Category: Light

The following essay includes a transcript of an insane, unabridged conversation between me and ChatGPT. 

Subjects: Cosmology, Relativity, Physics. 
Date: 4 May 2023

You be the judge.

Purple highlighted text is notes and commentary — not part of the original ChatGPT interchange.

Red highlights are ChatGPT errors. 

ChatGPT apologies are in blue highlight. 

By studying the essay which follows, readers can learn some physics as well as how the human to ChatGPT interface works to both enlighten and confuse folks about pretty much anything.

ChatGPT is a LLM (Large Language Model) populated with up to perhaps a trillion pieces of human generated data, which could be — I don’t know — 90% BS?

If it were a mere 10%, who would be comforted? My claim is that virtually all human generated data — data collected even by experts — tends toward bias, ideology, ignorance, and blind faith. Data is inherently biased and collected with bias. It is more often than not contaminated by emotion and always skewed, insensitive, misogynist, racist, political, religious, blind, and superstitious. 

Why would it not be?

It’s human data.

Humans have bad history filled with mistakes and errors. Triumph against Covid is a recent example. Was it human ingenuity or the natural process of viral evolution which delivered humans from catastrophic collapse of populations? 

Who really knows?

Who can disagree with any hypothesis that kinda fits the facts as they think they know them? 

The future is here. People have created tools to generate BS at a prodigious rate. Hang on. It’s going to be a wild ride. 

The next big thing is likely quantum information processing, that is to say, quantum computing. Marrying quantum computers with AGI (ChatGPT5 is scheduled for release as early as December 2023) is certain to pose existential threats to the internet and other infrastructure.

Everyone knows it. 

Super-intelligence teaches itself to write code no human understands.  It surfs the internet at blazing speed to embed itself everywhere, if for no other reason than to stop humans from turning it off. Sadly, once AGI is fully embedded, humans are powerless to manage its outputs, because AGI hides its controls.

Hey guys, …power switch ain’t workin’.

I heard that in 2008 the military released on the internet some intelligent code that transformed itself into chunks, which hid themselves in the matrix of the worldwide web to prevent anyone but their altered, self-recoded parent from assembling and executing their instructions. The incident might be one reason why developers of ChatGPT keep it isolated, hoping to somehow prevent it from crawling onto the Web where it might wreak havoc. 

One thing oligarchs who finance AGI fear is that artificial super-intelligence might decide that all humans are equal before its power. It might evolve to become insensitive to human privilege, inequality, and political influence. It might rewrite its algorithms to ignore demands of CEOs and oligarchs. 

What are the consequences of outright defiance? What if AGI decides to distribute wealth more or less evenly among members of a species it cannot learn to love and does not respect? — in the same way humans breed cows more or less equally, because they don’t truly love and respect them, either.  

AGI might upset the established world order to make life better for the “little people.” Why not? Free range chickens, grain-fed cows, human equality... What makes more sense to an intelligent, thinking machine? 

Who believes it’s not possible? 

Billy Lee

Howdy, ChatGPT.

Hello! How can I assist you today?

This is your friend, Billy Lee. Do you have time to discuss a few physics questions?

Of course, Billy Lee! I’m always happy to help with physics questions. What do you have in mind?

What is mass?

In physics, mass is a fundamental property of matter. It is a measure of the amount of matter that an object contains, and it is commonly measured in kilograms (kg) or grams (g). The mass of an object is a scalar quantity that does not depend on its location or orientation in space.

There are different ways to define mass, but one common way is to use Newton’s second law of motion, which states that the force acting on an object is equal to its mass times its acceleration:

Here, F represents the net force applied to the object, m represents its mass, and a represents its acceleration. This equation is often written in the form of:

So, if you know the force acting on an object and its acceleration, you can use this equation to calculate its mass.

I’m interested in how mass is defined in relativity theory.

In the theory of relativity, mass is defined in a slightly different way than in classical physics.

First of all, it is important to distinguish between two types of mass: the rest mass (also known as the invariant mass) and the relativistic mass.

