You can lead a horse to water

I thought I ought to say something about some of the conversations I have with some physicists. A recent example concerned gravity, and why light curves. I found myself talking to a guy doing a PhD called Erik Anson. At the end, I thought of the old adage: you can lead a horse to water, but you can’t make him drink. I am reminded of some of the conversations I had years ago with Young Earth Creationists. You can show them the strata, the fossils, and the radio dating, but none of it matters. They find a reason to dismiss the evidence because they are convictional. Note that I said convictional, not religious. Sadly, they aren’t the only people like that. Read this and weep:    

Erik Anson: In General Relativity, there is no requirement that a particle have mass to be affected by gravity. Gravity is a bending of spacetime; any particle traveling through curved spacetime will be affected.

Steven Spielman: True in Newtonian gravity as well. An orbit doesn’t depend on the object’s mass.

Erik Anson: Indeed, but if the mass is zero, Newtonian physics doesn’t really know how to deal with it. The best-available answer is to take the limit as mass approaches zero, but it still doesn’t really explain how a force defined by masses attracting each other would still somehow wind up affecting something massless. GR avoids this problem entirely, by modeling gravity using (a modified version of) Newton’s 1st Law, instead of (any version of) Newton’s 2nd Law. That’s the key here. In GR, there’s no mystery or hand-waving around why massless particles are affected.

John Duffield (me): I’m sorry guys, but light doesn’t curve because spacetime is curved. Spacetime curvature relates to the second derivative of potential, associated with the tidal force. Gravity is associated with the first derivative of potential. If you’re in a room where the force of gravity is precisely 9.8 m/s² at the ceiling and at the floor, there’s no spacetime curvature. But light still curves downwards. If the force of gravity is precisely 98 m/s² at both the ceiling and the floor, light would curve downwards all the more.

Erik Anson: If geodesics through a region of spacetime aren’t straight lines through space, then I’d call that region of spacetime “curved”. There would also be relative gravitational time dilation between the ceiling and floor, even if the acceleration were the same in both places. If you definition of “curved” is stricter than that, then fine. But that’s a collision of terminology, not an error in physics.

John Duffield: I’m sorry Erik, but it’s a gross error. The curvature of light through space is not the same as spacetime curvature. Here’s the typical depiction of Riemann curvature, which is synonymous with spacetime curvature:

CCASA image by Johnstone, see Wikipedia

Now zoom in to a portion of it. See the yellow arrow in the upper right? That represents a light beam. When you zoom in you can’t see any curvature on the plot. But you can see that the plot has a slope, and that the light beam is curved:

The slope of the plot represents g, and also the relative gravitational time dilation between the ceiling and floor. The curvature of the light beam is greater where g is greater. Not where the spacetime curvature is greater – which is where g changes most. See my “physics detective” article on how gravity works for details and references.

Erik Anson: You do realize that that “bowling ball on a trampoline” diagram is basically useless, right? This is relevant: Teaching Physics. Please explain, specifically, how each of my explanations was a “gross error”.

John Duffield: The bowling ball analogy isn’t useless. Not when you understand how gravity works. See my answer. You can think of it as a plot of the speed of light throughout an equatorial slice of the space around the Earth. Light doesn’t curve because spacetime is curved. It curves like any wave curves when there’s a gradient in wave speed. Einstein said the speed of light was constant in 1905, but only two years later in 1907 he was saying light curves in a gravitational field because the speed of light isn’t constant. He said it again in 1911, 1912, 1913, 1914, 1915, and 1916. He never changed his mind about it. Your first explanation was wrong on three counts: 1) gravity is not a bending of spacetime. A gravitational field is space that’s “neither homogeneous nor isotropic”. 2) Spacetime models space at all times, so there is no motion through it. 3) the deflection of light is twice the Newtonian deflection of matter, which you can understand by noting that only the horizontal components bend downward. Your second explanation is wrong because light doesn’t follow the curvature of spacetime, as I said above. I’m sorry Erik, but some of what you’ve been taught about GR is misleading. This has a major impact on things like Pernrose-Hawking singularity theorems. Here’s an excerpt from something else I’ve written:

