Does pressure resist acceleration?

[Xeinstein]

Suppose we have a box at rest that is filled with a uniform gas. We denote the volume by V and the pressure by p. Suppose next that we apply a small force to the box and accelerate it until it has a speed v. Once it is at speed v, the gas in the box has acquired a kinetic energy, so one might think that the total energy that we had to add to the box in order to accelerate the gas in it would have been equal to its kinetic energy. But this is not the whole story, because the Lorentz contraction has shortened the length of the box and therefore changed its volume. Making a box smaller when it contains a gas with pressure requires one to do work on it, in other words to put some energy into the gas. This extra energy represents the extra inertia of the gas.

The key question is: Is it harder to accelerate the gas because it takes work not only to accelerate the existing energy but also to compress the gas as the Lorentz contraction demands? In other words, the moving box will contract but the gas in it will resist the Lorentz-contraction of the box

 

[country boy]

Didn't you just do this one?

On 23 Jan 08, "Lorentz contraction of box filled with gas."

 

[russ_watters]

In its own frame, the box has not shrunk.

 

[pervect]

There are not any issues related to the Lorentz contraction of the volume of the box. This was addressed in the previous thread, and that issue should continue to be discussed in that thread.

The idea of "resisting acceleration" is essentially the idea of mass. The short answer is that pressure does not affect the mass (which is how I interpret the concept "resisting acceleration") of an isolated system of a box containing a pressurized gas.

Using the SR defintion of mass, pressure does NOT contribute to mass, ever. In some GR applications, however, pressure does contribute to mass. There are actually several concepts of mass in GR, one of the most relevant here is the concept of Komar mass. Note that the term "mass" actually has several different meanings! (We have the SR defintion, and we have several different GR definitions). This is not widely appreciated and occasaionally causes confusion, angst, and long arguments.

One might well ask then:

Is the SR mass of a box containing a pressurized gas different than the GR Komar mass? The answer to this question is no. The reason that the answer is no is that while the pressure in the interior of the box does contribute to the Komar mass, making it higher, the tension in the walls of the box also contributes to the Komar mass, making it lower. The net effect is that there is no change in the mass of the box due to the pressure terms.

This assumes that the box is an isolated system. If the box is not an isolated system, the answer gets more complicated.

 

[Xeinstein]

Didn't you just do this one?

On 23 Jan 08, "Lorentz contraction of box filled with gas."

That one has been hijacked
The question is this: The moving box will contract, but how about the gas, will the gas in it contract also? Will the gas resist the contraction of the box?

 

[1effect]

That one has been hijacked
The question is this: The moving box will contract, but how about the gas, will the gas in it contract also? Will the gas resist the contraction of the box?

The box does not become smaller in the frame comoving with it, so there is no work expanded in compressing the gas.
The total energy for the system box+gas at rest is

E_0=m_0c^2

where m_0 is the proper mass of the box+gas.
The total energy when the system has stopped accelerating and has reached cruising speed v is :

E_1=\gamma m_0c^2

If the system is accelerated slowly, there is no energy radiation, hence the same value m_0 is used in both expressions. This was also pointed out earlier by pervect.

The total work is:

W=E_1-E_0=(\gamma-1)m_0c^2

 

[pervect]

That one has been hijacked
The question is this: The moving box will contract, but how about the gas, will the gas in it contract also? Will the gas resist the contraction of the box?

I gave my answer, a good one, in #4 of that thread:

https://www.physicsforums.com/showpost.php?p=1583385&postcount=4

The short answer is that the moving box does not contract in its own frame, and that relativity is frame independent.

A fuller answer can be found in
https://www.physicsforums.com/showthread.php?t=117773

I get the impression that the simple answer is not satisfying you, and you either missed the longer answer above in the flurry, or that it is going over your head.

Perhaps we need to take a step back.

How about telling us a little bit about your background with respect to SR, so we can try to answer your questions in a manner that will be helpful to you?

Do you understand "frame independence"?

Do you understand that the box does not contract in its own frame? Do you understand the logic of working the problem in the simplest possible frame, and then applying the above principle of "frame independence" to get the correct answer in other frames?

I mentioned "invariant mass" before. Do you understand that concept, and its relevance to the answer to your question?

I have the feeling that communication just isn't happening here, and I'm afraid I don't know how to fix that.

 

[Xeinstein]

The box does not become smaller in the frame comoving with it, so there is no work expanded in compressing the gas.
The total energy for the system box+gas at rest is

E_0=m_0c^2

where m_0 is the proper mass of the box+gas.
The total energy when the system has stopped accelerating and has reached cruising speed v is :

E_1=\gamma m_0c^2

If the system is accelerated slowly, there is no energy radiation, hence the same value m_0 is used in both expressions. This was also pointed out earlier by pervect.

