it has momentum. Its stress-energy-momentum tensor is certainly not zero. So it can be a source of gravity, it has inertia, and it responds to gravity. […] relativity theory predicts … twice the deflection angle for a photon in a gravitational field than the deflection of a Newtonian particle.”
Almost a century of experiments plus hundreds of upvotes on Quora by physicists seem to validate Victor’s argument.
The photon is known to be the only massless, free-moving particle in the Standard Model of physics. Other massless particles are the gluon, the graviton, and of course the Higgs, discovered in 2012 at CERN. Europeans plan to build a Higgs factory to learn more about them. Gluons mediate the strong force. They don’t propagate through empty space. No one has yet observed even a single graviton. Higgs give fermions like quarks their mass.
Photons have an electric and magnetic structure. They are electromagnetic pulses of energy that emerge from atoms when electrons drop from a higher energy state to a lower one. When electrons shed energy, a pulse of electromagnetic radiation is emitted — a photon of light.
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Photons of light can be emitted from atoms at different frequencies — colors when wavelengths fall within the narrow range that humans see. These frequencies depend on the energy of electrons, which exist in many differently configured shells (or orbitals) within both atoms and molecules.
Wavelengths of light felt but not seen are called infrared; other invisible frequencies fall into broad categories such as radio waves, microwaves, x-rays, gamma rays and so on — all require instruments to detect.
Electromagnetic radiation is the medium through which humans observe and interact with everything knowable in the universe. Humans live inside an electromagnetic bubble that they are struggling to understand.
One thing most physicists understand is that a disturbing 95% of the energy and mass of the universe comes from a source no one can see. Physicists observe the effects of invisible (dark) matter and invisible (dark) energy by measuring the unusual dynamics of galaxies and by cataloging the physical organization and expansion of the universe itself.
These measurements make no sense unless folks assume that a lot of gravitationally interacting stuff is out there which no one has yet observationally confirmed. The missing mass is not debris or dark stars. The most exaggerated conjectures about how much mass and energy is scattered among the stars won’t come anywhere near enough to explain forces that make galaxies behave strangely.
Dark matter and energy don’t seem to be electromagnetic. Dark matter, if it exists, interacts with the mass of two-trillion galaxies and seems to refract their emitted light. Humans are blind to all of it.
Scientists postulate matter they call WIMPS, MACHOS, axions, and erebons. Each has a few properties necessary to make the universe work as observed, but none have all the required properties except perhaps erebons, if Roger Penrose’s Conformal Cyclic Cosmology (CCC) is someday verified.
Space-saturating foam of micro-sized black holes is another idea some have proposed. The problem is that theorists believe tiny black holes might be too stable to radiate electromagnetic waves or gravity waves.
Micro-holes lie in a sort of crevice of invisibility — unobservable by LIGO and LISA style gravity-wave sensors, yet too massive for current and future particle-colliders like CERN to create.
Because micro-holes don’t radiate light at any frequency, light telescopes will never find them. No imagined interaction of micro-holes is able to generate gravity-waves with enough disruptive power in spacetime to be detected. The nature of physics seems to suggest that no technology can be developed to confirm or deny the black-hole foam idea.
Perhaps the same dilemma faces dark matter detection. We know it exists, but physics says we can never find it. It will always lie just outside our reach doing its work in an invisible universe no one will ever see.
Worse, not one of the proposed forms of “dark” matter has ever been observed or identified. It is likely that no experiment currently scheduled will detect dark matter, which many physicists believe is “out there” and makes maybe four parts out of five of all the matter in the universe.
It’s an incredible paradox for conscious humans to live in a universe where they are blind to almost every important thing that is happening within and around them.
Humanoids are like fish which spend their lives swimming in streams buried deep inside caves. Spelunkers like me know that certain species of cave fish have no eyes. They lack all ability to see their world — as do we, it seems. As intelligent as people are, they don’t yet build sensors capable of confirming their notions about what the universe might actually be at large scales or small.
Oh well… someday maybe new discoveries will make our predicament evaporate away. The universe will reveal itself to humans, as we knew it would. Our dream to fully understand reality will come true.
Some day.
Scientists have sensible mathematics to show that if electromagnetic particles are massless, they must travel at an upper limit, called “c“. Over decades, folks decided that this constant is the speed of a photon in a vacuum; they decided that photons have no internal rest mass and travel in vacuum at a speed limit — the speed of light.
The truth might be more mysterious. No one knows what the upper limit of “c” is, because no one knows with certainty that space is truly empty or that massless particles exist.
When physicists say that certain particles are massless, they sometimes mean that they don’t interact with the Higgs Field, which is known to give mass to fermions, like quarks. They don’t mean they don’t have energy, specifically kinetic energy, which is a form of inertial mass, right? They also aren’t saying photons don’t interact gravitationally. They do, in a special way described by the geodesics of spacetime in Einstein’s General Relativity.
More on this idea later.
British physicist Brian Cox wrote in his book Why Does E = mc2 ? that the question about whether photons have rest mass is not yet settled.
It’s true that more than a few reasonable people seem to believe that photons traveling freely in the vacuum of space are massless. If they truly are then the permittivity constant “ε” in Maxwell’s equation can be established for electro-magnetic particles (like photons).
The formula below is used to calculate the speed of a massless electromagnetic particle; it is thought to be a maximum speed.
For now, ignore the μ term. It is the permeability (resistance) of vacuum to infusion by a magnetic field, which is determined by experiment. It is sometimes called the magnetic constant.
Epsilon (ε} is the permittivity (resistance) of vacuum to an electric field. It is sometimes called the electric constant.
”c” is the so-called ”universal speed limit.” It is called the lightspeed constant.
These three numbers — μ, ε, and c — help to define the maximum velocity of an electromagnetic wave, which most people believe is the archetypal photon (of light). They assume that the photon packet travels at the maximum allowable speed in a vacuum.
A problem with this view is that no one has proved that space is free; or that space has no weight; or that photons have no rest mass; or that undiscovered particles formed from forces other than electricity and magnetism don’t exist. A few scientists have said that there might be no such things as free space or massless photons. It is also possible that space presents less resistance to other phenomenon yet to be discovered.
