The mystery of mass is a myth

When you look around on the internet, you can find a whole host of articles about the mystery of mass. For example there’s a Guardian piece by Ian Sample, who says the origin of mass is “one of the most intriguing mysteries of nature”. Or there’s Concepts of Mass by Max Jammer, who says ”the notion of mass, although fundamental to physics, is still shrouded in mystery”. There’s also the ATLAS article by Michael Chanowitz, who talks about uncovering “the deep mystery of the origin of mass”. There’s just one little problem with all that, and it’s this: Einstein solved the mystery of mass over a hundred years ago.

The mass of a body is a measure of its energy-content

Einstein didn’t say mass was a mystery. He said “the mass of a body is a measure of its energy-content”. That was in 1905, in his famous E=mc² paper does the inertia of a body depend upon its energy-content? The answer is yes. As it happens he used L to denote energy rather than E, but that doesn’t matter. What matters is this: “If a body gives off the energy L in the form of radiation, its mass diminishes by L/c²”. A cooling body radiates energy, and in doing so, loses mass. Then when you heat the body up, it gains mass. It’s all very straightforward when you understand why. Unfortunately on a variety of websites you can read that the mass of a body is not a measure of its energy content. For example on Space.com you can read that the mass of an electron is “the interaction between an electron and the Higgs field. And that’s all there is to it”:

Higgs simulation from What the Higgs is going on with mass? by Paul Sutter in Space.com, image credit Lucas Taylor/CMS

The idea comes from the electroweak sector of the standard model, where the weak force is said to be mediated by massive vector bosons. They have to be massive because the force is short range.  See the Wikipedia Higgs mechanism article where you can read that according to Goldstone’s theorem, these bosons should be massless”. If they aren’t, the bosons aren’t gauge bosons, and the theory isn’t a gauge theory. And since electromagnetism is, the result would not be the electroweak theory. So a fix was needed, and it was provided by a number of contributors. They “discovered that when a gauge theory is combined with an additional field that spontaneously breaks the symmetry group, the gauge bosons can consistently acquire a nonzero mass”. Interestingly enough Peter Higgs’s original paper was rejected by Physics Letters in 1964 as not having any relevance to particle physics. So Higgs added a sentence at the end saying it implied “the existence of one or more new, massive scalar bosons”, then he submitted it to Physical Review Letters. It was called Broken Symmetries and the Masses of Gauge Bosons. It’s only a page and a half. You can read all about it in Higgs’s 2017 article on the prehistory of the Higgs boson. The trouble with all that is this: Einstein didn’t say the mass of a body was due to some interaction with some space-filling field. He said the mass of a body is a measure of its energy content, not something else. So somebody who says mass is something else, is saying Einstein was wrong. They’re also saying E=mc² is wrong. It isn’t. There is clearly something amiss somewhere. Sheldon Glashow didn’t call it “Weinberg’s toilet” for nothing.

The toilet of the Standard Model edifice

See Matthew Chalmer’s Particle Headache in the 12 November 2012 issue of New Scientist. That’s where you can read Guido Altarelli saying this: “The minimal standard model Higgs is like a fairy tale”. You can read more in Gian Francesco Giudice’s 2009 book A Zeptospace Odyssey. On page 173 he says this: “The most inappropriate name ever given to the Higgs boson is ‘The God particle’. The name gives the impression that the Higgs boson is the central particle of the Standard Model, governing its structure. But this is very far from the truth”. He also says “the Higgs sector is rather arbitrary, and its form is not dictated by any deep fundamental principle. For this reason its structure looks frightfully ad hoc”. Giudice tells us the mass of a body is the intrinsic energy of a body at rest, and tells us about E=mc². No problem there. The problem comes when he says “the Higgs mechanism accounts for about 1 per cent of the mass of ordinary matter, and for only 0.2 per cent of the mass of the universe. This is not nearly enough to justify the claim of explaining the origin of mass”. He also says the Higgs boson is “like the toilet of the Standard Model edifice”. I wonder if somebody is talking in code here, and I’m reminded of a house that had been used as a squat – the toilet was full of sh*t and it stank to high heaven. By the by, Giudice wrote an essay in 2017 on The Dawn of the Post-Naturalness Era, which featured an an imaginary conversation with Guido Altarelli”.  He’s also head of theory at CERN.

Mass is ambiguous

So yes, there is clearly something amiss. Especially since, as Matt Strassler says, the Higgs boson doesn’t get its mass from the Higgs field. Being generous, I suppose the situation isn’t helped by the way the word “mass” is ambiguous. It’s qualified in different ways to mean different things. There’s active gravitational mass, passive gravitational mass, and inertial mass. Then there’s invariant mass, intrinsic mass, and proper mass. And then there’s relativistic mass, effective mass, and rest mass. But active gravitational mass is a measure of energy, not mass. As Einstein said in 1916, “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. Passive gravitational mass is a measure of energy too. See the Wikipedia mass article, where you can read how “pure-energy” photons exhibit a behaviour similar to passive gravitational mass. Inertial mass is also a measure of energy. A photon is said to be massless, but it has a non-zero inertial mass. This is why as per the last line of Einstein’s E=mc² paper, radiation conveys inertia between the emitting and absorbing bodies:

Invariant mass is something you should forget about because the mass of a body varies with gravitational potential, which is why we have the mass deficit. Since intrinsic mass and proper mass are more of the same, you should forget about them too. Relativistic mass is another measure of energy – in Lev Okun’s 1989 Concepts of Mass you can read how Einstein cautioned against it. That leaves effective mass and rest mass. A photon exhibits an effective mass when you slow it down in glass. Let’s come back to effective mass later. For now, let’s focus on rest mass.

Unqualified mass is rest mass

When you see the word “mass” without qualification, what people usually mean is rest mass. That’s the mass of a body sitting there in front of you. It’s a measure of resistance to change-in-motion. A skateboard has a lot less mass than a car. It’s a whole lot easier to get a skateboard moving than it is to get a car moving. Then it’s a whole lot easier to stop the skateboard than it is to stop the car. Force equals mass times acceleration, and we know that the same force accelerates the skateboard aplenty but not the car. But Einstein said the mass of a body is a measure of its energy-content. So how does that work? Why is a body harder to push if it contains more energy? Like I said, it’s all very straightforward. That’s because of the wave nature of matter, and because most of the time, energy is kinetic energy, momentum is just another way of measuring it, and so is mass.

