A Principle Explanation of the “Mysteries” of Modern Physics
All undergraduate physics majors are shown how the counterintuitive aspects (“mysteries”) of time dilation and length contraction in special relativity (SR) follow from the light postulate, i.e., that everyone measures the same value for the speed of light c, regardless of their motion relative to the source (see this Insight, for example). And, we can understand the light postulate to follow from the principle of relativity, sometimes referred to as “no preferred reference frame” (NPRF). Simply put, if the speed of light from a source was only equal to ##c=\frac{1}{\sqrt{\epsilon_o \mu_o}}## (per Maxwell’s equations) for one particular velocity relative to the source, that would certainly constitute a preferred reference frame. Borrowing from Einstein [1], NPRF might be stated (see this Insight):
No one’s “sense experiences,” to include measurement outcomes, can provide a privileged perspective on the “real external world.”
While time dilation and length contraction follow “analytically” from the light postulate, there are those who do not consider the light postulate explanatory, since it does not provide “hypothetically constructed” mechanisms to “synthetically” account for time dilation and length contraction [2][3]. That is, the postulates of SR are “empirically discovered” principles offered without corresponding “constructive efforts.” In what follows, Einstein explains the difference between the two [4]:
We can distinguish various kinds of theories in physics. Most of them are constructive. They attempt to build up a picture of the more complex phenomena out of the materials of a relatively simple formal scheme from which they start out. Thus the kinetic theory of gases seeks to reduce mechanical, thermal, and diffusional processes to movements of molecules – i.e., to build them up out of the hypothesis of molecular motion. When we say that we have succeeded in understanding a group of natural processes, we invariably mean that a constructive theory has been found which covers the processes in question.
Along with this most important class of theories there exists a second, which I will call “principle-theories.” These employ the analytic, not the synthetic, method. The elements which form their basis and starting point are not hypothetically constructed but empirically discovered ones, general characteristics of natural processes, principles that give rise to mathematically formulated criteria which the separate processes or the theoretical representations of them have to satisfy. Thus the science of thermodynamics seeks by analytical means to deduce necessary conditions, which separate events have to satisfy, from the universally experienced fact that perpetual motion is impossible.
The advantages of the constructive theory are completeness, adaptability, and clearness, those of the principle theory are logical perfection and security of the foundations. The theory of relativity belongs to the latter class. In order to grasp its nature, one needs first of all to become acquainted with the principles on which it is based.
Here is why Einstein formulated special relativity as a principle theory [5, pp. 51-52]:
By and by I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results.
Despite the fact that “there is no mention in relativity of exactly how clocks slow, or why meter sticks shrink” (no “constructive efforts”), the “empirically discovered” principles of SR are so compelling that “physicists always seem so sure about the particular theory of Special Relativity, when so many others have been superseded in the meantime” [6].
As it turns out, we are in a similar position today with quantum mechanics (QM). For example, QM accurately predicts violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality all the way to the Tsirelson bound for Bell state entanglement without providing a corresponding constructive account (see this Insight, for example). This prompted Lee Smolin to write [7, p. 227]:
So, my conclusion is that we need to back off from our models, postpone conjectures about constituents, and begin again by talking about principles.
Other physicists are also calling for a principal account of QM. Chris Fuchs writes [8, p. 285]:
Compare [quantum mechanics] to one of our other great physical theories, special relativity. One could make the statement of it in terms of some very crisp and clear physical principles: The speed of light is constant in all inertial frames, and the laws of physics are the same in all inertial frames. And it struck me that if we couldn’t take the structure of quantum theory and change it from this very overt mathematical speak — something that didn’t look to have much physical content at all, in a way that anyone could identify with some kind of physical principle — if we couldn’t turn that into something like this, then the debate would go on forever and ever. And it seemed like a worthwhile exercise to try to reduce the mathematical structure of quantum mechanics to some crisp physical statements.
That QM accurately predicts the violation of the CHSH inequality to the Tsirelson bound without spelling out any corresponding constructive account prompted Smolin to write [7, p. xvii]:
I hope to convince you that the conceptual problems and raging disagreements that have bedeviled quantum mechanics since its inception are unsolved and unsolvable, for the simple reason that the theory is wrong. It is highly successful, but incomplete.
Of course, this is precisely the complaint leveled by Einstein, Podolsky, and Rosen (EPR) in their famous paper, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” [9]. In an equally famous paper (published after Einstein’s death), John Bell showed how any naïve “completion” of QM via hidden variables could conflict with the predictions of QM for two entangled particles (e.g., see this Insight) [10]. As long as the particles couldn’t communicate faster than light and didn’t have access to information about measurement settings until they were actually being measured, the outcomes for entangled particles with hidden variables would have to obey the “Bell inequality” (the CHSH inequality is a variation thereof). There are two-particle entangled states (“Bell states“) in QM that can violate the Bell inequality (and therefore, the CHSH inequality) and these violations are now experimentally well-confirmed. This “mystery” is in large part responsible for “the conceptual problems and raging disagreements that have bedeviled quantum mechanics.”
However, contra Smolin, we recently showed that Bell state entanglement does not render QM “wrong” or “incomplete” by extending NPRF to include the measurement of another fundamental constant of nature, Planck’s constant h [11][12][30]. As Steven Weinberg points out, measuring an electron’s spin via Stern-Gerlach (SG) magnets constitutes the measurement of “a universal constant of nature, Planck’s constant” [13, p. 3] (Figure 1). So if NPRF applies equally here, everyone must measure the same value for Planck’s constant h, regardless of their SG magnet orientations relative to the source, which like the light postulate is an “empirically discovered” fact. By “relative to the source” of a pair of spin-entangled particles, I mean relative “to the vertical in the [symmetry] plane perpendicular to the line of flight of the particles” [14, p. 943] (Figure 2). Thus, different SG magnet orientations relative to the source constitute different “reference frames” in QM just as different velocities relative to the source constitute different “reference frames” in SR.
