Lorentz contraction of box filled with gas

[1effect]

Oh really? What explanation am I using?

"The distance between the ships (once they reach final speed) is$L_0 \gamma$., but in the Earth frame it remains $L_0$.. That's length contraction, all right."

Not really: it is string stretching due to increased distance between the rockets. I have pointed that out to you.

The explanation given is the standard one that I use. The key--as in most relativity "paradoxes"--is the relativity of simultaneity.

Good, so we are in agreement.

Yes, the distance between the rockets does increase, which is what breaks the string. This is the same thing I've said several times when describing this "paradox".

We agree here as well.

But length contraction applies here--as always. The calculations on that site--the very same ones I would use--apply the Lorentz transformations to figure out that the distance between the rockets in their own frame is $L_0 \gamma$. Knock knock... who's there? Lorentz contraction, as always.

You are reaching here. While the proof does use the Lorentz transform (this is inescapable), it uses one of its consequences, the relativity of simultaneity while it does not use its other consequence, the length contraction.

If you are arguing against some strange idea where just moving past a string magically reaches out and puts stress on it: I agree, that's pretty silly.

Yes, this is a pretty silly interpretation of Lorentz contraction. Nevertheless, moving past the string makes the string appear shorter :-). Does the string become physically shorter?

But if you agree with that wiki site, which uses the Lorentz transformations (which imply length contraction and all the rest), then you must conclude that length "really" is contracted.

All I have been telling you is that length contraction, though a valid consequence of the Lorentz transforms, is not used in the wiki proof. As I said in the opening post, length contraction is not intrinsic for the explanation of the Bell's paradox.See the difference?

 

[1effect]

"Lorentz Contraction of Flux Quanta Observed in Experiments with Annular Josephson Tunnel Junctions", A. Laub et al., Phys. Rev. Lett. 75, 1372 - 1375 (1995).

Zz.

This is a very interesting one, the Tom Roberts FAQ lists no direct test of length contraction. Would it be possible for you to post the paper (or, at least, email me a copy)? Thank you.

 

[peter0302]

So does PV=nRT not work at relativistic speeds? Because n and R are certainly unaffected by Lorentz contraction. V however must decrease. If Pressure remains unchanged, that means that temperature would have to decrease as well, right?

 

[1effect]

So does PV=nRT not work at relativistic speeds? Because n and R are certainly unaffected by Lorentz contraction. V however must decrease. If Pressure remains unchanged, that means that temperature would have to decrease as well, right?

PV/T=nR=constant

kev and I just showed how P is frame invariant (P'=P), V'=V/gamma (due to length contraction). Therefore is must be that:
T'=T/gamma
Indeed, R.C.Tolman shows that in his chapter on relativistic thermodynamics. I don't have the book with me but I can get it and cite the correct page.

 

[ZapperZ]

This is a very interesting one, the Tom Roberts FAQ lists no direct test of length contraction. Would it be possible for you to post the paper (or, at least, email me a copy)? Thank you.

I only cited one that I know of, since that came out of a condensed matter experiment. Here are more:

"New experimental test of Lorentz’s theory of relativity", C.W. Sherwin Phys. Rev. A 35, 3650 - 3654 (1987).

"Test of special relativity in an ion storage ring", R. Grieser et al., Hyperfine Interactions 99, 135 (1996)

Zz.

 

[1effect]

PV/T=nR=constant

kev and I just showed how P is frame invariant (P'=P), V'=V/gamma (due to length contraction). Therefore is must be that:
T'=T/gamma
Indeed, R.C.Tolman shows that in his chapter on relativistic thermodynamics. I don't have the book with me but I can get it and cite the correct page.

Top of page 159. "Relativity, Thermodynamics and Cosmology".

 

[1effect]

I only cited one that I know of, since that came out of a condensed matter experiment. Here are more:

"New experimental test of Lorentz’s theory of relativity", C.W. Sherwin Phys. Rev. A 35, 3650 - 3654 (1987).

"Test of special relativity in an ion storage ring", R. Grieser et al., Hyperfine Interactions 99, 135 (1996)

Zz.

Are these tests of length contraction?

 

[Magic Man]

I guess it's pretty clear that you have no idea what length contraction (much less the subtler issue of the relativity of simultaneity) is all about.