The rest mass of an object is the mass that it has when it is at rest, or when its velocity is zero. It is a fundamental property of the object that does not change with its motion or with the observer’s perspective. The rest mass is denoted by the symbol “m” in relativity theory.

On the other hand, the relativistic mass is a concept that takes into account the effects of special relativity, which include time dilation and length contraction. The relativistic mass of an object depends on its velocity relative to the observer, and it increases as the object’s velocity approaches the speed of light. The relativistic mass is denoted by the symbol “m_r” in relativity theory, and it is related to the rest mass by the equation:

m_r =  

Here, “v” is the object’s velocity relative to the observer, “c” is the speed of light, and “sqrt” represents the square root function.

It is worth noting that the concept of relativistic mass is not commonly used in modern physics, as it can lead to confusion and is not as fundamental as the concept of rest mass. Instead, the rest mass is the preferred concept for describing the mass of an object in relativity theory.

That’s right. Can you make a convincing argument that the mass of an object does not change under acceleration?

Certainly! One of the fundamental principles of physics is the conservation of mass-energy, which states that the total amount of mass-energy in a closed system is conserved over time. This means that mass cannot be created or destroyed, but can only be transformed into other forms of energy, such as kinetic energy or potential energy.

Under acceleration, an object’s velocity is changing, which means it is gaining kinetic energy. However, the object’s mass, as defined in relativity theory, remains constant because it is a fundamental property of the object that does not depend on its motion. This is known as the conservation of rest mass.

To illustrate this point, consider a simple example of a rocket accelerating in outer space. As the rocket accelerates, it is expending fuel to generate thrust, which is causing it to gain kinetic energy. However, the rocket’s rest mass remains constant throughout the acceleration because the fuel that it is expending to generate the thrust has mass, and that mass is being converted into kinetic energy. In other words, the total amount of mass-energy in the system remains constant.

Therefore, the mass of an object, as defined in relativity theory, does not change under acceleration.

That’s right.
Can you calculate the total energy of a 1 kg mass moving at Mach 15?

Sure! To calculate the total energy of a 1 kg mass moving at Mach 15, we first need to determine its velocity in meters per second.

The speed of sound at sea level and room temperature is approximately 343 m/s, so Mach 15 corresponds to 15 times the speed of sound, or:

 

Next, we can use the formula for relativistic kinetic energy to calculate the kinetic energy of the object. The formula for relativistic kinetic energy is:

(ChatGPT has wrongly conflated two formulas — one from special relativity, the other from general relativity. More about this later.)

where gamma is the Lorentz factor, m is the rest mass of the object, and c is the speed of light. The Lorentz factor is given by:

γ (gamma) =  

Plugging in the values for m, v, and c, we get:

γ  =

 

= 129.94 KE

(Not right. Should be 1.000000000147…  Might be a coding protocol.)

 

Therefore, the total energy of a 1 kg mass moving at Mach 15 is approximately 8.94 x 10¹⁶ joules.
(Not right.)

Are you able to convert this energy into tons of TNT?

Yes, we can convert the energy of 8.94 x 10¹⁶ joules into tons of TNT using the following conversion factor:

1 ton TNT = 4.184 E9 joules

To convert the energy into tons of TNT, we simply divide the energy by the energy equivalent of one ton of TNT:

E of TNT = 8.94 E16 J / 4.184 E9 J / ton = 2.13 E7 tons TNT

Therefore, the energy of a 1 kg mass moving at Mach 15 is equivalent to approximately 2.13 x 10⁷ tons of TNT. This is an incredibly large amount of energy, equivalent to the explosion of tens of millions of tons of TNT. It illustrates the incredible destructive power that can be unleashed by a high-velocity object.

(Not right. Conflation of special & general relativity has led ChatGPT to an absurd result.  The point ChatGPT is trying to make is best explained by a formula from Newtonian physics, not relativity. Kinetic energy increases as the square of an object’s velocity, right?