Just as NPRF and the speed of light c produce the “mysteries” of time dilation and length contraction in SR, we showed that NPRF and Planck’s constant h produce the “mysteries” of Bell state entanglement and the Tsirelson bound for QM. Generally speaking, Bell spin state entanglement results from the conservation of spin angular momentum, and conservation principles and gauge invariance follow from Wheeler’s “boundary of a boundary” principle, ##\partial\partial = 0## [15][16][17] (Figure 3), which with NPRF underwrite all of physics [17][18].
Specifically, when Alice and Bob make their SG spin measurements at the same angle in the plane of symmetry (same reference frame), conservation of spin angular momentum dictates that they obtain the same result (both +1 or both -1) for the spin triplet states (opposite results for the spin singlet state). This suggests (naively) that if Bob makes his SG spin measurement at angle ##\theta## with respect to Alice (different reference frames), then he should obtain ##\cos{(\theta)}## when Alice obtains +1 in accord with the conservation of spin angular momentum (Figure 4). But, Bob can only ever measure ##\pm 1## per NPRF, just like Alice, so the conservation principle is constrained to hold only on average per NPRF (Figures 5 & 6). Thus, Bell state entanglement and the Tsirelson bound are “mysteries” precisely because of “average-only” conservation, which is conservation per NPRF (Figure 7). So we see that the principle of NPRF reveals an underlying coherence between non-relativistic QM and SR (Figure 8) where others have perceived tension.
For example, in his paper “On the Incompatibility of Special Relativity and Quantum Mechanics” Marco Mamone-Capria’s argument is based on “The EPR correlations … as a simple example of quantum mechanical macroscopic effects with spacelike separation from their causes” [19]. He points out that in 1972 Dirac wrote [20, p. 11]:
The only theory which we can formulate at the present is a non-local one, and of course one is not satisfied with such a theory. I think one ought to say that the problem of reconciling quantum theory and relativity is not solved.
And, Bell also voiced concerns about the compatibility of SR and QM based on quantum entanglement [21, p. 172]:
For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory.
Of course, we know QM is not Lorentz invariant and so it deviates trivially from SR in that fashion. In order to get QM from Lorentz invariant quantum field theory one needs to make low energy approximations [22, p. 173]. But, the charge of incompatibility based on QM entanglement actually carries serious consequences, because we have experimental evidence confirming the violation of the CHSH inequality per QM entanglement. So, if the violation of the CHSH inequality is in any way inconsistent with SR, then SR is being challenged empirically. By analogy, we know Newtonian mechanics deviates from SR because it is not Lorentz invariant. As a consequence, Newtonian mechanics predicts a very different velocity addition rule, so suppose we found experimentally that velocities do add as predicted by Newtonian mechanics. That would not merely mean that Newtonian mechanics and SR are incompatible, that would mean Newtonian mechanics has been empirically verified while SR has been empirically refuted. So, if one believes the violation of the CHSH inequality is in any way inconsistent with SR, and one believes the experimental evidence is accurate, then one believes SR has been empirically refuted. Clearly that is not the case, so their reconciliation as regards the violation of the CHSH inequality must certainly obtain in some fashion and here we see how the principle of NPRF does the job.
Further, contrary to Smolin and EPR, Bell state entanglement does not mean that QM is “incomplete” or “wrong.” Rather, QM is as complete as possible per the principles of ##\partial\partial = 0## and NPRF.
Given this result, one immediately wonders if general relativity (GR) can be brought into the mix via NPRF and the gravitational constant G. Of course it can and the associated counterintuitve aspect (“mystery”) in GR is the contextuality of mass. We already showed how this might resolve the missing mass problem without having to invoke non-baryonic dark matter [23][24].
Specifically, I am pointing out the well-known result per GR that matter can simultaneously possess different values of mass when it is responsible for different combined spatiotemporal geometries. Here “reference frame” refers to each of the different spatiotemporal geometries associated with one and the same matter source. Tacitly assumed in this result is of course that G has the same value in each reference frame, which is consistent with NPRF as applied to c and h above. This spatiotemporal contextuality of mass is not present in Newtonian gravity where mass is an intrinsic property of matter. For example, when a Schwarzschild vacuum surrounds a spherical matter distribution the “proper mass” ##M_{p}## of the matter, as measured locally in the matter, can be different than the “dynamic mass” ##M## in the Schwarzschild metric responsible for orbital kinematics about the matter [25, p. 126]. This difference is attributed to binding energy and goes as ##dM_p = \left(1-\frac{2GM(r)}{c^2r}\right)^{-1/2} \: dM##. In another example, suppose a Schwarzschild vacuum surrounds a sphere of Friedmann-Lemaitre-Robertson-Walker (FLRW) dust, as used originally to model stellar collapse [15, pp. 851-853]. The dynamic mass ##M## of the surrounding Schwarzschild metric is related to the proper mass ##M_{p}## of the FLRW dust, as joined at FLRW radial coordinate ##\chi_o##, by
\begin{equation}
\frac{M_p}{M} = \frac{3(2\chi_o -\sin(2\chi_o))}{4 \sin ^3(\chi_o)} \label{massratio}
\end{equation}
where
\begin{equation}
ds^2 = -c^2d\tau^2 + a^2(\tau)\left(d\chi^2 + \sin^2\chi d\Omega^2 \right) \label{FLRWmetric}
\end{equation}
is the closed FLRW metric [26]. I should quickly point out that this may prima facie seem to constitute a violation of the equivalence principle, as understood to mean inertial mass equals gravitational mass, since inertial mass can’t be equal to two different values of gravitational mass. But, the equivalence principle says simply that spacetime is locally flat [27, pp. 68-69] and that is certainly not being violated here nor with any solution to Einstein’s equations.