Nice attitude, thought this was meant to be a helpful site. My mistake I suppose...

 

[Doc Al]

Nice attitude, thought this was meant to be a helpful site. My mistake I suppose...

Actually, I am trying to be helpful. Despite your efforts to replace physics with "common sense" using the argument from incredulity.

Show me an experiment where it is proved that an object physically contracts with an increase in speed as measured in the frame of the object itself...

Can I assume you realize that length is not contracted in the frame of the object?

 

[ZapperZ]

Are these tests of length contraction?

The include tests of the length contraction, among other things.

I work with particle accelerators, and one of the things that people always have to model is the "bunch length" of the particles being accelerated. Often, people make transformation to the rest frame of the bunch length because some of the calculations to get certain part of the dynamics are easier in that frame. When they do that, a bunch of relativistic effects must always be included, and this includes the adjustments of the length of the bunch. In lab frame, the bunch length is always less than the bunch that we work with in the bunch frame. This manifest itself in our calculation of the space charge effects, for example.

This is why I'm a bit puzzled when it appears as if this part of SR is somehow talked about as if it is unverified. In particle accelerators, this is COMMON! This is before considering the fact that length contraction and time dilation are actually two sides of the same coin (refer to the muon evidence at sea level, and how that is reconciled within the muon frame as the contracted length of travel).

Zz.

 

[1effect]

The include tests of the length contraction, among other things.

I work with particle accelerators, and one of the things that people always have to model is the "bunch length" of the particles being accelerated. Often, people make transformation to the rest frame of the bunch length because some of the calculations to get certain part of the dynamics are easier in that frame. When they do that, a bunch of relativistic effects must always be included, and this includes the adjustments of the length of the bunch. In lab frame, the bunch length is always less than the bunch that we work with in the bunch frame. This manifest itself in our calculation of the space charge effects, for example.

This is why I'm a bit puzzled when it appears as if this part of SR is somehow talked about as if it is unverified. In particle accelerators, this is COMMON! This is before considering the fact that length contraction and time dilation are actually two sides of the same coin (refer to the muon evidence at sea level, and how that is reconciled within the muon frame as the contracted length of travel).

Well, I have pointed out that the most comprehensive web page for "Tests of SR" contains no tests for length contraction. The site has been recently updated. I emailed Tom Roberts a pointer to the paper you cited.

 

[pervect]

Nice attitude, thought this was meant to be a helpful site. My mistake I suppose...

We do try to help people who are genuinely interested in learning, as time permits. Arguing with people who don't understand relativity and are not really interested in learning just isn't productive for anybody.

 

[Dale]

The include tests of the length contraction, among other things.

I work with particle accelerators, and one of the things that people always have to model is the "bunch length" of the particles being accelerated. Often, people make transformation to the rest frame of the bunch length because some of the calculations to get certain part of the dynamics are easier in that frame. When they do that, a bunch of relativistic effects must always be included, and this includes the adjustments of the length of the bunch. In lab frame, the bunch length is always less than the bunch that we work with in the bunch frame. This manifest itself in our calculation of the space charge effects, for example.

This is why I'm a bit puzzled when it appears as if this part of SR is somehow talked about as if it is unverified. In particle accelerators, this is COMMON! This is before considering the fact that length contraction and time dilation are actually two sides of the same coin (refer to the muon evidence at sea level, and how that is reconciled within the muon frame as the contracted length of travel).

Zz.

Do the particles in the bunch interact with each other or is the interaction with the accelerator so much greater that the presence of the other particles can be neglected?

 

[ZapperZ]

Do the particles in the bunch interact with each other or is the interaction with the accelerator so much greater that the presence of the other particles can be neglected?

Depends on how much charge there is in a bunch, and how tightly they are clumped together. Above 1 nC, in a beam size of 1 cm in diameter and bunch length of about 9 ps, there's a lot of space charge effects, meaning the electrons in the bunch sees each other's repulsive coulomb charges. And when you get to 50 to 100 nC (which is often what I have to deal with), you need huge focusing magnetic field strength to keep them from flying apart.

Zz.

 

[dhris]

PV/T=nR=constant

kev and I just showed how P is frame invariant (P'=P), V'=V/gamma (due to length contraction). Therefore is must be that:
T'=T/gamma
Indeed, R.C.Tolman shows that in his chapter on relativistic thermodynamics. I don't have the book with me but I can get it and cite the correct page.