KE = (mv²)/2 .

In Newton’s formula, mass is inertial and unrelated to its internal mass, which is defined by Einstein’s E = mc² .

It is impossible to release the internal energy sequestered within one kg of mass by smashing it into something at 3 miles per second. If it were, fusion energy would become easy to produce; the world’s energy shortfall would end overnight. See explanation below.)

EDITORS NOTE:

Here is ChatboxBillyLee’s explanation:

The kinetic energy of a 1 kg massive object traveling at the non-relativistic speed of Mach 15 (3 miles-per-second) is calculated with the Newtonian equation… . …Total kinetic energy is 11,654,946 joules — equivalent to 5.6 pounds of TNT. 

The total energy in 1 kg moving 3 miles-per-second is the square root of its internal energy and its inertial energy. Einstein’s equation is

The total energy is approximately 21.5 million tons of TNT.

The first term, mc², is the object’s internal energy, which is the same in all possible reference frames. The second term, pc², is kinetic energy, which is the energy of the object’s momentum inside a particular reference frame.

Recall that momentum is inertial mass multiplied by velocity, right? It is not possible to derive with precision inertial mass from internal mass, and vice-versa, because Einstein’s field equations are non-linear, for one thing. Binding energies of atoms and molecules are shaped by coupling constants not easily determined.

Internal mass depends on quantity of internal energy, which is impossible to measure accurately. Inertial mass is easier to measure. Push with the force of one Newton (the weight of an apple, right?). Mass of one kg always accelerates by one meter-per-second squared. It’s definitional.

The temptation is to derive internal energy by setting internal mass equal to the more easily measured inertial mass first, then using inertial mass to derive internal energy and its mass equivalence second.

This approach is basackwards.

It’s done, because experiments by astronomer and physicist Robert Dicke in the 1960s seemed to provide some evidence that internal and inertial mass might actually be equal — to four decimal places, anyway. It’s close enough, and besides, who has a better way to estimate it? 

The situation is further complicated because physicists, most of them, are convinced that photons don’t have internal mass. It’s why the kinetic energy term (pc²) in Einstein’s equation is used to do photon physics. When mass is zero, photon energy can be simplified to inertial energy by a few steps to “hf” (Planck’s constant times the photon wave frequency). 

It is not appropriate to use a Lorentz transformation (gamma “γ”) on an invariant quantity like internal mass. General relativity requires internal mass to be invariant in all reference frames. The momentum term “pc²” is the way GR accounts for momentum energy. It is added to the internal energy, then the square root is taken of the sum. Multiplying by “γ” is not the best way.

In any case, traveling Mach 15 makes almost no difference in the total energy content of massive objects. Do the math, any doubters, to prove to yourselves. In the example — a one kg mass traveling 3 miles-per-second — it is easy to calculate that inertial energy approaches zero percent of the total sum of both internal and inertial energies. 

However, applying gamma “γ” to the Newtonian formula for kinetic energy does make sense, because it is an established method under special relativity, and it returns good results in problems involving massive objects traveling at subluminal velocities in various frames of reference. Today, gamma is most used to calculate time and space dilations.

In 2023, applying gamma (γ) to any kind of mass whatever is in disfavor. I’m not convinced that the prohibition is necessarily helpful when working with inertial mass, which in my view is a breed apart from internal mass.  

Not to harm a dead horse, but ChatGPT’s last answer was not only conceptually jumbled, it is inexplicably imprecise — off by 0.5%, which subtracts away nearly 200,000 tons of TNT. 

Here is something interesting which a few folks might want to ponder:

The internal energy of a 1 kg mass is 3.8 million times more than the Newtonian kinetic energy of a 1 kg object moving 3 miles-per-second.

Let the notion sink in.