Kinetic energy and momentum are two aspects of energy-momentum

A 10kg cannonball is a fairly massive body. You can heft it in your hands and feel the mass of it. Let’s say this cannonball is in space, and so are you. You’re wearing a spacesuit, and the cannonball is coming towards you at 10 metres per second. You might say this cannonball has kinetic energy KE=½mv². You might also say the cannonball has momentum p=mv. Now, turn on your backpack thrusters, and catch that cannonball. Apply a constant braking force for as long as it takes to bring that cannonball to a halt:

Astronaut image from the Inverse NASA astronauts article by Danny Paez, cannonball top right added by me

Kinetic energy is looking at this in terms of stopping distance. Momentum is looking at it in terms of stopping time. We divide by c to convert from one to the other, because c is distance divided by time. You cannot remove that cannonball’s kinetic energy without removing its momentum, which is why kinetic energy and momentum are two aspects of the thing called energy-momentum. Like electricity and magnetism, they are two sides of the same coin. But if you’ve ever looked closely at a coin, you will notice that it doesn’t just have a flip side. It has an edge. That coin has a third side. So does energy-momentum, because for mass, you divide by c again.

Photons are always moving

Of course when it comes to a photon in space, you would say it’s always moving at 299,792,458 m/s. This photon isn’t something you can slow down with your thrusters like the cannonball. Nor is it something you can speed up with your thrusters like the cannonball. It’s always moving at the speed of light. So it’s never at rest with respect to you. So rest mass doesn’t apply to a photon. That’s why the photon has no rest mass. Instead it has energy E=hc/λ and momentum p=h/λ, where h is Planck’s constant of action, c is the speed of light, and lambda λ is the photon wavelength. You cannot remove energy without removing momentum, so the photon has energy-momentum. And as per the Compton scattering example, the distinction between energy-momentum and inertia depends on who you say is moving. So how do you fix it so that the photon isn’t moving? You can’t accelerate to 299,792,458 m/s. You can’t chase a light beam and catch it up, as per Einstein’s thought experiment. That’s where Einstein said this: “if one were to pursue a light wave with the velocity of light, one would be confronted with a time-independent wave field. Such a thing doesn’t seem to exist, however”. However it does. Einstein didn’t know it in 1905, because the electron hadn’t been discovered for long. But you don’t pursue the light wave to be confronted with a time-independent wave field, you use another method. It sounds like a cheat, but it isn’t. Instead it’s simple. All you do is catch that photon in a mirror-box.

The photon in the mirror-box

There’s a handy little paper by Martin van der Mark and Gert (not the Nobel) ‘t Hooft called Light is Heavy. It talks about a balance scale, and explains why a box containing hot gas is heavier than a box containing cold gas. Imagine something like a gedanken spring steel box in space full of gedanken spring steel bullets ricocheting around inside. When you push the box, you have to push against the bullets bouncing off the side you’re pushing against. When I tap my magic wand and make those bullets move faster, you find it harder to get the box moving. So the box has more mass. Hence “although nothing at all is at rest inside the box, the gravitational mass is equal to the rest mass of the box as a whole”. Van der Mark and ‘t Hooft go on to replace the gas with light, whereupon the same principle applies. When you push the box, you have to push against the photons bouncing off the side you’re pushing against. When I tap my magic wand and increase the photon frequency, you find it harder to get the box moving. So the box has more mass. It’s heavier too, because gravity bends the light down so it exerts more force on the bottom of the box than the top:

Image from Light is Heavy by van der Mark and ‘t Hooft

The box is a body, and the mass of a body is a measure of its energy-content. So when you catch the massless photon in the mirror-box, it increases the mass of the system. The photon is still moving at the speed of light going around and around inside the box. But because its average location doesn’t change with respect to you, it’s effectively at rest with respect to you. You have effectively stopped the photon, and when you do so, its energy looks like inertia. And if that box is just the right size, the photon will look like a standing wave. Standing wave, standing field. It will look like a time-independent wave field. It will look like it’s standing still. Then when you open the box, what you’re holding in your hands is a radiating body that loses mass. The photon is out of the box in a flash. It departs at c from a standing start. But it wasn’t really a standing start. Because whilst the photon looked like a standing wave, it was always going around and around at c, all the time. Its path changed, that’s all. From a closed path to an open path. It all fits neatly with everything Einstein said about mass and energy. Apart from one little detail: there is no box. Because the electron is a photon in a box of its own making.

A photon in a box of its own making

The van der Mark and ‘t Hooft paper points out that elementary particles have non-zero spin, which “seems to imply that they all must have some sort of intrinsic dynamics”. You betcha. If the electron didn’t have any internal dynamics it wouldn’t have a magnetic moment. It wouldn’t go around in circles in a uniform magnetic field. So yes, “one could say matter is just ‘canned’ energy, a box with internal dynamics, and radiation is free energy”. That’s the size of it. That’s why the mass of a body is a measure of its energy content. The mass of an electron is not some measure of its interaction with distant objects, as per Mach’s principle. Nor is it some measure of its interaction with some kind of cosmic treacle. Because the electron isn’t a fundamental particle. It’s a 511 keV photon in a box of its own making. So is a positron, albeit with the opposite chirality. When you perform electron-positron annihilation it’s like opening one box with another, like each is the key to the other’s lock. Then each is a radiating body that loses mass. All of it. And then the boxes aren’t there any more:

Annihilation image from the CSIRO Australia Telescope National Facility

This is what E=mc² is all about, and it applies to an electron just as much as it applies to a cannonball or a car. I’ve bought the T-shirt, and it isn’t wrong. Einstein even referred to body and electron on the same line. And Einstein wasn’t even the first to think along such lines. JJ Thomson, who discovered the electron in 1897, called it a corpuscle. A corpuscle is a small body, and again: the mass of a body is a measure of its energy-content.