The total work is:

W=E_1-E_0=(\gamma-1)m_0c^2

Finally, I figure out what's wrong with your argument.
I can give you a hint: you jump around in different frames
In both the initial lab-frame and final co-moving frame, the box is at rest,
Then can we say the total work is zero? No, of course not
So it's clear that we must stay in one single frame, i.e. the initial lab-frame in which the box is moving at end of acceleration. In this frame, the moving box does indeed contract and compress the gas in it

 

[1effect]

Finally, I figure out what's wrong with your argument.
I can give you a hint: you jump around frames

No, everything is calculated from the frame the box was originally at rest. So , you continue to write nonsense.

In both the initial lab-frame and final co-moving frame, the box is at rest

Not really, the box gets accelerated up to speed v in the lab frame, as per your description. So, this is the second nonsense.

Then can we say the total work is zero? No, of course not
So we must stay at one frame, i.e. the initial, lab-frame

Exactly as I did.

In this frame, the moving box does indeed contract and compress the gas in it

Now, you are indeed mixing frames. Some moderator ought to close this thread. Pervect?

 

[Xeinstein]

No, everything is calculated from the frame the box was originally at rest. So , you continue to write nonsense.

Not really, the box gets accelerated up to speed v in the lab frame, as per your description. So, this is the second nonsense.

Exactly as I did.

Now, you are indeed mixing frames. Some moderator ought to close this thread. Pervect?

I don't think you understand relativity at all and continue to write nonsense.
It's clear from the similar thread, titled "Lorentz contraction of box filled with gas", that you are wrong about Lorentz-contraction. Your biggest problem is that somehow, you believe Lorentz-contraction is an illusion, Not real. In fact, most people in the forum of that thread disagree with you and you couldn't explain, in the lab-frame, why the thin thread between two spaceships breaks in the Bell spaceship paradox.

I think it's obvious that you jump around in different frames, from the initial lab-frame to the final co-moving frame. You said that the box does not become smaller in the frame co-moving with it, I think that's well-known and we all agree with it. But you can't extrapolate that and claim Lorentz-contraction of moving object is Not physically real. So the question is: does the box become smaller in the lab-frame (in which the box is moving)? If yes, will it compress the gas in it? you can find the answer in Schutz's book: Gravity from the Ground Up, at page 194; This is the kind question that really test your understanding of Lorentz-contraction.

Would you be surprised if I tell you that Schutz disagree with you and claim "pressure does resist acceleration"? Since Schutz is such a big shot in relativity, I don't think you have a chance...

In his book "Gravity from the Ground Up", page 194, in the box of 15.4 Investigation: How pressure resists acceleration" It says: it is harder to accelerate the gas because it takes work not only to accelerate the existing energy but also to compress the gas as the Lorentz-contraction demands.

Here is the link to that page in the book: Gravity from the Ground Up
http://books.google.com/books?id=P_...ts=eYBnh8oGoa&sig=ZkzEIBINItUiFyMW5-uvjt1kMus
I hope you can learn something about Lorentz-contraction from Schutz's book

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

If the contraction is "Not physical", then can you tell us why the thin thread connected between two spaceships break in Bell's spaceship paradox?

Firstly, "Bell's paradox" is a thought experiment, not a real one, so it has no bearing on my statement pertaining to the absence of experimental confirmation for length contraction.

Secondly, here is a very good explanation. The calculations do not use length contraction.

 

[1effect]

I think it's obvious that you jump around in different frames, from the initial lab-frame to the final co-moving frame.

I think that anybody that knows physics realized already that both E_0 and E_1 are calculated in the same frame. I cannot help you if you don't know elementary relativity.

So the question is: does the box become smaller in the lab-frame (in which the box is moving)? If yes, will it compress the gas in it? you can find the answer in Schutz's book: Gravity from the Ground Up, at page 194; This is the kind question that really test your understanding of Lorentz-contraction.

The box does not become smaller. A moving observer will measure it thru light signals as being smaller.

Would you be surprised if I tell you that Schutz disagree with you and claim "pressure does resist acceleration"? Since Schutz is such a big shot in relativity, I don't think you have a chance...

In his book "Gravity from the Ground Up", page 194, in the box of 15.4 Investigation: How pressure resists acceleration" It says: it is harder to accelerate the gas because it takes work not only to accelerate the existing energy but also to compress the gas as the Lorentz-contraction demands.

Here is the link to that page in the book: Gravity from the Ground Up
http://books.google.com/books?id=P_...ts=eYBnh8oGoa&sig=ZkzEIBINItUiFyMW5-uvjt1kMus
I hope you can learn something about Lorentz-contraction from Schutz's book

Yes, I read the book. It is interesting to note afew things:

-you already knew the answer when you started your threads
-what you did not know, and this is really interesting for the mainstream people watching this thread, is that Schutz made a mistake on the page you are citing (p.194). It happens to the very best, even to famous professors :-)

Can you spot the mistake?

I had to snip your ramblings on the Bell's paradox.

 

[Xeinstein]

I gave my answer, a good one, in #4 of that thread:

https://www.physicsforums.com/showpost.php?p=1583385&postcount=4

The short answer is that the moving box does not contract in its own frame, and that relativity is frame independent.

Do you mean that the length of the box is "frame independent"? It's the same in all frames? I think only the space-time interval is "frame-independent", but the distance or length is Not.