The idea that ”dark” matter and energy must exist to make the universe behave the way it does is compelling to many physicists. If true, it is possible — though light travels nearly 300 million meters-per-second — it is not traveling at the maximum speed of a generic, massless particle. The electric constant (ε)might need to be adjusted.
A decrease in the permittivity (resistance) of space (ε) — made obvious by inclusion of vast number of photons in the cosmic microwave background — drives ”ε” to be smaller and ”c” to be larger, right?
New particles, dark and as yet undiscovered, might do the same. The consequences could be significant.
Determining the upper speed of a massless particle requires a form of circular reasoning that is currently based on the measurement of the velocity of photons in a vacuum, which is called the speed of light.
The measured velocity of light in a vacuum is now an established constant of nature with a fixed value that doesn’t change regardless of the frame of reference. Modern labs have measured both the frequencies and wavelengths of various colors of light; multiplying the two numbers together always yields the same result — the speed of light.
Knowing the speed of light permits physicists to establish a value for ε by working backwards in the wave equation to solve for the electric permittivity of space. The value of “ε” falls easily from Maxwell’s Equations to a precision of 12 places.
It can’t be any other way. But is it the right way?
Here’s the problem: Physicists have measured mass in photons during experiments at the linear accelerator lab at Stanford University, SLAC.
In superconductors, photon mass has been measured to be as high as 1.2 eV.
Photon mass has been observed in wave guides and in plasmas.
Fact is, photons have inertial mass, which is a measure of their energy as calculated from their wavelengths or frequencies. In relativity theory, energy and mass are measured in the same units, electron-volts, because in the theory, mass and energy are equivalent.
Click this link to view CLOSER TO TRUTH interview with Raphael Bousso.
Cosmologist, Raphael Bousso, believes that empty space has weight, which is a measure of the cosmological constant, which is a measure of dark energy.
Space seems to be saturated like a sponge with something that gives it energy or force or weight if you will. The weight of empty space determines the size of the universe and some of its fundamental laws. Universes beyond our own with different weights of space can be larger or smaller and obey different rules.
Most physicists agree that photons become massive when they travel through transparent materials like glass, where they slow down by as much as 40%.
The problem is that these observations conflict with both the Heisenberg and the Schrodinger view of quantum mechanics, which is the most tested and confirmed model physicists have. Modern ideas seem to work best when photon mass is placed on the energy side of the mass-energy column. Otherwise, the presence of internal mass suggests that photons can be restrained to a defined size, which drives their momentums to infinity.
The truth is that it is not possible to prove that photons are massless. The stress-energy-momentum tensor in Einstein’s equation of General Relativity implies that photons can be both the source and the object of gravity. I’m referring to this tensor as “mass” and leaving it there for others to dispute. A rabbit hole for courageous readers to explore is the concept of pseudotensor, which this essay will avoid.
It is also not true that a photon can never be at rest either. Lab techs do unusual things with photons during experiments with lasers and superconductors — including slowing photons down and even stopping some (with supercooled helium-4). Right?
Another problem is the electromagnetic nature of light. The electric part of a light-wave carries enough energy to move an electron up and down. The magnetic part carries the same energy but its motion creates a force that pushes electrons outward in the same direction as the light. It’s why light-sails work in space. Oscillating magnetic fields push light forward. Otherwise, light might stand in one place and simply jiggle. But is light-speed the best magnetic fields can do?
Electromagnetism could be irrelevant in the search for an upper speed limit “c“, because “c” might prove to be the result of an unknown set of particles with properties outside the current boundaries of the Standard Model.
Massless particles, — undiscovered ones anyway — might not be electromagnetic. Humans might be biologically unfit to detect them; unable to measure their properties.
For those who might be rolling their eyes, remember that physicists claim that 95% of the mass and energy required to make the universe behave the way it does is missing. They call the missing stuff “dark” because they can’t find it. Excuse me should anyone catch me rolling my eyes.
Some theorists have speculated that “dark photons” might exist to help fill in the gaps. The popular TV show How the Universe Works actually repeated the idea in an episode of its latest series. The writers were probably referring to axions, which some physicists propose are similar to photons except that they have mass and are slower moving.
Photons are bosons. They are force carriers for electrons, correct?
Maybe folks should try to accept the notion that nothing in physics prevents bosons like photons from having mass or from taking on mass when they whiz over and through atoms and molecules (in glass and water, for example) where some physicists conjecture, they stimulate the release of polaritons in their wake. Jiggling electrons that lack the energy to jump states emit polaritons, which seem to add enough equivalent mass to photons to slow them down. Think of polaritons as light-matter wavelets.
Massive, gravitationally interacting photons are not required to be “dark.” If photons are the darkmatter, axions are unnecessary to solve certain problems both in cosmology and the Standard Model. No experiment will find them.
I mentioned that three other particles are presumed to be massless: the gluon, the graviton, and the Higgs boson.
To review, the gluon is not easily observed except in particle colliders where it lives briefly before decaying into other particles; it is confined among the protons and neutrons in the nuclei of atoms. The graviton, on the other hand, has never been observed. The Higgs boson was discovered in 2012. CERN plans to build a Higgs factory someday to explore its properties.
The only particle available to physicists right now that enables them to establish the permittivity of space and compute the velocity of massless particles is the photon.
That’s it.
If the photon has internal mass, i.e., rest mass, everything changes.
Let’s hop into a rabbit hole for a moment and go back a step: What if massless, non-electromagnetic particles mediate entanglement, for example? Wherever paired electrons are found, entanglement rules, right?
Everyone knows that entanglement violates laws of logic and physics. No one can make sense of it.
What if massless non-electromagnetic particles entangle the electromagnetic particles of the subatomic world? If they travel a thousand or ten-thousand times the speed of light, they will present an illusion over short planetary scales that entanglement is instantaneous. No instrument or lab will detect the difference.
What are the consequences if massless non-electromagnetic particles travel at a billion times the speed of light? Maxwell’s equations won’t apply to particles like these.