Are not gross bodies and light convertible into one another?

Take a look at the conceptual development of Einstein’s mass-energy relationship by Wong Chee Leong and Yap Kueh Chin. Note their introduction. In 1704, over three hundred years ago, Sir Isaac Newton knew that gross bodies and light were convertible into one another. That’s what pair production and annihilation do. We’ve known about pair production and annihilation since 1932, the thick end of a hundred years. They convert light into matter, and vice versa. Simply by changing the wave path from an open path to a closed path, and vice versa. We start with two high-energy photons, we perform gamma-gamma pair production such that a photon interacts with a photon, and the result is an electron and a positron. Because each photon ends up interacting with itself, and stays interacting with itself, wrapped and trapped as a spin ½ particle. The result is mass, and all we did was convert linear momentum into angular momentum. To do this we had to convert some other linear momentum into angular momentum, because of conservation of angular momentum, and because those photons are the only tool in the box. Not only that, but they are the box. The electron has mass because a photon interacts with itself, not with something else. When it does, we don’t call it momentum any more, we call it mass. We don’t call it a photon any more. We call it an electron. We don’t call it light any more. We call it matter. That’s why we have the strange theory of light and matter. How absurd it gets.

As to why all this isn’t common knowledge I just don’t know. The wave nature of matter is common knowledge. So is electron diffraction. So is the Einstein-de Haas effect, and the Poynting vector. Why isn’t the flip-side symmetry between energy and mass common knowledge? Perhaps the underlying issue is a change of interpretation wherein people think mass is mysterious because they think of energy as some kind of abstract book-keeping thing. Or just the capacity to do work. Or just the property of a thing. Einstein didn’t think that. He thought of energy as thing in its own right. Energy is the one thing we can neither create nor destroy. The thing that’s really fundamental. In his E=mc² paper Einstein used an L for Lagrangian instead of an E for energy, but his meaning is clear. He said this: “If a body gives off the energy L in the form of radiation, its mass diminishes by L/c²”. Radiation is a form of energy. The photon isn’t some billiard-ball thing that has energy. The photon is energy. And matter is made of it. I think the best way to really grasp this is by taking a closer look at Compton scattering:

Image from Rod Nave’s hyperphysics

In Compton scattering some of the incident photon energy is converted into electron kinetic energy. The electron gets kicked aside and the photon is deflected. The photon changes direction and its wavelength increases because it loses energy. The electron is accelerated in the usual sense and the photon is decelerated in the vector sense. Do another Compton scatter on this self-same photon, and another and another ad infinitum, and in the limit there’s no photon left. You can take all the kinetic energy away from a fast-moving cannonball, and you’re still left with a cannonball. But it isn’t the same for a wave. When you take all the kinetic energy away from a wave in the surf, it just isn’t there any more. So the wave is energy. It’s the same for a photon. When you take all the kinetic energy away from a wave in space, it just isn’t there any more. So the photon is kinetic energy. Perform Compton scattering repeatedly with the self-same photon, and in the end it has been entirely converted into the kinetic energy of electrons. And yet, and yet: in pair production, you can make an electron and a positron out of a photon. So the electron is kinetic energy too. But now this kinetic energy is hidden. We call it mass-energy. Or potential energy. Or field energy. Only there’s angular momentum in this field, and a secret Poynting vector going around and around. Because of this, electrons have their dipole magnetic moment, and go round in circles, helixes, or spirals in a uniform magnetic field. Or drift in a non-uniform magnetic field. That’s why we have magnets. That’s why when you annihilate that electron with a positron you see 511 keV photons racing away at the speed of light. From a standing start. Because in atomic orbitals and everywhere else, electrons exist as standing waves. Standing wave, standing field. Standing waves that only look like they’re standing still.

Electron mass is resistance to change-in-motion for a wave going around and around

This is why the mass of a body is a measure of its energy content. If there is no energy content, there is no body. Photon energy or photon momentum is a measure of resistance to change-in-motion for a wave moving linearly at c. Electron mass is resistance to change-in-motion for a wave going around and around at c. That’s it. It’s as simple as that. That’s all there is to it. Matter is made of energy and that’s the only ingredient. The rest mass of an electron is a measure of how much energy is in there going around and around in circles at c, going nowhere fast. The electron’s energy is 511 keV and its rest mass is 511 keV/c², only it isn’t really at rest. The electron’s kinetic energy is a measure of the extra energy that makes it move. It tells you how fast this energy that’s going nowhere fast, is going somewhere. But it can never go as fast as light because it is light, going around and around. Accelerating an electron can be likened to stretching a helical spring. Getting the electron moving is like deforming an open circle of spring steel into one turn of a helix. The energy required increases as we attempt to deform it further. As we accelerate more and more, the helix is effectively stretched straighter and straighter. But a photon travels at c, it can’t travel in a straight line at c and still be going around in circles at c. It would have to go faster than light to do that. And light doesn’t go faster than light. So matter can’t travel as fast as light. Matter can’t go faster than the light from which it’s made.

Mass can vary

Not in vacuo, anyway. Cherenkov radiation is akin to a sonic boom, because the speed of electrons can exceed the phase velocity of light in water. Light is slowed down in a material such as water. When you slow down a photon it exhibits an effective mass. Some of its energy-momentum is effective as mass. When you slow it down further, more of its energy-momentum is effective as mass. When you slow it down to an effective speed of zero by trapping it in a mirror-box, all of its energy-momentum is effective as mass. Hence as Henri Poincaré said, “what we call mass would seem to be nothing but an appearance”. The lesson to learn is that there’s no substantial difference between effective mass and mass, there’s just a sliding scale between the two. So, if the speed of a photon varied a little as it propagated through free space, its mass would vary a little. Of course, we’re confident that this doesn’t happen for photons, but oranges are not the only fruit, and quark is not the only cheese. Talking of which, there is such a thing as the mystery of quark mass. A proton consisting of two up quarks and a down quark has a mass of 938MeV. A neutron consisting of an up quark and two down quarks has a mass of 940MeV. A π+ pion consisting of an up quark and a down antiquark has a mass of 140MeV. A ρ+ rho meson consisting of an up quark and a down antiquark has a mass of 770MeV. Something doesn’t add up here:

Image from Rod Nave’s hyperphysics

It sounds as if there’s something wrong here. I am reminded of quantum electrodynamics, the first quantum field theory. It suffered from the “problem of infinities”, so much so that some authors say most workers in the field doubted its correctness, whilst others say physicists were so overwhelmed by the problems that they believed a conceptual change was needed. It didn’t happen.

