What space contracts in Special Relativity?

[Mentz114]

That reinforces my point--that it isn't a consistent approach to talk about properties with respect to objects. If you take an extended object, such as a train, and start accelerating it, there IS no such thing as "the rest frame of the object" because in general, different parts of the object are traveling at different speeds.

Irrelevant. I'm talking about inertial motion.

Take a "rigid" rod that initially has length L when at rest. Gently acceleratBut the fact that it has a geometric explanation doesn't negate the length contraction and time dilation, it just explains it.

From what I understand of this, it re-inforces my point that length contraction does not need to be explained any further. The object does not need to be contracted. Where does it say in SR that the object contracts ?

Can you come up with an experiment that shows that the object contracted ? Say the pole in the barn-pole scenario ?

 

[WannabeNewton]

Where does it say in SR that the object contracts ?

Such a statement only has meaning relative to a choice of frame. In the inertial frame (modulo spatial rotations) in which the rod is initially at rest before being Born rigidly accelerated, it certainly does contract continuously during the acceleration phase and remains at a single contracted length after being brought to a constant velocity. On the other hand, in the rest frame of any given particle in the rod the spatial distances to neighboring particles in the rod will remain constant for all time because the entire time-like congruence of particles in the rod is Born rigid.

 

[dEdt]

WannabeNetwon

I won't pretend that my interpretation of SR isn't contentious -- in fact, I'd go as far as to say that it's a minority position. However, I will continue to passionately advocate for it because it is the correct interpretation. (Incidentally, it was in poor taste that you accused me of being ignorant of the literature in the philosophy of relativity. I've read most of Harvey Brown's work on the matter, including his book Physical Relativity, and have been thoroughly convinced by his arguments. On the other hand the papers countering his position, such as John Norton's "Why Constructive Relativity Fails", have been very feeble replies in my opinion.)

You begin by asserting that

In other words [length contraction] falls out of chronogeometric assumptions of SR whereas [in the Lorentz ether theory it] is a consequence of dynamics.

It's worth noting that, despite how confidently you state it, this interpretation of length contraction appears nowhere in Einstein's writings (at least that I'm aware of), even after he was introduced to Minkowski's work and even after his formulation of General Relativity. To the contrary, after Pauli wrote his review article on relativity, which contained the passage

Should one, then, completely abandon any attempt to explain the Lorentz contraction atomistically? We think that the answer to this question should be No. The contraction of a measuring rod is not an elementary but a very complicated process. It would not take place except for the covariance with respect to the Lorentz group of the basic equations of electron theory, as well as of those laws, as yet unknown to us, which determine the cohesion of the electron itself.

, Einstein enthusiastically praised it, writing that

Whoever studies this mature and grandly conceived work might not believe that its author is a twenty-one year old man. One wonders what to admire most, the psychological understanding for the development of ideas, the sureness of mathematical deduction, the profound physical insight, the capacity for lucid, systematical presentation, the knowledge of the literature, the complete treatment of the subject matter, or the sureness of critical appraisal.

For what it's worth, Eddington, who was responsible for introducing relativity to the English-speaking world, wrote that

There is really nothing mysterious about the FitzGerald contraction. It would be an unnatural property of a rod pictured in the old way as continuous substance occupying space in virtue of its substantiality; but it is an entirely natural property of a swarm of particles held in delicate balance by electromagnetic forces, and occupying space by buffeting away anything that tries to enter.

I hope these quotes convince you that the interpretation of length contraction, time dilation etc. as "geometric phenomena" is quite recent.

It's also an unsatisfactory interpretation in my opinion. To see why, we first have to ask ourselves, what is geometry? Without going into the level of rigor that would satisfy a mathematician, a geometry is a collection of things called points, obeying certain axioms, along with a way of assigning a number for every pair of points, this function being called the metric. Special Relativity gives us a way of creating a spacetime geometry, with events serving as the geometry's points, because the quantity $\eta_{\alpha\beta}\Delta x^\alpha\Delta x^\beta$ serves as a useful metric due to the fact that this quantity takes the same form in all inertial coordinate systems.

But here's the key point: the only reason we assign a such a metric to the set of events is because the laws of physics are Lorentz invariant. Otherwise, the quantity $\eta_{\alpha\beta}\Delta x^\alpha\Delta x^\beta$ would play no role in the laws of physics and hence would be completely useless. In other words, it is the symmetry properties of the dynamical laws of physics that create a spacetime geometry, not the other way around. So to explain length contraction in geometric terms is an indirect way of explaining it in terms of the dynamical laws of nature.

