Robert A. Wilson commented on something I posted over at Triton Station:
Certainly, one can hardly argue with the principle of general relativity as a fundamental physical principle. The various forms of the equivalence principle, on the other hand, presume that we already know what mass is – which we clearly don’t.
I’ve invited Robert to elaborate a bit here. So Robert, I agree with you on the principle of general relativity but could you explain what you mean when you say we don’t know what mass is and how that relates to the equivalence principle?
Thank you. I will try to explain what I mean without becoming too controversial, but I warn you now that I may not succeed. When I was first drawn in to the problem of thinking about grand unified theories or theories of everything, I started, as a group theorist, to try to understand the underlying group theory. This I failed to do, as it did not make sense as group theory. Therefore I started to look at the physics, and in particular to try to identify what is the most fundamental problem, because of course there was no chance at all that I could address all the problems. After a while, I identified the problem of mass as the fundamental problem. This means different things to different people, but it certainly includes things like dark matter (what is all this extra mass that we seem to need, and where does it come from?), neutrino
oscillations (do neutrinos really have mass, and if so, why can’t we measure it?). These two problems on their own are to me a clear indication that we do not understand the concept of mass. So I set out to look for experimental properties of mass that theory does not explain. I found lots of strange coincidences that I could not understand, and tried to ask any physicists who would listen, what these coincidences could possibly mean? I was somewhat surprised by the response, which was pure anger, and a complete and utter refusal to even begin to look at the experimental evidence.
The concept of mass is a fundamental concept in all physical theories, and without it we can hardly imagine a theory of physics at all. But already in Newtonian mechanics, mass was two separate concepts, of inertial and gravitational mass, and the problem has only got worse since then. Local experiments have not yet succeeded in distinguishing inertial from gravitational mass, so there may not be a local distinction. But on large scales (galaxy scales) and small scales (sub-proton scales) mass clearly does not behave in the way that we are used to in our kitchens and gardens. For practical purposes, our concept of mass works pretty well from the proton scale to the Solar System scale, and perhaps another 6 orders of magnitude on one side or the other. But that’s not good enough for a theory of everything.
When I approached the problem from a group-theoretical point of view, considering the internal symmetries of elementary particles, including the symmetries of spin, (weak) isospin, generations and so on, and combined this theoretical investigation with the experimental evidence, including the astronomical evidence for the way we are moving through the universe, also described in terms of group theory, it gradually became clear that the very concept of mass is a geocentric concept. In simple terms, this is because the universe is completely quantised, but mass is not. In a quantum universe, it is theoretically impossible for mass to be a universal concept. It isn’t possible to argue against this on physical grounds, because it is a mathematical theorem. You might deny it, but the universe cannot.
Well, there’s a lot to unpack here and for starters I’ll just address a few points.
“But already in Newtonian mechanics, mass was two separate concepts, of inertial and gravitational mass…”
This long standing separation of mass into multiple concepts because of the separate historical developments of those concepts seems like nothing more than a case of arrested analytic development. It has long been known gravitational and inertial mass are the same thing. That fact is sometimes referred to as the Galilean equivalence principle. This becomes unsurprising if, by virtue of that fact, it is simply asserted that mass is a property of matter, independent of any particular measurement regime. That a great deal of time and energy are still spent testing the “equivalency” is ridiculous because the two masses are are not separate things; they are the same thing – an identity.
“But on large scales (galaxy scales) and small scales (sub-proton scales) mass clearly does not behave in the way that we are used to in our kitchens and gardens.”
That this fact is considered surprising is itself surprising. That things behave differently on vastly different scales should be obvious because scale matters – even in your kitchen. Drop a tennis ball on your foot and there will be no significant consequence; drop a bowling ball on your foot and you’ll probably need medical attention. In the case of the vast scale difference between our solar system and a galaxy, it was the naive expectation that the rotation curves of galaxies should display a “Keplerian decline” that was the primary driver for the birth, in the 1980s, of the modern dark matter concept.
So, if we simply define mass as a property of matter and define matter as any three dimensionally localized object with the property of rest mass, you can then note that since to the best of our knowledge E/m=c^2, it follows that a given quantity of mass has an energy equivalent. That does not mean that mass and energy are identical – clearly they are not.
If we then define fundamental energy as electromagnetic radiation, we can then state that matter is the 3D form of energy and energy is the 4D form of matter. This is especially relevant to the cosmological scale >100Gly where matter, energy and their interactions in hybrid systems like galaxies are the fundamental components that observations present to us.
“In simple terms, this is because the universe is completely quantised, but mass is not. In a quantum universe, it is theoretically impossible for mass to be a universal concept.”