Because it seems that speeds of subatomic particles like photons are able to increase as their masses approach zero, it is possible that “c” could be orders of magnitude faster than the speed of a photon — that is, the speed of light — if it turns out that photons harbor tiny but significant rest masses.
I’m not advocating this notion. Let’s crawl out of the rabbit hole. I’m suggesting only that such a state of affairs is possible, because the assumption that photons at rest are massless — that internal mass of photons is always zero — though reasonable and desirable to justify models, is not yet settled according to some physicists.
And there is, of course, the phenomenon of entanglement which no one can explain.
Here’s speculation that should blow the mind of any thinking person: Could photons, if shown to have internal mass, be the stuff that make the galaxies move in the non-intuitive ways they do?
Yes, some physicists argue that the upper limit on the internal (rest mass) of a photon must be less than 10-52 kilograms, which is about 5.6E-17 eV for folks who think that way. (Multiply mass by the speed of light twice to make the conversion and divide by 1.60218E-19 Joules per eV.)
5.6E-17 eV doesn’t seem like much mass at all until folks realize that the minimum number of photons in the universe might be as high as 1090. This number is ten billion times the number of atoms in the universe. It means that the internal mass contribution from photons alone could easily exceed 1038 kilograms if the upper limit proposed by some is used to perform the calculation.
Do the math, anyone who doesn’t believe it.
Guess what?
Prepare for a letdown.
Based on the conjectured eVs, the mass of all material in the visible universe is in the neighborhood of 1053 kilograms. The video below will help the reader understand how this value and others are calculated. The mass of the visible universe turns out to be 1,000 trillion times more than the conjectured internal mass of all photons.
Think about it.
Is it enough mass to account for the galaxy anomalies seen by astrophysicists? To any reasonable mind the answer is obviously, no. But this conclusion is not the end of the story.
Those who study astronomy know that the outer stars in galaxies seem to move at roughly the same speed as the inner. Yet the galaxies aren’t flying apart.
By way of contrast, the planets in solar systems like ours travel slower the farther away they orbit from their sun. If Neptune orbited as fast as Earth, it would fly away into deep space.
A recalibration to account for the internal mass of photons of light (which seems to always be discounted) does not at first blush offer the gravitational heft that astrophysicists require to make everything on galactic scales fall into place.
The cosmic background radiation — which is nothing more than photons that decoupled close to the beginning of time — saturates the universe like vinegar in a sponge, right? It is distributed evenly across all space for as far as human-built instruments can see.
The CMB makes an annoying hum in radio telescopes no matter their focus or where they point. Photons with tiny internal masses or no mass at all will have no influence on the understanding by astrophysicists of how the universe behaves.
Neutrinos, which seem to oscillate between three (or perhaps four) as yet undetermined massive states, might at times take on values below the actual mass-value of photons — if photons turn out to be more massive than most believe. The laws of physics require that neutrinos less massive than massive photons, should they exist, must travel superluminally (faster than light). Agreed?
Several “discredited” observations have reported faster-than-light neutrinos, including the unexpected outcome of the infamous OPERA experiment, which inspectors eventually blamed on a loose fiber-optic cable that was ever-so-slightly longer than it should have been.
OK. It seems reasonable. Who can argue?
Scientists who believe that superluminal neutrinos actually exist don’t speak up, perhaps out of fear for their careers. They probably couldn’t get their opinions published anyway, right?
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Crackpot ideas that later prove valid is how science sometimes works. It’s how science has become the mess that it is — a chaos of observations that can’t make sense out of 95% of what is going on all around; a plethora of experimental results that don’t quite match the work of theorists.
The super-brilliant people who paint the mathematical structures of ultimate reality rely on physicists to smear their masterworks with the muds of perturbation, renormalization, and a half dozen other incomprehensible substrates to get the few phenomenon folks think they understand to look right and make sense. Theory and experiment don’t seem to match-up as well as some folks think they should more times than not.
A minor recalibration based on the acceptance of photons as quantum objects with tiny, almost unmeasurable masses will not change ideas about the nature of the universe and what is possible, because the upper-bound on photon masses might be undervalued — perhaps by a factor of billions.
Theorists like Nima Arkani-Hamed work on abstract geometries called amplituhedrons to salvage notions of massless particles while simplifying calculations of scattering probabilities in quantum mechanics. It seems to me like hopeless adventures doomed to fail. But in fairness so did Columbus’s exploration for new worlds.
To be a serious candidate for dark matter, a typical microwave photon should have an average mass of nearly .05 eV (electron volts), which is about 9 x 10-38 kilograms. If multiplied by the number of photons ( 1090 ), the photon masses add almost miraculously to become 85% of the theoretical mass of the universe.
(1E90)*(9E-38) = 9E52. (9E52) / .85 = 1E53 kg.
It’s the same number conjectured by dark-matter advocates.
To qualify for dark matter means that a typical or average photon must have close to one ten-millionth of the mass of an electron.
Only then does everything fall into place like it should.
Pull out the calculator, anyone who doesn’t believe it.
Einstein, in his famous 1905 paper on special relativity, showed that mass is equivalent to the energy of an object divided twice by a constant, which is “c” squared, right?
Later, he added a second term to the internal energy of a particle which is its inertial energy, pc2 . Simplified, this term equals hf for a massless photon. The total energy of any object is the square root of the sum of its internal energy and its inertial energy.
If Einstein is taken at his word, then the inertial mass of a photon is a function of its characteristic frequency — i.e. the inertial mass of a photon is equal to
where “h” is the Planck constant and “c” is the speed of light. The internal mass, should any exist, can be discounted.
An argument can be made from Einstein’s equations that the mass of a photon might be times larger. A factor of 1.414… won’t change the argument. It strengthens the point but is, in the end, not important enough to include in an article that is already overly long. Curious readers can review the reasoning in my essay General & Special Relativity.
If the average photon has an inertial mass of .05 eV, it requires that — all else being equal — the combined photon energy in a non-expanding universe would lie in the range of infrared light, a frequency in this case of 12E12 Hz, which is sometimes referred to as far-infrared.