A problem in the foundations of particle physics

In their 1993 essay on the conceptual foundations and the philosophical aspects of renormalization theory, Tian Yu Cao and Silvan Schweber say “serious doubt has often been cast on the whole program”. They describe QED as a conceptually unstable theory, and say a stubborn historian might reject it. They also say renormalization “took the framework of QFT as given, and made no attempts to alter its foundations”. They go on to say that “what is hidden in the locality assumption is an acknowledgment of our ignorance of the structure of the electron”. Could a similar issue apply elsewhere? Yes. See asymptotic freedom and QCD – a historical perspective by David Gross dating from 2004. He says “by the 1950s the suspicion of field theory had deepened to the point that a powerful dogma emerged – that field theory was fundamentally wrong, especially in its application to the strong interactions”. And that “the feeling of most was that renormalization was a trick”, one that “simply swept the infinities under the rug”. He also said “quarks had not been seen, even when energies were achieved that were ten times the threshold for their production”. And that “the non-relativistic quark model simply did not make sense. The conclusion was that quarks were fictitious, mathematical devices”. That sounds interesting. Let’s investigate this. Let’s take a look at what the proton is, and what it is not.

NEXT

1. Hi John, another high quality article. You mentioned a photon in a box of its own making. That is one of ideas I have explored in a lot of detail I will write about it at an appropriate time. The thing that got me thinking in that direction in the first place was, in part, the lecture I did on Schroedinger’s wave equation. The solution is for an electron in a box. The box is actually a voltage potential box. If the localized energy of of the electron as a standing wave is creating its own box, then the actual situation is consistent with Schroedingers assumption. The wave equation solution in a finite sized box gives the electron energy levels constrained to specific levels. If voltage and mass / quantity of energy is equated with gravitational potential then given enough energy an electron can climb out of a local energy well, like an atom, and you have the photo electric effect. There is a lot more to explore in cubic geometry and it relation to, and transformation to spherical geometry. Incidentally, once you know that Schroedingers wave equation is solved for the electron in a box, it explains why the cat came in to illustrate macroscopic versus atomic level objects. If the electron is constrained in an atomic box and the cat is made of atoms, then it is ridiculous to consider the cat in the box.

1. Sorry Andy, the above comment was in the spam folder. I can’t see why I’m afraid. I guess you repeated it. Utmost apologies for the inconvenience, but I was “under attack” a couple of weeks back, and set up a long list of words in the spam detector. I’ve since changed tack, so I hope the problem doesn’t recur. But please save your comment before posting just in case.

2. Hi John, excellent work again. I was particularly interested in you description of a photon in a box of its own making as it ties in with many of my thoughts regarding cubic topology. However, I intend to write ore on that at another time. It does however remind me of my introductory lectures in semi-conductor physics. The solution to the Schroedinger wave equation is presented as the solution for an electron in a box. The box in question appears to be the voltage potential field of the atom which is a vertical sided potential forming a box that constrains the electron, and in which only certain energy levels are allowed due to the self-interference of wave trapped in the box. This fits with the idea of a standing wave electron that you have talked about, which is able to only take on quantised levels of energy from photons due to the energy level constaints of the box it is constrained within. Once you realise that the box the electron is in is an atomic size box, of a couple of nano-meters in side length, the story of Schroedinger’s cat can be seen to be ridiculous as it was supposedly, originally intended to be. Cats are made up of atoms as are all macroscopic objects. Therefore, the quantum box is inside the cat and it makes no sense for the cat to be inside the box. No matter how good probability maths is at describing the subatomic situation the out come is photons and electrons moving in very regular numbers between atoms to bring about the behaviour we observe at a macroscopic level. So macroscopic events and the probability description of the subatomic situation are incompatible. However, if you consider what is going on inside the atom as actual trapped waves of electromagnetic potential, rather that probability waves things make a lot more sense. I suspect that physics suffers from a psychological problem called “functional fixedness”. It is the inability to discriminate two interpretations for things that appear the same from one point of view. So, because the wave equation maths appear to look like probability expressions the mathematicians say, because we are using equations with the form of probability expressions, the real world situation they represent must relate to probability. They overlook the that the wave nature of electromagnetism can give rise to expressions of the same form. The same form but describing voltage potential distribution, not probability. Also, because they are looking for point particle solutions rather than considering that everything is just waves of electromagnetic potential of different lengths distributed in space and often wrapped back around on themselves in loops of helical electromagnetism. Waves, have a finite wavelength. Particles are infinitesimal mathematical concepts. If you view the particle as a description of the effect of the wave energy related to a point described by the wave centre in space, then you have two viewpoints that can be mutually compatible. Rather than a particle wave duality paradox. Keep up the good work. I look forward to your next blog.

1. Thanks Andy. I’ve just added a paragraph to this one about Gian Francesco Giudice.
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There’s an interesting thing about the electron in the box. When you treat the electron itself as a photon in a box, and then move the box around and around a proton in little circles, the standing-wave photon that “fits in the box” has a longer wavelength. Hence the system features less kinetic energy. Hence negative binding energy, wherein the bound electron has less mass-energy than the free electron. The proton is also affected of course, but not so much. I talk about the proton next.

3. Hello. I posted a comment with some links, but it seems it didn’t passed the spam filter.
You can download a book from there. It talks exactly about what you describe here: Matter is just confined light. From there, John A. Macken is able to describe almost all phenomena that takes place in the universe. Its a fascinating reading.