I have to admit that I don’t understand what you are trying to say here. This may be because I am of the opinion that the commonly agreed upon concept of the Cosmos as a Universe has no scientific merit (see https://thisislanduniverse.com/2022/02/26/another-day-another-anti-universe-rant/). From that point of view, the universe you speak of is an imaginary construct.
I’ll leave it there for now. There is much to discuss. Regards,
Bud
Hmmm. I’m not sure we’ll get very far with this discussion. The concepts that I regard as non-existent are ones you think are beyond discussion, and the ones you think are non-existent are ones I think are beyond discussion. You think that mass exists and the universe doesn’t. I think that the universe exists and mass doesn’t.
Hi Robert,
Perhaps you’re right. I had some sense as I wrote my previous comment that our views are far more divergent than they had appeared to be in past discussions. In particular we seemed to agree on the distinction between math and physics as separate disciplines and that math was only a tool of physics, and not a branch thereof.
I also have to disagree with your comment that I consider my concepts (of mass and the Cosmos) as beyond discussion. I presented logical arguments based on empirical facts for my views. I’m more than willing to discuss those arguments with someone who disagrees with them. It seems to me that all you presented by way of supporting your own views were assertions of those views. For instance:
“When I approached the problem from a group-theoretical point of view, considering the internal symmetries of elementary particles, including the symmetries of spin, (weak) isospin, generations and so on, and combined this theoretical investigation with the experimental evidence, including the astronomical evidence for the way we are moving through the universe, also described in terms of group theory, it gradually became clear that the very concept of mass is a geocentric concept.”
The logical structure here reduces to:
1. I considered group theory (math).
2. I considered some observations (physics).
3. I concluded that mass is a geocentric concept.
As presented the logic is purely subjective. I see no way to objectively evaluate it in scientific terms. Now there may well be some sound objectively logical arguments buried in there but it’s not at all obvious what they might be.
Any such discussion, if it is to be scientific, must be couched in logical arguments that must in turn be grounded in empirically verifiable claims. If for instance, the Universe of your model is simply an axiomatic truth and therefore not subject to factual analysis then a scientific discussion or evaluation of your model is not possible; it can only be relevant to math space not physics.
Again, I don’t hold any views that I consider to be beyond discussion. If you hold some aspects of your model as axiomatically true, then you are correct, we are unlikely to have any fruitful discussions re scientific issues. That is unfortunate.
You misunderstand me. I take nothing as axiomatic in physics. The conclusions I have come to are arrived at after years of work, and the reasons I have come to these conclusions are described in my papers, on the arXiv and elsewhere, and (in diluted form) on my blog. They are absolutely grounded in empirically verifiable claims. One of the reasons I get so frustrated with arguments with physicists is that they refuse to discuss the empirical data, and whenever the going gets tough they resort to dogmatic statements of theory. Even when the theory is not supported by any empirical evidence at all.
Let’s take this back to the nominal topic- mass and the equivalence principle. My view is that mass is a measurable property of matter. If it is not clear what I mean by that, please let me now.
Your view seems to be, “that the very concept of mass is a geocentric concept.” In all honesty I don’t understand what you mean by that – in terms of physics. Can you elaborate?
OK, let’s go back to the beginning. In the beginning, inertial mass was defined by Newton’s second law m = F/a, and gravitational mass by Newton’s law of gravity M = ar^2/G. In Newtonian mechanics, these are defined to be the same. All is well and good for 200 years. But then cracks started to appear in Newtonian mechanics, which was no longer adequate to explain all empirical data. At that stage we know that there is something wrong with Newtonian mechanics, but it is meaningless to ask the question in isolation of whether inertial and gravitational mass are equivalent. It is the set of assumptions as a whole that is falsified by empirical observation, not any individual assumption. So you can assume the equivalence principle and modify Newtonian dynamics (MOND, as discussed on tritonstation), or modify the equivalence principle. I have nothing to say on this subject that hasn’t been said already, and it is not relevant to my argument.
With the demise of Newtonian theory as a “theory of everything”, new definitions of mass were required and appeared, first Einstein’s definition
and then Dirac’s definition in terms of the wave-function. The new equivalence principle is that Dirac’s mass is equivalent to Einstein’s mass. It is this version of the equivalence principle that I take aim at. It is easy to prove mathematically, in fact, that these two definitions cannot be equivalent, but that is not what we are talking about – we want empirical evidence.