(Set equivalent-mass equal to .05 eV (8.9E-38 kilograms) and solve for frequency.) The frequency approaches the lower energy microwave part of the light spectrum.
Note:For perspective, one eV is the energy (or mass equivalent) of a near-infrared photon of frequency 242E12 Hz, which approaches from below the higher-energy visible-light part of the light spectrum.
The mass equivalence of the inertial energy of 1E90 infrared photons is sufficient to hold the universe together to prevent runaway expansion caused by repulsion due to the gravity constant Λ in Einstein’s equation for General Relativity.
Do the math.
I know what some people might be thinking: Didn’t the 29 May 1919 solar eclipse, which enabled observers to confirm Einstein’s theory of General Relativity, demonstrate that photons lack internal mass? Didn’t Eddington’s experiment prove wrong Newton’s idea that photons, which he called corpuscles, were massive objects?
Maybe. Maybe not. Maybe internal mass isn’t necessary. There is enough energy in the inertial term of Einstein’s equation to yield the required mass.
Unlike massive particles where internal energy far outweighs inertial energy, for photons, inertial energy is dominant. Even if science admits to a small amount of internal mass in photons, it is their inertial energy that dominates.
I found a good mathematical argument for light mass on Quora by Kyle Lochlann, an academic in relativity theory. Here is the link:
Be sure to read comments to his answer — especially those who find math incomprehensible, which might be nearly everyone who reads my blog.
After all, Newton’s theory of gravity predicted that the light from stars would deflect near the Sun at only half what Eddington’s experiment clearly showed. Eddington’s eclipse proved Einstein’s theory — the geodesics of spacetime bend in the presence of massive objects like stars.
Many concluded that photons followed the geodesics of spacetime, because photons lacked mass equivalence of any kind. Newton erred about pretty much everything involving gravity and light, some said.
But their conclusion can’t be right, can it? Doesn’t their conclusion ignore what the math of Einstein’s formulas actually says?
Won’t it make more sense to say that the geodesics of spacetime constrain and overwhelm whatever internal and inertial mass photons might possess? Doesn’t it make more sense to convert the frequency-related inertial energy of photons to mass to better explain their behavior near objects like the Sun?
Evidence exists that light-mass is a thing and that it matters. Einstein included a mass-equivalence term for light in his tensors for general relativity. Frank Wilczek, MIT Nobel laureate, is famous for insisting that the mass of anything at all is its energy content. The energy of light is in its frequency, its momentum, which is a measure of its mass.
It’s true that light does not seem to interact with the Higgs field. Nevertheless, the energy of light seems to interact gravitationally with ordinary matter. The interaction is not measurable when photon numbers are small. When photon numbers are huge, perhaps it is.
A single photon in the presence of the Sun has no chance. When 10E90 photons saturate a space that is almost entirely devoid of matter, photons can shape a universe — especially when their number is 10 billion times the number of atoms.
It seems possible, at least to me.
According to data gathered by the NASA WMAP satellite, ordinary matter in the observable universe amounts to a little more than 1/4 of a neutron per cubic meter of space. It amounts to 253.33E6 electron-volts of mass. Everything else WMAP observed was “cold dark matter” and “dark energy”.
How many .05 eV photons does it take to flood a cubic meter of space with enough mass-equivalence to reduce the mass-energy of 1/4 of a neutron to 15% of the total? How many photons are required to sum to 85% of the energy WMAP attributed to “cold dark matter”? It turns out that the number is 34 billion photons per cubic meter.
The question is: how many photons are there?
The observable universe has an estimated volume in the neighborhood of 1E80 cubic meters, right? Yes, it might be as much as 4 times that number.
The lower-bound number of photons in the observable universe is 1E90. It might be ten times more.
It turns out that the number photons per cubic meter in the universe must be somewhere close to 25 billion. 25 is pretty darn close to 34. Since all the numbers are estimates with large margins of error, it’s possible that everything will fall into place as it should if and when the statistics of the universe are ever known with precision.
Could photons of light might be the “cold” dark matter everyone is searching for?
A single neutron has no chance when it is bathed in 136 billion .05 eV photons, which surround and envelop it on all sides from every direction. It makes a kind of quantum scale Custer’s Last Stand for random neutrons, right?
When scientists look at the universe today, they see an accelerating expansion. They see in the cosmic background radiation photons that have slipped from infrared into longer, less energetic microwave wavelengths which no longer have enough mass-equivalence to hold the universe together.
As light stretches into longer and longer wavelengths through interaction mechanisms such as Compton scattering and other processes (like the push of “dark energy” or the less popular gravitational tug of parallel universes), light frequencies and energies diminish.
Eventually, when the total of all light falls below an average frequency of 12E12, the equivalent mass of the 1E90 primordial photons loses its grip; it becomes unable to hold the universe together.
Near the beginning of time when photons were orders-of-magnitude higher in frequency than now, their stronger gravitationally-equivalent-masses pulled together the structures astronomers study today, like stars and galaxies.
But now scientists seem to be witnessing a runaway expansion of the universe. Light has stretched and dimmed into the microwave and radio-wave frequencies where its mass-equivalence is unable to hold together the universe as it once was.
Because we can’t detect it, isn’t it possible that dark energy and dark matter don’t exist? That is to say, the idea that dark matter and energy are necessary to account for observations is no more than a conjecture made necessary by a misbehaving universe of unusual galaxies. But direct observational evidence for dark matter and energy is the part of the conjecture that is missing. No one has ever seen any.
What astronomers are observing instead is faraway galaxies that existed billions of years ago when the mass-equivalent energy of photons was greater than it is now.
The intact universe of galaxies seen in the night sky today, which is photographed with high-resolution space-borne telescopes, is not up to date in any sense at all, except that it is the view of an ancient past that goes back almost to the beginning of time depending on how deep into space anyone looks.
Everyone who cares about astronomy knows it’s true.
To qualify as a candidate for dark matter means that a photon must have close to one ten-millionth of the mass of an electron. It seems like a reasonable ratio, right?