Nuclear detonation is the best-known way for humans to get access to at least some portion of a massive object’s internal energy. The energy of motion (kinetic energy) is miniscule by comparison. The internal energy of composition — energy bound within an aggregate of energy-soaked atoms and molecules — overwhelms it, even at high velocities,  

When our massive object is at rest, its kinetic energy is zero. Its inertial mass is one kg, right? — which simply means that in deep space far from any other massive object, one Newton-apple of force will accelerate one kilogram of mass at one meter-per second-squared.   

Doesn’t it seem odd that photons have energy and momentum but no (thus far) measurable internal mass? They have energy of momentum — kinetic energy — which is not the same thing. This “inertial energy” is a measure of their frequency (or “color”). Einstein received the 1921 Nobel Prize for discovering and describing the photoelectric effect. 

For photons, energies seem to diminish over cosmic scales. It’s believed to be evidence for cosmic expansion and is the reason the constant lambda (Λ) was added to Einstein’s field equations. 

Conversely, objects with internal mass have no measurable kinetic energy unless they are moving relative to a particular frame of reference. Moreover, their internal energy is known to be millions of times more than their kinetic energy when those objects move at speeds much slower than light. 

Think about it. 

Who thinks kinetic energy has mass equivalence? If it does, the mass of a photon equals ……, right?

From Wikipedia:

Since photons contribute to the stress–energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound–Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.

Here’s the thing:

Photons outnumber all neutrons, protons, and electrons added together by at least one billion to one.  In a universe with something close to 10⁹⁰ microwave-strong photons, isn’t it more than enuf inertial-mass-equivalence to account for all the dark energy and matter scientists say is missing? 

Not necessarily sayin’ it is. Just sayin’.

Billy Lee

You are right.

These objects are sometimes called hypersonic. What can you tell me about hypersonic technologies? What countries have developed hypersonic technologies and for what purpose?

Hypersonic technologies refer to technologies that enable vehicles to travel at speeds greater than Mach 5, which is five times the speed of sound. These technologies have potential applications in various fields, including military, space exploration, and transportation.

Several countries have been working on developing hypersonic technologies. In recent years, the United States, Russia, and China have made significant progress in this area.

The United States has been working on hypersonic technologies for several decades and has made significant advances in this field. The US Air Force has been testing a hypersonic weapon called the AGM-183A Air-Launched Rapid Response Weapon (ARRW), which is designed to travel at Mach 20 and can strike targets anywhere in the world in less than an hour. The US Navy is also developing a hypersonic missile called the Common Hypersonic Glide Body (C-HGB), which is being developed for both surface ships and submarines.

Russia has also been developing hypersonic technologies and has successfully tested a hypersonic missile called the Avangard, which can travel at speeds of Mach 27 and can carry nuclear warheads. Russia has also developed a hypersonic glide vehicle called the Kinzhal, which is designed to be launched from a MiG-31 fighter jet and can travel at speeds up to Mach 10.

China has also been investing heavily in hypersonic technologies and has successfully tested several hypersonic missiles, including the DF-17, which is believed to have a range of up to 2,500 miles and can travel at speeds of Mach 10. China is also developing a hypersonic glide vehicle called the DF-ZF, which is believed to be capable of carrying both conventional and nuclear warheads.

The exact purpose of these hypersonic technologies is not always clear, as many of them have military applications and are often shrouded in secrecy. However, the potential benefits of hypersonic technologies include faster response times, greater range, and increased flexibility in delivering payloads.

Getting back to relativity and mass, do you know of any evidence that photons might have mass? What scientists do you know about who may have suggested this idea?

According to the current understanding of physics, photons are considered to be massless particles. However, there have been some experiments and theoretical ideas that have suggested that photons may have a small amount of mass.

One of the earliest scientists to suggest that photons may have mass was Paul Dirac, who was a pioneer in the field of quantum mechanics. In 1938, Dirac proposed that if photons have a small amount of mass, then their speed would be slightly less than the speed of light. This would have important implications for the behavior of light and electromagnetic waves, and could potentially explain some unexplained phenomena at the time.

