Lorentz contraction of box filled with gas

Click For Summary
The discussion centers on the behavior of a gas-filled box when accelerated, particularly regarding Lorentz contraction and pressure changes. It is established that while the box experiences length contraction from an external observer's perspective, the pressure inside remains constant in the box's own frame due to the principles of relativity. The calculations demonstrate that the force exerted by gas molecules is reduced by a factor of gamma, and this reduction balances with the contraction of the box's area, leading to no change in pressure. The conversation also touches on the implications of these principles for solid materials, suggesting that Lorentz contraction does not induce stress in materials in the same way it does in gases. Overall, the pressure and volume of the gas are invariant in the box's reference frame, emphasizing the relativity of motion.
  • #31
Doc Al said:
I don't get it. On the one hand you say that we agree, and yet on the other hand you seem to think that somehow there's an "explanation" of the Bell spaceship paradox that doesn't imply length contraction. 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.

There are many,many explanations of the "Bell paradox". Some include length contraction. You are using one of the explanations (the more simplistic one). Have a close look at the wiki detailed explanation, as I pointed out, it does not use length contraction. As you can see, the calculations prove that it isn't the string that contracted but the distance between the rockets that increased resulting into stretching the string.
Length contraction is not intrinsic for the explanation of Bell's paradox.
 
Last edited:
Physics news on Phys.org
  • #32
Doc Al said:
The "modern view" is that length contraction is quite "real" (albeit a kinematic/geometric effect of space-time), as is time dilation and the relativity of simultaneity. This is not the first time that "common sense" has been put to shame by careful mathematical argument and--more importantly--experimental evidence.

But not "real" in a physical sense. How can it honestly shrink physically simply because of its speed... What is measured or observed from a different frame is not the reality of the physical object.

It also wouldn't be the first time that "careful mathematical argument" had been put to shame because of blind faith over common sense. 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...
 
  • #33
1effect said:
There are many,many explanations of the "Bell paradox". Some include length contraction. You are using one of the explanations (the more simplistic one).
Oh really? What explanation am I using?
Have a close look at the wiki detailed explanation, as I pointed out, it does not use length contraction.
The explanation given is the standard one that I use. The key--as in most relativity "paradoxes"--is the relativity of simultaneity.
As you can see, the calculations prove that it isn't the string that contracted but the distance between the rockets that increased resulting into stretching the string.
Length contraction is not intrinsic for the explanation of Bell's paradox.
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". 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.

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. 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.
 
  • #34
Magic Man said:
But not "real" in a physical sense. How can it honestly shrink physically simply because of its speed... What is measured or observed from a different frame is not the reality of the physical object.

It also wouldn't be the first time that "careful mathematical argument" had been put to shame because of blind faith over common sense. 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...

"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.
 
  • #35
Magic Man said:
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...
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.
 
  • #36
Doc Al said:
Oh really? What explanation am I using?

"The distance between the ships (once they reach final speed) isL_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?
 
Last edited:
  • #37
ZapperZ said:
"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.
 
  • #38
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?
 
  • #39
peter0302 said:
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.
 
  • #40
1effect said:
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.
 
  • #41
1effect said:
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".
 
  • #42
ZapperZ said:
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?
 
  • #43
Doc Al said:
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...
 
  • #44
Magic Man said:
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. :wink:

Magic Man said:
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?
 
  • #45
1effect said:
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.
 
  • #46
ZapperZ said:
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.
 
  • #47
Magic Man said:
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.
 
  • #48
ZapperZ said:
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?
 
  • #49
DaleSpam said:
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.
 
  • #50
1effect said:
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.
 
  • #51
dhris said:
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.
 
  • #52
1effect said:
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.
 
  • #53
dhris said:
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.
 
  • #54
1effect said:
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.
 
  • #55
dhris said:
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 ?
 
Last edited:
  • #56
1effect said:
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.
 
  • #57
dhris said:
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 :-)
 
  • #58
1effect said:
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.
 
  • #59
dhris said:
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?
 
  • #60
1effect said:
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.
 

Similar threads

I Car, wheels and Lorentz contraction of the road: Is this a Paradox?
  • · Replies 72 ·
3
Replies
72
Views
6K
Lorentzian contraction of a box increases the pressure inside?
  • · Replies 14 ·
Replies
14
Views
3K
B Does shortness from length contraction have a real physical effect?
  • · Replies 12 ·
Replies
12
Views
2K
I Is There Experimental Evidence That Contradicts Time Contraction Predictions?
  • · Replies 5 ·
Replies
5
Views
2K
B SR vs GR - Visual Difference between Length Contraction
  • · Replies 11 ·
Replies
11
Views
3K
B Calculating Time taken to reach speed with Time Dilation
  • · Replies 18 ·
Replies
18
Views
2K
Does pressure resist acceleration?
  • · Replies 89 ·
3
Replies
89
Views
19K
I Can this experiment break Lorentz symmetry?
  • · Replies 35 ·
2
Replies
35
Views
821
I Potential energy and the gravitational field of a collapsing cloud of gas
  • · Replies 1 ·
Replies
1
Views
1K
Is inertial mass of gas the same as its rest mass
  • · Replies 1 ·
Replies
1
Views
2K