Hawking did not understand gravity

Unfortunately many physicists are unaware of it. For example, one of Stephen Hawking’s “seminal” papers was singularities and the geometry of spacetimedating from 1966. On page 26 he referred to the Schwarzschild metric and the “apparent” singularity at r=2m. He said it was “simply due to a bad choice of coordinates”. On page 76 Hawking talked of “such a strong gravitational field that even the ‘outgoing’ light rays from it are dragged back”. It’s clear Hawking had never read Einstein’s fundamental ideas and methods of the theory of relativity. That’s where Einstein explained why light curves. It’s clear that Hawking did not understand that a gravitational field is a place where “the speed of light is spatially variable”. He didn’t know that in a gravitational field, “light speeds up as it ascends from floor to ceiling”. He didn’t know that in a strong gravitational field, outgoing light rays aren’t dragged back. They speed up even more. Hawking didn’t understand the first thing about gravity, so he didn’t understand the first thing about black holes either. If you think that’s bad, it gets worse. A lot worse…

Erik Anson: Oh, I see. You read some things that Einstein wrote about variable speed of light, which results from time dilation (it’s always cc as measured by clocks and meter sticks that the light is passing by), and now you think you understand GR better than actual physicists who did actual GR calculations. Forgive me if I can’t take you seriously.

John Duffield: I understand GR better than some. I also understand that we use the local motion of light to define the second and the metre, and then use the second and the metre to measure the local speed of light. That’s why we always measure the local speed of light to be 299,792,458 m/s. Duh! It’s a risible schoolboy error. It’s a tautology. Magueijo and Moffat talked about that in their Comments on “Note on varying speed of light theories”.

The variable speed of light doesn’t result from time dilation. It results from a concentration of energy in the guise of a massive star “conditioning” the surrounding space, this effect diminishing with distance. It affects c = 1/√(ε₀μ₀). Hence an optical clock goes slower when it’s lower because light goes slower when it’s lower. Not because some magical mysterious thing called time goes slower. Note that it wasn’t just Einstein talking about the variable speed of light. It was Irwin Shapiro too. His 1964 paper was all about what we now call the Shapiro delay. He said this: “the speed of a light wave depends on the strength of the gravitational potential along its path”. Also note Is The Speed of Light Everywhere the Same? by PhysicsFAQ editor Don Koks. The answer is no. It varies in the room you’re in. If it didn’t, g would be zero.

Like I was saying, I’m afraid the GR you’ve been taught is, in some respects, misleading. I know this because I’ve read the Einstein digital papers, Hence I know how gravity works. It’s quite straightforward. But amazingly, most professional physicists and cosmologists don’t.

Erik Anson: It’s not a “risible schoolboy error”. We no longer measure the speed of light at all; it’s fixed, by definition, as a result of previous measurements that determined it to be uniform in the relevant (local) sense. There is no confusion here, no circularity of reasoning, as you’re trying to imply. If you assume that the world’s physicists missed something that basic, rather than entertaining the possibility that you missed something, then you need a reality check. And possibly a refresher on Bayes’ Theorem. It’s not just light clocks that slow down. Everything slows down, e.g., rates of particle decay. Time dilation is a thing. All physical processes get slowed down, by an equal amount. That is entirely equivalent to just saying that time is passing more slowly, and so that’s what we do. You are vastly over-estimating your understanding of GR relative to actual physicists, and your emphasis on Einstein’s original papers is rather odd. You do realize that science builds on itself, right? GR isn’t holy scripture, more “pure” when it’s from the original source material.

John Duffield: It absolutely is a risible schoolboy error. The speed of light is fixed by definition? That’s Humpty Dumpty physics. Yes physicists like Kip Thorne really did miss something that basic. But don’t think all the world’s physicists have. I haven’t. Nor did Irwin Shapiro. Or Don Koks, or John Moffat or Jo Magueijo. Or Ned Wright. He doesn’t say light curves because spacetime is curved. Instead he says this: “In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light. The figure below shows a bundle of rays passing the Sun at various distances”:

Gif from Ned Wright’s Deflection and Delay of Light

Don’t think what you’ve been taught is what the world’s physicists think. Do your own research and think for yourself. Remember that people like Kip Thorne peddle time travel. That’s pseudoscience. I suspect some other things you’ve been taught are too. Remember Leonard Susskind’s elephant and the event horizon, where the elephant is in two places at once? That’s pseudoscience too. This isn’t:

1912: “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”.

1913: “I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis”.

1914: “In the case where we drop the postulate of the constancy of the velocity of light, there exists, a priori, no privileged coordinate systems.”

1915: “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”.

1916: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity”.

1920: “Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.

In a nutshell, the GR you’ve been taught is an ersatz version of the real thing. One that promotes misinformation and doesn’t even tell you how gravity works. Even though Einstein did. You might not want to believe it coming from me, but one day you will.

