B Any plausible explanation for dynamical length contraction?

[Dale]

No, it is not à la carte, as you suggest, @Dale . Your future is either there or it isn't...

It absolutely is a la carte. That is the whole point of an interpretation.

Let's take a step back. A theory is a mathematical framework with a mapping from the math to experiment. This mapping from math to experiment is sometimes called the minimal interpretation. The framework together with the minimal interpretation is the minimum necessary for doing science. The minimal interpretation allows you to challenge the mathematical framework experimentally using the scientific method.

Now, it is possible to go beyond the original mathematical framework and make a whole new mathematical framework, perhaps even with its own minimal interpretation. If that new framework and new minimal interpretation make all of the same experimental predictions as the original, then it is called a reformulation of the original. They are not considered separate theories, and usually there is a clear mathematical way to derive one framework from the other. For example, Newton-Cartan gravity is a geometrical reformulation of Newtonian gravity wherein gravity is represented as spacetime curvature. This is not general relativity, it is Newtonian gravity, but it shares a lot of the math with general relativity. In particular, in standard Newtonian gravity gravity is a real force, but in the Newton-Cartan reformulation gravity is a fictitious force.

It is also possible to go beyond the original mapping from the math to experiment and include mappings from the math to other concepts, usually philosophical in nature. This is called an interpretation, meaning an interpretation beyond the minimal interpretation. An interpretation, by definition, cannot be queried experimentally because all of the mappings between the math and experiment are already contained in the minimal interpretation.

So, if we want to be consistent with how the world works, then what must we do? Ultimately, experiment is what we use to assess how consistent our concepts are with the world. Things that can be determined by experiment reflect some fact about the world itself and things that cannot (even in principle) be determined by experiment do not reflect some fact about the world itself.

Neither interpretations nor reformulations can be distinguished by experiment, even in principle. All reformulations of a theory and all interpretations of a theory agree on all experimental predictions. Thus neither interpretations nor reformulations reflect some fact about the world itself. They are only concepts in our mind, and as such, we can change our mind about them without coming into conflict with how the world works.

 

[alexandrinushka]

Let's not. For starters, the currently accepted theories of matter and energy consistent with SR are all variants of QFT which makes no sense with a BU interpretation (it is fundamentally non-deterministic). So, essentially all practicing physicists functioanlly reject the coupling argued by the philosophers you insist on believing.

"Einstein's synchronization method is the only genuine one" is utter nonsense as to the claim it is the only one. The universe does not care how or whether we synchronize clocks.
"there is no such thing as a superfluous absolute frame" is a statement of faith, similar to religion. There is no way to prove or disprove it, as a matter of principle.

You invent a quandary the simply does not exist. If you don't like BU, don't use it. Note that the Ellis of Hawking and Ellis "Large Scale Structure of spacetime" strenuously argues that QFT forbids the validity of BU. Most disagree with the "forbids" aspect of this, but the point is that one of greatest relativity theorists of the last 50 years totally rejects the BU interpretation.

Thanks a lot for your post, I will check your resources. I needed to hear that ^^

 

[alexandrinushka]

It absolutely is a la carte. That is the whole point of an interpretation.

Let's take a step back. A theory is a mathematical framework with a mapping from the math to experiment. This mapping from math to experiment is sometimes called the minimal interpretation. The framework together with the minimal interpretation is the minimum necessary for doing science. The minimal interpretation allows you to challenge the mathematical framework experimentally using the scientific method.

Now, it is possible to go beyond the original mathematical framework and make a whole new mathematical framework, perhaps even with its own minimal interpretation. If that new framework and new minimal interpretation make all of the same experimental predictions as the original, then it is called a reformulation of the original. They are not considered separate theories, and usually there is a clear mathematical way to derive one framework from the other. For example, Newton-Cartan gravity is a geometrical reformulation of Newtonian gravity wherein gravity is represented as spacetime curvature. This is not general relativity, it is Newtonian gravity, but it shares a lot of the math with general relativity. In particular, in standard Newtonian gravity gravity is a real force, but in the Newton-Cartan reformulation gravity is a fictitious force.

It is also possible to go beyond the original mapping from the math to experiment and include mappings from the math to other concepts, usually philosophical in nature. This is called an interpretation, meaning an interpretation beyond the minimal interpretation. An interpretation, by definition, cannot be queried experimentally because all of the mappings between the math and experiment are already contained in the minimal interpretation.

