Lorentz contraction of box filled with gas

[1effect]

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

Why don't you take a minute to explain this to kev in a constructive way?
Pressure in relativity is represented by the diagonal elements of the energy-stress tensor.
For motion along x-axis, the terms corresponding to the y and z axis (p_yy and p_zz) are invariant but the term along the direction of motion, p_xx, is not.
This can be explained mathematically by the tensor transformation . This can also be explained intuitively by the fact that p_xx is proportional to the time derivative of the momentum in the direction of motion (dp/dtau) which, in turn is proportional to the derivative of the particle speed with respect to proper time (dw_resultant/dtau). We have seen this earlier in this thread. If +w and -w is the particle speed wrt the box and if the box speed wrt the lab is v, one gets:

w_resultant+=(v-w)/(1-vw/c^2) for particles hitting the front wall (lower pressure because the wall is "running away from the particles)

w_resultant_=(v+w)/(1+vw/c^2) for particles hitting the trailing wall (higher pressure because the wall is "running towards the particles)

The above is an oversimplified explanation,good enough to just to give an intuitive feel, the tensor explanation is the rigorous one.

The above brings about a very interesting point:

What is the relativistic correspondent to the law of ideal gasses: pV/T=const?
What is the correct meaning of p in the above law? It cannot be any of the p_xx,p_yy,p_zz components, is it the norm of the vector? this requires some thought.

 

[Dale]

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".

I don't know what better evidence exists of the correctness of a physical principle than being able to build a functioning device using that principle. Maybe that isn't considered "experimental" but rather "engineering" evidence, but I have to say that it works for me.

 

[pervect]

Why don't you take a minute to explain this to kev in a constructive way?
Pressure in relativity is represented by the diagonal elements of the energy-stress tensor.
For motion along x-axis, the terms corresponding to the y and z axis (p_yy and p_zz) are invariant but the term along the direction of motion, p_xx, is not.
This can be explained mathematically by the tensor transformation . This can also be explained intuitively by the fact that p_xx is proportional to the time derivative of the momentum in the direction of motion (dp/dtau) which, in turn is proportional to the derivative of the particle speed with respect to proper time (dw_resultant/dtau). We have seen this earlier in this thread. If +w and -w is the particle speed wrt the box and if the box speed wrt the lab is v, one gets:

w_resultant+=(v-w)/(1-vw/c^2) for particles hitting the front wall (lower pressure because the wall is "running away from the particles)

w_resultant_=(v+w)/(1+vw/c^2) for particles hitting the trailing wall (higher pressure because the wall is "running towards the particles)

The above is an oversimplified explanation,good enough to just to give an intuitive feel, the tensor explanation is the rigorous one.

The above brings about a very interesting point:

What is the relativistic correspondent to the law of ideal gasses: pV/T=const?
What is the correct meaning of p in the above law? It cannot be any of the p_xx,p_yy,p_zz components, is it the norm of the vector? this requires some thought.

If you have a box of particles , the momentum per unit time transferred to the front of the box by the particles must equal the momentum per unit time transferred to the back of the box. This must be true in all frames.

See for instance

https://www.physicsforums.com/showthread.php?t=117773

(This is unfortunately not a textbook reference, but something I worked out. There may be minor typos).

Much of this thread has been about differences in interpretation of what "pressure" means. To talk about the "pressure" of a gas in a moving frame, one must define what one means. Presumably this would be the force / unit area, or the total momentum transferred to the walls of the box per (unit area * unit time).

One issue that arises is that there can be subtle differences between the stress-energy tensor used in GR, and that used in engineering, due to the handling of "convective terms".

See the warning in the Wikipedia article http://en.wikipedia.org/w/index.php?title=Stress-energy_tensor&oldid=186028100

Warning: In solid state physics and fluid mechanics, the stress tensor is defined to be the spatial components of the stress-energy tensor in the comoving frame of reference. In other words, the stress energy tensor in engineering differs from the stress energy tensor here by a momentum convective term.

significant confusion is possible here by one person using the engineering definitions and another person using the GR definitions.