PS: everything slows down because of the wave nature of matter. See page 26 of Schrödinger’s quantization as a problem of proper values, part II. He said ““let us think of a wave group of the nature described above, which in some way gets into a small closed ‘path’, whose dimensions are of the order of the wave length”. He was talking about the electron.

Erik Anson: You continue to be stuck a century in the past. Why are you quoting Einstein and Schrödinger like scripture, instead of just talking about GR and QM? Also, please stop making assumptions about what I’ve been taught. Feel free to check out my profile, and my answers.

John Duffield: I’m not stuck a century in the past. I’ve referred to Einstein, Schrödinger, Shapiro, Magueijo, Moffat, Koks, and Wright to show you that I’m not just making this stuff up. Don’t be so quick to dismiss Einstein because you think you know better. You don’t.

As for your answers, I thought this one was interesting: Is it right to say the electromagnetic field fills all spacetime the way water fills all of a swimming pool. You measure the speed of light to be the same regardless of your speed because of the wave nature of matter. See the other meaning of special relativity by Robert Close. PS: I was pleased to see you say spacetime is not a physical object. That means light doesn’t curve because spacetime is curved, doesn’t it?

I thought this one was interesting too: Can the aether that Michelson-Morley disproved be related to the dark matter we haven’t found? You might like to read this: Aether theories – Wikipedia. And Einstein’s Leyden Address, where he referred to a gravitational field as space that’s “neither homogeneous nor isotropic”. Einstein also said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. Space has its vacuum energy. When it’s inhomogeneous the extra energy has a mass equivalence and a gravitational effect.

But I thought your answer to this was the best: Why are scientists always so ready to dismiss new ideas and never break current protocol? LOL! No reply necessary.

Erik Anson: I’m not “dismissing Einstein because I think I know better”. But, neither was he always right. The best of his ideas about GR are part of modern GR. The wave nature of matter in no way determines how we measure the speed of light, because we measure the speed of light with macroscopic instruments that are in the classical limit anyway. And, yes, I’m aware that gravitational energy produces its own gravitational effect. So are all the physicists doing the dark matter calculations, because that’s just standard GR. When we talk about missing gravitational sources (dark matter), that’s even when we include the (very small) contribution from the gravitational energy itself. Please stop assuming that physicists have no idea what they’re doing, especially when you haven’t actually checked whether your claims work mathematically.

John Duffield: The bottom line is this, Erik: some elements “modern GR” flatly contradict Einstein, and are wrong. This then impacts some aspects of cosmology. I recommend you read that paper by Robert Close. Think about the raisin-cake analogy, and remember this: space expands between the galaxies but not within. Conservation of energy means every galaxy is sitting in a region of space where the energy-density is greater than the surrounding space.

Erik Anson: >> some elements “modern GR” flatly contradict Einstein, and are wrong. Evidence for this? If you have evidence that modern GR is “wrong”, that would be groundbreaking. On the other hand, if you’re just calling it “wrong” because it contradicts your interpretation of an opinion of Einstein’s from before we had all the evidence we do now… yeah, no, that’s not how science works. Science is based on evidence, not deifying scientists, even the greats. >> Think about the raisin-cake analogy. I prefer to think about the actual physics, rather than a cartoon version of the physics designed to convey some part of what’s going on to the general public. >> space expands between the galaxies but not within. Sure. >> Conservation of energy means every galaxy is sitting in a region of space where the energy-density is greater than the surrounding space. The energy density of space? No, conservation of energy has no such implication. But, of course, galaxies are denser than not-galaxies, so if you’re not talking about vacuum energy, then it’s trivially true (just not relevant to the discussion). Also, keep in mind that dark matter clouds preceded the formation of galaxies. In fact, the distribution of dark matter pretty much determined where the galaxies formed in the first place. So, trying to explain away dark matter via the effects of galaxies would be a bit of a temporal paradox. Please stop trying to lecture me on something that you only know in terms of analogies and prose, when I’ve studied the actual physics.

John Duffield: The evidence is that NIST optical clocks go slower when they’re lower. Now, you might claim that this is evidence that time goes slower at the lower elevation. But open up an optical clock. Can you see any time flowing through it? No. Is a clock some kind of cosmic gas meter, but with time flowing through it instead of gas? No. There’s no evidence of anything called time inside that clock. But there’s ample evidence that there’s light inside that clock. Now replace the optical clocks with relativity’s favourite gedanken clocks – parallel mirror light clocks. The lower clock goes slower, like this:

Gif image by Brian McPherson

See it? The lower clock goes slower because light goes slower when it’s lower, just like Einstein said. And that’s the reason why light curves downwards. Not because it follows the curvature of spacetime. How can it, when spacetime is not a physical object?