A fuller answer can be found in
https://www.physicsforums.com/showthread.php?t=117773

I get the impression that the simple answer is not satisfying you, and you either missed the longer answer above in the flurry, or that it is going over your head.

Perhaps we need to take a step back.

How about telling us a little bit about your background with respect to SR, so we can try to answer your questions in a manner that will be helpful to you?

Do you understand "frame independence"?

Do you understand that the box does not contract in its own frame? Do you understand the logic of working the problem in the simplest possible frame, and then applying the above principle of "frame independence" to get the correct answer in other frames?

Yes, I do understand "frame independence" and the box does not contract in "its own frame". I think that's well-known and we all agree with. So that's not the question.
The question is this: Does the box contract in "the lab-frame" in which the box is moving? If yes, will it compress the gas in it? That's all we need to know.

 

[1effect]

Yes, I understand that the box does not contract "in its own". I think that's well-known and we all agree with. So that's not the question.
The question is this: Does the box contract "in the lab-frame" in which the box is moving? If yes, will it compress the gas in it?

The answers are "no" and "no".

 

[pervect]

Do you mean that the length of the box is "frame independent"? It's the same in all frames?
Do you believe that Lorentz-contraction of moving object is "an illusion" or it's real?

The length of the box depends on who observes it. Length is therefor not a frame-independent quantity.

Whether or not you consider length to be "real" depends on your philosophy. "Real" is a very vague term. "Independent of the observer" is a much more precise term. When you say "real" I think you probably mean "independent of the observer", but it's hard to be sure. If you mean something else by *real*, please give a short example of what you mean by "real", and some examples. (Are bricks real? How do you know they are real). Please try not to get too far into the philosphy in this forum, however - but sometimes a little philosphical disussion is unavoidable in order to answer non-philoophical questions.

The length of a physical object is thus not a property of the object alone. It is depends both on the object, and on the observer - specifically on the frame in which the observer resides.

For an example of a property of a physical object that is a property of the object alone, consider the Lorentz interval, or proper length, of the object.

Now, onto energy, mass, and momentum.

The box also has energy, momentum, and mass. The energy and momentum of the box depend on the observer. This is the same in relativity as it is in Newtonian mechanics - the kinetic energy of an object depends both on the object and who observers it.

In relativity, the energy and momentum together comprise the energy-momentum 4-vector. The energy-momentum 4-vector, however, is not a property of the box alone - like length, it depends on both the box and the observer. (But it transforms in standard and well understood manner, making it very useful and fundamental).

The invariant mass of the box, however, is a quantity which depends only on the box, *if* we assume that the box is an isolated system (as it is in this example). This invariant mass can be computed from the energy momentum 4-vector. To make the equations simple, chose units such that c=1. Then the invariant mass of the box is E^2 - |p|^2, where E is the energy of the box, and |p| is its momentum

I haven't responded to the rest of your post, because you're getting off on the wrong track :-(.

 

[marcus]

Does pressure resist acceleration?

I just want to reply to the question that the thread title asks. Yes.
Pressure contributes inertia. Inertia resists acceleration.

However this does not have much to do with the Lorentz contraction and that box example. The best thing to do, I think, is to forget about Lorentz contraction, and the box of gas, and special relativity

Suppose we have a box at rest that is filled with a uniform gas. We denote the volume by V and the pressure by p. Suppose next that we apply a small force to the box and accelerate it until it has a speed v. Once it is at speed v, the gas in the box has acquired a kinetic energy, so one might think that the total energy that we had to add to the box in order to accelerate the gas in it would have been equal to its kinetic energy. But this is not the whole story, because the Lorentz contraction has shortened the length of the box and therefore changed its volume. Making a box smaller when it contains a gas with pressure requires one to do work on it, in other words to put some energy into the gas. This extra energy represents the extra inertia of the gas.

The key question is: Is it harder to accelerate the gas because it takes work not only to accelerate the existing energy but also to compress the gas as the Lorentz contraction demands? In other words, the moving box will contract but the gas in it will resist the Lorentz-contraction of the box

I think other people have pointed out that the Lorentz contraction does not change the pressure measured in the box. So this line of reasoning seems fruitless.

Instead, think of the sun. I believe that part of the gravitational attraction of the sun, which the Earth feels, is due to the pressure in the core (as a simple consequence of the GR equation). Part of it is due to the kinetic energy associated with the temperature at the core. Besides the obvious contribution of particle masses, the gravitational mass of the sun is compounded of several things, including pressure.

The gravitational mass and the inertia of the sun are the same. Therefore a portion of the inertial mass of the sun is contributed by the pressure-----the pressure everywhere in the sun contributes somewhat, but I mentioned the core pressure especially because I suspect it is high enough to have a noticeable effect.

It would be fun to know the percentage of the mass of the sun which is attributable to internal pressure. Maybe someone more knowledgeable than I has a source for this. Please correct me if I am wrong. I'm just reasoning from the Einstein field equation of GR, which in effect features both energy density and pressure on the right hand side.