 

[Mentz114]

Such a statement only has meaning relative to a choice of frame. In the inertial frame (modulo spatial rotations) in which the rod is initially at rest before being Born rigidly accelerated, it certainly does contract continuously during the acceleration phase and remains at a single contracted length after being brought to a constant velocity. On the other hand, in the rest frame of any given particle in the rod the spatial distances to neighboring particles in the rod will remain constant for all time because the entire time-like congruence of particles in the rod is Born rigid.

Yes, but I've already said I'm talking about an effect that happens between inertial timelike worldlines. I don't see how rigidity affects the measurement of a moving rod between inertal frames.

 

[WannabeNewton]

(Incidentally, it was in poor taste that you accused me of being ignorant of the literature in the philosophy of relativity. I've read most of Harvey Brown's work on the matter, including his book Physical Relativity, and have been thoroughly convinced by his arguments. On the other hand the papers countering his position, such as John Norton's "Why Constructive Relativity Fails", have been very feeble replies in my opinion.)

While I apologize for my presumption, I would think a person who is aware of the contention would pay more caution in advocating the (as you put it) "minority position" as if it was unequivocally established in current literature. In other words, your previous posts give off the impression that said position is incontestable whereas the philosophical literature says otherwise so you should have elucidated that disclaimer. A fruitful discussion would entail both the pitfalls and the advantages of a constructive, dynamical explanation of length contraction by means of microscopic interactions.

It's also an unsatisfactory interpretation in my opinion.

This, on the other hand, I would say is not a minority view. Unfortunately the chronogeometric framework of SR provides such an elegant derivation (not explanation) of length contraction that a constructive, dynamical explanation is often eschewed.

Thanks for the historical quotes! I had seen Pauli's quote before but never the other two, and they are definitely on the convincing side.

 

[Mentz114]

WannabeNetwon

I won't pretend that my interpretation of SR isn't contentious --
...
...
...
But here's the key point: the only reason we assign a such a metric to the set of events is because the laws of physics are Lorentz invariant. Otherwise, the quantity $\eta_{\alpha\beta}\Delta x^\alpha\Delta x^beta$ would play no role in the laws of physics and hence would be completely useless. In other words, it is the symmetry properties of the dynamical laws of physics that create a spacetime geometry, not the other way around. So to explain length contraction in geometric terms is an indirect way of explaining it in terms of the dynamical laws of nature.

What you are talking about is not an interpretation of SR but some other theory. I wish you'd said this at the beginning instead of claiming a lot of false stuff about SR.

 

[dEdt]

What you are talking about is not an interpretation of SR but some other theory. I wish you'd said this at the beginning instead of claiming a lot of false stuff about SR.

You can disagree with this interpretation, but it is an interpretation of special relativity. What would make you say otherwise?

 

[stevendaryl]

Irrelevant. I'm talking about inertial motion.

You said:

But a property of an object has the value that the object itself assigns.

That didn't sound like it was restricted to objects moving inertially. But if you do restrict it to objects moving inertially, does that mean that objects that are accelerating don't have properties?

Where does it say in SR that the object contracts ?

Well, if you assume that an object is gently accelerated in the direction of its length in such a way that it always has the same length L in its instantaneous rest frame, then it follows that its length in any single rest frame contracts continuously. (Where, as I said, "length in a frame" means the distance between endpoints measured simultaneously in that frame.)

 

[Mentz114]

You can disagree with this interpretation, but it is an interpretation of special relativity. What would make you say otherwise?

Because SR does not try to explain the geometric effects. They are easily deduced from the geometry.

That has to be left to another theory.

 

[Mentz114]

You said:
That didn't sound like it was restricted to objects moving inertially. But if you do restrict it to objects moving inertially, does that mean that objects that are accelerating don't have properties?

It was meant so. If something is accelerating, does that mean it can never be or have been inertial ?

Well, if you assume that an object is gently accelerated in the direction of its length in such a way that it always has the same length L in its instantaneous rest frame, then it follows that its length in any single rest frame contracts continuously. (Where, as I said, "length in a frame" means the distance between endpoints measured simultaneously in that frame.)