 

[Xeinstein]

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

No one is trying to suggest otherwise. The question is how to measure the length of a moving object? It's not straitforward as you might imagine.
To properly measure the length of a moving object, we must measure the position of both ends at the same time in our inertial frame. However, an observer at rest on the moving object would not agree that the measurements were made at the same time. The observer at rest with respect to the moving object, using her own clocks, would say that the position of the front end was measured at an earlier time than the position of the back end. So both agree that a measurement of length of a moving rod yields a shorter length than the measurement made in the frame of the rod. This is called the Lorentz contraction. This contraction is real in any sense of the word as you can think of.

 

[Xeinstein]

The other posters have already demonstrated the mistake here quite well, but I would encourage you to think about this further.

What about a solid rod of steel? Even fairly small changes in length (strain) of a steel bar result in enormous changes in pressure (stress) within the bar. At relativistic speeds the stress and strain would be far beyond the failure point of the steel.

Since you cannot have something failing in one frame and being unstressed in another frame then you must come to the conclusion that Lorentz-contraction does not cause material stress (pressure) in general.

I think you mixed up two different things.
Supposed the box is reinforced with rod of steel. When we accelerate the box filled with gas, the Lorentz contraction is inevitable. But the contraction will Not induce any mechanical stress in the rod itself. However, the gas inside the box has more energy since its volume has changed due to Lorentz contraction of the box

 

[Dale]

I think you mixed up two different things.
Supposed the box is reinforced with rod of steel. When we accelerate the box filled with gas, the Lorentz contraction is inevitable. But the contraction will Not induce any mechanical stress in the rod itself. However, the gas inside the box has more energy since its volume has changed due to Lorentz contraction of the box

I wasn't mixing anything up. I wasn't talking about boxes or gas at all, I was only talking about stress in metal rods. My point was only that the natural unstrained length of a piece of steel is frame-variant.

 

[Xeinstein]

I wasn't mixing anything up. I wasn't talking about boxes or gas at all, I was only talking about stress in metal rods. My point was only that the natural unstrained length of a piece of steel is frame-variant.

No body is saying that the natural unstrained length of a piece of steel is "frame-invariant", So we both agree there is No enormous changes in pressure (stress) within the steel bar

What about a solid rod of steel? Even fairly small changes in length (strain) of a steel bar result in enormous changes in pressure (stress) within the bar. At relativistic speeds the stress and strain would be far beyond the failure point of the steel.

Since you cannot have something failing in one frame and being unstressed in another frame then you must come to the conclusion that Lorentz-contraction does not cause material stress (pressure) in general.

 

[Dale]

No body is saying that the natural unstrained length of a piece of steel is "frame-invariant", So we both agree there is No enormous changes in pressure (stress) within the steel bar

What about a solid rod of steel? Even fairly small changes in length (strain) of a steel bar result in enormous changes in pressure (stress) within the bar. At relativistic speeds the stress and strain would be far beyond the failure point of the steel.

Ahh, I see. Sorry, that was intended to be a "proof by contradiction". If Lorentz contraction were to cause material stress then you would get failure in one frame and not in another. That is a contradiction so the assumption (Lorentz contraction causes material stress) must be false. The rest was a handwaving explanation about why not.

 

[Xeinstein]

Ahh, I see. Sorry, that was intended to be a "proof by contradiction". If Lorentz contraction were to cause material stress then you would get failure in one frame and not in another. That is a contradiction so the assumption (Lorentz contraction causes material stress) must be false. The rest was a handwaving explanation about why not.

I think the original post is kind of misleading. I'm glad it has been cleared up, Thank you...

Consider what happens when we accelerate a box filled with gas. We have to expend a certain amount of energy to accelerate the box, In Newtonian mechanics, this energy goes into the kinetic energy of the box: as its speed increases so does its kinetic energy. This happens in relativity too, of course, but in addition, we have to spend some extra energy because the box contracts.

The Lorentz contraction is inevitable: the faster the box goes, the shorter it gets. But this shorting does Not come for free. The box is filled with gas, and if we shorten the box we reduce the volume occupied by the gas. This compression is resisted by pressure, and the energy required to compress the gas has to come from somewhere. It can only come from the energy exerted by the applied force. This means the force has to be larger (for the same increase in speed) that it would be in Newtonian mechanics, and this in turn means that the box has a higher inertia, by an amount proportional to the pressure in the box.