Yes, the energy density of space. A gravitational field is a place where it varies. Because it’s a place where space is “neither homogeneous nor isotropic”. Unfortunately the FLRW metric “starts with the assumption of homogeneity and isotropy of space”. This is not a good assumption!

I’ve studied the actual physics, Erik. Sorry if what I’m saying sounds like a lecture. If I can make amends, is there anything that puzzles you? I might be able to offer something useful.

Erik Anson: >> The evidence is that NIST optical clocks go slower when they’re lower. This is a prediction of GR, both as originally formulated and as used in the modern day. You can’t use an accurate prediction of a theory as evidence that that theory is wrong. Also, non-optical clocks also go slower due to gravitational time dilation. Your argument doesn’t really make sense, here. >> Yes, the energy density of space. A gravitational field is a place where it varies. Not really, no, except insofar as the field itself has energy density. >> Because it’s a place where space is “neither homogeneous nor isotropic”. Unfortunately the FLRW metric “starts with the assumption of homogeneity and isotropy of space”. This is not a good assumption! It’s an approximation, and that approximation is very good at the large scales at which it’s actually applied. Nobody uses the FLRW metric to try to understand stellar motion in a galaxy. >> I’ve studied the actual physics, Erik. Then why do you keep making factually incorrect statements about it? And why are you making your arguments exclusively in terms of lay explanations? You may have a different definition of “study” than I do. I don’t mean “read about”, I mean “learn how to actually do”.

John Duffield: The evidence I gave you is evidence that Einstein’s GR is right, and that the GR you’ve been taught is, in some respects, wrong. You think the speed of light is constant, and that light curves because spacetime is curved. That’s wrong. You surely know the latter doesn’t make sense, because you know spacetime isn’t a physical object.

Yes, the energy-density of space. Space isn’t nothing. See Einstein talking about field theory in 1929. He referred to the electromagnetic field and the gravitational field, and said it can “scarcely be imagined that empty space has conditions or states of two essentially different kinds”. According to Einstein, a field isn’t something separate from space. It isn’t something that exists in space. It’s a state of space.

People take the FLRW metric as gospel, then spend 20 years down a mine in a futile search for WIMPs because they don’t know that space is inhomogeneous just about everywhere.

I’ve studied the actual physics, see this, and I’m not making factually incorrect statements. Yes, I think my definition of study is different to yours. My definition includes doing my own research and gaining an understanding of things like gravity. Yours seems to be accepting everything you’re told at UW and rejecting Einstein along with the hard scientific evidence that delivers understanding. But let’s not dwell on our differences. Like I said, is there anything that puzzles you? I might be able to offer something useful. Otherwise, let’s agree to differ on go our separate ways. OK, it’s 18:48 here in England, time for tea!

Erik Anson: >> The evidence I gave you is evidence that Einstein’s GR is right. Yes. >> and that the GR you’ve been taught is, in some respects, wrong. No. It is in no way evidence of that, because “the GR I’ve been taught” makes that same prediction. This is very basic. Bayes’ Theorem 101, really. I have no idea how you can be misunderstanding this. >> Yes, the energy-density of space. I have already explained why this doesn’t work the way you want it to. >> People take the FLRW metric as gospel, then spend 20 years down a mine in a futile search for WIMPs because they don’t know that space is inhomogeneous just about everywhere. The search for WIMPs has almost nothing to do with the FLRW metric. Please stop making uninformed claims. >> I’m not making factually incorrect statements. Sure you are. I’ve pointed some out. >> My definition includes doing my own research and gaining an understanding of things like gravity. Yours seems to be accepting everything you’re told at UW and rejecting Einstein along with the hard scientific evidence that delivers understanding. This is a laughably inaccurate description of the situation. >> is there anything that puzzles you? I might be able to offer something useful. Plenty of things puzzle me, but I doubt you have anything useful to offer, given the unscientific nature of your arguments thus far.

John Duffield: It’s been interesting talking to you Erik. You don’t understand how gravity works, and nothing I show you is going to change that. Because you think you know better than Einstein, Shapiro, Magueijo, Moffat, Koks, Wright, and me. Yes, I’ve learned something very useful about why are scientists always so ready to dismiss new ideas and never break current protocol? Thanks. Over and out.

Eric Anson: You have no substantial reply, so you put words in my mouth and bluster. Got it. Have a nice life.

I let him have the last word. The moral of the tale is this: you can lead a horse to water, but you can’t make him drink. And you can lead a PhD to knowledge, but you can’t make him think.