1. the physics detective

Sorry about that. I’ve been getting a lot of spam recently. I unspammed it, here it is. I’ve seen John Macken’s material before, and I’d say he’s barking up the right tree, though with some things that need fixing. By and large I’d say more and more people are homing in on the correct physics and seeing that the Standard Model has serious issues. I’ll take a look at the links you posted. But I can’t do that right now because it’s a full house here. Happy Christmas!

4. John,

What happens to a photon in a lightbox when you lower it to the event horizon of a black hole?
Does the velocity go to zero?
Does the mass go to zero?
Does the energy to zero?
Does the frequency go to zero?
Is the photon still there but frozen or does it completely disappear, never to return?

1. Don, as far as I can tell, the speed of the photon inside the box goes to zero because c is reducing. However conservation of energy says the energy doesn’t change. I know we say E=mc² which would then imply that the mass is reducing, but that doesn’t feel right. Otherwise a black hole made up of a zillion photons in lightboxes would have zero mass.
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The frequency doesn’t change. See page 149 of Relativity, the Special and General Theory where Einstein said “an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated“. The frequency of the ascending photon doesn’t change, nor does the frequency of the descending photon. However if light is totally stopped the frequency is academic. As far as I can tell the photon is still there, but it’s reduced to a immobile “pressure pulse in space”. As such it contributes to the black hole’s gravitational field.

1. Anders

The picture I like to imagine is the frequency going so high that the wavelength hits the Planck length, essentially maxing out, so that the energy density of space inside the black hole is as high as it can possibly be. Space is “full”.
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So the wave is there but the distance it covers is virtually zero, which means that its speed is zero. And of course, all waves inside the event horizon interact and get in the way of all other waves (or the arrested reflection of one and the same wave if you will), creating the ultimate traffic jam. It’s a big box that’s filled with light to capacity and therefore is black.
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(And maybe all the light within is polarized the same way.)
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This way the energy doesn’t go to zero; if it did there would be no mass and no gravitational field around it, and we know that the opposite is the case.

1. I quite like that picture, Anders. But IMHO the frequency of the upward photon doesn’t decrease. Instead we see red shift at a higher elevation because the upward photon was emitted at a lower frequency. Flip this around and it means the frequency of the downward photon isn’t changing. But yes, I think the spatial lenergy density maxes out and space is “full”. It’s as if it’s reached some kind of compressional elastic limit. I’m not sure if the individual waves retain their individual identity in a place like this. Like Greg was saying. this reminds me of a BEC.

1. Anders

Thanks John. And yes you’re right, I had reservations about the frequency variation but wanted to throw it at the wall, but it makes more conservation-of-energy sense to abandon that. I still think the light is trapped in there somehow, carrying the total energy which doesn’t change or leak out. I like the BEC state description too with its low temperature and slowing of light by interference.
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Now if the energy is what it is, maybe we should look at the equation from the perspective of mass: m=E/c². The lower the speed of light, the higher the mass. I don’t know if that impacts matter falling toward the event horizon (because its inertia increases), but inside the icebox it would mean monstrous mass for a given E when c is close to zero. Until we divide by exactly zero and it breaks down – I don’t believe in infinities and singularities in the real world so let’s call it virtually zero.

1. Anders

It occurred to me that to keep E = hc/λ unchanged, the wavelength must decrease with c. That would mean proportional compression and slowing of light in gravity, for a given photon frequency.

2. I’m not sure we are talking about a monstrous mass here Anders. Note what I said in the article about the cannonball. Its kinetic energy is a measure of stopping distance, and its momentum is a measure of stopping time. These two measures are two sides of the energy-momentum coin. The difference between them is a division by c, but you cannot reduce the energy without reducing the momentum. I think it’s similar for mass where there’s another division by c. It’s the “third side of the coin”, as it were. Hence I think m=E/c² is an SR expression that doesn’t really work in a GR situation where c is varying. To be honest, I don’t like to see a c in any expression to do with gravity. Such as rₛ = 2GM/c². Which contains an M for mass!

2. John,

I have learned so much from reading your articles that I must thank you for eliminating much of my confusion. However, this simple thought experiment can reveal more.

You said that the mass of a photon in a lightbox is due to the photon hitting the sides of the box. If the photon is not hitting the sides of the box then there cannot be any mass. That would also agree with the fact that any massive object falling in a gravitational field loses mass. So I think anything reaching the event horizon has no mass.

But the million-dollar question is, does the energy go to zero? I think energy does go to zero. If we look at the equation E = mc² and plug in a mass of zero or the speed of light as zero, it predicts zero energy. So Einstein’s equation agrees. Then there is the equation for the energy of a photon: E = hc/λ. Plug in a c of zero and the energy is zero. So that equation also agrees. Also, when scientists try to cool something down to absolute zero degrees, they keep taking energy out and the motion of whatever they are cooling gets slower and slower. These scientists are always talking about achieving zero energy.

So why does a black hole have so much mass? It takes an infinitely long time for anything to reach the event horizon. This universe is less than 14 billion years old. I think the vast majority of the mass has not reached the event horizon and will not for trillions of years.

I wonder if the energy of all the mass falling into a black hole can be simulated?

