In summary, the author provides a concise overview of the light postulate, the principle of relativity, and how these two principles follow from each other. He also discusses how the superselection rule for the fundamental physical constants can be derived from these two principles.
  • #1
RUTA
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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...

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  • #2
I enjoyed this, esp the image of other universal constants working the same as c.

it seems like a chicken and egg problem a little (QM superselection rules and NPRF physical constants) but at least they are both chickens.
 
  • #3
Jimster41 said:
I enjoyed this, esp the image of other universal constants working the same as c.

it seems like a chicken and egg problem a little (QM superselection rules and NPRF physical constants) but at least they are both chickens.

Thnx. Would you mind expanding on that second comment for me? A referee said something similar, so I'm curious what exactly brought that to mind :smile:
 
  • #4
Which comes first, the partition that provides the correct equivalence relation on average for (c,h,G, b?) or the equivalence relation that dictates partition?
 
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  • #5
Jimster41 said:
Which comes first, the partition that provides the correct equivalence relation on average for (c,h,G, b?) or the equivalence relation that dictates partition?
Which is the superselection rule as you see it?
 
  • #6
I’m going to go with “partition”, and venture even further... that is what physical chemistry sort of is.
 
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  • #7
Jimster41 said:
I’m going to go with “partition”, and venture even further... that is what physical chemistry sort of is.
Let's look at SR. Here is the explanatory hierarchy as we present it in our paper:

NPRF --> everyone measures c --> time dilation and length contraction --> relativity of simultaneity (different partitions of spacetime).

So, NPRF is not the equivalence relation, but it is the ultimate basis for our equivalence relation, which is strictly speaking the synchronized proper time of the comoving observers for either Alice or Bob (or ... ). Here we have NPRF/equivalence relation leading to the partition. Now let's flip it:

Relativity of simultaneity --> time dilation and length contraction --> everyone measures c --> NPRF.

For QM we have:

NPRF --> everyone measures h --> average-only conservation and Bell state correlations --> relativity of data partition (different partitions of Bell state data).

Again, NPRF isn't the equivalence relation, but it is the ultimate basis for it. Now let's flip it:

Relativity of data partition --> average-only conservation and Bell state correlations --> everyone measures h --> NPRF.

If you go with the equivalence relation as fundamental, you have one and the same rule leading to two different consequences. If you go the other way, you have two different rules with the exact same consequence. I think physicists would prefer the former, since they tend to be reductionists (explain more and more with less and less" per Weinberg). The other way makes NPRF look like an amazing coincidence.
 
  • #8
hmm. I sort of read the table in the article up and down and that's why "at least both are chickens" aha. And I guess I see NPRF as exactly that pretty neat coincidence between relativity of simultaneity and the discrete partitioning of information for Bell observers in different frames.

to me these sound like accurate historical accounts of "what happened"
RUTA said:
Relativity of simultaneity --> time dilation and length contraction --> everyone measures c --> NPRF.
RUTA said:
Relativity of data partition --> average-only conservation and Bell state correlations --> everyone measures h --> NPRF.

So, I guess I see NPRF as a statement of "connected fact" rather than pejorative "amazing coincidence".
 
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  • #9
Jimster41 said:
hmm. I sort of read the table in the article up and down and that's why "at least both are chickens" aha. And I guess I see NPRF as exactly that pretty neat coincidence between relativity of simultaneity and the discrete partitioning of information for Bell observers in different frames.

to me these sound like accurate historical accounts of "what happened"

So, I guess I see NPRF as a statement of "connected fact" rather than pejorative "amazing coincidence".
That could be true :smile:
 
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  • #10
Actually, I prefer

“Time dilation and length contraction --> Relativity of simultaneity -->everyone measures c --> NPRF.”

“Average-only conservation and Bell state correlations --> Relativity of data partition --> everyone measures h --> NPRF.”
 
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  • #11
I bought and am reading the book you recommended, "Universal Constants in Physics". Thnx for pointing that out, Jimster41.
 
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  • #12
And I just bought your book (Kindle) for morning coffee.
 
  • #13
I've started a thread in the BSM forum zeroing in only on the subtopic of a discussion of references [23] and [24] in the Insights article. https://www.physicsforums.com/threads/explaining-dark-matter-and-dark-energy-with-minor-tweaks-to-gr.994343/
 
  • #14
ohwilleke said:
I've started a thread in the BSM forum zeroing in only on the subtopic of a discussion of references [23] and [24] in the Insights article. https://www.physicsforums.com/threads/explaining-dark-matter-and-dark-energy-with-minor-tweaks-to-gr.994343/

Moderator's note: That thread has been put in moderation for review. On an initial look, it is much too long and much too broad for a single thread discussion; a single thread discussion should be focused on one particular reference, and ideally on one particular question raised by that reference.