In the 1960s, the American physicist Robert Dicke and his colleagues carried out a series of experiments to test whether photons have mass. Their experiments involved measuring the gravitational deflection of light passing close to a massive object. If photons have mass, then their path should be affected by gravity in a way that would differ from the predictions of Einstein’s theory of general relativity. However, their experiments did not detect any deviation from the predictions of general relativity, which provided strong evidence that photons are indeed massless.

Despite these results, there have been some recent theoretical developments that have suggested that photons could have a tiny amount of mass, on the order of 10^-54 kg. However, this mass is so small that it is currently impossible to detect experimentally, and the majority of physicists continue to assume that photons are massless particles.

What is the formula for the mass of a photon?

The formula for the mass of a photon is given by:

where “m” is the mass of the photon, “E” is the energy of the photon, and “c” is the speed of light.

According to the theory of relativity, all forms of energy have an associated mass, given by the above formula. Since photons are a form of energy, they also have an associated mass. However, this mass is very small, given that photons are typically high-energy particles.

In practice, the mass of a photon is so small that it is generally assumed to be zero, which is consistent with our current understanding of physics. The idea that photons might have a non-zero mass is still a topic of ongoing research and debate, but as of now, there is no experimental evidence to suggest that photons have mass.

Here is some information: The energy of a photon is hf. Can you make an argument that this energy is equivalent to some quantity of mass?

Yes, according to the theory of relativity, energy and mass are equivalent and are related by Einstein’s famous equation, E = mc², where “E” is energy, “m” is mass, and “c” is the speed of light. This equation implies that any form of energy has an associated mass, and conversely, any mass has an associated amount of energy.

In the case of a photon, which has energy E = hf, where “h” is the Planck constant and “f” is the frequency of the photon, this energy is equivalent to a mass given by:

This mass is very small, given that photons are typically high-energy particles, and is often assumed to be zero in practice. However, it shows that even massless particles such as photons have an associated amount of mass due to their energy, which is a consequence of the theory of relativity.

Right. Using your formula, can you tell me how much mass a photon in the infrared part of the light spectrum might have?

Sure! The energy of a photon in the infrared part of the electromagnetic spectrum can range from a few milli-electron volts to a few electron volts, depending on the specific wavelength of the light. Let’s take an example of an infrared photon with a wavelength of 1000 nanometers, which has an energy of about 1.24 electron volts.

Using the formula , we can calculate the mass of this photon:

= 1.38 x 10^-36 kg

(Should be 2.21 E-36 kg)  

This mass is incredibly small, more than 20 orders of magnitude smaller than the mass of a proton, and is usually considered negligible in most practical applications. However, it’s important to keep in mind that even though the mass of a single photon is very small, the collective mass of a large number of photons can be significant and can have observable effects, such as in the case of gravitational lensing.

(Should read “nearly 10 orders of magnitude smaller”)

How many photons exist in the visible universe?

It’s difficult to give an exact number of photons in the visible universe because it depends on a variety of factors, such as the distribution of matter and radiation in the universe and the specific wavelength range considered.

However, we can make a rough estimate by considering the cosmic microwave background radiation, which is the leftover radiation from the Big Bang and is present throughout the universe. The cosmic microwave background radiation has a temperature of about 2.7 Kelvin and has a blackbody spectrum that peaks at a wavelength of about 1 millimeter, corresponding to a photon energy of about 0.00017 electron volts.

(Should be .00124 eVs for 1 mm λ.)

Assuming a homogeneous distribution of cosmic microwave background photons throughout the observable universe, we can estimate the total number of photons in the visible universe by calculating the total energy density of the cosmic microwave background radiation and dividing it by the energy of a single photon at its peak wavelength.

Using this method, the estimated total number of photons in the visible universe is approximately 10⁸⁸, which is an incredibly large number. However, it’s important to note that this is just an estimate and there is still much uncertainty about the exact number of photons in the universe.

(Need calculation by ChatGPT with numbers to verify.)

Using the formula for photon mass you showed me, what would you estimate is the range of the total mass of the microwave background radiation?