 

[yuiop]

The Lorentz contraction is inevitable: the faster the box goes, the shorter it gets. But this shorting does Not come for free. The box is filled with gas, and if we shorten the box we reduce the volume occupied by the gas. This compression is resisted by pressure, and the energy required to compress the gas has to come from somewhere. It can only come from the energy exerted by the applied force. This means the force has to be larger (for the same increase in speed) that it would be in Newtonian mechanics, and this in turn means that the box has a higher inertia, by an amount proportional to the pressure in the box.

Hi Xeinstein,

Can I take it you are still not convinced that the pressure would remain constant (frame invarient) in the box accelerated to constant velocity relative to us?

 

[Xeinstein]

Hi Xeinstein,

Can I take it you are still not convinced that the pressure would remain constant (frame invarient) in the box accelerated to constant velocity relative to us?

I don't know if it's true or not that the pressure would remain constant (frame invarient) in the box accelerated to constant velocity relative to us.
I think if the pressure is part of energy-momentum/stress-energy tensor, then it would not remain constant (frame-varient).

Do you agree that the gas in the box has more energy since its volume has changed due to Lorentz-contraction of the box?

 

[yuiop]

I don't know if it's true or not that the pressure would remain constant (frame invarient) in the box accelerated to constant velocity relative to us.
I think if the pressure is part of energy-momentum/stress-energy tensor, then it would not remain constant (frame-varient).

I am no expert on the stress-energy tensor of GR but I am pretty sure the pressure referred to in that context is not the same as pressure in the context of the gas laws. The stress energy tensor is used in the context of gravity and applies to a massive body even when there is no atmosphere present.

Do you agree that the gas in the box has more energy since its volume has changed due to Lorentz-contraction of the box?

I don't think it is as simple as that. Certainly objects with angular momentum slow down (and so lose angular kinetic energy) when they are moving relative to us. This is a consequence of time dilation. I think we also showed that tranverse components of the gas particles slow down when the box is moving relative to us (and that the pressure remains constant). If anything, everything points towards the moving system losing energy by our measurements if we ignore the increase in kinetic energy of the system components due to their relative linear motion wrt us. In other words if we have a solid brick movig relative to us it would have increased kinetic energy simply because of its motion relative to us. If we looked closer at the particles that make up the brick they would appear to be spinning and/or vibrating slower than when the brick was at rest wrt us. It is difficult to make a case for kinetic energy due to motion relative to us as being due to increased internal energies.

 

[peter0302]

This is a consequence of time dilation.

Hm. Perhaps this is the answer then. Gas pressure is ultimately caused by the kinetic energy of the gas. Since the clock of the moving object slows down relative to the stationary observer, so does the speed, and therefore, kinetic energy, and, therefore, temperature, of the gas.

However, the volume also decreases with Gamma.

So using PV=nRT, where both Volume and Temperature decrease, Pressure remains constant.

 

[dhris]

Hi Xeinstein,

Can I take it you are still not convinced that the pressure would remain constant (frame invarient) in the box accelerated to constant velocity relative to us?

I hope he's not convinced of it, because it's not true.

 

[yuiop]

I hope he's not convinced of it, because it's not true.

Please show a calculation or link showing how it not true.

1effect and myself have gone to the trouble to show the calculations of why we think it is true. You have not shown your calculations or demonstrated where ours are wrong.

 

[dhris]

Please show a calculation or link showing how it not true.

1effect and myself have gone to the trouble to show the calculations of why we think it is true. You have not shown your calculations or demonstrated where ours are wrong.

It has been explained about 4 times in this thread already. If you go back and read it you can see where 1effect was finally convinced that your calculation did not predict that the pressure is invariant. For god's sake, he even made a post addressing the explanation to you directly.

 

[yuiop]

It has been explained about 4 times in this thread already. If you go back and read it you can see where 1effect was finally convinced that your calculation did not predict that the pressure is invariant. For god's sake, he even made a post addressing the explanation to you directly.