I have examined lots of empirical evidence, including besides the astronomical evidence for MOND, also the flyby anomaly, the Pioneer anomaly, inconsistent measurements of G, mass drift of copies of the IPK, the muon g-2 anomaly, kaon oscillations, neutrino oscillations, measurement of polarisation of entangled photons, measurements of the electron/proton mass ratio, and many others. In my papers I have argued from various different ones of these, or combinations, that the empirical evidence shows that the Einstein mass and the Dirac mass cannot be the same. However, we have the same philosophical problem as before, that all I have really shown is that the complete set of assumptions of modern physics is inconsistent. Which was already known.
So, if I say that the Einstein mass and the Dirac mass are not equivalent, I am really using this as a shorthand for saying that we need a new definition of mass in order to progress beyond the current models of physics towards a new “theory of everything”. Either way, I think that the conclusion as I originally worded it, or in the equivalent form “we clearly do not understand mass” is valid. You will notice that I did not say anything about whether the equivalence of Einstein and Dirac mass is “true” or “false” – it is a meaningless question.
If you want me to elaborate on the empirical evidence, I might single out the proton/electron mass ratio, although this is probably the most controversial of all the evidence I mentioned. Modern measurements of this mass ratio all use the Dirac equation as the definition of mass, and have only a very distant relationship to any concept of Einstein mass, so that we can take it that the Dirac mass ratio is 1836.152…, fixed to this accuracy in the 1973 CODATA adjustment of recommended values of fundamental physical constants.
In the 1969 CODATA adjustment, there was a lot of discussion about whether to do the analysis with quantum electrodynamics (QED) or without (WQED), as the results were slightly different in the two cases. WQED doesn’t use the Dirac equation, so is reliant ultimately on the Einstein mass, but supplemented by Maxwell’s equations and the laws of electromagnetism. What the 1969 paper shows, and discusses over several pages, is a significant tension between different experimental measurements over the period 1949 to 1967. Ultimately this tension was put down to unexplained experimental uncertainties, but I put forward the suggestion that, just possibly, it might have been a real effect, caused by a drift over time between the Einstein mass (defined by gravity and classical electromagnetism) and the Dirac mass (defined by QED).
To investigate this, one needs to look at the variation over time of the gravitational environment of the experiments. Local effects such as variations in the strength of gravity, or the latitude of the experiment, or the twice-daily tides, can certainly be excluded, but global effects such as the slow variation in tilt of the Earth’s axis are a possible source of systematic error that changes over time. Indeed, this is essentially the only variable that could plausibly have such an effect. So I looked at the variable and did some modelling. And I found that the electron/proton mass ratio happened to be exactly equal to the sine of the angle of tilt, divided by twice the number of days in a year, in March 1973. And in June 1963, and in August 1967. But at no other time in the past 15000 years.
You can take this is as a meaningless coincidence if you like. But I take it as a definition of the equivalence of Einstein and Dirac mass, that was adopted by the physics community in 1973. To support this position, I tried to fit the empirical data from 1949-67 to the change in axial tilt, and found the best fit with a 22% Einstein to 78% Dirac proportion, that eliminates the tension found in the 1969 paper. This proportion represents a mixing between gravitational and electromagnetic effects of mass, and it may or not be relevant that this proportion is equal to the mixing between QED and the weak force, as implemented in the Feynman calculus..
Sorry, I meant August 1957, not August 1967.
I see the problem. You are defining mass in mathematical terms while I’m defining it in physical terms. The two approaches can be fit together in the context of our understanding that math is a modelling tool in physics. So let’s begin with a physical definition that can then be elaborated mathematically. The simplest form of mass is rest mass. Rest mass is a property of matter; matter is any three dimensionally localized object with the property of rest mass.
The equation you presented as Einstein’s definition of mass isn’t really a definition so much as it is a mathematical description of the relationship between matter and energy. Simplifying to rest mass the equation it is just m=E/c^2. Rearranging it to E/m=c^2, we explicitly get the well known, empirically demonstrated relationship. There is a mass-energy equivalence dependent on the omni-directional expansion rate of an expanding spherical wavefront of electromagnetic energy. The physical and mathematical descriptions dovetail nicely.
However interesting, the distinction you draw between Einstein’s (GR) mass and Dirac’s mass is essentially a distinction between two mathematical models that are known to be incompatible. That has nothing to do with the observed equivalence of inertial and gravitational masses, known as the “weak” equivalence principle, nor do I see any connection with the extensions thereof known as the Einstein and Strong principles, neither of which are actually principles so much as conjectures of mathematical convenience.
BTW, you’ve mentioned your blog several times. I’d be happy to check it out but you haven’t provided a link. Thanks.
FWIW here are my thoughts on how wave/particle duality and the nature of mass/gravity/dark matter could be explained with Special Relativity.