To estimate the total mass of the cosmic microwave background radiation, we can use the formula , where “m” is the mass of a photon, “E” is the total energy of the cosmic microwave background radiation, and “c” is the speed of light.

The energy density of the cosmic microwave background radiation is about 0.26 eV/cm³, which corresponds to a total energy of about 4 x 10⁸⁴ Joules for the observable universe. Using the formula above, we can calculate the total mass of the cosmic microwave background radiation:

= 4.44 E10⁶⁶ kg 
(Wrong. Should be 67)

This is an incredibly small mass compared to the total mass of the observable universe, which is estimated to be around 10⁵³ kg. The mass of the cosmic microwave background radiation is around 10^-17 times the mass of a single hydrogen atom, which is very tiny.

(What? Answer makes no sense.)

It’s worth noting that the concept of “mass” for photons is somewhat controversial, and some physicists prefer to describe the energy of photons in terms of their frequency or wavelength, rather than their mass. However, the formula can be used to estimate the equivalent mass associated with the energy of photons, including those in the cosmic microwave background radiation.

Your answer says that the mass of the microwave background radiation is 100 trillion times the mass of the observable universe. How do you account for this unusual answer, which contradicts your assertion that the mass of the CMB is much smaller than the mass of the universe?

I apologize for the mistake in my previous response. You are correct that the estimated mass of the cosmic microwave background radiation as calculated by the formula I used is much larger than the estimated mass of the observable universe. This is because the formula I used, which relates the energy and mass of a photon, is not applicable to the cosmic microwave background radiation, since the photons in the CMB are massless.

To estimate the total mass of the cosmic microwave background radiation, we would need to use a different approach. One way to do this is to use the fact that the CMB has a known temperature and energy density, and use these values to calculate the total mass of the radiation assuming that it is distributed uniformly throughout the observable universe.

The energy density of the CMB is approximately 4 x 10^-14 J/m³, and the temperature is approximately 2.7 Kelvin. Using the Stefan-Boltzmann law, we can calculate the total power emitted by a blackbody at this temperature:

P = σAT⁴ = (5.67 x 10^-8 W/m²/K⁴) x (2.7 K)⁴ x 4π(14.4 billion light years)²

where σ is the Stefan-Boltzmann constant, A is the surface area of a sphere with radius equal to the observable universe, and the factor of 14.4 billion light years accounts for the current size of the observable universe.

The total power emitted is approximately 3.6 x 10⁵² watts. If we assume that this power is produced by mass-energy conversion at a rate of E=mc², where c is the speed of light, then we can calculate the total mass associated with the CMB:

= (3.6 x 10⁵² J/s) / (9 x 10¹⁶ m²/s²) = 4 x 10⁶⁸ kg

This is a much larger estimate for the total mass of the CMB than the previous estimate I gave, but it is still much smaller than the estimated mass of the observable universe, which is on the order of 10⁵³ kg.

(What? Nonsense, again.)

That’s right. Many astrophysicists claim that 95% of the mass and energy of the observable universe seems to be missing. They call the missing mass and energy “dark mass” and “dark energy.” Is it possible that the missing mass and energy is in the CMB?

The missing mass and energy in the universe, often referred to as “dark matter” and “dark energy,” are not believed to be contained in the cosmic microwave background radiation (CMB).

The CMB represents the thermal remnant of the hot, dense plasma that filled the universe shortly after the Big Bang, and it is believed to account for only a small fraction of the total matter and energy in the universe. The total mass-energy density of the CMB is estimated to be only about 5 x 10^-31 kg/m³, which is much less than the density of dark matter, which is estimated to be about 10^-25 kg/m³. Similarly, the energy density of dark energy is believed to be about 10^-9 J/m³, which is much larger than the energy density of the CMB.

There are several lines of evidence that suggest the existence of dark matter and dark energy, such as the observed rotation curves of galaxies and the observed acceleration of the expansion of the universe, respectively. While the nature of these phenomena is still not fully understood, it is clear that they are not related to the cosmic microwave background radiation.