Below is I believe the post 1effect addressed to me that you are referring to:

Why don't you take a minute to explain this to kev in a constructive way?
Pressure in relativity is represented by the diagonal elements of the energy-stress tensor.
For motion along x-axis, the terms corresponding to the y and z axis (p_yy and p_zz) are invariant but the term along the direction of motion, p_xx, is not.
This can be explained mathematically by the tensor transformation . This can also be explained intuitively by the fact that p_xx is proportional to the time derivative of the momentum in the direction of motion (dp/dtau) which, in turn is proportional to the derivative of the particle speed with respect to proper time (dw_resultant/dtau). We have seen this earlier in this thread. If +w and -w is the particle speed wrt the box and if the box speed wrt the lab is v, one gets:

w_resultant+=(v-w)/(1-vw/c^2) for particles hitting the front wall (lower pressure because the wall is "running away from the particles)

w_resultant_=(v+w)/(1+vw/c^2) for particles hitting the trailing wall (higher pressure because the wall is "running towards the particles)
...

Take this line:

"w_resultant+ = (v-w)/(1-vw/c^2) for particles hitting the front wall (lower pressure because the wall is "running away from the particles)".

1effect is suggesting that there is less pressure on the front wall because the wall is moving away from particles. What he is forgetting is that those particles rebound with lower velocity because the wall is moving away. Those rebounding particles (with lower velocity) now hit the rear wall with lower velocity which contradicts the next line:

"w_resultant- = (v+w)/(1+vw/c^2) for particles hitting the trailing wall (higher pressure because the wall is "running towards the particles)

Although 1effect is partly right that some of the particles hitting the rear wall have a higher impact velocity imparting a higher impulse he has not allowed for the slow particles that have been slowed down by colliding with the receding front wall. Any fast particles colliding with the rear wall rebound even faster (they gain momentum from the rear wall) and so the fastest particles in the system are the ones heading towards the front wall which compensates for the fact the front wall is receding and reducing the impact. The slowest particles in the system are the ones heading towards the rear wall that compensates for the rear wall "running towards the particles".

A detailed calculation for the longitudinal collisions is complicated and I will only do it if I have to and I don't believe even that would convince you.

Here are some simple observations that should show pressure is invariant without even having to do the calculations:

1) If pressure gauges are attached to all faces of the box then when the box is accelerated relative to us we will not see any changes on any of the pressure gauges that relates to the relative velocity of the box. Agree?

2) It is widely accepted that that transverse force under the Lorentz transformation is reduced by a factor of gamma. The faces of the box parallel to the motion of the box have areas that are also reduced by gamma. Therefore the pressure on the parallel faces is invariant. It is also widely accepted that longitudinal force parallel to the motion is invariant under the Lorentz transformation. The longitudinal force of the gas acts on the faces transverse to the direction of box's motion and those area of those faces (the front and rear faces) does not change as they are not subject to length contraction. The longitudinal force of the gas and the area it acts on are both invariant and so the pressure on those faces must be invariant too. Agree?

The Wikipedia article on the stress-energy tensor refers to “In particular, Tii represents a pressure-like quantity, normal stress,” Normal stress is a “pressure-like" quantity. A "pressure-like" quantity is not exactly the same thing as the pressure of a gas in the normal sense as far as I know. Maybe the senior experts here can advise on that.

 

[1effect]

Below is I believe the post 1effect addressed to me that you are referring to:



Take this line:

"w_resultant+ = (v-w)/(1-vw/c^2) for particles hitting the front wall (lower pressure because the wall is "running away from the particles)".

1effect is suggesting that there is less pressure on the front wall because the wall is moving away from particles. What he is forgetting is that those particles rebound with lower velocity because the wall is moving away. Those rebounding particles (with lower velocity) now hit the rear wall with lower velocity which contradicts the next line:

"w_resultant- = (v+w)/(1+vw/c^2) for particles hitting the trailing wall (higher pressure because the wall is "running towards the particles)

Although 1effect is partly right that some of the particles hitting the rear wall have a higher impact velocity imparting a higher impulse he has not allowed for the slow particles that have been slowed down by colliding with the receding front wall. Any fast particles colliding with the rear wall rebound even faster (they gain momentum from the rear wall) and so the fastest particles in the system are the ones heading towards the front wall which compensates for the fact the front wall is receding and reducing the impact. The slowest particles in the system are the ones heading towards the rear wall that compensates for the rear wall "running towards the particles".