In the Standard Model, only neutrinos are less massive than electrons. No one knows what the mass of each of the three “flavors” of neutrinos is, but when added they are less than 0.12 eV — about 2.4 times the equivalent-mass of infrared photons and about one four-millionth of the mass of electrons. It seems possible to me that the mass of at least one of the flavors of neutrinos will be less than the conjectured equivalent-mass of an infrared photon packet.
Neutrons and protons are, by contrast, 2,000 times “heavier” than electrons.
I am asking working physicists to reexamine estimates that claim the mass of a photon can be no more than trillions of times less than the mass of an electron.
The claim can be found at the back of articles in science journals as well as in blogs across the internet. For me, the idea seems ridiculous on its face. The energy-equivalent mass of photons varies with frequency, but only the lowest energy radio wave photons can hope to approach the low equivalent-mass estimated in the latest publications.
Scientists might want to revisit the mass of a photon and the methodology of its measurement. The stakes are high, and science doesn’t have many options. Hope — like the energy of ancient photons — is fading.
Science would be served best if scientists started from scratch to reexamine every assumption and lab procedure. The search for dark matter has become an expensive and compulsive quest that seems futile, at least to me. Several costly experiments have reached disappointing dead ends, which are reviewed in the “VICE on HBO” video located near the start of this essay.
What if photons of light really are the dark matter, which is hiding in plain sight waiting to be discovered by anyone who dares to look at the problem with fresh eyes?
What if the delay between the observations of the CMB (cosmic microwave background) and the structure of the universe is a natural disconnect in time and space that misleads folks to believe that mass must be “out there”, when it has in fact long since dissipated?
From another perhaps opposite perspective, what if photons are instead stimulating emissions from virtual particles as they travel at fantastic speeds through the vastness of space? What if these emissions add mass to photons sufficient to bring them to the “dark matter” threshold, as they do in materials like glass?
Such a state of affairs would imply that not all photons travel the same speed in the so-called vacuum of “empty” space. It is a heretical idea, for sure — a can of worms, perhaps to some, but hey! — you can catch a lot of fish with a can of worms.
A photon is a packet of electromagnetic oscillations built-up from many frequencies. Superposition of these frequencies adds to give a photon its characteristic frequency from which its equivalent mass can be calculated. Right?
Use imagination to think of the many ways a higher “speed limit” that is mandated by the existence of massive photons might work to stimulate the interest of a space-traveling civilization to explore the universe, which ordinary folks begin to understand is more accessible, more reachable than anyone thought possible.
Consider the number of inexplicable phenomena that would make sense if particles thought to have zero internal mass don’t really exist, and photons, gluons, gravitons, and Higgs bosons aren’t the only ones.
Recalibration might save a lot of time and effort in the search for the putative missing energy and mass of the universe.
Should “dark” particles exist whose internal mass is less than that of photons, they will likely move at superluminal speeds that make them difficult to track. To influence stars, their number would have to dwarf photons. Such an idea strains credulity.
A counterproposal by Roger Penrose speculates that dark matter particles might have the mass of the eye of a flea; he calls them “erebons.” These particles are electromagnetically invisible, but their huge masses relative to other particles in the Standard Model make them gravitationally compelling.
Erebons decay; evidence for their decay should be showing up in data collected by LIGO detectors.
So far persuasive evidence for erebons has not been found.
For scientists and explorers, the access-barrier to a universe shaped and configured by massive photons will most certainly shrink — perhaps thousands to millions of times.
The stars and galaxies that people believed were unreachable might finally fall within our grasp.
Or — perhaps less optimistically and more cynically — the mass-equivalent energy of 1E90 photons might by now be so severely degraded that nothing can save a universe that has already come undone and flown away into an abyss that humans will never see.
The radiation-evidence from a catastrophe of disintegrating galaxies that has already occurred won’t reach Earth-bound viewers for perhaps billions of years.
Should humans survive, our progeny — many millions or billions of years from now — may “see” in the vastness of space a cold and diminished radio-wave radiation that hums in a soul-less vacuum devoid of galaxies and visible light. Microwave light will by then be nothing more than a higher-pitched, prehistoric memory.
Roger Penrose says that the fluid dynamics of an exhausted universe devoid of matter will become indistinguishable from the singularity that gave its start. A new universe will ignite from the massless, radiation-ashes of the old.
Human-nature forces us to want to know more; most folks want to search for and find the answers to the questions that will determine the fate of all life on Earth and in the vast stretches of spacetime that remain beyond our reach.
Is the universe within our grasp, or has it already disintegrated?
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
People assume they see nothing, but in every case, when they look closely — when they investigate — they find something… air, quantum fluctuations, vacuum energy, etc.
QUESTION: Is this a large-scale view of the universe or a sub-microscopic view of vacuum energy and quantum fluctuations? Can anyone tell? The universe is not empty. Everywhere anyone looks, at all scales, it seems like there is no such thing as nothing.
Everyone finds no evidence that a state of nothing exists in nature or is even possible.
Physicists know this for sure: there can be no state of absolute zero in nature — not for temperature; not for energy; not for matter. All three are equivalent in important ways and are never zero — at all scales and at all time intervals. Quantum theory — the most successful theory in science some will argue — claims that absolute zero is impossible; it can’t exist in nature.
There can be no time interval exactly equal to zero.
Time exists; as does space (which is never empty); both depend for their existence on matter and energy (which are equivalent).
Einstein said that without energy and matter, time and space have no meaning. They are relative; they vary and change according to the General Theory of Relativity, according to the distribution and density of energy and matter. As long as matter and energy exist, time can never be zero; space can never be empty.
People can search until their faces turn blue for a physical and temporal place where there is nothing at all, but they will never find it, because a geometric null-space (a physical place with nothing in it) does not exist. It never has and never will. Everywhere scientists look, at every scale, they find something.
We ask the question, Why is there something rather than nothing?
Physicists say that nothing is but one state of the universe out of a google-plex of other possibilities. The odds against a state of nothingness are infinite.
Another glib answer is that the state of nothing is unstable. The uncertainty principle says it must be so. Time and space do not exist in a place where nothing exists. Once the instability of nothing forces something, time and space start rolling. A universe cascades out of the abyss, which has always existed and always will. Right?