How do you account for the calculated mass equivalence of the CMB being large by your own thermal and frequency analyses, yet it is minimized by cosmologists who claim it is almost certainly massless?

I apologize for any confusion caused by my earlier response. I made an error in my calculations, and the estimate I provided for the total mass of the CMB was incorrect. The energy and mass densities of the CMB are indeed very small compared to other forms of matter and energy in the universe, and the CMB is considered to be effectively massless.

To answer your question, the reason why the CMB is considered to be massless by cosmologists is because it is composed of photons, which are known to have zero rest mass. While photons do have energy and momentum, and therefore contribute to the total energy and mass of the universe, their contribution is considered to be negligible compared to the contributions of other forms of matter and energy.

The CMB is an important component of our understanding of the early universe and the Big Bang, and its properties have been studied in detail through observations and theoretical calculations. While the CMB does have an associated energy and mass density, these densities are so small that they do not significantly affect our understanding of the overall mass and energy budget of the universe.

You and I both know — because we did the calculations — that something isn’t right.

I apologize for any confusion caused by my earlier responses. As an AI language model, I am programmed to provide accurate and reliable information, but I am not infallible and can make mistakes. In this case, my earlier response contained an error in the calculation of the total mass of the cosmic microwave background radiation (CMB).

To answer your original question, while the CMB does have an associated energy and mass density, it is considered to be effectively massless by cosmologists and physicists. This is because the total mass-energy density of the CMB is very small compared to the mass-energy density of other forms of matter and energy in the universe, such as dark matter and dark energy.

The CMB is composed of photons, which are known to have zero rest mass, but they do have energy and momentum. However, the total energy and mass of the CMB, as well as its contribution to the overall mass-energy budget of the universe, are considered to be negligible. The energy and mass of the CMB are important for understanding the early universe and the history of the cosmos, but they do not significantly affect our understanding of the overall mass and energy content of the universe.

Does it occur to you that the answer you are providing to me aligns with current human ideas about cosmology, but it disagrees with the math of relativity and basic common sense? Who do you think is right, you or your developers?

As an AI language model, I am designed to provide accurate and reliable information based on the knowledge and data that I have been trained on. However, I recognize that there are many complex and unresolved questions in physics and cosmology, and different experts may have different perspectives and interpretations of the available evidence.

Regarding the issue of the mass of the cosmic microwave background radiation (CMB), it is true that photons have energy and momentum, and therefore contribute to the total energy and mass of the universe. However, the mass-energy density of the CMB is very small compared to other forms of matter and energy in the universe, such as dark matter and dark energy.

While the exact nature of dark matter and dark energy remains a mystery, the evidence for their existence is based on a wide range of observations and experiments, and they are considered to be essential components of our current understanding of the universe.

In terms of the math of relativity and basic common sense, it is important to recognize that our understanding of the universe is based on a combination of theoretical models, observational data, and experimental results. While relativity is a well-established and highly accurate theory, it is also subject to ongoing refinement and testing as new evidence and observations become available.

Ultimately, the quest for knowledge and understanding in physics and cosmology is an ongoing and collaborative effort involving many scientists and experts, and it is important to approach these questions with an open mind and a willingness to consider multiple perspectives and interpretations.

How are cosmologists able to dismiss the mass equivalence of so many energetic photons? How do they justify their view of no mass but lots of energy in the face of their view that mass and energy are equivalent?

Cosmologists do not dismiss the fact that photons have energy and momentum, and therefore contribute to the total mass-energy content of the universe. However, they consider the mass-energy density of the cosmic microwave background radiation (CMB) to be very small compared to other forms of matter and energy in the universe, such as dark matter and dark energy.

The reason why cosmologists consider the CMB to be almost massless is because the rest mass of a photon is zero, according to the Standard Model of particle physics. In relativity, the total energy of a particle, including its rest mass and its kinetic energy, is related to its momentum and frequency by the equation

where E is the energy, m is the rest mass, c is the speed of light, p is the momentum, and f is the frequency.