A detailed calculation for the longitudinal collisions is complicated and I will only do it if I have to and I don't believe even that would convince you.

Here are some simple observations that should show pressure is invariant without even having to do the calculations:

1) If pressure gauges are attached to all faces of the box then when the box is accelerated relative to us we will not see any changes on any of the pressure gauges that relates to the relative velocity of the box. Agree?

2) It is widely accepted that that transverse force under the Lorentz transformation is reduced by a factor of gamma. The faces of the box parallel to the motion of the box have areas that are also reduced by gamma. Therefore the pressure on the parallel faces is invariant. It is also widely accepted that longitudinal force parallel to the motion is invariant under the Lorentz transformation. The longitudinal force of the gas acts on the faces transverse to the direction of box's motion and those area of those faces (the front and rear faces) does not change as they are not subject to length contraction. The longitudinal force of the gas and the area it acts on are both invariant and so the pressure on those faces must be invariant too. Agree?

The Wikipedia article on the stress-energy tensor refers to “In particular, Tii represents a pressure-like quantity, normal stress,” Normal stress is a “pressure-like" quantity. A "pressure-like" quantity is not exactly the same thing as the pressure of a gas in the normal sense as far as I know. Maybe the senior experts here can advise on that.

The point I made is that, while the components transverse to v are invariant (i.e. p_yy, p_zz), the component along v (p_xx) is not. This comes out directly from the transformation of the energy-stress tensor.

 

[dhris]

A detailed calculation for the longitudinal collisions is complicated and I will only do it if I have to and I don't believe even that would convince you.

This calculation will show you that the pressure on this face is different from that on the others. This can easily be seen from the tensor calculation, which is the correct way to do it.

1) If pressure gauges are attached to all faces of the box then when the box is accelerated relative to us we will not see any changes on any of the pressure gauges that relates to the relative velocity of the box. Agree?

Nobody is disputing that measurements made in the rest frame don't change (post-acceleration that is). That's obvious. You're talking about transforming the pressure, though, and it is not invariant under a Lorentz transformation as you can't seem to stop claiming.

2) It is widely accepted that that transverse force under the Lorentz transformation is reduced by a factor of gamma. The faces of the box parallel to the motion of the box have areas that are also reduced by gamma. Therefore the pressure on the parallel faces is invariant. It is also widely accepted that longitudinal force parallel to the motion is invariant under the Lorentz transformation. The longitudinal force of the gas acts on the faces transverse to the direction of box's motion and those area of those faces (the front and rear faces) does not change as they are not subject to length contraction. The longitudinal force of the gas and the area it acts on are both invariant and so the pressure on those faces must be invariant too. Agree?

We've been over and over this in the thread. Yes, the transverse components in the tensor are not changed, but the component in the direction of motion does change. Therefore, you can't claim that "pressure" is invariant under the Lorentz transformation.

Normal stress is a “pressure-like" quantity. A "pressure-like" quantity is not exactly the same thing as the pressure of a gas in the normal sense as far as I know. Maybe the senior experts here can advise on that.

They call it "pressure-like" because there can be normal stresses in solids, but we don't usually call it pressure in that case. But the pressure appearing in the stress-energy tensor for a perfect fluid in the Wikipedia page is indeed the pressure you are thinking of. I can't imagine what "senior expert" you want to hear from. Pressure is a component of the stress energy tensor so your claim that it is a Lorentz invariant is wrong. I'm not going to argue with you about it any more because otherwise I will be here for the rest of my life. But please stop spreading this misinformation.

 

[yuiop]

This calculation will show you that the pressure on this face is different from that on the others. This can easily be seen from the tensor calculation, which is the correct way to do it.


Nobody is disputing that measurements made in the rest frame don't change (post-acceleration that is). That's obvious. You're talking about transforming the pressure, though, and it is not invariant under a Lorentz transformation as you can't seem to stop claiming.