Also, that thread is asking for people's "gut check" opinions, which is off topic and doesn't lead to fruitful discussion.
 
  • #15
RUTA said:
relativity of simultaneity (different partitions of spacetime)

Relativity does not partition spacetime into two regions with respect to a particular event. It partitions spacetime into three regions: the past light cone, the future light cone, and the spacelike separated region. This partitioning, for any given event, is invariant.

It seems to me that the above fact should be taken into account in any attempt to provide an explanation.
 
  • #16
I only just started chapter two of the book. The chapter is titled “Block Universe from Special Relativity” looking forward to it. My gut reaction to your comments above (FWIW):

There is only ever Alice and Bob.
And
Invariant except for differential aging
(I get that both measure the same second... and yet their seconds aren’t the same)

the first thought leaves me wishing I had a clearer picture of some of the more complicated Bell experiments... ones with more than two detectors etc. What does the math even look like when you are trying to simultaneously resolve three of Schrodinger’s cats? I’m guessing it has to be done pair-wise?
 
  • #17
PeterDonis said:
Relativity does not partition spacetime into two regions with respect to a particular event. It partitions spacetime into three regions: the past light cone, the future light cone, and the spacelike separated region. This partitioning, for any given event, is invariant.

It seems to me that the above fact should be taken into account in any attempt to provide an explanation.
That is a different partition altogether. I'm talking about partitions per surfaces of simultaneity for any given observer. The partition I'm talking about is therefore observer dependent, which is key to the entire explanation.
 
  • #18
RUTA said:
I'm talking about partitions per surfaces of simultaneity for any given observer.

Yes, I know that.

RUTA said:
The partition I'm talking about is therefore observer dependent

No, it's coordinate dependent. Which means that, according to the standard way that GR is interpreted, it has no physical meaning, since only invariants have physical meaning.
 
  • #19
PeterDonis said:
No, it's coordinate dependent. Which means that, according to the standard way that GR is interpreted, it has no physical meaning, since only invariants have physical meaning.
The coordinates are associated with the observer here and they certainly do have physical meaning for the observer, they represent what that observer will measure.
 
  • #20
RUTA said:
The coordinates are associated with the observer here

But there's no unique way of doing that. In SR, if the observer is inertial forever, there is at least a coordinate chart that is picked out by the observer's state of motion--but in our real universe spacetime is not flat and no observer is ever inertial forever.

RUTA said:
they certainly do have physical meaning for the observer, they represent what that observer will measure.

Only on the observer's worldline. The coordinates picked by an observer on Earth don't represent what the observer directly measures in the Andromeda galaxy since the observer can't directly measure anything there.
 
  • #21
PeterDonis said:
But there's no unique way of doing that. In SR, if the observer is inertial forever, there is at least a coordinate chart that is picked out by the observer's state of motion--but in our real universe spacetime is not flat and no observer is ever inertial forever.

Only on the observer's worldline. The coordinates picked by an observer on Earth don't represent what the observer directly measures in the Andromeda galaxy since the observer can't directly measure anything there.
We rarely have to worry about GR corrections. And we do use distant coordinates all the time in making measurements, e.g., probes around distant planets.
 
  • #22
RUTA said:
We rarely have to worry about GR corrections.

Perhaps in a practical sense this is true for many problem domains. But you are talking about foundations. For foundations, the fact that GR is more accurate than SR is critical.

RUTA said:
we do use distant coordinates all the time in making measurements, e.g., probes around distant planets

We use coordinates to describe the results of measurements. We do not use coordinates to make measurements. Measurement results are invariants. Coordinate values are not.
 
  • #23
PeterDonis said:
Perhaps in a practical sense this is true for many problem domains. But you are talking about foundations. For foundations, the fact that GR is more accurate than SR is critical.

We use coordinates to describe the results of measurements. We do not use coordinates to make measurements. Measurement results are invariants. Coordinate values are not.
The comparison I'm talking about is the relativity principle of SR as applied to c with its application in QM to h. The theoretical structure of GR in no way undermines that relationship and does not add anything to the analysis. The coordinate values can (and usually do) correspond to or directly relate to measured values, e.g., SG magnet angles. The point of a coordinate system is, as the name states, to "coordinate."
 
  • #24
RUTA said:
The theoretical structure of GR in no way undermines that relationship and does not add anything to the analysis.

To me, that's because your analysis is limited in scope, which, as I said, doesn't seem viable if you are talking about foundations. For example, your analysis doesn't cover gravity.
 