 

[Xeinstein]

Does pressure resist acceleration?

I just want to reply to the question that the thread title asks. Yes.
Pressure contributes inertia. Inertia resists acceleration.

However this does not have much to do with the Lorentz contraction and that box example. The best thing to do, I think, is to forget about Lorentz contraction, and the box of gas, and special relativity
I think other people have pointed out that the Lorentz contraction does not change the pressure measured in the box. So this line of reasoning seems fruitless.

I don't think it has anything to do with pressure change or not. If you check Schutz's calculation in his book, the pressure p is a constant but the volume of the gas does change (page 194 in his book: Gravity from the Ground Up). So this is not the question

Instead, think of the sun. I believe that part of the gravitational attraction of the sun, which the Earth feels, is due to the pressure in the core (as a simple consequence of the GR equation). Part of it is due to the kinetic energy associated with the temperature at the core. Besides the obvious contribution of particle masses, the gravitational mass of the sun is compounded of several things, including pressure.

The gravitational mass and the inertia of the sun are the same. Therefore a portion of the inertial mass of the sun is contributed by the pressure-----the pressure everywhere in the sun contributes somewhat, but I mentioned the core pressure especially because I suspect it is high enough to have a noticeable effect.

It would be fun to know the percentage of the mass of the sun which is attributable to internal pressure. Maybe someone more knowledgeable than I has a source for this. Please correct me if I am wrong. I'm just reasoning from the Einstein field equation of GR, which in effect features both energy density and pressure on the right hand side.

Hello Marcus,

So we both agree "pressure resists acceleration", but how?
Since you are one of the knowledgeable "Astro/Cosmo Guru", so let me ask you an honest question, The question is this: Does the box contract "in the lab-frame" in which the box is moving? If yes, will it compress the gas in it?
Please Note: If both the box and the gas contract at the same time, then there is No compression. If somehow the box contracts but the gas does Not, then the box has to compress the gas in it. In other words, will the gas resist the contraction of the box, as Lorentz-contraction demands. That's all we need to know.

 

[Xeinstein]

The length of the box depends on who observes it. Length is therefor not a frame-independent quantity.

The invariant mass of the box, however, is a quantity which depends only on the box, *if* we assume that the box is an isolated system (as it is in this example). This invariant mass can be computed from the energy momentum 4-vector. To make the equations simple, chose units such that c=1. Then the invariant mass of the box is E^2 - |p|^2, where E is the energy of the box, and |p| is its momentum

I haven't responded to the rest of your post, because you're getting off on the wrong track :-(.

>>> because you're getting off on the wrong track
Why? Just because I asked you an honest question.

The question is this: Does the box contract "in the lab-frame" in which the box is moving? If yes, will it compress the gas in it?
Please Note: If both the box and the gas contract at the same time, then there is No compression. If somehow the box contracts but the gas does Not, then the box has to compress the gas in it. In other words, will the gas resist the contraction of the box, as Lorentz-contraction demands. That's all we need to know.

 

[pervect]

>>> because you're getting off on the wrong track
Why? Just because I asked you an honest question.
Did you delete or modify some of the text in your previous posts?
Somehow, there are a few sentences missing?
I remember something like this "pressure dose Not resist acceleration"

It seems to me that you are pushing your own point of view, which as nearly as I can tell is incorrect, rather than asking questions and trying to understand the answers.

I really *am* trying to get you on the right track, right now in my opinion you are going off on a non-productive tangent and basically "not getting it".

Some of the issues involved here are subtle. So let's start with some of the issues that are not.

What I'd ideally like for you to come away with from this thread is an understanding of the concept of invariant mass in special relativity (and if not that much, at least a desire to learn more about it), and how this concept relates to "resistance to acceleration".

If we could accomplish that much, it might be time to get into the GR issues, which are also present.

 

[Xeinstein]

In its own frame, the box has not shrunk.

Hello russ_wallers,

We all agree that "in its own frame", the box has not shrunk.
So that's Not the question. The question is this: Does the box contract "in the lab-frame" in which the box is moving? If yes, will it compress the gas in it? In other words, will the gas resist the contraction of the moving box, as Lorentz-contraction demands? That's all we need to know, thanks...

 

[1effect]

Does the box contract "in the lab-frame" in which the box is moving?
If yes, will it compress the gas in it? ...

"No" and "no". How many times do u need to ask the same question?

 

[matheinste]

Hello all.

I have been following this thread and in general i am out of my depth but it does throw up a question which seems relevant to me.

The box is contracted in the "moving" frame as observed from the "stationary" frame. Are the sizes of molecules of the gas and their separation distances also affected by the relative motion.

At a more fundamental level is everything affected dimensionally by the relative motion.

Matheinste.

 

[1effect]

Hello all.

I have been following this thread and in general i am out of my depth but it does throw up a question which seems relevant to me.

The box is contracted in the "moving" frame as observed from the "stationary" frame. Are the sizes of molecules of the gas and their separation distances also affected by the relative motion.