So, if we want to be consistent with how the world works, then what must we do? Ultimately, experiment is what we use to assess how consistent our concepts are with the world. Things that can be determined by experiment reflect some fact about the world itself and things that cannot (even in principle) be determined by experiment do not reflect some fact about the world itself.

Neither interpretations nor reformulations can be distinguished by experiment, even in principle. All reformulations of a theory and all interpretations of a theory agree on all experimental predictions. Thus neither interpretations nor reformulations reflect some fact about the world itself. They are only concepts in our mind, and as such, we can change our mind about them without coming into conflict with how the world works.

Thanks a lot for your message, @Dale . It really is helpful and I appreciate you taking time to bring this home to my mind.

 

[alexandrinushka]

Guys, I want to thank you for your patience and for bearing through my rambling, fears and pain points. I have learned a lot from this exchange, specifically that I should study a bit more Physics and keep a more open mind (not just jump to conclusions from minimal interpretations and feel like I have cracked the mystery of the entire universe with one theory).
I admit I have read more Metaphysics than Physics in my life (to a ratio of 100 to 1, I guess) and it is very easy to "get married" to an idea when it is vehemently sold by philosophers. Nothing against philosophers though. From my readings, I can tell most of them are brilliant and many have double PhDs in Math/Physics and Philosophy. But often they swear by something and then, a month later, another just as brilliant guy publishes an article about why the previous one was wrong. As so on and on and on. It is tiring at times. Probably the "shut up and calculate" attitude is a good one to adopt from times to times.

I understand how frustrating it may be to pass some ideas that are obvious to you to some newbie. I have been teaching myself (Russian, in my case) and at times I felt my student was not making an effort or refusing to understand on purpose. Usually it is not true.
Neither was I trying to argue just for the sake of it or from unwillingness to understand something. Most of the time I tend to admit an error as soon as I understand I have erred.

Anyway, this thread has been useful to me and I have definitely (alas, after some have been obliged to phrase the same thing in several different ways) learned a lot.
So thank you @Dale , @PeroK , @PAllen and @PeterDonis

This thread stays open, of course, but I have personally drawn the conclusions I needed from this exchange and do not intend to be especially active on it, unless pinged or mentioned.

 

[Dale]

Just one piece of advice. When I have a question about “reality” the first thing I do is sit down and figure out what sort of experiment could be done to answer the question.

If there is no such experiment then I am done, the question wasn’t a question about “reality” as I had mistakenly thought. Sometimes I try to figure out why it isn’t a question about “reality”, but usually I just don’t even bother with it.

If there is an experiment then I see if I can find a paper where that experiment has been done or at least analyzed fully. If I cannot find such a paper then I might try to analyze it myself, but generally such topics are beyond me. Those wind up being the most frustrating, but they are rare.

 

[anuttarasammyak]

I understand how frustrating it may be to pass some ideas that are obvious to you to some newbie. I have been teaching myself (Russian, in my case) and at times I felt my student was not making an effort or refusing to understand on purpose. Usually it is not true.

I would just mention here in my school days the originally Russian text on introduction of relativity theory by Landau and Zhukov enlighted me so much. I am still loving the latter part written by Zhukov for its plain and clear mathematics. I admire you can read it and other excellent works of Landau in original Russian.

 

[Rene Dekker]

I am late to the party, and won't comment on the good philosophical discussion, but like to comment on your original question. I have always found it easier to understand and accept length contraction, by viewing it as a rotation instead.

We are all familiar with normal rotations in 3D space, and don't think much about the effects that it has. Imagine a rod is lying some distance away on the its side, perpendicular to your viewing direction, such that you see the full length of the rod. If I now rotate the rod, then it appears to shrink in size to you. We normally don't think about it that way, because our brain compensates for that immediately. But if you would take photographs before and after the rotation, and compare those, then the rod appears to have shortened. After the rotation you would also see one of its short ends, and one end would be further away than the other.

Something similar happens with length contraction with a faster moving rod. It is kind of like a rotation in time. The rod appears shorter, you see one of its short ends, and one end would be "further away" in time than the other. If you look at the mathematics of it, then it is also more like a rotation than a contraction.