Think about it. It’s not complicated.
People seem to ignore the plain fact that no one has ever observed even a little piece of nothing in nature. There is no evidence for nothing.
Could it be that the oft-asked question — Why is there something rather than nothing? — is based on a false impression, which is not supported by any evidence?
Cosmic microwave background radiation is a good example. It’s a humming sound that fills all space. Eons ago CMB was visible light — photons packed like the molecules of a thick syrup — but space has expanded for billions of years; expansion stretched the ancient visible light into invisible wavelengths called microwaves. Engineers have built sensors to hear them. Everywhere and at every distance microwave light hums in their sensors like a cosmic tinnitus.
Until someone finds evidence for the existence of nothing in nature, shouldn’t people conclude that something exists everywhere they look and that the state of nothing does not exist? Could we not go further and say that, indeed, nothing cannot exist? If it could, it would, but it can’t, so it doesn’t.
Why do people find it difficult, even disturbing, to believe that no alternative to something is possible? Folks can, after all, imagine a place with nothing in it. Is that the reason?
Is it human imagination that explains why, in the complete absence of any evidence, people continue to believe in the possibility of null-spaces — and null-states — and empty voids?
Photons are mysterious quantities of light which have both wave and particle properties. The odd thing: physicists say they have zero rest mass. All their energy comes from their frequencies, which are invisible fields of electricity and magnetism that oscillate in a symbiotic dance of orthogonality.
A physical packet (quantum) of vibrating light (a photon) can be said to have zero mass (despite having momentum, which is usually described as a manifestation of mass), because it doesn’t interact with a field now known to fill the so-called vacuum of space — the Higgs Field.
Odder still: massive bodies distort the shape of space and the duration of time in their vicinities; packets of vibrating light (photons), which have no mass, actually change their direction of travel when passing through the distorted spacetime near massive bodies like planets and suns.
Maybe people cling to their belief in the concept of nothingness because of something related to their sense of vision — their sense of sight and the way their eyes and brains work to make sense of the world. Only a tiny interval of the electromagnetic spectrum, which is called visible light, is viewable. Most of the light-spectrum is invisible, so in the past no one thought it was there.
The photons people see have a peculiar way of interacting with each other and with sense organs, which has the effect of enabling folks to sort out from the vast mess of information streaming into their heads only just enough to allow them to make the decisions necessary for survival. They are able to see only those photons that enter their eyes. Were it otherwise humans and other life-forms might be overwhelmed by too much information and become confused.
Folks don’t see a lot of the extraneous stuff which, if they did observe it, would immediately disavow them of any fantasies they might have had about a state of nothingness in nature.
If we were not blind to 99.999% of what’s out there, we wouldn’t believe in the concept of nothing. Such a state, never observed, would seem inconceivable.
The reason there is something rather than nothing is because there is no such thing as nothing. Deluded by their own blindness, humans invented the concept of ZERO in mathematics. Its power as a place holder convinced them that it must possess other magical properties; that it could represent not just the absence of things that they could count, but also an absolute certainty in measurement that we now know is not possible.
ZERO, we have learned, can be an approximation when it’s used to describe quantum phenomenon.
When the number ZERO is taken too seriously, when folks refuse to acknowledge the quantum nature of some of the stuff it purports to measure, they run into that most vexing problem in mathematics (and physics), which deconstructs the best ideas: dividing by zero, which is said to be undefined and leads to infinities that blow-up the most promising formulas. Stymied by infinities, physicists have invented work-arounds like renormalization to make progress with their computations.
Because humans are evolved biological creatures who are mostly blind to the things that exist in the universe, they have become hard-wired over the ages to accept the concept of nothingness as a natural state when, it turns out, there is no evidence for it.
Anyone who has witnessed the birth of their own child understands that the child does not emerge from nothing, but is a continuation of life that goes back eons.
The phenomenon of life and death has added to the confusion. We are born and we die, it seems. We were once nothing, and we return to nothing when we die. The concept of non-existence seems so right; the state of non-being; the state of nothingness, so real, so compelling.
But we are fools to think this way — both about ourselves and about nature itself. Anyone who has witnessed the birth of their own child understands that the child does not emerge from nothing but is a continuation of life that goes back eons. And we have no compelling evidence that we die; that we cease to exist; that we return to a state of nothingness.
No one remembers not existing. None of us have ever died. People we know and love seem to have died, physically, for sure. But we, ourselves, never have.
Those who make the claim that we die can’t know for sure if they are right, because they have never experienced a state of non-existence; in fact, they never will. No human being who has ever lived has ever experienced a state of non-existence. One has to exist to experience anything.
Why is there something, not nothing? Because there is no such thing as nothing. There never will be.
A foundation of modern physics is the Heisenberg Uncertainty Principle, right? If this principle is truly fundamental, then logic seems to demand that nothing can be exactly zero.
Nothing is more certain than zero, right? The Uncertainty Principle says that nothing fundamental about our universe can have the quale of certainty. The concept of nothing is an illusion.
An alternative to nothing, is something. Something doesn’t require an explanation. It doesn’t require properties that are locked down by certainty. Doesn’t burden-of-proof lie with the naysayers?
Find a patch of nothing somewhere in the universe.
It can’t be done.
The properties of things may need to be explained — scientists are always working to figure them out. People want to know how things get their properties and behave the way they do. It’s what science is.
Slowly, surely, science makes progress.
Billy Lee
Afterthought: The number ZERO is a valid place holder for computation but can never be a quantity of any measured thing that isn’t rounded-off. When thought about in this way, ZERO, like Pi (π), can take on the characteristics of an irrational number, which, when used for measurement, is always terminated at some arbitrary decimal place depending on the accuracy desired and the nature of the underlying geometry.
Working with ZERO is tricky. Dividing by ZERO is never allowed, which is what was done in the second-to-last line to give the result: 2 = 1. Remember: (a – b) = 0, because a = b.
The universe might also be pixelated, according to theorists. Experiments are being done right now to help establish evidence for and against some specific proposals by a few of the current pixel-theory advocates. If a pixelated universe turns out to be fact, it will confound the foundations of mathematics and require changes in the way small things are measured.
