B Why aren't standard rods and clocks affected by LC and TD?

[stevendaryl]

Well if you restrict to 2-dimensional Minkowski diagrams you are right. But not in the more realistic 4-dimensions.
The problem is the symmetry in this case doesn't address the issue of the stability of measuring rods and clocks in the absence of rigid rulers, that is the sense of Einstein's lament.

Could you relate this concern with nonideal clocks and measuring rods back to your original post? You were asking why ideal clocks and measurement rods are assumed to be unaffected by Lorentz contraction and time dilation. But that's not true, so isn't the original question answered?

I'm having trouble understanding your concern about nonideal clocks and rods. Is it that you are worried that the actual clocks and rods used in tests of SR might be affected by acceleration in such a way as to mimic the effects of SR? And so tests of SR might not be conclusive?

 

[loislane]

Ah, but they are affected by relativistic effects (GR and SR). That's actually why they're useful. Standardized objects are objects that are forced to do something very precise by nature. Let's take the type-1A supernovas. They are forced to emit a certain spectrum of light. So if you know that when the light's wavelength was when it was emitted, e.g. $\lambda$, and you observe it with a wavelength of $\lambda '$, you can figure out how much the wavelength has been stretched whilst it traveled across spacetime, e.g.

\frac{\lambda '}{\lambda} = a

where a is a parameter that comes from GR. Thus, by knowing how much the light has been stretched due to GR, you can use GR to reverse engineer (reconstruct) the distance that the supernova is away from you.

Not exactly. It is because the assumption about physical validity of ideal clocks and rods unaffected by LC/TD is undoubtedly confirmed empirically by the stability of atoms and their spectra that we can do that "reverse engineering".

 

[Dale]

Well if you restrict to 2-dimensional Minkowski diagrams you are right. But not in the more realistic 4-dimensions.

Even in 4D spacetime 3 degrees of freedom for Born rigid motion are more than enough to investigate the LT.

The problem is the symmetry in this case doesn't address the issue of the stability of measuring rods and clocks in the absence of rigid rulers

Again, so what? Why does that issue need to be addressed?

If we assume that the laws of physics have the appropriate symmetries then we get the Lorentz transform, regardless of whether or not those laws include rigid objects. This is the point of the symmetry approach, it does not depend on any specific laws, it comes directly from the symmetries.

I just don't see a problem here.

 

[loislane]

Could you relate this concern with nonideal clocks and measuring rods back to your original post? You were asking why ideal clocks and measurement rods are assumed to be unaffected by Lorentz contraction and time dilation. But that's not true, so isn't the original question answered?

The concern is Einstein's actually. I'm trying to come to terms with it.

I'm having trouble understanding your concern about nonideal clocks and rods. Is it that you are worried that the actual clocks and rods used in tests of SR might be affected by acceleration in such a way as to mimic the effects of SR? And so tests of SR might not be conclusive?

Not at all. Non inertial frames and accelerations hace not entered the discussion and they are anyway taken care by the clock postulate. SR tests are conclusive.

 

[loislane]

Even in 4D spacetime 3 degrees of freedom for Born rigid motion are more than enough to investigate the LT.

Not if you include rototranslations and those are motions found in physics.
Actually if you read Laue's paper you'll learn that infinite dof's are needed in Minkowski geometry for rigid bodies.

Again, so what? Why does that ah issue that needs to be addressed?

If we assume that the laws of physics have the appropriate symmetries then we get the Lorentz transform, regardless of whether or not those laws include rigid objects. This is the point of the symmetry approach, it does not depend on any specific laws, it comes directly from the symmetries.

I just don't see a problem here.

Ok, that's great. How dou you interpret Einstein's concern in that quote.

 

[FieldTheorist]

Not exactly. It is because the assumption about physical validity of ideal clocks and rods unaffected by LC/TD is undoubtedly confirmed empirically by the stability of atoms and their spectra that we can do that "reverse engineering".

I'm sorry, but this post is incoherent. Could you please rephrase this in a way where the central equations/concepts/reasoning are made explicit, rather than implicit? I'm afraid I can't answer a question (or know if I have the requisite knowledge to even attempt to answer the question) if the question is vague and unclear.

 

[loislane]

I'm sorry, but this post is incoherent. Could you please rephrase this in a way where the central equations/concepts/reasoning are made explicit, rather than implicit? I'm afraid I can't answer a question (or know if I have the requisite knowledge to even attempt to answer the question) if the question is vague and unclear.

I don't find it incoherent on rereading but perhaps it needs to be read after post #16 to understand it. Sorry for assuming you read the whole thread.

 

[Dale]

Not if you include rototranslations and those are motions found in physics.

Those motions don't correspond to any Lorentz transform. Any motion which corresponds to a Lorentz transform (more generally any Poincare transformation) can be achieved through Born rigid motion only.

How dou you interpret Einstein's concern in that quote

I interpret it as the concern of a person before the symmetry approach had been developed.

 

[PeterDonis]

H-N theorem says what you write between parenthesis only.

Yes, but the fact that any rigid motion at all in SR must be Born rigid was already known, so H-N didn't need to state it explicitly. In more technical language, any rigid motion in SR must be described by a congruence of timelike worldlines with zero expansion and shear (which is what "Born rigid" means); that was known before H-N proved their theorem. The H-N theorem gives the conditions required for a congruence of timelike worldlines to have zero expansion and shear.

This was already settled by Laue in 1911 when it showed that rigid bodies cannot exist in SR

No, that's not what he showed. You need to spend some time actually looking at the science instead of reading pop science.

 

[PeterDonis]

An ideal measuring rod is one that keeps its shape while being (gently accelerated)

Technically, no, an ideal measuring rod is one that is not being accelerated at all. As I noted in a previous post, the geometry of Minkowski spacetime can be constructed using only inertial frames, i.e., only rods and clocks in inertial motion. Adding accelerated measuring rods with the property you describe is a useful convenience, but is not fundamentally necessary.

 

[PeterDonis]

The OP question has been answered. Thread closed.