Thus, contrary to what some believe about SR, QM, and GR collectively, these theories are comprehensive (not “incomplete” as claimed in [7] and [9]) and coherent (not “in conflict” as claimed in [19] and [20]). In order to appreciate the beauty of these theories collectively, one need only view them per the principles of ##\partial\partial = 0## and NPRF with their associated “mysteries” corresponding to c, h, and G, respectively. I close with this quote from Wolfgang Pauli [28, p. 33]:
‘Understanding’ nature surely means taking a close look at its connections, being certain of its inner workings. Such knowledge cannot be gained by understanding an isolated phenomenon or a single group of phenomena, even if one discovers some order in them. It comes from the recognition that a wealth of experiential facts are interconnected and can therefore be reduced to a common principle. In that case, certainty rests precisely on this wealth of facts. The danger of making mistakes is the smaller, the richer and more complex the phenomena are, and the simpler is the common principle to which they can all be brought back. … ‘Understanding’ probably means nothing more than having whatever ideas and concepts are needed to recognize that a great many different phenomena are part of a coherent whole.
Figure 1. A Stern-Gerlach (SG) spin measurement showing the two possible outcomes, up (##+\frac{\hbar}{2}##) and down (##-\frac{\hbar}{2}##) or +1 and -1, for short. The important point to note here is that the classical analysis predicts all possible deflections, not just the two that are observed. The difference between the classical prediction and the quantum reality uniquely distinguishes the quantum joint distribution from the classical joint distribution for the Bell spin states [29].
Figure 2. Alice and Bob making spin measurements on a pair of spin-entangled particles with their Stern-Gerlach (SG) magnets and detectors in the xz-plane. Here Alice and Bob’s SG magnets are not aligned so these measurements represent different reference frames.
Figure 3. The boundary of a boundary is zero. The oriented plaquettes bound the cube and the directed edges bound the plaquettes. As you can see from the picture, every edge has oppositely oriented directions that cancel out. Thus, the boundaries of the plaguettes (the edges), which bound the cube, sum to zero.
Figure 4. The angular momentum of Bob’s particle ##\vec{S}_B = \vec{S}_A## projected along his measurement direction ##\hat{b}##. This does not happen with spin angular momentum because Bob must always measure ##\pm 1##, no fractions, in accord with NPRF.
Figure 5. A spatiotemporal ensemble of 8 experimental trials for the spin triplet states showing Bob’s outcomes corresponding to Alice’s +1 outcome when ##\theta = 60^\circ##. Blue arrows depict SG magnet orientations and yellow dots depict the measurement outcomes. Spin angular momentum is not conserved in any given trial, because there are two different measurements being made, i.e., outcomes are in two different reference frames, but it is conserved on average for all 8 trials (six up outcomes and two down outcomes average to ##\cos{(60^\circ)}=\frac{1}{2}##).
Figure 6. Average View for the Spin Triplet States. Reading from left to right, as Bob rotates his SG magnets relative to Alice’s SG magnets for her +1 outcome, the average value of his outcome varies from +1 (totally up, arrow tip) to 0 to -1 (totally down, arrow bottom). This obtains per conservation of spin angular momentum on average in accord with no preferred reference frame. Bob can say exactly the same about Alice’s outcomes as she rotates her SG magnets relative to his SG magnets for his +1 outcome. That is, their outcomes can only satisfy conservation of spin angular momentum on average in different reference frames, because they only measure ##\pm 1##, never a fractional result. Again, just as with the light postulate of special relativity, we see that no preferred reference frame leads to a counterintuitive result. Here it requires quantum outcomes ##\pm 1 \left(\frac{\hbar}{2}\right)## for all measurements leading to the “mystery” of “average-only” conservation.
Figure 7. Bub’s version of Wheeler’s question “Why the quantum?” is “Why the Tsirelson bound?” The “constraint” is the principle of “conservation per no preferred reference frame”.
Figure 8. Comparing SR with QM according to no preferred reference frame (NPRF). Because Alice and Bob both measure the same speed of light c, regardless of their motion relative to the source per NPRF, Alice(Bob) may claim that Bob’s(Alice’s) length and time measurements are erroneous and need to be corrected (length contraction and time dilation). Likewise, because Alice and Bob both measure the same values for spin angular momentum ##\pm 1## ##\left(\frac{\hbar}{2}\right)##, regardless of their SG magnet orientation relative to the source per NPRF, Alice(Bob) may claim that Bob’s(Alice’s) individual ##\pm 1## values are erroneous and need to be corrected (averaged, Figures 5 & 6). In both cases, NPRF resolves the “mystery” it creates. In SR, the apparently inconsistent results can be reconciled via the relativity of simultaneity. That is, Alice and Bob each partition spacetime per their own equivalence relations (per their own reference frames), so that equivalence classes are their own surfaces of simultaneity and these partitions are equally valid per NPRF. This is completely analogous to QM, where the apparently inconsistent results per the Bell spin states arising because of NPRF can be reconciled by NPRF via the “relativity of data partition.” That is, Alice and Bob each partition the data per their own equivalence relations (per their own reference frames), so that equivalence classes are their own +1 and -1 data events and these partitions are equally valid.
References
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PhD in general relativity (1987), researching foundations of physics since 1994. Coauthor of “Beyond the Dynamical Universe” (Oxford UP, 2018).
See Section 3.2.1 of this paper: https://www.mdpi.com/1099-4300/22/5/551/htm for the role of Newton's 2nd law. That's not in the book.
I don’t think of a spacetimesource element as “real”. It just represents the relational nature of quantum exchanges of energy-momentum.
In a private conversation is best :-)
Yes that’s it
This article https://arxiv.org/pdf/2107.02089.pdf was just posted on another thread I've been following. You might be interested in reading Section 5.1 "De Broglie-Bohm theory"
My Insight has nothing to do with the dBB interpretation nor have I ever published anything to do with dBB, so I don't know why you expected me to engage in a discussion of dBB. If you want to see how the relativity principle + h underwrites QM just as the relativity principle + c underwrites SR, see https://arxiv.org/abs/2106.12043 written for physics educators. It references our relevant publications if you're interested.