  • #25
PeterDonis said:
To me, that's because your analysis is limited in scope, which, as I said, doesn't seem viable if you are talking about foundations. For example, your analysis doesn't cover gravity.
The relationship between SR and QM that we point out is valid, so de facto it is independent of gravity. Indeed, the principle relating them (relativity principle) and dd = 0 hold across all theories of physics, Newtonian and modern. Thus, it is clear that we don't need a theory of everything to do foundations of physics.
 
  • #26
RUTA said:
The relationship between SR and QM that we point out is valid, so de facto it is independent of gravity.

You can't possibly know this without a theory of quantum gravity that has been experimentally confirmed. All you can know without that is that the relationship is valid under conditions where gravity can be ignored.

RUTA said:
we don't need a theory of everything to do foundations of physics.

As long as your definition of "foundations of physics" is ok with the fact that claims based on theories that are known to have a limited domain of validity cannot be asserted as valid outside that domain.
 
  • #27
PeterDonis said:
You can't possibly know this without a theory of quantum gravity. All you can know without that is that the relationship is valid under conditions where gravity can be ignored.

Not as long as your definition of "foundations of physics" is ok with the fact that claims based on theories that are known to have a limited domain of validity cannot be asserted as valid outside that domain.
We can possibly know what is shown deductively in the paper. It's not a matter of opinion, we are stating mathematical and empirical facts. Now, it may be the case that what we are observing and describing mathematically in current experimental situations does not extrapolate to other experimental situations. But, that's the point of physics -- to articulate empirically discovered principles/laws/regularities/constraints, extrapolate them theoretically, and test the extrapolations. What we point out in https://www.mdpi.com/1099-4300/22/5/551/pdf is that dd = 0 and the relativity principle that held for Newtonian physics and E&M are still holding in modern physics. We then outline how one might extrapolate to theories of quantum gravity based on those principles. That's one way to use foundations of physics.
 
  • #28
RUTA said:
We then outline how one might extrapolate to theories of quantum gravity based on those principles.

Ok, I need to read that part of the Insight more carefully. The phrase "matter can simultaneously possesses different values of mass when it is responsible for different combined spatiotemporal geometries" doesn't seem correct to me, but perhaps I'm misunderstanding what it's intended to mean.
 
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  • #29
References [23] and [24] make some very bold claims (namely that dark energy and dark matter are chimeras of improper application of GR thus explaining the CMB, galaxy rotation curves, clusters, and dark energy phenomena). Are there any other groups that have concurred in that conclusion?
 
  • #30
ohwilleke said:
References [23] and [24] make some very bold claims (namely that dark energy and dark matter are chimeras of improper application of GR thus explaining the CMB, galaxy rotation curves, clusters, and dark energy phenomena). Are there any other groups that have concurred in that conclusion?
There are lots of other fits, we share some in those papers. No one has anything compelling at this point. I’d like to get back and develop the physics, but I’ve been too busy working on foundations stuff 🙂
 
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  • #31
PeterDonis said:
The phrase "matter can simultaneously possesses different values of mass when it is responsible for different combined spatiotemporal geometries" doesn't seem correct to me

After further perusal of the paper, I think the choice of words here is misleading. What is being described in the paper is simply the fact that the externally measured mass of a gravitationally bound system in GR is not equal to the "naive" sum of the masses of its constituents--where "naive" sum means we just add up the locally measured masses of the constituents instead of actually doing a proper integral with a proper integration measure that takes the spacetime geometry into account. The difference between the "naive" sum and the externally measured mass of the system as a whole is usually referred to as "gravitational binding energy".

All of that is fine, but the phrase "different combined spatiotemporal geometries" is misleading. There is only one spacetime geometry in any given spacetime in GR. What I called the "locally measured mass" of a constituent of a gravitationally bound system above is the mass that would be measured by an observer co-located with the constituent, in a local inertial frame in which spacetime curvature can be ignored. But the fact that spacetime curvature can be ignored in such a local measurement does not mean it isn't there; the actual spacetime geometry is still curved, and doesn't change when we go from a local measurement on a single constituent to an external measurement of the system as a whole.

I also don't think "contextuality for mass" is an appropriate term in this context. All of the measurements being described are invariants; they don't depend on who is measuring them or what other measurements are being done in combination with them. So I don't see any valid analogy with contextuality in QM.
 
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  • #32
PeterDonis said:
After further perusal of the paper, I think the choice of words here is misleading. What is being described in the paper is simply the fact that the externally measured mass of a gravitationally bound system in GR is not equal to the "naive" sum of the masses of its constituents--where "naive" sum means we just add up the locally measured masses of the constituents instead of actually doing a proper integral with a proper integration measure that takes the spacetime geometry into account. The difference between the "naive" sum and the externally measured mass of the system as a whole is usually referred to as "gravitational binding energy".

The two different values of mass for one and the same matter are obtained properly using the local metric.