 

[vanhees71]

I think one has to distinguish two things:

(1) "length contraction" as a purely kinematical effect. Here the physical situation is that one has some solid body (e.g., a rod) that is at rest as a whole in some inertial frame. Then this rod has a well-defined "proper length", $L_0$, given by the length as measured in this inertial rest frame. The important point is that "measuring the rod's length" means that an arbitrary observer reads off the spatial coordinates of the ends of the rod in a momentary inertial frame, where he or she is at rest and defines the length in the usual way using Euclidean geometry with the result that he get's the lengths in direction of boost contracted by the inverse Lorentz factor $1/\gamma=\sqrt{1-\beta^2}$ while lengths in direction perpendicular to the boost direction are unchanged in comparison to the proper lengths as defined in the restframe of the body.

(2) Deformation due to acceleration

This is more complicated, because it involves the dynamics and inner structure of the body you measure, and indeed there cannot be a rigid body. This becomes most clear when assuming a rigid body a la Born, which turns out to have only 3 degrees of freedom and admitting only a specific set of possible "rigid motions".

A famous example is the rotating disk. You can have a rotation of the disk around its center with constant angular velocity as a rigid motion, but it is not possible to bring such a "Born rigid disk" continuously from rest in an inertial frame in this rigid rotation. Of course, the resolution of this paradox is that there is no Born rigid disk in nature and in fact you can bring the disk into this state of rigid rotation, but the in fact elastic body must necessarily deform. A nice discussion about the "Ehrenfest paradox" concerning a rotating "rigid disk" can be found in Eddington, The mathematical theory of relativity, where he however also uses a specific simplified description of the disk as a "incompressible body", where he defines incompressibility locally.

 

[phyti]

alexandrinushka;

A metal rod can be measured, heated, and measured again, revealing a change in dimension, all occurring in a single ref. frame. Materials can be transformed via various processes, thus there are no 'rigid' objects. Changes in dimension and composition are a common part of physics.

Here is an example of physical length contraction.

 

[Nugatory]

Yet it does not seem to me one can employ the same reasoning when it comes to length.

If you have not already done so, you may want to spend some quality time with Bell's spaceship paradox - Google will work here. The observed physical phenomenon is that the string breaks, but only in one frame can we explain this as dynamical length contraction of the string.

 

[PeterDonis]

The observed physical phenomenon is that the string breaks, but only in one frame can we explain this as dynamical length contraction of the string.

Actually, what "contracts" is not the actual length of the string but its "unstressed" length, the length it would have if no force were being applied to it. But a force is being applied to it, from the spaceships, and in the frame in which the ships are originally at rest, that force keeps it at the same length (i.e., prevents it from contracting as it otherwise would since it is moving).

 

[PeterDonis]

does a dynamical length contraction contradict any current physical law?

No. John Bell's paper on how to teach special relativity, the one in which he introduced the Bell spaceship paradox, had this as one of its main points.

 

[PeterDonis]

John Bell's paper on how to teach special relativity

Link here:

https://www.semanticscholar.org/pap...Bell/1a53126db535ced288804e357f6d1e88a7ca995f

 

[PeterDonis]

I would therefore be grateful if you could share the paper you are talking about.

Unfortunately I can't find a link to it. I thought it was in the comment thread I linked to earlier but it doesn't seem to be.

The basic argument of the paper was the same as the one I gave in my Insights article.

 

[PeterDonis]

if you don't mind, I might at some point PM you for more details

That's fine.

 

[Nugatory]

Actually, what "contracts" is not the actual length of the string but its "unstressed" length,

And here I thought that I was being so clever by not putting any dangerous adjectives in front of the word "length"

But seriously, kidding aside, one of the virtues of Bell's thought experiment is that it requires us to think about the actual physics, what would stress and strain gauges measure and why.

 

[PeterDonis]

It has been refuted by Petkov

Petkov correctly points out that presentism (the view that only the "present", defined as all events in spacetime that are simultaneous with some chosen event, exists) is not consistent with SR (because SR says that the "present", so defined, is frame-dependent, and physics can't depend on frame-dependent quantities). Here he agrees with Stein.

His "refutation" of Stein is based on his claim that Stein failed to consider that SR shows that spacetime is four dimensional. (I haven't read Stein's article so I can't comment on whether that claim of Petkov's is correct.) But the statement that spacetime is four dimensional is much weaker than the block universe claim. My Insights article gives an example of why: the alternative I proposed in that article, to consider the past light cone of a chosen event as "real" (or "fixed and certain" as I phrased it in the article), is not even considered by Petkov, and since a light cone is also four-dimensional, it is perfectly consistent with the four dimensionality of spacetime as shown by SR. So Petkov might have "refuted" Stein, but he has not established that the block universe is the only possibility consistent with SR.

 

[robphy]

Here is an example of physical length contraction.