1. Don:
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Go back to the falling electron. It’s like a photon in a box of its making. A gravitational field is a place where there’s a gradient in the speed of light. This refracts some of the “round-and-round” kinetic energy into downward kinetic energy. Hence the round-and-round kinetic energy is reducing. Hence the mass is reducing whilst the total energy stays the same. If the electron keeps on falling, the increasing downward speed will approach the local speed of light, at which point I think the electron breaks up and you see a gamma burst.
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Your motionless photon in a box at the event horizon is something different. The photon isn’t hitting the side of the box, so there is no mass, but if you’re also at the event horizon, you’re motionless too, so you can’t push it. However the energy content is the same, and the mass of a body is a measure of its energy content. So the mass is unchanged. On the way there if E is unchanged and c is reducing then E = mc² says m is increasing. However c goes to zero so I think equation E = mc² doesn’t really work in this situation. Ditto for E = hc/λ.
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As for the million-dollar question, I know of no situation wherein conservation of energy does not apply. And note this article: What is energy? At the fundamental level, I think energy is “a volume of stressed space”, and that hasn’t changed. The photon at the event horizon is still a lump of space pushing outwards on the surrounding space, so contributing to the gravitational field. As such the “active gravitational mass” is non-zero, and that’s said to be equivalent to the inertial mass. A photon moving at the speed of light has no rest mass, but it has an inertial mass. Catch the photon in a box and it isn’t moving relative to you so it’s effectively at rest, so now it has rest mass too. If the photon is motionless at the event horizon, IMHO the same applies.
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It takes an infinitely long time for the downward photon to reach the event horizon, because it’s slowing down to zero. But remember the hailstone analogy. That’s “simulating” the energy of all the mass falling into a black hole. A water molecule doesn’t pass through the surface of the growing hailsttone. Instead it gets surrounded by other water molecules, and the surface passes through it. The result is one big solid lump. I think it’s similar for a black hole, which I think of as a “frozen star”. It’s like one great big round lump where space is as dense as it can get. Where the speed of light is zero. That means the usual mechanism for falling down just isn’t there. Which I think is really interesting.

5. Don, I really like John’s previous exploration of The Frozen Star concept. And his speculation that the photons and other particles could also be part of a possible BEC mixture.

1. I also like John’s concept that a black hole is a frozen star. I am just saying that I don’t think that all the mass has reached the event horizon.

6. John, I just don’t believe that things stuck in an event horizon can have zero motion which would mean zero energy. I have been trying to point out there are problems of such an assumption. But I believe I have stumbled on to a better explanation. In a strong gravitational field, everything accelerates towards the center of gravity until they cannot go any faster. The velocity of everything approaches the speed of light. Objects acquire more energy and become more massive. Objects stop accelerating when they reach the speed of light. They appear to be not moving when viewed by an outsider observer but instead, they are moving very fast. You still have your frozen snowball and I have my motion.

7. the physics detective

Don: zero motion doesn’t mean zero energy. In its most fundamental form energy, appears to be “spatial pressure”. It’s this that results in a gravitational field. Not the motion of this spatial pressure, like what we see with a photon. A photon still causes gravity even when it’s configured as a standing wave with no apparent motion, like the photon in the box. Ditto if it isn’t moving because it’s at a place where the “coordinate” speed of light is zero.
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A strong gravitational field is a place where there’s a steep gradient in this “coordinate” speed of light, so there’s a problem with your scenario. The downward speed of an electron increases because the speed of light is reducing, and falling bodies do not slow down. That means the electron would have to end up falling faster than the speed of light. That just can’t happen, so the result is, I think, a gamma-ray burst. Have a read of this: https://physicsdetective.com/firewall/ .
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Also note that when it comes to gravity, we have the mass deficit, see this: https://en.wikipedia.org/wiki/Binding_energy#Mass%E2%80%93energy_relation. That’s because gravity converts potential energy into kinetic energy. When a brick hits the ground this kinetic energy gets dissipated, so you’re left with a mass deficit. The falling brick is not gaining any energy. Conservation of energy applies. Instead you do work on the brick when you lift it up. You add energy to it. As a result, its mass increases. It’s the flip side of the mass deficit.

1. John, thanks for responding to my poorly thought out comment.

I am still trying to understand what your “spatial pressure” is. When I think of pressure I think of lbs/in². I don’t think you mean that so I get confused. What kind of pressure do you mean? How does it extend beyond a massive body? How does it pass through all materials uninhibited?

Also, when a photon gets to the event horizon, do the electro and magnetic waves freeze at some random magnitude? Are they still waving but not moving in any direction. Or are they a standing wave? Do the electric and magnetic fields still exert force?

I agree, falling objects in a gravitational field will lose mass when they are stopped and they lose all their kinetic energy. When an electron approaches an event horizon, does it lose so much mass and energy that it decays into a photon? Do other subatomic particles do the same?

1. the physics detective

Sorry to be slow replying Don. Spatial pressure is exactly that. Space has this elastic nature, waves run through it. Einstein’s stress-energy-momentum tensor has a shear stress term and an energy-pressure diagonal, and it “describes the density and flux of energy and momentum in spacetime”. Think of the universe as something like a squeezed-down stress ball. It has this “cosmic pressure”. That’s what Schrodinger called it. Now open your fist and watch it expand. Only the pressure through the universe isn’t uniform. When there’s a pressure gradient in space, we call it a gravitational field. It extends beyond a massive body because matter is made of energy and at the fundamental level, ,energy appears to be the same thing as space. So you can emulate a massive body in space by injecting space in space. See where I talked about the hypodermic in how gravity works. It passes though all materials uninhibited because atoms don’t consists of 99% empty space. That figure is wrong by 1%.
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When a photon gets to the event horizon, it stops. I view the photon as a soliton, a single electromagnetic wave. Once it’s stopped it isn’t waving, it’s now like a bulge in space. A pulse of pressure. Yes, we now have a standing wave. I don’t think this exerts electromagnetic force, but I do think it exerts gravitational force.
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I think that when an electron approaches an event horizon, it loses so much mass that it’s no longer stable, and it decays into one or more gamma photons and/or neutrinos. The result is a gamma ray burst. I think the same happens to other subatomic particles. In all cases energy is conserved. Gravity converts potential energy, which is mass-energy, which is internal kinetic energy, into external kinetic energy. This cannot happen without limit.

1. John, from your previous statement I believe you are saying that massive bodies inject space into space creating pressure. Does this mean that a vacuum bottle with an internal pressure of 0 lbs/in² in the orbiting space station would increase in pressure if it was brought down to the surface of the Earth? In fact, any closed rigid container would have a change in internal pressure whenever its distance from the center of the Earth was changed. Do you agree with this statement?