I don't know if the conclusion that P'=P is correct. This would imply that pressure is a scalar quantity, when in fact it is a component of the stress-energy tensor.

 

[1effect]

I don't know if the conclusion that P'=P is correct. This would imply that pressure is a scalar quantity, when in fact it is a component of the stress-energy tensor.

Feel free to look over the computations here. It is all elementary SR, no GR.

 

[dhris]

Feel free to look over the computations here. It is all elementary SR, no GR.

First of all, you use a transformation law for the area that does not apply to all the faces of the box. The face with normal parallel to the motion is not changed in the way you specified. Secondly, your transformation of the speed, w'=w/gamma, is not the way that velocities transform in relativity.

The pressure is a component of the stress-energy tensor, which means that's how it transforms. Nothing to do with GR.

 

[1effect]

First of all, you use a transformation law for the area that does not apply to all the faces of the box. The face with normal parallel to the motion is not changed in the way you specified. Secondly, your transformation of the speed, w'=w/gamma, is not the way that velocities transform in relativity.

You are incorrect, it was specified quite clearly that we (kev and I ) are working with the Oz or Oy directions (i.e. perpendicular to the direction of motion Ox). The derivation is valid for all 4 surfaces parallel with the direction of motion.

I can also show that the pressure is different for the remaining two surfaces perpendicular on the direction of motion since the particle speed is:

(v+w)/(1+vw/c^2) and (v-w)/(1-vw/c^2)

The pressure is a component of the stress-energy tensor, which means that's how it transforms. Nothing to do with GR.

So, can you show the calculations?Do you get different results than I did? I think pervect promised the same thing but he never pursued the issue.

 

[dhris]

I can also show that the pressure is different for the remaining two surfaces

Right, so if the pressure is different on those two surfaces, you can't conclude that the pressure is invariant under the transformation. That's my point.

 

[1effect]

Right, so if the pressure is different on those two surfaces, you can't conclude that the pressure is invariant under the transformation. That's my point.

The conditions have been established by this post, for particles moving along the z axis only.
So both my calculations and kev's are correct. Do you have any calculations to show for yourself ?

 

[dhris]

The conditions have been established by this post.
So both my calculations and kev's are correct. Do you have any calculations to show for yourself ?

The pressure is the component of the stress-energy tensor. Look here:
http://en.wikipedia.org/wiki/Stress-energy_tensor#Relativistic_stress_tensor_for_an_idealized_fluid

That means it's not a scalar and thus not invariant under Lorentz transformations. What calculation do you want? To do the transformation correctly, you start with that tensor and transform it using a Lorentz matrix. I don't see any reason for me to write that all out.

 

[1effect]

The pressure is the component of the stress-energy tensor. Look here:
http://en.wikipedia.org/wiki/Stress-energy_tensor#Relativistic_stress_tensor_for_an_idealized_fluid

That means it's not a scalar and thus not invariant under Lorentz transformations. What calculation do you want? To do the transformation correctly, you start with that tensor and transform it using a Lorentz matrix. I don't see any reason for me to write that all out.

I had a hunch that you will waive your arms :-)

 

[dhris]

I had a hunch that you will waive your arms :-)

I clearly pointed out what was wrong with your calculation, but for some reason that's not enough. So no, I don't feel like wasting 20 minutes writing out the matrix transformation for you just so you can link your original post again.

 

[1effect]

I clearly pointed out what was wrong with your calculation, but for some reason that's not enough. So no, I don't feel like wasting 20 minutes writing out the matrix transformation for you just so you can link your original post again.

A quick check on how the diagonal elements transform for the energy-stress tensor shows that elements p_yy and p_zz are invariant under transformation. Exactly what I showed with elementary methods. Do you want me to do the calculations for you?

 

[dhris]

A quick check on how the diagonal elements transform for the energy-stress tensor shows that elements p_yy and p_zz are invariant under transformation.

That's right. But the third component isn't, so the pressure is not invariant under the Lorentz transformation, which is what I understood you to be saying earlier.

 

[1effect]

That's right. But the third component isn't, so the pressure is not invariant under the Lorentz transformation, which is what I understood you to be saying earlier.