For now, it seems that Pi and ZERO — indeed, all measurements involving irrational numbers — are probably best used when truncated to reflect the precision of Planck’s constant, which is the starting point for physicists who hope to define what some of the properties of pixels might be, assuming of course that they exist and make up the fabric of the cosmos.
In practice, pixelization would mean that no one needs numbers longer than forty-five or so decimal places to describe at least the one-dimensional properties of the subatomic world. According to theory, quantum stuff measured by a number like ZERO might oscillate around certain very small values at the fortieth decimal place or so in each of the three dimensions of physical space. A number ZERO which contained a digit in the 40th decimal place might even flip between negative and positive values in a random way.
The implications are profound, transcending even quantum physics. Read the Billy Lee Conjecture in the essay Conscious Life, anyone who doesn’t believe it.
One last point: quantum theory contains the concept of superposition, which suggests that an elementary particle is everywhere until after it is measured. This phenomenon — yes, it’s non-intuitive — adds weight to the point of view that space is not only not empty when we look; it’s also not empty when we don’t look.
Billy Lee
Comment by the Editorial Board:
Maybe a little story can help readers understand better what the heck Billy Lee is writing about. So here goes:
A child at night hears a noise in her toy-box and imagines a ghost. She cries out and her parents rush in. They assure her. There are no ghosts.
Later, alone in her room, the child hears another sound, this time in the closet. Her throbbing heart suggests that her parents must be lying.
Until she turns on the light and peeks into her closet, she can’t know for sure.
Then again, maybe ghosts fly away when the lights are on, she reasons.
In this essay, Billy Lee is trying to reassure his readers that there is no such thing as nothing. It’s not real.
Where is the evidence? Or does nothing disappear when we look at it?
Maybe ghosts really do fly away when we turn on the lights.
Communicating with distant spacecraft in the solar system is cumbersome and time consuming because the distances are huge and no one can send signals faster than the speed-of-light. A signal from Earth can take from three to twenty-two minutes to reach Mars depending on the position of the two planets in their orbits. Worse, the Sun blocks signals when it lies in their path.
As countries explore farther from Earth to Mars and beyond, these delays and blockages will become annoying. The need to develop a technology for instantaneous communication that can penetrate or bypass the Sun will become compelling.
Quantum particles are known for their ability to “tunnel” through or ignore barriers — as they clearly do in double-slit experiments where electrons are fired one at a time to strike impossible locations. So, looking to quantum processes for signaling might be good places to start to find solutions to long-range communication problems.
NOTE FROM THE EDITORIAL BOARD, May 8, 2019: Sixteen months after Billy Lee published this post, the Chinese launched the Mozi satellite. It successfully carried out the first in a series of experiments with entangled quantum particles over space-scale distances. This technology promises a quantum encrypted network by the end of 2020 and a global web built on quantum encryption by 2030. The Chinese seem to be on the cusp of both FTL communication (through teleportation of information) and quantum encryption.
If scientists and engineers are able to develop quantum signaling over solar-system-scale distances, they might discover later that adding certain tweaks and modifications will render the Sun transparent to our evolving planet-to-planet communications network.
Indeed, the Sun is transparent to neutrinos — the lightest (least massive) particles known. In 2012, scientists showed they could use neutrinos to send a meaningful signal through materials that block or attenuate most other kinds of subatomic particles.
But this article is about faster than light (FTL) communication. Making the Sun transparent to inter-planetary signaling is best left for another article.
Quantum entanglement is the only phenomenon known where information seems to pass instantly between widely placed objects. But because the information is generated randomly, and because it is transferred between objects that are traveling at speeds at or below the speed-of-light, it seems clear to most physicists that faster-than-light (FTL) messaging can’t come from entanglement, certainly, or any other process — especially in light of Einstein’s assertion of a cosmic speed-limit.
Proposals for FTL communications based on technologies rooted in the quantum process of entanglement are usually dismissed as crack-pot engineering because they seem to be built on fundamental misunderstandings of the phenomenon.
Difficulties with the technology are often overlooked — such as spontaneous breaking and emergence of entanglement; progress seems impossible to skeptics. Nevertheless, there may be ways to make FTL happen, possibly. The country that develops the technology first will accrue advantages for their space exploration programs.
In this essay I hope to explain how FTL messaging might work, put my ideas into a blog-bottle and throw it into the vast cyber-ocean. Yes, the chances are almost zero that the right people will find the bottle, but I don’t care. For me, it’s about the fun of sharing something interesting and trying to explain it to whoever will listen.
Maybe a wandering NSA bot will detect my post and shuffle it up the chain-of-command for a human to review. What are the odds? Not good, probably.
Anyway, two serious obstacles must be overcome to communicate instantly over astronomical distances using quantum entanglement. The first is the problem of creating a purposeful signal. (To learn more about entanglement click the link in this sentence to go to Billy Lee’s essay, Bell’s Inequality. The Editors)
The second problem is how to create the architectural space to send signals instantly to a distant observer. Knowledgeable people who have written about the subject seem to agree that both obstacles are insurmountable.
Most scientists say FTL communication is impossible. This post suggests a way to engineer around the impossibility.
Why? It’s because the states of an entangled pair of subatomic particles are not determined until one of the particles is measured. The states can’t be forced; they can only be discovered — and only after they are created by a measurement.
Once one particle’s state is created (randomly) through the mechanism of a measurement, the information is transferred to the entangled partner-particle instantly, yes, but the particles themselves are traveling at the speed-of-light or less. The randomly generated states carried by these entangled particles aren’t going anywhere for very long faster than the speed-limit of light.
How can these difficulties be overcome?
Although the architectural problem is the most interesting, I want to address the purposeful-signal problem first. A good analogy to aid understanding might be that of an old-fashioned typewriter. Each key on a typewriter when pressed delivers a unique piece of information (a letter of the alphabet) onto a piece of paper. A person standing nearby can read the message instantly. Fair enough.
Imagine setting up a device which emits entangled pairs of photons; rig the emissions so that half the photons when measured later will be polarized one way, half the other. No one can know which photons will display which state, but they can predict the overall ratio of the two polarities from a “weighted” emitter.