By the way, what do you mean by "physical"?
(I ask because it is ambiguous [to me] in the literature of "length contraction".)

You might be interested in my GeoGebra visualization of the "causal diamond" or "light-clock diamond" (the intersection of light-cones) https://www.geogebra.org/m/pr63mk3j (which is based on https://www.geogebra.org/m/XFXzXGTq the spacetime diagram of the Michelson-Morley apparatus).

 

[PAllen]

Petkov correctly points out that presentism (the view that only the "present", defined as all events in spacetime that are simultaneous with some chosen event, exists) is not consistent with SR (because SR says that the "present", so defined, is frame-dependent, and physics can't depend on frame-dependent quantities). Here he agrees with Stein.

Actually, presentism can't be refuted as long as an advocate of it accepts that the 'true present' is inherently undetectable, while still being 'real'. That is, one simply posits, as an axiom that there exists an undetectable foliation of spacetime (taken as mathematical model) defining the 'real' present. An axiom is not subject to refuation, only demonstration of conflict with reality. However, in this case, the indistinguishability of LET from BU in physical predictions, implies this axiom cannot be refuted by observations. [Note, my definition of presentism is slightly different from yours - there is no claim that the true present, defining what really exists moment to moment, is related to simultaneity for any observer, defined by any particular convention. It might be, but we could never know which observer, or which convention.]

 

[phyti]

By the way, what do you mean by "physical"?
(I ask because it is ambiguous [to me] in the literature of "length contraction".)

You might be interested in my GeoGebra visualization of the "causal diamond" or "light-clock diamond" (the intersection of light-cones) https://www.geogebra.org/m/pr63mk3j (which is based on https://www.geogebra.org/m/XFXzXGTq the spacetime diagram of the Michelson-Morley apparatus).

A measurable change in dimension in the direction of motion vs. an apparent visual image change.
Here is another example specific to the MMX.

 

[alexandrinushka]

Petkov correctly points out that presentism (the view that only the "present", defined as all events in spacetime that are simultaneous with some chosen event, exists) is not consistent with SR (because SR says that the "present", so defined, is frame-dependent, and physics can't depend on frame-dependent quantities). Here he agrees with Stein.
His "refutation" of Stein is based on his claim that Stein failed to consider that SR shows that spacetime is four dimensional. (I haven't read Stein's article so I can't comment on whether that claim of Petkov's is correct.) But the statement that spacetime is four dimensional is much weaker than the block universe claim. My Insights article gives an example of why: the alternative I proposed in that article, to consider the past light cone of a chosen event as "real" (or "fixed and certain" as I phrased it in the article), is not even considered by Petkov, and since a light cone is also four-dimensional, it is perfectly consistent with the four dimensionality of spacetime as shown by SR. So Petkov might have "refuted" Stein, but he has not established that the block universe is the only possibility consistent with SR.

So wait. The past light cone is real. The intersection between the past light cone and future light cone is real (we call if "the present moment"), but the future light cone is not real yet. Right? How is this different from the growing block universe?

 

[PeterDonis]

The past light cone is real.

I said "fixed and certain" in my Insights article, but we can use "real" to mean that for this discussion.

The intersection between the past light cone and future light cone is real (we call if "the present moment")

No. The past light cone does not include its apex, the single point called "the present moment", and nor does the future light cone. We can take the "present moment" to be "real" if we take it to become fixed and certain as soon as we experience it. But that does not mean it's an intersection of the past and future light cones.

the future light cone is not real yet.

Yes.

How is this different from the growing block universe?

Because, first, what becomes "real" from moment to moment in the view I was suggesting in the Insights article is not the entire future light cone of any given moment, or even just the portion of it that is in the past light cone of the next moment, but the points that are in the past light cone of the next moment but weren't in the past light cone of the previous moment. This includes points that were not in the future light cone of the previous moment (though just an infinitesimal amount of them).

And second, because the growing block universe says that what becomes "real" from moment to moment is not a tiny set of points that is in the past light cone of the next moment but wasn't in the past light cone of the previous moment, but an entire spacelike 3-surface's worth of points.

 

[Dale]

the single point called "the present moment",

I tend to use “here and now” instead because “the present moment” is too easy to misconstrue as a spacelike surface of simultaneity instead of a single event. Taking about these things is always difficult since the language hasn’t evolved to have commonly accepted words for all of these concepts.

 

[vanhees71]

The only adequate language for "modern physics" is math ;-)).