PeterDonis said:
All of that is fine, but the phrase "different combined spatiotemporal geometries" is misleading. There is only one spacetime geometry in any given spacetime in GR.

One solution obtained by combining two other solutions. Standard GR, nothing misleading here.

PeterDonis said:
What I called the "locally measured mass" of a constituent of a gravitationally bound system above is the mass that would be measured by an observer co-located with the constituent, in a local inertial frame in which spacetime curvature can be ignored. But the fact that spacetime curvature can be ignored in such a local measurement does not mean it isn't there; the actual spacetime geometry is still curved, and doesn't change when we go from a local measurement on a single constituent to an external measurement of the system as a whole.

Again the meaning of "mass" in the two solutions is unambiguous and intuitive. In the cosmology part, it is just dust density times co-moving volume. In the Schwarzschild part, it is obtained by rotational dynamics. In both cases, the observers are in inertial frames (following geodesics). Again, standard GR, nothing unusual.

PeterDonis said:
I also don't think "contextuality for mass" is an appropriate term in this context. All of the measurements being described are invariants; they don't depend on who is measuring them or what other measurements are being done in combination with them. So I don't see any valid analogy with contextuality in QM.

Thus, one and the same matter has two different values of mass -- one obtained by inertial observers inside the matter and one obtained by inertial observers in orbit around the matter. This differs from the usual notion of binding energy, e.g., a free neutron has one mass and a bound neutron has another mass. In that case, the mass is different at different times, the context changes temporally. Here the mass is different in different regions of space, it is the same in each spatial region at all times. Either way, the mass of matter is clearly a function of the context, thus the phrase.

There is nothing "crank" about this result, it's not like this idea slipped past referees and editors at different journals. No referee or editor has ever questioned the result or the terminology because it comports with GR.
 
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  • #33
RUTA said:
one and the same matter has two different values of mass -- one obtained by inertial observers inside the matter and one obtained by inertial observers in orbit around the matter.

I see what you mean, but I still think your language is misleading. An inertial observer in orbit around an object made of matter is not measuring the "dynamic mass" of individual small pieces of matter in the object; he's mesauring the "dynamic mass" of the whole object. He has no way of separating that into individual pieces.

The inertial observer inside the matter, OTOH, is measuring the "proper mass" of the individual piece of matter with which he is co-located. He cannot directly measure the mass of the whole object. He can only calculate it using observations and assumptions.

RUTA said:
This differs from the usual notion of binding energy

In the sense that, in your description, the spacetime is not stationary (since the FRW region cannot be stationary), yes, this is true. However...

RUTA said:
e.g., a free neutron has one mass and a bound neutron has another mass.

...this is stated incorrectly, IMO. A correct statement would be that a system containing bound neutrons (such as an atomic nucleus) has a mass that is smaller than the sum of the free masses of its constituents (for example, the mass of a deuteron is less than the mass of a free proton plus the mass of a free neutron). A measurement of the mass of the bound system cannot be separated into a measurement of the "bound mass" of individual constituents: you can't separate the measured mass of a deuteron into "mass of a bound proton" and "mass of a bound neutron".
 
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  • #34
RUTA said:
One solution obtained by combining two other solutions.

Just to be clear, you mean that the spacetime in this solution has a region which is Schwarzschild and a region which is FRW, with a boundary between them, correct?

[Edit: This is in reference to the example in ref. 24 in the article.]
 
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  • #35
PeterDonis said:
Just to be clear, you mean that the spacetime in this solution has a region which is Schwarzschild and a region which is FRW, with a boundary between them, correct?

[Edit: This is in reference to the example in ref. 24 in the article.]
Correct.

In order that the DM fits are compelling, we would need to derive theoretical predictions for the fitting factors currently found empirically (for galactic rotation curves, galactic cluster mass profiles, CMB anisotropies) using contributions from those boundary terms. Again, that's just a simplification, but no one is ever going to solve Einstein's equations for a real galaxy. What we need to do is at least motivate the fitting factors via other measurements (luminosity, temperature, etc.). Then check the theoretical (approximated) predictions for the fitting factors against those obtained empirically. The work done to date was simply to find out whether or not the inverse square law functional form is reasonable (the answer there is clearly affirmative), so we know what we're looking for in the GR formalism. Have you done the fits for these data using MOND, various modified gravity theories, and the different DM models? If so, you'll see that our result is on par with all of those (I did all those and showed the comparisons in our papers). Anyway, finding theoretical predictions for the fitting factors should be possible, but I've been working on other questions in foundations that I find more interesting :-)

What I find more interesting than finishing the "no-DM-GR-is-correct model" is showing how the whole of physics is coherent, contrary to popular belief. And, I found a big piece of that by answering Bub's question, "Why the Tsirelson bound?" So, I've been busy these past two years working on the consequences of that answer.
 
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