1. No. The pressure I’ve spoken about isn’t gas pressure. It’s the “pressure of the vacuum”. So your vacuum bottle with an internal air pressure of 0 lbs/in² would register 0 lbs/in² at all elevations. I don’t know how you would actually measure this “pressure of the vacuum”. I’m not even sure if pressure is really the right word. But Schrodinger spoke of “cosmic pressure” in 1918, and the stress-energy momentum tensor has an energy-pressure diagonal, so it seems like the best word available.

1. John, thanks for giving me more clarity on what you mean by pressure. Personally, I find it very confusing to use the word pressure as the stuff gravity creates to slow light.

The video https://www.youtube.com/watch?v=CUjt36SD3h8 claims that materials have an equivalent electromagnetic wave frequency that interferes with the frequency of light to slow the propagation speed of light. Maybe neutrons and protons transmit some sort of wave that interferes with light to slow the speed of light. Maybe they transmit gravitational waves.

The article https://physics.stackexchange.com/questions/342625/do-electromagnetic-waves-interact-with-gravitational-waves says that gravitational and electromagnetic waves do interact but I don’t understand the details.

1. I think that video by Don Lincoln is pretty good. But the speed of light varying with gravitational potential isn’t the same as the speed of light varying in glass. The glass can behaves as a prism, separating the light by frequency to yield a rainbow. That just doesn’t happen with gravitational lensing: the slowing-down of light in a gravitational field is not frequency dependent. And don’t forget that it’s a concentration of energy that causes gravity, not just matter. So it can’t be neutrons and protons transmitting waves that causes gravity. See what I said in https://physicsdetective.com/the-theory-of-everything/ about the photon. See the second image, and note this: “As for the cells in the upper portion of the picture, note that most of them are twisted, with a spin-1 characteristic. You have to rotate them by 360° before they look the same again. Now look up the centre, where the cells are rectangular. They have a spin-2 characteristic”. Even a photon results in a gravitational field. If you had a zillion out-of phase photons all offset from one another by a small amount, the whole grid would look like the central section, and the result would be a gravitational field. See the 7th and 8th images in that article. In a way, the photon is a gravitational wave as well as an electromagnetic wave. Do gravitational waves and electromagnetic waves interact? Yes of course. When the gravitational wave is passing through, photons go slower.

1. John, thanks for letting me know that gravity doesn’t create a rainbow when bending light. I was wondering about that.

I read your TOE article and I get some of it but most of it is beyond my Physics understanding. I am learning slowly.

In my previous message, I suggested that gravity slows light because gravity is actually some type of wave that interferes with all other types of waves such as matter, energy, and electromagnetic waves. But now I am thinking that gravity is a transverse wave and the gravitational waves that physicists detect are longitudinal changes in the normally steady waves of gravity. Does this make sense to you?

1. Gravitational waves are said to be quadrupole waves, Don. And quadrupole waves are said to be transverse waves, but more compicated than the usual dipole waves. See this section of the Wikipedia article:
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https://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_passing.
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Also note this in the history section: When Einstein published his general theory of relativity in 1915, he was skeptical of Poincaré’s idea since the theory implied there were no “gravitational dipoles”. Nonetheless, he still pursued the idea and based on various approximations came to the conclusion there must, in fact, be three types of gravitational waves (dubbed longitudinal–longitudinal, transverse–longitudinal, and transverse–transverse by Hermann Weyl)..
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I’ve never written an article on gravitational waves. I don’t doubt they exist, because I think waves are more fundamental than fields, and neutron stars do lose energy. But I’ve never actually researched gravitational waves. Maybe I should. I’ve been meaning to write an article about LIGO.
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Meanwhile note that any concentration of energy has a gravitational effect, so a photon isn’t just an electromagnetic wave, it’s a gravitational wave too. Only that aspect of it is so weak you wouldn’t notice it.

1. Anders

I hope that you will write an article on gravitational waves, John. They are an important part of the puzzle.
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I see them as similar to a cosmic tsunami – an immense pressure wave of energy in the sea of space, distorting the dimensions of spacetime along its path, but not affecting gravity itself, per se. Different kind of energy. Gravity isn’t a wave, there are no gravitons.
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I like to imagine gravity as essentially a feature of electromagnetism, when EM energy is bound in a stable configuration. A gravitational field would then be where a concentration of energy makes local EM fields tend to cancel out (or in the case of black holes completely cease to exist), causing nearby objects to naturally seek the lower EM potential, which means “downward” motion.
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I have no idea if this makes sense!

2. I’m not sure gravitational waves are an important part of the puzzle, Anders. Photons propagate long distances because they’re solitons, but for all I know a gravitational wave spreads out like a sound wave. A tsunami in a very large ocean would end up being the tiniest ripple on a far distant shore. Or even undetectable.
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I think you’re right about gravity being a feature of electromagnetism, because c varies and c = 1/√(ε₀μ₀). For an analogy, imagine space is some sort of stiff elastic lattice. You grab it with your left hand and twist anticlockwise to emulate the electromagnetic field of an electron. Then you grab it with your right hand and twist clockwise to emulate the electromagnetic field of a proton. The opposite twists cancel, so there’s no net electromagnetic field. However both twists pull in the lattice, so they don’t net to nothing. Gravity of course is an outward push rather than an inward pull, but I think the analogy is still of some use.
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I think what you said makes sense, but it’s simpler than you think. A wave curves if there’s an orthogonal gradient in wave speed, and there clearly is, because optical clocks go slower when they’re lower. The you take note of the wave nature of matter and liken the electron to a wave in a closed path. The horizontal component of the path veers downwards, so the electron falls down. I’m sure this is why the GR deflection of light is twice the Newtonian deflection of matter. Because the horizontal component of the path is half the total closed path.

3. John, I think you are right about light waves also being gravitational waves. Are neutrons and protons also electromagnetic waves and also gravitational waves?
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I think the gravitational component of electromagnetic waves is very low energy.
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The reason why a gravitational wave passes through everything is the energy of a single wave can not transfer enough energy to act as a quantum particle and be absorbed. That is why gravitons can not be detected.
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However, if you get enough gravitational waves in a unit of space, the resulting energy density can slow the speed of light waves. Another way of looking at this is to imagine that light waves and gravitational waves keep waving at the same frequency and amplitude but they interfere with each other which slows the effective rate of forward movement. In other words, a photon requires more time to transfer its entire quantum of energy from one place to another.