No, they are not. Uniform relative motion does not affect either the size of the molecules, nor the separation distances between molecules. The box does not contract, either in the proper frame , nor in the observer frame, so the pressure remains constant.

The above is not true for the general case of non-uniform (accelerated) motion. In this situation, the outcome depends heavily on the way of accelerating the objects.

 

[Doc Al]

We all agree that "in its own frame", the box has not shrunk.
So that's Not the question. The question is this: Does the box contract "in the lab-frame" in which the box is moving? If yes, will it compress the gas in it? In other words, will the gas resist the contraction of the moving box, as Lorentz-contraction demands? That's all we need to know, thanks...

You seem to have a misconception about the nature of the Lorentz contraction. You seem to be thinking of it as an active process, as opposed to a transformation of measurements between frames. Example: Imagine a can of beer sitting on the table. A rocket ship goes by at high speed and--amazingly enough--observers on the rocket are able to perform measurements of the beer can as they fly by. Is the can and its contents Lorentz contracted? Of course! Does that somehow increase the pressure in the can? Do you expect anything unusual to happen to the can of beer? Do you think that pressure can somehow increase so as to burst the can as viewed in the frame of the rocket? I'm being a bit facetious, but I hope you see the point.

Of course, subtle things can happen when you accelerate an object. (See all the discussions about the Bell spaceships.) But your first sentence said "We all agree that "in its own frame", the box has not shrunk." That implies that you have accelerated the box in such a way as to preserve its proper length (as opposed to stretching or squashing it), thus you have introduced no stresses on the box or its contents whatsoever.

 

[Doc Al]

Are the sizes of molecules of the gas and their separation distances also affected by the relative motion.

Of course. As measured from the moving frame.

No, they are not. Uniform relative motion does not affect either the size of the molecules, nor the separation distances between molecules.

As measured from the "stationary" frame, the separation distances between molecules will be contracted.

 

[1effect]

Of course. As measured from the moving frame.


As measured from the moving frame, the separation distances between molecules will be contracted.

Sure, as a measurement process, not as an active process (see your previous post to Xeinstein).
Interestingly enough, this is the error in the Schutz text, Schutz takes the contraction as an active proces when he calculates the mechanical work p\Delta V resulting from such contraction. This type of contraction, due to measurement effects, cannot be responsible for any mechanical work. Subtle are the ways of relativity.

 

[Doc Al]

I think matheinste was clearly talking about observations made in the moving frame:

The box is contracted in the "moving" frame as observed from the "stationary" frame. Are the sizes of molecules of the gas and their separation distances also affected by the relative motion.

To answer his question "No" just adds to the confusion.

Otherwise, I agree with you. And, for the life of me, I don't understand what Schutz was doing. (I don't have his book; just going by what I see on that link.)

 

[1effect]

I think matheinste was clearly talking about observations made in the moving frame:
To answer his question "No" just adds to the confusion.

Otherwise, I agree with you. And, for the life of me, I don't understand what Schutz was doing. (I don't have his book; just going by what I see on that link.)

Happens to the very famous :-)

 

[1effect]

No, that's Not true. In either frames ,the lab frame (the box is moving) or the box co-moving frame (the box is at rest), pressure does Not increase, it's the same before or after acceleration. If you follow Schutz's calculation in his book, the pressure is a constant but the volume of the gas Does change, that's Lorentz-contraction all right

Here's the link to his calculation :
http://books.google.com/books?id=P_...ts=eYBnh8oGoa&sig=ZkzEIBINItUiFyMW5-uvjt1kMus

The point is that Schutz made a mistake, \Delta V=0 this is why the pressure does not change. For the 5-th time.

 

[yuiop]

The point is that Schutz made a mistake, \Delta V=0 this is why the pressure does not change. For the 5-th time.

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.

 

[yuiop]

We all agree that "in its own frame", the box has not shrunk.
So that's Not the question. The question is this: Does the box contract "in the lab-frame" in which the box is moving? [/QOUTE]

Yes, if the box is accelerated relative to the lab then it will physically length contract relative to its length when it was at rest in the lab. Of course an observer that co-moving with the box will not be able to measure this length contraction. It is only measurable by the observer with relative motion to the box.

If yes, will it compress the gas in it? In other words, will the gas resist the contraction of the moving box, as Lorentz-contraction demands? That's all we need to know, thanks...

Lorentz contraction demands that length (and volume) contracts. Lorentz contraction does not demand that that gas resists the contraction.

Despite real physical length contraction the pressure does not increase. I have gone to great lengths to demonstrate this in another thread by several methods. Here is yet another way of looking at it but this is more informal than the other arguments I gave in the "Proof that gas pressure is invariant" thread:

In classical experiments to determine the gas laws they found that when the temperature of a quantiy of enclosed gas is reduced that the volume reduced by a proportinal amount if the pressure is kept constant. The constant pressure means that the gas does not "resist" the contraction in volume as the temperature is reduced. Temperature can be thought of as a measure of the average kinetic energies of the particles in the sample of gas. Be warned however that temperature is a complex subject and there are several interpretations of exactly what we mean by temperature when we consider the relativistic case. In a simplyfied viewpoint reducing the kinetic energy of the particles in the box relative to the box is similar to reducing the temperature of the gas and results in a reduction of volume without any change of pressure. When the box is accelerated to a velocity relative to us, time dilation basically causes the particles to slow down in a manner similar to reducing the temperature and this combined with the contracted volume of the box is consistent with no change in pressure and with no "resistance" to contraction of the box and no resistance to the acceleration of the box due to gas compression.