We've been over and over this in the thread. Yes, the transverse components in the tensor are not changed, but the component in the direction of motion does change. Therefore, you can't claim that "pressure" is invariant under the Lorentz transformation.


They call it "pressure-like" because there can be normal stresses in solids, but we don't usually call it pressure in that case. But the pressure appearing in the stress-energy tensor for a perfect fluid in the Wikipedia page is indeed the pressure you are thinking of. I can't imagine what "senior expert" you want to hear from. Pressure is a component of the stress energy tensor so your claim that it is a Lorentz invariant is wrong. I'm not going to argue with you about it any more because otherwise I will be here for the rest of my life. But please stop spreading this misinformation.

Well now we have a new paradox, the "pressure paradox". We place a piston on the rear face of the pressure box that is held in place by a spring. When the box is moving we know the force exerted by the spring is invariant yet the pressure on the rear face is increased due to the stress-energy tensor. The paradox is why does the piston not move if the pressure acting on the piston is greater than the force of the spring retaining it? The piston obviously does not move in the rest frame of the box.

 

[Dale]

So using PV=nRT, where both Volume and Temperature decrease, Pressure remains constant.

It is fairly dangerous to use the standard form of laws in SR and simply assume that they still remain valid.

Here is P a 4-scalar or is it a tensor? If it is a 4-scalar then what is the corresponding 4-vector of which P is the norm? V is notoriously difficult to define in SR due to issues of simultaneity, usually I think it is a timelike 4-vector. So if V is a 4-vector and P is a tensor or a scalar then is T a 4-vector?

I don't know the answer to any of these, but using the ideal gas law in SR is not a simple matter of writing the traditional expression.

 

[peter0302]

Well, I asked earlier if PV=nRT held in SR and no one answered.

BTW, V and P are both scalar.

 

[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.

There are some serious problems with the author's claims. The factor in their paper is
sqrt(1-v^2/cbar^2) where cbar is the speed of light in their junction
(about 0.05 c). True Lorentz contraction involves the vacuum speed of
light, c, not cbar.

 

[Xeinstein]

More correctly said:

-the modern view is that the contraction is not physical, it is just a geometric (trigonemetric) artifact of the Lorentz-Einstein transforms : http://en.wikipedia.org/wiki/Length_contraction#A_trigonometric_effect.3F

-we do not have any experimental confirmation to the contrary :
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Length_Contraction

That's nonsense
Lorentz-contraction is "Real" in any sense of the word you can think of

 

[matheinste]

Hello all.

i am a little confused by all these knowledgeable arguments for and against various effects due to relatively moving systems. My understanding is that the effects such as time dilation, length contraction etc are results of a transformation of the fundamental dimensions of spacetime, at least i think that is what is predicted by relativity. IF this is true then surely all physical dimensions and derived units change pro rata and basically everything is conserved. This is a rather naive view but is it more or less correct.

Matheinste.

 

[1effect]

Hello all.

i am a little confused by all these knowledgeable arguments for and against various effects due to relatively moving systems. My understanding is that the effects such as time dilation, length contraction etc are results of a transformation of the fundamental dimensions of spacetime, at least i think that is what is predicted by relativity. IF this is true then surely all physical dimensions and derived units change pro rata and basically everything is conserved. This is a rather naive view but is it more or less correct.

Matheinste.

As measured by a distant observer in relative motion, distances shrink, frequencies change (relativistic Doppler effect). The objects themselves do not shrink.

 

[matheinste]

Hello 1effect.

Still confused. I cannot see how distances shrink but objects do not. The dimensions of an object are the measurements of its extension in space and these extensions in space are, surely, distances.

I do of course realize that for an observer in his own frame the action of his being observed has no effect on his own observations and so neither distances or sizes of objects or perception of time change for him.

I need to clear up the fundamentals before i can progress with my queries and my immediate question is are the changes in distance and time fundamental transformations in the values of the dimensions of spacetime. I believe they are.

Thankyou for your reply. Matheinste.