The relativity principle applied to the measurement of the speed of light c constitute the postulates of SR. As of now, 116 years after the publication of SR, we have nothing else to explain time dilation, length contraction, and the relativity of simultaneity. The relativity principle is not considered "nonobvious" in physics. On the contrary, it has been widely accepted since Galileo. What we showed in our publications (reviewed in this Insight) is that you can recover all of denumerable-dimensional QM with the very same relativity principle applied to the measurement of another fundamental constant of Nature, Planck's constant h. If you believe this principle account of QM lacks explanatory value, then you must also believe the postulates of SR lack explanatory value. You wouldn't be alone in that belief, but the vast majority of physicists disagree and all introductory physics textbooks introduce SR via its postulates.
In order to provide a "constructive" account of QM (as required for a proper "interpretation"), one will have to give up something cherished. That's what all the no-go theorems tell us. Since I love special relativity (I got my PhD in general relativity) and SR also lacks any constructive account, I have recently decided that I can live without a constructive account of QM as long as I can find a "principle" account of it as compelling as that for SR (relativity principle and light postulate). And, I have done so (explained in this Insight and others referenced therein). Indeed, this principle account of QM uses the same relativity principle applied to a different constant of Nature, h ("Planck postulate"). I'm content with that :-)
There are lots of references for the non-locality given in the Wiki article https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory
dBB is non-local, i.e., it uses a faster-than-light causal mechanism (pilot wave). Thus, if you use dBB to explain Bell-inequality-violating QM correlations, you must pick a preferred frame to maintain definite causal ordering. It has nothing to do with the aether. This is a very common complaint against dBB, you can find it addressed in virtually every paper dealing with the dBB interpretation.
The problem with Bohm is the use of a preferred frame. This looks a lot like the situation Einstein found himself in (quote from forthcoming in Am. J. Phys. by Moylan):
Even "Einstein was willing to sacrifice the greatest success of 19th century physics, Maxwell’s theory, seeking to replace it by one conforming to an emission theory of light, as the classical, Galilean kinematics demanded" before realizing that such an emission theory would not work (J. Norton, “Einstein’s Special Theory of Relativity and the Problems in the Electrodynamics ofMoving Bodies that Led him to it,” https://www.pitt.edu/~jdnorton/papers/companion.pdf). So, now that we know QM follows from the relativity principle applied to Planck's constant h, just like SR follows from the relativity applied to the speed of light c, (https://arxiv.org/abs/2106.12043), I have to believe Einstein would again defer to relativity principle :-)
(cited in our in our Scientific Reports paper and attached here). We reject the subjective nature of QBism, opting instead for one, self-consistent objective account of physical reality (represented by the block universe of shared, self-consistent classical information). And it makes perfect sense given that we're advocating for the fundamentality of principle explanation, i.e., principle explanation doesn't necessarily require a constructive counterpart. If you believe physics is in the business of identifying constraints on experience, as QBism claims, then the constraint "no preferred reference frame" is quite reasonable without a corresponding causal mechanism.
POs are not necessarily human, they can be actual or hypothetical data collection devices, e.g., the probe that just landed on an asteroid or a hypothetical probe of some spacetime location inside a star.
Both Alice and Bob always measure h (##\pm \frac{\hbar}{2}## to be precise) for their spin measurements of the Bell spin state in question. Both are justified in saying the other is the one who has to average their outcomes to obtain the "correct" value of spin to satisfy conservation of spin angular momentum. Just like time dilation and length contraction where Alice(Bob) tells Bob(Alice) that his(her) clocks are slow and his(her) meter sticks are short, both are right. That is the "weird" consequence of conservation per NPRF, i.e., the relativity principle applied to the measurement of h.
Dynamical explanation in physics is still absolutely legit in our view, it's just not fundamental. In my opinion, anything that can be explained dynamically should be, since our experience is dynamical. I only resort to the more fundamental principle/adynamical/Lagrangian explanation as a last resort, e.g., in dealing with closed timelike curves, origin of the universe, delayed choice, etc. All this is covered in our book, as you'll see. Chapters 7 & 8 cover the reconciliation of our dynamical experience of time with adynamical or block universe physics. You can also read our Entropy paper. At 35 pages it's long, but still shorter than Chapters 7 & 8
The "conservation part" of the mystery of entanglement is not found in the mysteries of time dilation and length contraction. The fact we are pointing out in our Scientific Reports paper (as outlined in the ScienceX News article) is that all of these mysteries stem from the application of the relativity principle ("no preferred reference frame" NPRF) to a fundamental constant. And while this principle explanation of the mysteries is true (principle explanation = mathematical consequences of empirical facts), there are still no (consensus) constructive accounts. And these mysteries are very very old. So, what do we make of these facts?
As I suggest in the ScienceX News article, perhaps we don't always need an explanation based on a causal mechanism. That's where the ScienceX News article ends, but we go further in our Scientific Reports paper. There we suggest that principle explanation is just as valid as constructive explanation when physics is viewed per Mermin's QBism (cited therein):
In other words, physics provides constraints on experience. If that's the way you view physics, then a constraint such as NPRF is very reasonable. That's where the Scientific Reports paper ends, but we go further in our Entropy paper. In that paper, we provide a mathematical model of consciousness whereby all of physics follows from two axioms (empirical principles), one of which is NPRF. And that shows how the mysteries of physics are related to the hard and combination problems of consciousness, and how neutral monism resolves them all. The bottom line: the physics we have is beautifully coherent and comprehensive (although not finished, since we still need quantum gravity of course).
You might also like to read this Insight which explains an "unreasonable consequence" of superquantum correlations as presented in Bub and Bub's book.