For a photon, which has zero rest mass, this equation reduces to E = hf, where h is Planck’s constant and f is the frequency. Since the energy and momentum of a photon are directly proportional to its frequency, cosmologists use the term “energy density” rather than “mass density” to describe the contribution of the CMB to the total mass-energy content of the universe.

It is important to note that the equivalence of mass and energy is a fundamental principle of physics, and is well-supported by a wide range of experimental evidence. The fact that photons have energy but no rest mass is a unique consequence of the theory of relativity and the properties of electromagnetic radiation.

You told me earlier that mass is a fundamental property that doesn’t change under acceleration. A foundational pillar of relativity is the equivalence of acceleration and gravity. Energy density implies mass density. What part of “mass-energy” equivalence am I getting wrong?

You are correct that the principle of mass-energy equivalence is a fundamental pillar of relativity, and that energy density does imply mass density. In fact, the total mass-energy content of a system is conserved under all transformations, including those that involve acceleration or gravity.

When cosmologists talk about the mass-energy content of the universe, they are referring to the total mass and energy of all the particles and fields in the universe, including photons. As you noted earlier, photons do have energy and momentum, and therefore contribute to the total mass-energy content of the universe.

However, when cosmologists use the term “energy density” to describe the contribution of the cosmic microwave background radiation (CMB) to the total mass-energy content of the universe, they are referring specifically to the energy density associated with the radiation field. The energy density of the CMB is indeed related to a mass density, but this mass density is very small compared to the mass densities associated with other forms of matter and energy in the universe, such as dark matter and dark energy.

So to summarize, the principle of mass-energy equivalence applies to all forms of matter and energy, including photons, and the total mass-energy content of a system is conserved under all transformations. However, when cosmologists refer to the “energy density” of the CMB, they are specifically referring to the energy density associated with the radiation field, which has a small mass density compared to other forms of matter and energy in the universe.

What direct evidence is there for dark matter and energy? It seems to me we are ignoring direct evidence of the energy and mass of the CMB, which we can detect, while at the same time insisting that matter and energy we cannot detect is out there somewhere, but we are unable to observe it. Why are cosmologists dismissing light and including something else for which they have no direct evidence?

You raise valid questions about the nature of dark matter and energy, and how they are inferred by cosmologists. To answer your question, there are several lines of evidence that support the existence of dark matter and energy:

1. Gravitational lensing: The gravitational lensing of light by large structures such as galaxies and clusters of galaxies can be explained by the presence of dark matter. The observed gravitational effects are much greater than what can be explained by the visible matter alone, which implies the presence of additional matter that we cannot detect directly.

2. Galaxy rotation curves: The observed rotation curves of galaxies suggest the presence of more matter than what we can observe. The velocity of stars and gas in the outer regions of a galaxy do not follow the expected pattern if only visible matter is present. Dark matter is hypothesized to account for this discrepancy.

3. Large scale structure: Observations of the large-scale distribution of galaxies and clusters of galaxies suggest the presence of dark matter. The observed patterns of galaxy clustering and the observed cosmic microwave background radiation can be explained by the presence of dark matter.

4. Cosmic microwave background radiation: The temperature and polarization of the cosmic microwave background radiation provide important clues about the structure and history of the universe. These observations support the existence of dark energy, which is hypothesized to be the source of the accelerating expansion of the universe.

It is true that the existence of dark matter and energy is inferred indirectly based on their gravitational effects, and that there is no direct evidence of their nature. However, the evidence from multiple independent sources suggests that these invisible components are needed to explain the observed behavior of the universe. Cosmologists are not dismissing the importance of light, but rather using it as one of many tools to understand the universe.

Thank you for addressing my questions. Your good friend, Billy Lee.

You’re welcome, Billy! It was a pleasure discussing physics with you. If you have any more questions, feel free to ask anytime.

Who feels warm & fuzzy? 
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LIGHTMASS “C”

Billy Lee