 

[1effect]

Hello 1effect.
I need to clear up the fundamentals before i can progress with my queries and my immediate question is are the changes in distance and time fundamental transformations in the values of the dimensions of spacetime. I believe they are.

Thankyou for your reply. Matheinste.

Yes, they are indeed fundamental transformations in the values of the dimensions.

 

[matheinste]

Hello 1effect.

I am still not happy with the answer but it is a bit unfair of me to continue this discussion in someone elses thread so i will probably start a new one by again asking the same question.

Matheinste.

 

[1effect]

So I suppose we all agree that the moving box does contract in the "lab-frame" in which the box is moving. It takes 100 replies to get to this point or conclusion. We are making progress.
Now the next question is this: will the box compress the gas in it? In other word, will the gas resist the contraction of the box as Lorentz-contraction demands?

You have received the answers several times already : "no" and "no"

 

[Xeinstein]

You have received the answers several times already : "no" and "no"

Do you realize you are probably the only person in this thread/forum claim length does Not contract in the observer frame in which the box is moving? If that's the case, then you are seriously mistaken. For the 5-th time

In the following quote, kev explains why you are mistaken:

If by $$\Delta V=0$$ you are saying that change in volume due to relative motion is zero, then that implies that change in length due to relative motion is also zero and you are seriously mistaken.

If change in length (length contraction) is imaginary then change in clock rate (time dilation) is also imaginary, because they go hand in hand. There is plenty of experimental evidence that time dilation is not imaginary.

You might have noticed that Einstein and Lorentz state that $L = L_o \sqrt(1-v^2/c^2)$ and not $L=L_o$ which is what $\Delta V=0$ and $\Delta L=0$ implies.

Why does Special Relativity have all those those complicated transformation formulas if no real physical transformations occur? Why does anybody bother if they are all imaginary and have no consequences? Kind of makes relativity pointless.

What's Lorentz-contraction? Is it an illusion or is it real?
First, we need to know how to measure the length of a moving object? It's not straightforward as you might think. To properly measure the length of a moving object, we must measure the position of both ends at the same time in our inertial frame. However, an observer at rest on the moving object would not agree that the measurements were made at the same time. The observer at rest with respect to the moving object, using her own clocks, would say that the position of the front end was measured at an earlier time than the position of the back end. So both agree that a measurement of length of a moving rod yields a shorter length than the measurement made in the frame of the rod. This is called the Lorentz contraction. This contraction is real in any sense of the word you can think of.

 

[AVentura]

If I accelerated a train to a relativistic speed I would observe a contraction of its length.

But if I accelerate two electrons (or atoms) independently at the same rate I do not observe the distance between them to reduce at all from what it was when they were moving slowly. (Picture two separate Linacs aligned on the same axis, their electrons will not affect one another, otherwise Linacs in different hospitals would be pulling each other's electrons out of their guides!)

Why the two different results? Because the atoms in the train are in a lattice. If you try to accelerate the front of the train independently of the back you will rip it in half. But an observer who is already moving the same direction as the train would claim the front started first, and that's why it ripped in half; no paradox. But the train will rip in half.

 

[granpa]

when an objects moves it really does contract or at least it occupies less space (same thing?). but to that object the rest of the universe appears to be moving and therefore contracted. did the universe contract just because this one object moved? of course not.

the length of an object is the distance between the front and back at one instantaneous moment. imagine that the object is moving past a line of stationary, perfectly synchronized clocks. since, to the moving object, the clocks APPEAR (even after compensating for light travel time) to be out of synch, the line of clocks will also appear to be shorter.

so length contraction is both real and illusory. the moving object really contracts. while everything else only appears to the moving object to contract.

this is similar to the twin paradox where only one of the twin actually ages less even though it appears as though both are time dilated.

 

[matheinste]

Hello granpa.

--------- contraction is both real and illusory. the moving object really contracts. while everything else only appears to the moving object to contract.---------


Length contraction, like time dilation in SR is symmetric. Both observers in relative motion see length contract and time dilate in the other frame. In their own frame of course they see nothing change.

Matheinste.



-----so length contraction is both real and illusory. the moving object really contracts. while everything else only appears to the moving object to contract.-----

 

[granpa]

thats what i said