You understood wrong. I told you here that p_xx isn't, why don't you pay attention? It is much easier to pay attention than to make up strawmen and beat them up, isn't it? :-)

So, the elementary derivation and the tensor-based derivation agree. Are we done?

 

[dhris]

You understood wrong. I told you here that p_xx isn't, why don't you pay attention? It is much easier to pay attention than to make up strawmen and beat them up, isn't it? :-)

No, it is what you were claiming originally. I wrote "I understood" in my last post just to be polite.

 

[Dale]

Depends on how much charge there is in a bunch, and how tightly they are clumped together. Above 1 nC, in a beam size of 1 cm in diameter and bunch length of about 9 ps, there's a lot of space charge effects, meaning the electrons in the bunch sees each other's repulsive coulomb charges. And when you get to 50 to 100 nC (which is often what I have to deal with), you need huge focusing magnetic field strength to keep them from flying apart.

Zz.

Then it sounds like "real physical length contraction" to me. The interaction between particles in a bar of steel are EM, the interaction between particles in a bunch are EM, length contraction is demonstrated for the bunch, it seems unreasonable to think it is not confirmed for materials in general.

 

[1effect]

Then it sounds like "real physical length contraction" to me. The interaction between particles in a bar of steel are EM, the interaction between particles in a bunch are EM, length contraction is demonstrated for the bunch, it seems unreasonable to think it is not confirmed for materials in general.

Looks like.

 

[Magic Man]

Can I assume you realize that length is not contracted in the frame of the object?

That was my whole point and the issue I had. I read the previous posts as trying to suggest otherwise.

 

[ZapperZ]

Then it sounds like "real physical length contraction" to me. The interaction between particles in a bar of steel are EM, the interaction between particles in a bunch are EM, length contraction is demonstrated for the bunch, it seems unreasonable to think it is not confirmed for materials in general.

I can cite another paper here from accelerator physics:

The variation of the pulse width of a bunch with a mean energy of 19.1 and 36.8 MeV with the electric charge of the bunch through a 0.5-m-long drift space is shown in Fig. 7. Initial pulse widths of 0.55, 1.1, and 2.2 ps are considered here. It is observed that the pulse elongation is weaker as the mean energy increases due to the Lorentz contraction.

M. Uesaka et al., Phys. Rev. E 50, 3068 (1994).

There's a lot more of stuff like this in accelerator physics. So it is puzzling why someone would claim that there's no "experimental evidence".

Zz.

 

[peter0302]

PV/T=nR=constant

kev and I just showed how P is frame invariant (P'=P), V'=V/gamma (due to length contraction). Therefore is must be that:
T'=T/gamma
Indeed, R.C.Tolman shows that in his chapter on relativistic thermodynamics. I don't have the book with me but I can get it and cite the correct page.

So _temperature_ depends on reference frame? Does this mean that a fast moving object appears to glow red hot to a stationary observer, but looks perfectly normal to a distant observer going at the same speed?

 

[yuiop]

So _temperature_ depends on reference frame? Does this mean that a fast moving object appears to glow red hot to a stationary observer, but looks perfectly normal to a distant observer going at the same speed?

Actually we were claiming (if the classic gas laws hold in the relativistic context) that the gas in the box moving relative to us, must appear to cool if the volume appears to get smaller and the pressure remains constant.

Admittedly, there is a problem with this viewpoint. If the box has extreme relative motion the gas might appear as Bose-Einstein condensate in our frame and not in the rest frame of the box. Obviously some other interesting physical laws must be at play that prevents this happening.

 

[1effect]

So _temperature_ depends on reference frame? Does this mean that a fast moving object appears to glow red hot to a stationary observer, but looks perfectly normal to a distant observer going at the same speed?

"Appears" is key. For a distant observer , lengths "appear" to be contracted, time "appears" to be dilated, temperature "appears" to be lowered. This is why we try to do measurements in the proper frame , not in a distant frame. When this is not possible (try measuring the temperature of a fast moving meteorite), we compensate the results of our remote measurements by applying the appropriate relativistic corrections.

 

[dhris]

... the pressure remains constant.

Please stop repeating this. It is wrong. The pressure is not invariant under a Lorentz transformation.