I'm not surprised you haven't heard of superquantum correlations. I started working in foundations in 1994 and didn't hear about superquantum correlations until 2018. We published a book on foundations of physics in 2018 and Jeff Bub asked us to give a talk on it for his seminar. After a few hours of discussion we were walking from the restaurant to our car when Bub said, "What I really want to know is, Why don't we observe superquantum correlations? They don't violate no-superluminal-signaling, so why are they not found in Nature?" Silberstein and I didn't know what he was talking about. Answering his question (they violate "conservation per NPRF") is what ultimately led to this Insight.
The bolded phrase is correct. I wrote up a series of Insights articles on this very topic:
https://www.physicsforums.com/insights/does-gravity-gravitate/
The short version is, the answer to the title question (does gravity gravitate?) can be either yes or no, depending on how you interpret it. The things MTW is talking about are part of the interpretation of the question that leads to a no answer. But the way Deur is using nonlinear effects is part of the interpretation of the question that leads to a yes answer. Both interpretations are valid; they just show that the question itself as originally stated is ambiguous, and the ambiguity can be resolved into two different questions that have different answers.
That debate isn't just over the dark energy case, although that's the case Sean Carroll chose to use to illustrate the issue in his blog post about "energy is not conserved". The debate applies to any spacetime that is not stationary, including the many non-stationary spacetimes with no cosmological constant (such as all of the FRW spacetimes with no cosmological constant).
So while I agree that not having to have a cosmological constant is a nice feature, I don't think Deur's model "solves" any general problem about "mass-energy not being conserved in GR". The same problem, if you think it's a problem, is there in FRW spacetime with no cosmological constant, which is basically where Deur's model would end up as a model of the universe as a whole (modulo some corrections due to the other effects in his model, that also don't affect the "conservation" issue as far as I can see).
The cosmological constant in GR is not "global"; it's just non-dynamical–it's an extra effective energy density that is just there regardless of anything else that happens. In quantum field theory it just corresponds to a nonzero vacuum expectation value of energy, which is a perfectly good local quantity.
The last sentence leads to what I think is a better way to describe what problem is solved by not having to have a cosmological constant. All attempts to estimate from QFT what a nonzero vacuum expectation value of energy should be, if there is one, come up with answers 120 or so orders of magnitude larger than the observed value they are supposed to be explaining. Deur's model makes that problem go away, which is certainly nice, but again, I don't think "solving a problem with mass-energy not being conserved" is a good way to describe why it's nice; "eliminating the problem of the huge mismatch between theoretical and experimental values of the cosmological constant" would be better.
Can you elaborate on this?
This struck me when I was reading the article you linked to; I think this is a very nice feature of the model.
I'm a little confused by this statement in the article:
"Deur's approach does not reproduce the conclusions of conventional classical General Relativity in the weak gravitational fields and spherically asymmetric systems where it dark matter and dark energy phenomena are observed"
At least as regards the effects I described in post #84 (particularly the first one), I don't see how this is correct. AFAIK it is perfectly true that conventional models of galaxies, the ones in which the discrepancy between mass inferred from luminosity and mass inferred from rotation curves is observed, are Newtonian and do not include any post-Newtonian terms, which means they do not include any effects of nonlinearity in the EFE. Those post-Newtonian terms and nonlinear effects are certainly present in principle, and in this respect Deur simply seems to be arguing that, contrary to the assumption underlying conventional models, those effects are not in fact negligible for galaxies. Since the magnitude of those effects is extremely hard to estimate from first principles (it's not feasible to numerically solve the Einstein-Infeld-Hoffman equations for a system of ##10^{11}## bodies), the arguments underlying the conventional assumption that they are negligible are heuristic, and so proposing a model that challenges those assumptions does not strike me as being inconsistent with GR.
Some of the other effects mentioned (such as the confinement invoked to account for dark energy effects) are not, as I understand it, present at all in classical GR, so the article's remark would apply to those; but the article doesn't seem to be drawing any distinction of this kind, it just seems to be making a blanket statement that none of Deur's claimed effects are present in classical GR, and that seems to me to be too strong.
I'm not sure about all aspects of the analogy between SR and QM that is described in the paper.
I agree that all observers in relativity having to measure ##c## for the speed of light, regardless of their state of motion, is analogous to all observers in QM having to measure ##\pm \hbar / 2## for spin, regardless of their choice of measurement direction. And I agree that the latter fact requires that, when analyzing conservation of angular momentum in QM, the best we can possibly do is the "average conservation" that the paper describes.
I'm not sure how length contraction or time dilation correspond to the spin "corrections" that have to be made to verify "average conservation", since length and time aren't conserved quantities and the contracted lengths and dilated times that a given observer assigns to objects in motion relative to him are not "corrections" applied to any calculation of conservation.
I'm wondering, though, if the latter issue could be addressed by looking at energy and momentum instead of time and length, since they are "corrected" by the same factors and they are conserved quantities. That would still leave as a difference between SR and QM the fact that the SR conservation laws are not average only.
These are good points, I would like to see the same things for Deur's proposed model.
Actually, from what I can see, the effects described in the 2009 Deur paper I linked to, and the 2020 paper @ohwilleke linked to, are classical effects and should be present in a classical GR model. His investigation was motivated by considering graviton-graviton interactions in a quantum field theory of a spin-2 field, but the actual Lagrangian he presents in the 2009 paper is classical; it's just a power series expansion of the standard Einstein-Hilbert Lagrangian around a zero order flat metric.