In another post you asked if length contraction of the gas particles themselves results in a reduction of pressure in the moving frame. The answer is no. According to the gas laws the pressure within a container is independant of the size or mass of the gas molecules (to a first aproximation). The formula PV = nRT contains no term for the size or mass of the molecules, only the number of molecules (n). This is of course for an ideal gas.

 

[1effect]

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.

This is not what Doc Al and I are talking about.
Have u read starting with post 23?

 

[yuiop]

This is not what Doc Al and I are talking about.
Have u read starting with post 23?

I have re-read the posts and it is still not clear what you mean by \Delta V=0.

Could you clarify what you mean?

In post #22 you state :

The box does not contract, either in the proper frame , nor in the observer frame, so the pressure remains constant.

Have you changed your position on that statement?

When the box is moving relative to an observer the observer will measure the box to be length contracted. Whether that length contraction is real or not depends on whether it was the box that accelerated relative to the observer or whether the observer accelerated relative to the box.

To give a further example. Say we have 2 observers at rest with respect to each other and each with an identical box of gas. Observer A with his box accelerates to velocity v relative to observer B. Both observers will measure the other observer's box to be contracted. We can express this situation as:

(Volume A) < (Volume B) according to observer B

and

(Volume B) < (Volume A) according to observer A.

The expression

[(Volume A) < (Volume B)] AND [(Volume B) < (Volume A)]

is a logical contradiction as they both cannot be true at the same time.

We can resolve the contradiction by saying that the box that accelerated (box A) really length contracted while the volume of box B only appears to have length contracted. Box B never accelerated so it has not undergone any physical change. The apparent length contraction of box B according to observer A comes about because A is making measurements with rulers that length contracted during his acceleration and with clocks that are running at a slower rate due to his time dilation.

We can apply this logic to the Twin's paradox. Twin A accelerates away from twin B for a while. Both twins measure the ageing rate of the other twin to be slower than their own ageing rate. However when twin A returns twin B discovers that twin A really was ageing slower while twin A realizes that his measurement of twin B's slower ageing rate was an illusion. This is because A was making measurements with rulers and clocks that have physically altered during acceleration.

In the case of the twins and time dilation we can show that for at least one observer the Lorentz transformations have a real outcome. One twin really is older than the other one.

 

[1effect]

I have re-read the posts and it is still not clear what you mean by \Delta V=0.

Could you clarify what you mean?

In post #22 you state :


Have you changed your position on that statement?

When the box is moving relative to an observer the observer will measure the box to be length contracted. Whether that length contraction is real or not depends on whether it was the box that accelerated relative to the observer or whether the observer accelerated relative to the box.

To give a further example. Say we have 2 observers at rest with respect to each other and each with an identical box of gas. Observer A with his box accelerates to velocity v relative to observer B. Both observers will measure the other observer's box to be contracted. We can express this situation as:

(Volume A) < (Volume B) according to observer B

and

(Volume B) < (Volume A) according to observer A.

The expression

[(Volume A) < (Volume B)] AND [(Volume B) < (Volume A)]

is a logical contradiction as they both cannot be true at the same time.

We can resolve the contradiction by saying that the box that accelerated (box A) really length contracted while the volume of box B only appears to have length contracted. Box B never accelerated so it has not undergone any physical change. The apparent length contraction of box B according to observer A comes about because A is making measurements with rulers that length contracted during his acceleration and with clocks that are running at a slower rate due to his time dilation.

We can apply this logic to the Twin's paradox. Twin A accelerates away from twin B for a while. Both twins measure the ageing rate of the other twin to be slower than their own ageing rate. However when twin A returns twin B discovers that twin A really was ageing slower while twin A realizes that his measurement of twin B's slower ageing rate was an illusion. This is because A was making measurements with rulers and clocks that have physically altered during acceleration.

In the case of the twins and time dilation we can show that for at least one observer the Lorentz transformations have a real outcome. One twin really is older than the other one.

the box does not accelerate, it is in uniform motion.

 

[yuiop]

the box does not accelerate, it is in uniform motion.

If the box has always been moving at velocity (v) with respect to us and we have no history of the box (or ourselves) accelerating then there is insuffient information to determine if the contraction of the volume (V) is "real" or "apparent".

Either way we would measure the box to contracted according to \Delta V = V_0 - V_0 \sqrt{1-v^2/c^2}.

How do you justify \Delta V =0 ?

 

[1effect]

If the box has always been moving at velocity (v) with respect to us and we have no history of the box (or ourselves) accelerating then there is insuffient information to determine if the contraction of the volume (V) is "real" or "apparent".