With respect to you, I don't think this is a useful discussion.

 

[stevendaryl]

With respect to you, I don't think this is a useful discussion.

Well, you asked where in SR it says that moving objects shrink, and I answered that question.

 

[Sugdub]

I think it's more accurate to say there there are an infinite number of different ways to describe the configuration of the rod, one for each reference frame.

Let's step away from something as complicated as a rod and look at something simpler, like a point charge. Figure 1 shows the electric field produced by a stationary point charge...Figure 2 shows the electric field produced by a moving charge... Clearly there's a difference between the two electric fields -- a difference that arises from the point charge's motion.

An observer at rest relative to the point charge will always see Figure 1, while an observer moving relative to the will always see Figure 2. Is it correct to say that there are two (or more) different configurations of the electric field? I don't think so. Better to say that there are two different descriptions of the electric field...

(my emphasis)
The electric field is not observable, so observers won't see it, irrespective of their relative motion. The theoretician who decides to select an IRF in which the electric charge is at rest will represent the electric field as shown in Figure 1. Conversely a theoretician who selects another IRF in which the charge is in relative motion will invoke a representation alongside Figure 2 for the electric field induced by the same charge. SR imposes this constraint. But eventually the predictions made by both theoreticians concerning the outcome of observations and measurements will be identical, assuming they invoke Lorentz-invariant laws. The SR theory impacts our formal representation of the electric field, however changing IRF has no observable consequences.

Sure, from a moving POV the charge distribution/rod looks different. But nothing happened to the rod, because there's no physical difference between inertial motion and rest.

None of these arguments demonstrate more than the fact that things are different when measured (described ?) from a moving POV. Which we expect. But the rod is unchanged by this...

(my emphasis)
If the theoretician selects an IRF showing the rod at rest, he/she will describe the rod using its proper length. Should another theoretician select another IRF showing the rod in inertial motion, then he/she will invoke another representation of the same rod with a contracted length and altered internal forces as well (btw forces are not observable). SR imposes this constraint. All such changes will impact the theoretical analysis which will then differ between both theoreticians. Indeed the SR theory impacts how theoreticians formally describe the rod. But ultimately their respective predictions concerning what can be seen or measured by any observer will be identical, assuming they invoke Lorentz-invariant laws. The SR theory impacts our formal representation of the rod, however changing IRF has no observable consequences.

Conversely, changing observation conditions, for example changing the relative speed between an observer and the observed rod, I mean a genuine change in the experimental conditions, will definitely trigger a change in the outcome of the measurement performed by the observer. This change is not dealt with by SR, it is not formalized through a change of the IRF. As soon as you use words like “see”, “looks”, “view” or “POV”, you need to specify the relative motion of the “observer” to whom these words relate, in respect to the rod. You also need to specify which physical mechanism (light rays, ...) propagates the relevant information toward the “observer”, including of course the propagation speed. Eventually you will overlay a difference between what the moving “observer” can “measure” or “see” as compared to what he/she would have actually measured if at rest in respect to the rod. In other words the “observer” becomes part of the scenario. Overall what can be seen by the moving observer is a compound of an SR-compatible description of the rod and a Doppler effect overlay.

I recommend that in a first instance you eliminate any direct or indirect reference to the “observer” in order to first find an agreement on whether the rod shrinks or not (or better: to determine what this expression actually means), irrespective of it being “observed”, therefore eliminating the mix between the SR-impact on the formal description of the rod and the Doppler-effect on the outcome of measurements by a moving observer.

In a second raw, it will be interesting to consider how the rod “looks” from the “POV” of a moving “observer”. But for this second step, you will be keen in avoiding the usual confusion between the velocity of the rod in respect to the IRF you select for the formal representation of the scenario on the one hand, and the velocity of the rod in respect to the observer (who is part of the scenario) on the other hand. The representation frame (IRF) chosen by the theoretician for performing his/her analysis is a different concept than the observation frame chosen by those who perform the experiment.

Hopefully both contributors can accept my wording.

 

[Mentz114]

Well, you asked where in SR it says that moving objects shrink, and I answered that question.

Thank you. But as I've said, the object does not shrink, the measurement made is subject to relativistic length contraction. It is not necessary for anything to shrink in order for the measurement to give a smaller value than the rest length. So relativity does not say that an object shrinks as an effect of inertial motion.