A particle travelling at the speed of light, from its own frame of reference, arrives as soon as it leaves. If its position is constrained via oscillation (or orbiting motion), then its position is undefined, it occupies all positions all the time from its own perspective, i.e. it behaves as a wave. However an observer(or ‘measurer’) would see the particle with a definite position at any point in time, if they could observe the particle they would see a particle oscillating at the speed of light with its position defined and changing through time. Those different perspectives could account for the wave/particle duality.
If a particle is oscillating at the speed of light, then for the particle, time is frozen, The frozen time for the particle causes time to slow in the surrounding space via self-interaction. That distortion in the speed of time causes the gravitational effect since the net motion of another oscillating particle will be in the direction where time is running slower. Allowing the gravity/time distortion to feedback(self -interact) for a second time causes the ‘dark matter’/MOND effect.
In summary I am suggesting that gravity/mass is a result of the distortions in the speed of time due to Special Relativity and self-interaction.
The problem as I see it is not the difference between a mathematical definition of mass and a physical definition, so much as the fact that there is no physical definition of mass. You prove this by giving a completely circular “definition” by saying that mass is a property of matter, and that matter is something that has mass. This simply isn’t a definition of anything.
You are correct to say that the distinction between Einstein mass and Dirac mass is quite different from the distinction between inertial and gravitational mass. This is something I pointed out in my comment on 1st April (which wasn’t a joke, by the way!). The only connection between the two dichotomies is that they both point clearly to the fact that we do not understand mass.
The only reason I didn’t put a direct link to my blog is because it’s in the metadata of my comments, and you can find it by clicking on my name in tritonstation and anywhere else that doesn’t censor my comments. Explicitly, it is at https://robwilson1.wordpress.com
Defining mass as a fundamental, measurable property of matter is a straightforward physical definition of the term mass. Note that matter is not being defined as mass but as a phenomenon that has two fundamental properties, it is any 3D localized object with rest mass. The definition is not circular because mass is only one property of matter – they are not the same thing.
The relationship the between matter and energy which first arose in the context of relativity theory and is a well established fact. That relationship seems to me to be a fundamental property of matter, one in which mass takes part, so perhaps a more complete definition should be: Mass is a fundamental and measurable property of matter that can be converted to an equivalent amount of energy as 3D matter is converted to 4D energy in accord with the relationship E/m=c^2.
“The only connection between the two dichotomies is that they both point clearly to the fact that we do not understand mass.”
But there is no dichotomy between inertial and gravitational mass if you define mass as a property of matter. That was also a fundamental point of Einstein’s General Relativity.
There is nothing there that I recognise as a definition. Just because you can *measure* mass, doesn’t mean you can define it. If you measure mass in different ways, you might be measuring different things. All the evidence points to the fact that different types of measurements do indeed measure different concepts of mass. All the evidence points to the fact that mass is *not* a fundamental property of matter. It is measurable, certainly, but it is not fundamental.
It’s not at all clear what you would recognise as a definition since I’m more or less just describing the physics that underlies E/m=c^2, which is what you cited as definitional of rest mass. What the justification is for the claim that different measurements record different values for mass, rather than different models calculating different results, is not clear; the Einstein-Dirac example you cited does not establish that at all.
Nothing you’ve cited supports the physically dubious proposition that mass isn’t fundamental; it may not be fundamental in your model but it appears to be quite fundamental in empirical reality which is where all scientific models need to be based.
Well, I’ve done my best to explain my point of view without writing a whole book about it. If you’re not convinced by the examples I’ve given here, you can read many more on my blog and in my papers, where I give the details and the references to support my arguments.
The history of physics is full of “more or less” definitions and concepts that “appear to quite fundamental in empirical reality”, that have been abandoned as a deeper reality has become apparent. My argument is that “mass” is one of those concepts, but since the deeper reality is not yet apparent, the argument falls on deaf ears.
The reification of mass is the ultimate cause of the theoretical necessity for an infinite amount of information to be contained in a finite number of particles, which not only causes the UV catastrophe (and for that matter the IR catastrophe) in all QFTs, but is the impetus behind the rampant mathematicism in physics, that you rightly condemn.
Mass is an observed and measured property of all material bodies – it is not a reified, pre-existing relational concept – in the way that spacetime is. If you find a theoretical problem with regard to an infinite amount of a reified human concept like information, well that’s a theoretical problem that resides entirely within the theoretical model that has the problem. There is no physics involved.
That is your opinion. My opinion is different. Mass is not a single concept, it is two concepts. If you cannot separate the two concepts, then you have the same problem that conventional physics has.
If by two concepts you mean inertial vs gravitational mas, you might want to consider this:
https://www.sciencedirect.com/science/article/pii/S1355219813000695