Either way we would measure the box to contracted according to \Delta V = V_0 - V_0 \sqrt{1-v^2/c^2}.

How do you justify \Delta V =0 ?

do you understand the xchange with Doc Al?

 

[matheinste]

Hello again.

Just to clear up some confusion on my part. In answer to a previous query in this thread it was confirmed by Doc Al that an observer in the "stationary" frame would see the separation distances of the gas molecules in the "moving" frame contracted. It was not explicitly stated that the size of the gas molecules is also contracted. I believe this to be so but would like it to be clear, if it is a fect, so we can all accept it as i feel it has relevance to a rerstricted, non accelerated version of the original post.

Matheinste.

 

[Doc Al]

I'd say that any linear dimension along the direction of motion will be measured as contracted, whether its the distance between molecules or the "size" of the molecules themselves.

 

[matheinste]

Thankyou Doc Al.

This means to me that any, and every effect depending only on the linear dimensions and clock rates of a system will not be changed by any inertial relative motion. I am also assuming that every physical process ultimately depends upon these fundamental dimensions of length and time. In other words every term in the mathematiacl formulation of a physical law dependent on these dimensions will either be unaffected or proportionately affected so as to leave the numerical result unaltered. Obviously the observed measurement of length and time being, fundamental and not derived, will be affected.

I have no idea how things behave in accelerated frames so this scenario is probably not relevant to the original post.

Not very well put but, nor put with confidence, but i think you can get the idea.

Mateinste .

 

[yuiop]

Hello again.

Just to clear up some confusion on my part. In answer to a previous query in this thread it was confirmed by Doc Al that an observer in the "stationary" frame would see the separation distances of the gas molecules in the "moving" frame contracted. It was not explicitly stated that the size of the gas molecules is also contracted. I believe this to be so but would like it to be clear, if it is a fect, so we can all accept it as i feel it has relevance to a rerstricted, non accelerated version of the original post.

Matheinste.

Say the box is moving along the x-axis with velocity v relative to the "stationary" frame.

In the rest frame of the box some of the molecules are bouncing up and down the y-axis with velocity u. So even in the rest frame of the box the molecules are length contracted in the y direction because the gas molecules are not at rest except at zero degrees Kelvin. To the observer in the stationary frame the y component of the molecules bouncing up and down is reduced by time dilation so they are less length contracted than they are in the rest frame of the box. In the rest frame of the box the molecules bouncing left to right parallel to the x-axis also have average velocity u. From the stationary frame the forward velocity of the molecules is greater than u but the molecules going from the front wall to rear wall on their return journey at moving at a velocity of less than u from the point of view of the observer in the stationary frame. So to the observer in the stationary frame some of the molecules are actually longer than they are in the rest frame of the box.

You should be able to see that the change in shape of the molecules is complex and not restricted to just the x-axis parallel to the motion of the box. You should also be aware that (as I said in an earlier post) the ideal gas law is independent of the shape, size or mass of the molecules for an ideal gas.

The ideal gas law is PV=nRT

where

P = Pressure of the gas
V = Volume of the gas
n = Number of gas molecules
R = The gas constant
T = Absolute temperature of the gas.

Like I said... no mention of size, shape or molecule mass in the ideal gas law.

I guess you just don't agree that time dilation applies to gas molecules too.

 

[Doc Al]

I'd say that any linear dimension along the direction of motion will be measured as contracted, whether its the distance between molecules or the "size" of the molecules themselves.

Kev makes an important point in his post #39 that I failed to emphasize here: The observed length contraction of a molecule depends on the relative velocity of the molecule, not just the speed of the box.

 

[yuiop]

Thankyou Doc Al.

This means to me that any, and every effect depending only on the linear dimensions and clock rates of a system will not be changed by any inertial relative motion. I am also assuming that every physical process ultimately depends upon these fundamental dimensions of length and time. In other words every term in the mathematiacl formulation of a physical law dependent on these dimensions will either be unaffected or proportionately affected so as to leave the numerical result unaltered. Obviously the observed measurement of length and time being, fundamental and not derived, will be affected.

I have no idea how things behave in accelerated frames so this scenario is probably not relevant to the original post.

Not very well put but, nor put with confidence, but i think you can get the idea.

Mateinste .

First of all, it seems we can answer every question simply by saying nothing changes according to an observer at rest with system under observation. However, this viewpoint has difficulty explaining things like why two twins age differently when brought back together. There may be other physical phenomena that that occur due to relatistic motion in the sense that they can be measured after the event when the system is brought to rest. One example is Thomas precession. A gyroscope sent in a orbit around the Earth will not be pointing in exactly the same direction after each complete orbit. This is a real measurable effect and is in fact being measured the in Gravity Probe B. They are still clearing the noise from the data of that experiment but the precession seems to be there under the noise. Sagnac invented a gyroscope without any moving parts that is in regular comercial use. It is doubtful that the Sagnac effect would have been discovered by someone who had the viewpoint that nothing really changes in a moving system.