4. Are neutrons and protons also electromagnetic waves and also gravitational waves? I think so Don. I think the electron is a photon in a “trivial knot” configuration, and a proton is a photon in a “trefoil knot” configuration. I also think electron capture does what it says on the tin.
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I just don’t know about those gravitational waves I’m afraid. But it seems you can’t shield anything from gravity. So it sounds reasonable that you can’t shield anything from a gravitational wave either. Which makes me think there’s not much energy exchange between a gravitational wave and a photon. Which makes sense, since there’s no energy exchange between a gravitational field and a photon. In gravitational redshift, the photon is emitted at a lower frequency. It doesn’t lose energy as it ascends.
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I just don’t believe in gravitons I’m afraid. Not as messenger particles. I think of a gravitational wave as a graviton. I think of an electromagnetic wave as a photon. But virtual photons, the so-called messenger particles of the electromagnetic interaction, are virtual. Ditto for virtual gravitons, the so-called messenger particles of the gravitational interaction. They are virtual as in not real. They do not exist.
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Re “However, if you get enough gravitational waves in a unit of space, the resulting energy density can slow the speed of light waves”. I think that’s the wrong way to look at it. If a gravitational wave is passing through, you will notice a slowing down in the speed of light. Not locally of course. You’ll see distant pulsars appearing to speed up.
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As for “imagine that light waves and gravitational waves keep waving at the same frequency and amplitude but they interfere with each other”, I just can’t enthuse about that. A photon is an electromagnetic wave, and it’s also a gravitational wave. But there’s only one wave there. See https://physicsdetective.com/the-theory-of-everything/. This is the important bit: “You should associate twisted cells with electromagnetism, and flattened cells with gravity. But in doing so, you should note that the twisted cells are also flattened”. And this “So Maxwell never lined up his transverse undulations like ducks in a row, then pushed them together so that they were all slightly out of phase. So he never saw that the result was a gravitational field”. Well, that’s my take on it anyway.

5. uncertainH

Sometimes I wonder if the reason the photon and gravity wave behave as they do is because they are manifestations of the same thing – the distortion of space. If massless photons combine into knots, and then exhibit what we measure as charge and mass, and since we also know that the electromagnetic field of the new configuration didn’t just appear out of nowhere, it originated from the electromagnetic field of the photons, then does it not follow that the spatial distortion, curvature, or pressure on ghost like jelly, whatever you want to call it, also originated from the photon?

6. UncertainH: yes, I think so. See the theory of everything where I refer to William Kingdon Clifford’s 1870 space theory of matter. Clifford said “I hold in fact:
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(1) That small portions of space are in fact of a nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them.
(2) That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave.
(3) That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or etherial.
(4) That in the physical world nothing else takes place but this variation, subject (possibly) to the law of continuity”.
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I think that’s about it. Space waves, and we make matter out of those waves.

8. Pablo Pantooka

Einstein equated mass ONLY with “REST-energy”
and stressed that over and over during his December 1934 Gibbs Lecture. The term and distinction of “REST-energy” is crucial. He did not equate mass with total energy. Einstein’s great discovery was that of the REST- energy. E=mc2 is not even true and just a pop-sci version… E0=mc2 is the correct actual Einstein equation.

Einstein himself did not at all approve of relativistic mass whatsoever. He was adamant and aggressive about it in his letters.

9. John, I have been rethinking our conversation about mass and something doesn’t make sense. If we consider that water in a dam loses energy when it goes down and through hydro-electric generators to create electric energy, the water must lose energy. This would indicate that all objects falling in gravitational fields lose energy and mass, especially approaching a black hole. Or, maybe the law of conservation of energy is not valid when altitude is changed in a gravitational field.
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I expect that someone has already done measurements to determine if mass changes with altitude since we have launched so many objects into orbit.

10. Don: yes, the water loses energy. See the Wikipedia binding energy article:
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https://en.wikipedia.org/wiki/Binding_energy#Mass%E2%80%93energy_relation
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Note how it mentions the mass deficit. Gravity converts internal kinetic energy, which is mass energy, into external kinetic energy. People tend to call this energy gravitational potential energy, and some say it’s stored in the field, but it isn’t. As for black holes, see my firewall article where I refer to Friedwardt Winterberg’s 2001 paper gamma ray bursters and Lorentzian relativity. He says a falling body erupts into a gamma ray burst on the way into a black hole. I think he’s right. . .
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I don’t think anybody has done an experiments to measure the mass change. It’s very small for the Earth, and the change affects your measuring device too, so you might not measure any change.

1. John, thanks again for responding to my poorly thought out comment. I sound like a broken record.

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I was trying to show that energy and mass approach zero as things approach an event horizon due to a loss of gravitational potential energy. I thought that would support the equations E=mc2 and E=hc/λ which indicate energy decreases as the speed of light approaches zero.

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However, I found this video (https://www.popularmechanics.com/space/a14524087/black-holes-mass-energy/) that says the gravitational potential energy for a non-rotating black hole and a rotating black hole are 6% and 42% of the original mass respectively. While I don’t have the knowledge to verify the calculations I now realize gravitational potential energy has nothing to do with the speed of light and everything to do with the distance from the center of gravity of the black hole. This information eliminates gravitational potential energy as a significant factor for decreasing mass.

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So then I wondered if the equations E=mc2 and E=hc/λ are valid at an event horizon.

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Looking at E=hc/λ I realized that if energy is constant then the equation predicts that the wavelength approaches zero as c approaches zero. This is more likely than energy approaching zero. I am OK with non-massive things not losing gravitational potential energy and having constant energy. Also, the equation I should be using is E=hf which allows energy to be a constant if the frequency is constant. You always say that frequency doesn’t change as light ascends or descends. I don’t know how you know this but I’m OK with that too.

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Now I think E=mc2 probably only works for Special Relativity, and not where there is a gravitational field.

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