It seems to me that there are basically two classical effects he is describing:
(1) Nonlinearity in the Einstein Field Equation, which leads to terms in a post-Newtonian expansion that amount to adding a ##\ln(r)## term to the Newtonian potential, which in turn adds a ##1 / r## term to the Newtonian force, which is basically the same thing that MOND does, but now without requiring any modification to GR;
(2) Non-sphericity, the fact that a galaxy is a flattened disc and not a sphere, which, according to Deur, prevents different nonlinear effects under #1 above from canceling out. If this is correct, it is very interesting, because it would mean that the effects he is talking about would not be visible in a spherically symmetric model of the sort I have been considering in framing the questions I've asked. Which unfortunately makes checking the whole thing a lot harder, since there are no known closed form solutions for the flattened disc case (which is why Deur has to rely on numerical simulations).
You're misunderstanding my point here. I am not saying that the application of your claimed GR effect in the paper was backwards. I am saying that the only GR effect I can come up with that could apply to ##M_L##, which is where you say the change needs to happen, is in the opposite direction from what it would need to be to resolve the issue your claimed effect is supposed to resolve. That observation in itself doesn't tell me that anything specific in the paper is wrong; it just tells me that, whatever your claimed GR effect is, if it exists, it can't be any of the ones I can come up with. Which is why I keep asking questions to try to help me figure out what your claimed GR effect is, since if it exists it must be something different from any of the ones I have come up with.
No, that's not all you have seen from me. You have also seen specific, simple questions from me. You have not answered my latest one, in post #76. Can you answer it?
Most of what I have posted in this discussion has not been about that at all. It has been about the GR effect claimed in your paper which I have not been able to understand.
I am not trying to criticize or disparage the scholarly process. I am certainly not trying to claim that the journal should not have published your paper. That is entirely up to them. I am also not at all saying that your Insights article should not have been written or that PF should not have published it.
I am just trying to understand the heuristic argument you are making in the paper regarding the presence of a GR effect with the claimed properties. Lecturing me on the scholarly process does not help me with that at all. What would help me with that would be if you would answer the questions I posed in post #76. If you're not going to do that, I'll just bow out of the discussion since I have nothing further either to gain from it or to contribute to it.
You may not respect the authorities and/or your colleagues in the community, but you nonetheless have to get them to sign off on your ideas if you want your ideas distributed and/or recognized by that community. I understand PF only allows Insights based on ideas that have successfully passed this process. My Insight is based 100% on that process. I have not seen you post any references refuting anything in my Insight that have passed that process. All I've seen from you are value judgments and unsupported beliefs regarding what is a highly tangential point of the Insight, i.e., principle explanation in modern physics. For example, what do you think about the ScienceX News article I linked earlier?
If you can cite a no-go theorem having passed the scholarly process, you will save me a lot of time in the future. Otherwise, you're wasting a lot of my time responding to your unsupported beliefs and value judgments. I'm sorry, I just can't spare the time in that direction, Peter.
A more pertinent paper by Deur for this discussion might be this one:
https://arxiv.org/pdf/0901.4005.pdf
This is ref. 3 in the paper linked to in the quote above, and appears to be the original paper presenting his proposed effect and estimating its impact on galaxy rotation curves.
Btw, I should clarify something: nothing I have said should be taken as claiming that this statement just quoted is wrong. In fact I don't understand the claims being made in the paper about things like "globally determined" vs. "locally determined" mass, or how an observer in the surrounding FLRW dust region in what I quoted in my previous post just now can measure ##M_p##. What I am trying to figure out is whether I don't understand because I've missed something, or because the paper is actually wrong in its claims about the existence of an effect within standard GR that has the necessary properties.
So far, the responses I have gotten have moved me in the direction of "the paper is actually wrong", but that's still just opinion on my part because I still have not gotten a response which helps me to make sense of the parts of the paper that I can't understand. In my previous post I tried to frame a simple question that focuses on one particular part that I can't understand, in the hope that I will get a response that helps me to understand it. I may still not agree with it even after I understand it, but I would much prefer, if I am going to end up disagreeing, to be able to do so with confidence that I understand the claim I am disagreeing with. That is why I have persisted in asking questions.
The question is this: how will each of these observers obtain the masses they are said to obtain in the above?
I'll give what I understand to be the answer for the observer in the Schwarzschild vacuum region: this observer puts a test object into orbit about the "galaxy" (which in this model is actually a collapsing FLRW dust region, but let's ignore that and assume it's a stationary compact region like a galaxy) and measures its orbital parameters, and uses the well-known equations for orbits in Schwarzschild spacetime to derive the mass ##M## of the central object.
So to rephrase the question: first, is my understanding above correct? And if it isn't, what is the correct description of how the observer in the Schwarzschild vacuum region will measure his ##M##?
And second, how will the other observer, the one in the surrounding FLRW dust region, measure ##M_p##? What I am looking for is an explicit description of a measurement procedure similar to what I described above for the Schwarzschild observer. I have speculated about this in previous posts, but since you are saying I have misunderstood the paper, I will refrain from speculating. I would like you (@RUTA) to tell me.
I don't accept arguments from authority. In fact, when I see someone retreat into an argument from authority, my Bayesian prior is to raise my estimate of the probability that their claims are mistaken. Just to help you calibrate your estimate of me, I posted a thread in the relativity forum not too long ago proposing that an argument by Schild that is presented in MTW is erroneous. The thread is linked below if you care to read it; there is quite a bit of good discussion by a number of PF members, several of whom raised good points I had not thought of:
https://www.physicsforums.com/threa…me-dilation-imply-spacetime-curvature.919181/
If that's the only response you can give, I'm afraid we have reached an impasse. But I'll try and frame a simpler question that might elicit a more helpful response from you in a follow-up post.
No. I have no idea who these people are or what expertise they have in GR.
I won't respond to the rest of your post since I don't see any basis there for a constructive discussion. But, as I said, I'll try to frame a simpler question in a follow-up post.
I'll check that out, thnx.
The judges at the Gravity Research Foundation, journal referees, and journal editors disagree with you there, as it received Honorable Mention and was published.