Call the 50/50 ratio, letter “A”. Now imagine configuring another emitter-system to project 3 of 4 photons polarized one way; 1 of 4 another — after measurement. Call the 3 to 1 ratio “B”. If engineers are able to construct and rig weighted emitters like these, they will have solved half of the FTL communication problem.
Although no one can know the state of any single particle until after a measurement, engineers could identify the ratio of polarization states in a large number sent from any of the unique emitter-configurations they design.
This capability would permit them to build a kind of typewriter keyboard by setting up photon emitters with enough statistical variation in their emission patterns to differentiate them into as many identifiable signatures as needed — perhaps an entire alphabet or — better yet — some other symbolic coding array like a binary on-off signaling system perhaps. In that case, one configuration of emitter would suffice, but designers would need to solve other technical problems involving rapid signal-sequencing.
To send a purposeful-signal, engineers might select an array of emitters and rapid-fire photons from them. If they selected an “A” (or perhaps an “on”) emitter, 50% of the photons would register as being in a particular polarization state after they were measured. If they chose “B”, 75% would register, and so on. After measurements on Earth, the entangled bursts of particles on their way to Mars would take on these ratios instantly.
I believe it might be possible to build emitter-systems someday — emitter systems with non-random polarization ratios. If not, then as is sometimes said at NASA, Houston, we have a problem. FTL communication may not be designable.
On the other hand, if engineers build these emitters, then we can know for sure that when measured on Earth, the entangled photon-twins in the Mars-bound emitter-bursts will display the same statistical patterns; the same polarization ratios. Anyone receiving bundles of entangled-photons from these encoded-emitters will be able to determine what they encode-for by the statistical distribution of their polarities.
Ok. Assume engineers build these emitter-systems and set up a keyboard. How might they ensure that when someone presses a key the letter sent is seen immediately by a distant observer?
How might the architectural geometry of the communication space be configured?
This part is the most interesting, at least to me, because its success doesn’t depend on whether anyone sends a single binary-signal or a zoo of symbols — and it’s the most critical.
It does no one any good to instantly communicate polarization states to bunches of photons traveling at the speed of light to Mars. The signals take three to twenty-two minutes to get there, whoever tells them instantly what state to be in or not. We want the machines on Mars to receive messages at the same time we send them.
How can we do that?
Maybe the method is becoming obvious to some readers. The answer is: photons in Earth-bound labs aren’t measured until their entangled twins have had time enough to travel to Mars (or wherever else they might be going). Engineers will entrap on Earth the photons from each “lettered” emitter and send their entangled twins to Mars. The photons from each “lettered” emitter on Earth will circulate in a holding bin (a kind of information-capacitor), until needed to construct a message.
As entangled twins reach the Mars Rover (for example), anyone can “type-out” a message by measuring the Earth-bound photons in the particular holding bins that encode the “letters” — that is, they can start the process that takes measurements that will induce the polarization-ratios of the “lettered” emissions used to “type” messages. Instantly, the entangled particle-bursts reaching Mars will take on these same polarization-ratios.
I hear folks saying, Wait a minute! Stop right there, Billy Lee! No one can hold onto photons. You can’t store them. You can’t trap or retain them, because they are impervious to magnets and electrical fields. No one can delay measurements for five milliseconds, let alone five minutes or five days.
Well, to my mind that’s just a technical hurdle that clever people can jump over, if they set their minds to it. After all, it is possible to confine light for for short periods with simple barriers, like walls.
Then again, electrons or muons might make better candidates for communication. Unlike photons, they are easily retained and manipulated by electromagnetic fields.
Muons are short-lived and would have to be accelerated to nearly light-speed to gain enough lifespan to be useful. They are 207 times heavier than electrons, but they travel well and penetrate obstacles easily. (Protons, by comparison, are nine times heavier than muons.)
The National Security Agency (NSA) photographs every ship at sea with muon penetrating technology to make sure none harbor nuclear weapons. Muons are particles some engineers are already comfortable manipulating in designs to give the USA an edge over other countries.
We also have a lot of experience with electrons. Electrons are long-lived — they don’t have to be accelerated to near light-speeds to be useful. Speed doesn’t matter, anyway.
Entangled particles don’t have to travel at light-speed to communicate well, nor do they have to live forever. Particles only need enough time to get to Mars (or wherever they’re going) before designers piggyback onto their Earth-bound entangled partners to transmit instant-messages.
Inability to communicate instantly with distant probes like the Mars Rover is degrading our ability to conduct successful missions inside the solar system.
Even if it takes days or weeks for bursts of entangled-particles to travel to Mars (or wherever else), it makes no difference. Engineers can run and accumulate a sufficiently robust loop of streaming emissions on Earth to enable folks, soon enough, to “type” out FTL messages in real time whenever necessary.
As long as control of and access to the emitted particle-twins on Earth is maintained, people can “type out” messages (by measuring the captive Earth-bound twins at the appropriate time) to impose and transfer the statistical configuration of their rigged polarization ratios (or spins in the case of electrons or muons) to the Mars-arriving particle-bursts, creating messages that a detector at that far-away location can decode and deliver, instantly.
The challenge of instant-return messaging could be met by employing the same technologies on Mars (or wherever else) as on Earth. The trick at both ends of the communication pipe-line is to store (and if necessary replenish) a sufficient quantity of the elements of any possible communication in streaming particle-emission capacitors.
Tracking and timing issues don’t require the development of new technologies; the engineering challenges are trivial by comparison and can be managed by dedicated computers.
Discharging streaming information capacitors to send ordered instant messages in real-time is new — perhaps a path forward exists that engineers can follow to achieve instant, long-range messaging through the magic of quantum entanglement.
The technical challenges of designing stable entanglement protocols that will enable an illusion of instant messaging that is both useful and practical are formidable, but everything worth doing is hard — until it isn’t.
times larger. A factor of 1.414… won’t change the argument. It strengthens the point but is, in the end, not important enough to include in an article that is already overly long. Curious readers can review the reasoning in my essay 
, 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?
.
.