You've totally misunderstood what was published. Your analysis is so far off the mark, I would have to reproduce most of the paper to correct it here. Think carefully about your assertion, Peter. You're claiming that the authors, judges, referees, and editors all missed the fact that the application of the effect was backwards. But, it's obvious to you. Doesn't that give you pause at all?
Is that your basis for a no-go theorem?
Unfortunately, the reasons given above are totally misguided.
That is true.
Do you have any calculations or references to support your beliefs here? Because the reasons given above are totally erroneous. You have totally misunderstood the paper and I don't have the time to help you there, my friend.
This is probably where I see the disconnect.
First, as I think I've said before, I don't think "heuristically" is enough. You can't just assume the effect you want to be there actually is there in a solution that is applicable to a galaxy and our observations of it. You have to show that the effect is there and of the right general order of magnitude. Just assuming it's there because it appears to be there in a different solution is not enough.
Second, the "fact" you are talking about, even in the solution you explicitly examine (collapsing FRW surrounded by Schwarzschild vacuum surrounded by expanding FRW), is not an effect that produces what you are looking for, as you are describing it later in your post. More on that below.
This is simply invalid handwaving. "GR allows for simultaneously differing mass values for one and the same matter" is not a magic wand. It's a specific statement about a specific pair of measurements, and it has a specific effect, and that effect is not what you're looking for.
A correct application of "GR allows for simultaneously differing mass values for one and the same matter" would look like this:
The mass ##M_L##, because it is obtained from observed luminosities, is a sum of "locally measured" masses–masses that would be measured by an observer in the same local region of the galaxy as the stars whose luminosities are being observed. Those are the masses that appear in the mass-luminosity relationships that are being used.
The mass ##M_R##, because it is obtained from observed rotation curves, is a sum of "externally measured" masses–masses that would be measured by an observer in the vacuum region outside the system. (There are some technicalities to this, but I think it's reasonable for the case under consideration.)
GR allows "externally measured" masses to be different from "locally measured" masses for systems like galaxies, because the latter include the effects of gravitational binding energy while the former do not. But that effect, as I've already noted, is in the wrong direction: "locally measured" masses are larger than "externally measured" masses, not smaller. So if the only matter in a galaxy is luminous matter, we would expect a GR correction to make ##M_L > M_R##, which is the opposite of what we need. (Also, the magnitude of this correction is small; it is of rough order of magnitude ##G M / c^2 R##, where ##R## is some appropriate value for the radius of the galaxy. For all galaxies we know of, this correction is a tiny fraction of a percent at best.)
GR also includes spatial curvature, which is not included in the standard Newtonian models of galaxies, but as I've already said, this does not affect either ##M_R## or ##M_L##; it only affects our estimate of average density.
There is no other GR effect I know of that is applicable here. The only other thing you discuss in the paper that seems at all relevant is the claim on p. 5, after equation (7), that observers in the exterior FRW region will somehow measure ##M_p## instead of ##M##; I have already explained why I don't find that claim to be valid. The only thing I would add to that here is that, as far as I can tell, any such effect, if it were valid, would affect how we infer ##M_R## from observations, not how we infer ##M_L##; but you are saying in what I've quoted above that your claimed effect changes how we infer ##M_L##.
As an empirical finding, this is fine. But it does not support any claim that there is a valid GR correction that will produce such a functional form. I don't see how there can be one, for the reasons given above. And as I've already remarked, and you have agreed, you are not deriving your functional form from any underlying GR equations; you are just assuming it as an ansatz and seeing how it fits the data. So the fact that it fits the data well does not provide any support for the claim that there is in fact a valid GR correction that leads to your ansatz.
So if your functional form turns out to be valid (i.e., if it doesn't turn out to be just another way of representing the effects of dark matter), I think it will be because it is a reasonable approximation to some underlying effect that is not present in GR, but is present in some modified theory (possibly derived from quantum gravity) that includes effects that are not present in GR. (I personally think this is extremely unlikely, but that's just my opinion; once we actually have a working theory of gravity, possibly quantum gravity, that goes beyond GR, we'll see what it says.)
When you adjoin the FRW and Schwarzschild solutions, the comparative mass can be equal, larger, or smaller, and the matter can be surrounded by vacuum or vice-versa, as I explain in the corresponding AJP paper. That fact alone is used heuristically as follows.
##M_R## is inferred from orbital speeds (or other data in the cases of mass profiles of X-ray clusters and anisotropies in the angular power spectrum of the cosmic microwave background) by assuming Newtonian gravity supplies the centripetal acceleration for UCM of the orbiting stars and gas. When the orbital speeds are measured (via redshifts) we find ##M_R## is much larger than ##M_L##. So, we are considering a correction to Newtonian gravity for a situation that otherwise doesn't seem to warrant it (very small spatial curvature). The correction we proposed is simply to replace ##M_L## in the Newtonian acceleration with a corrected value, since the mass of the matter responsible for the acceleration is being measured in two different ways and GR allows for simultaneously differing mass values for one and the same matter. We found a functional form for correcting ##M_L## that rivals or beats all competitors across three different astronomical matter distributions — galactic, galactic cluster, and cosmological. That is interesting because no other approach works as well across all three distributions. The rivals we compared are:
1. Two different DM distribution models (Burkett and NFW). The functional forms for these DM distributions are not based on any knowledge of the physics for these hypothetical and unlikely (as shown by Carroll) particles.
2. Correction to Newtonian physics (MOND). The ad hoc change of Newtonian acceleration at large scales. There is a relativistic counterpart for this now, but it's ugly and does not satisfy local conservation (not divergence-free).
3. Two different corrections to GR (MSTG and STVG). These are also otherwise unmotivated and do not satisfy local conservation.
Again, none of the rivals match our fits using our simple functional form for the correction of ##M_L## across all three matter distributions. Keep in mind that we're not talking about a new phenomenon here. The missing mass phenomenon was introduced in the 1930's (e.g., Zwicky, F: On the masses of nebulae and clusters of nebulae. The Astrophysical Journal 86, 217-246 (1937)). So, after 80+ years these are still our best guesses.
Conclusion, maybe it's reasonable to consider the idea from GR that matter can simultaneously possess different values of mass based on spatially different measurement contexts. We already know it's true for different temporal contexts, e.g., free neutron mass greater than bound neutron mass. So, is this such a stretch?
That's the best I can do, Peter. Hope it suffices.
On further thought, this way of putting it, while it is correct, might not really get at the issue I'm trying to describe. So let me try it another way.
Suppose we know ##M_R## for some galaxy but we don't know ##M_L## (say we can't see the galaxy directly because it's obscured by a dust cloud, but we've been sent rotation curve data for the galaxy by some alien civilization that isn't behind the dust cloud). What value for ##M_L## would we predict from our knowledge of ##M_R##? Or, to put it another way that makes the logic clearer, what value for total luminosity for the galaxy would we predict from our knowledge of ##M_R##, if we assume that all the matter in the galaxy is luminous (stars) and has similar properties to stars in our own galaxy?
The Newtonian prediction is simple: we expect ##M_L = M_R##, so we just apply some expected distribution of stellar luminosities, plug those into an integral for total luminosity, and use known mass-luminosity relationships to apply the appropriate weighting factors in the integral so that the total mass, given our assumed distribution of stellar luminosities (which we can translate into an assumed distribution of stellar masses) comes out to ##M_L##. This kind of calculation, since it gives an answer for total luminosity that is significantly larger than the total luminosity we actually observe, is the basic argument used by proponents of dark matter: there must be non-luminous matter present to make up the total mass that is needed to account for the observed rotation curves.
Since in actual fact we observe ##M_L < M_R## by some significant factor, if we want to avoid dark matter (and if we also want to avoid modifying our theory of gravity, which is what the paper under discussion wants to do–it wants to find a solution within GR), we need to find some non-Newtonian effect that would modify the above prediction procedure. The first obvious non-Newtonian effect to consider is gravitational binding energy: in Newtonian gravity, binding energy doesn't affect mass, but in GR, it does. However, this effect is in the wrong direction: it leads us to expect ##M_L > M_R## in the above prediction procedure (i.e., it leads us to expect a larger total luminosity than what we would infer by assuming ##M_L = M_R## in the above procedure), because gravitational binding energy is negative; the mass measured "from the outside" by something like rotation curves is smaller than the mass measured "from the inside", by an observer locally that is next to some particular star, and that locally measured mass is what is correlated with the luminosity in our known mass-luminosity relationships. This kind of effect is what I was thinking of in post #65, but I incorrectly mixed it up with space curvature.
A second non-Newtonian effect to consider is space curvature; but as I noted in my previous post (quoted above), that doesn't affect either ##M_R## or ##M_L## in the above prediction procedure (i.e., it doesn't affect the total luminosity we would infer from rotation curve data). It just affects the proper volume we assign to the galaxy, which means it affects the average density we expect a local observer, inside the galaxy, to measure.
So neither of those non-Newtonian effects can account for our observation that ##M_L < M_R##. And I am not aware of any other non-Newtonian effect that would be significant in this scenario, nor does the paper appear to me to suggest one; it only suggests one of the above two, neither of which work.
Actually, on thinking this over some more, I think I have misstated this a bit. Including non-Newtonian effects of the kind implied by "two different measurements of mass for one and the same matter" (which means correcting for things like spatial curvature) should not change either ##M_L## or ##M_R##. What it should change is our calculation of how much proper spatial volume the mass occupies, i.e., it should change our estimate of the average density (more precisely, proper density, the density measured by an observer locally inside the galaxy) of the matter in a galaxy, as compared to a Newtonian calculation (our estimate of average proper density should be reduced–more spatial volume for the same mass). But it should not change the mass we infer from rotation curves or luminosity at all, because those estimates are independent of our estimate of the average density.
What I am calling the "error" there is the discrepancy between ##M_R## and ##M_L## when using standard methods to estimate both. So there is an error. I am trying to understand how your proposed method resolves it. See below.
This doesn't answer my question, because I can't make what you're describing here give an answer that resolves the discrepancy. I don't understand how to relate what you are saying in the paper to what I am calling ##M_R## and ##M_L##, or how what you are describing in the paper corrects the discrepancy between the two. The only sense I can make of "two different measurements of mass for one and the same matter" gives an answer that makes the discrepancy worse, not better, for the reason I gave in post #65 (it doesn't change ##M_L## and it makes ##M_R## larger, not smaller). So I'm confused. I am hoping that if you give explicit answers to the two questions I gave, it will help to resolve, or at least reduce, my confusion.
There is no error, they are two different measurements of mass for one and the same matter, as allowed per GR. You can map them one to the other as I showed in the paper.
This was my initial read as well, based on the usage of the terms "proper mass" and "dynamical mass" — basically, that the non-Newtonian effects mean that the "proper mass", which includes corrections for things like spatial curvature, is a better thing to plug into the dynamical equations than the "dynamical mass", which does not include those corrections. However, that can't be the right answer because, as I noted in an earlier post, the correction is in the wrong direction: the corrections due to things like including spatial curvature make the estimate for ##M_R## larger, not smaller.
Perhaps it will also help if I give what I take to be the answers to these questions that would be given by a proponent of (A) dark matter, and (B) MOND.
(A1) ##M_R## is correct, but ##M_L## is too small because it only counts luminous matter.
(A2) There is other matter present, dark matter, which is not luminous and so can't be counted that way. When we add in the mass of dark matter, we get ##M_L + M_D = M_R##, which fixes the discrepancy.
(B1) ##M_L## is correct, but ##M_R## is too large because it is estimated using the wrong dynamical equations.
(B2) MOND changes the dynamical equations so that ##M_R## is smaller and matches ##M_L##, which fixes the discrepancy.