 

[matheinste]

Hello Doc Al and Kev.

Your comments have been taken on board of course accepted.

I will follow the this post with a more enlightened interest

Thankyou Matheinste.

 

[pervect]

First of all, it seems we can answer every question simply by saying nothing changes according to an observer at rest with system under observation.

One should perhaps be more formal and say that we can analyze the system in any frame we chose, and that it's usually best to chose the simplest one. This is a simple, but important point, that can hardly be stressed enough. But that leads us to point #2.

However, this viewpoint has difficulty explaining things like why two twins age differently when brought back together.

Actually, it doesn't have any difficulty at all in explaining this. Only one twin is in an inertial frame. Other twins are in a non-inertial frame for at least part of the journey. There are many correct ways of analyzing the later case, and all of them get the same answer.

The difficulty in attempting to explain the Sagnac effect by this line of reasoning also involves the fact that there is no single inertial frame that describes the observer in question.

 

[yuiop]

..

Actually, it doesn't have any difficulty at all in explaining this. Only one twin is in an inertial frame. Other twins are in a non-inertial frame for at least part of the journey. There are many correct ways of analyzing the later case, and all of them get the same answer.

The difficulty in attempting to explain the Sagnac effect by this line of reasoning also involves the fact that there is no single inertial frame that describes the observer in question.

I think it fair to say that newcomers to relativity that are first taught the totally symmetrical and strictly formal version of Special Relativity that is constrained to inertial frames only, are genuinely perplexed by so called paradoxes like the the Twin's paradox. Every year, there are hundreds of questions about the twin's paradox and endless arguments that perhaps could be avoided by introducing earlier in the education process (or stressing more) the concept that acceleration breaks the symmetry. Just my point of view.

Beyond that, I have no quibble with your statement that one of the twins is not in an inertial frame and that the Sagnac effect is not an inertial frame, but in my experience newcomers find these concepts genuinely puzzling when trained to think in terms of symmetrical inertial frames only.

 

[AstroRoyale]

I'm not sure what is being argued here as things have gotten off track, but here's a go of it. The Pressure of a gas is not a lorentz invariant, it does change WHEN MEASURED IN DIFFERENT FRAMES.

<br /> T^{&#039;}= \Lambda^{T} T \Lambda<br /> with<br /> T=diag[\rho, p, p ,p]<br /> and \Lambda is the boost matrix which I&#039;m too lazy to typeset. <br /> [\tex]<br /> <br /> If the pressuse is 1 atm in the rest frame of the gas, then it will not be 1 atm WHEN MEASURED BY AN OBSERVER IN THE MOVING FRAME. However, if you were a physics student living in the box that is moving at some relativistic speed, say 0.5c, you will measure 1 atm every time. This is the essence of relativity, that in the box there is NO experiment to determine if the box is in uniform motion.

 

[yuiop]

I'm not sure what is being argued here as things have gotten off track, but here's a go of it. The Pressure of a gas is not a lorentz invariant, it does change WHEN MEASURED IN DIFFERENT FRAMES.

<br /> T^{&#039;}= \Lambda^{T} T \Lambda<br /> with<br /> T=diag[\rho, p, p ,p]<br /> and \Lambda is the boost matrix which I&#039;m too lazy to typeset. <br /> [\tex]<br /> <br /> If the pressuse is 1 atm in the rest frame of the gas, then it will not be 1 atm WHEN MEASURED BY AN OBSERVER IN THE MOVING FRAME. However, if you were a physics student living in the box that is moving at some relativistic speed, say 0.5c, you will measure 1 atm every time. This is the essence of relativity, that in the box there is NO experiment to determine if the box is in uniform motion.

<br /> <br /> I assume you are talking about the stress tensor here. We had a long discussion about this in the &quot;Proof of the invariance of gas pressure&quot; thread where we concluded that the pressure calculated in the stress energy tensor is not the same thing as regular gas pressure. Regular gas pressure is a Lorentz invariant. See <a href="https://www.physicsforums.com/showthread.php?t=213016" class="link link--internal">https://www.physicsforums.com/showthread.php?t=213016</a>

 

[AstroRoyale]

Yes, T is the stress energy tensor, and as far as I know T=diag(\rho, p,p,p)
is THE stress/energy tensor of an ideal gas. What do you suppose that p in the stress energy tensor is, if it is not the pressure as you claim?

 

[yuiop]

Yes, T is the stress energy tensor, and as far as I know T=diag(\rho, p,p,p)
is THE stress/energy tensor of an ideal gas. What do you suppose that p in the stress energy tensor is, if it is not the pressure as you claim?

I have no idea what the p in the stess energy tensor is as I am no expert on tensors. Pervect knows more about these things and he tends to agree in the tread I linked to that that stress energy tensor pressure and ideal gas pressure may not be the same thing. Pervect points out that engineers and physicists have different definitions of pressure and that may be the root of the disagreement. As far as I know, Pervect is the main author of thie article on the stress-energy tensor in Wikipedia. http://en.wikipedia.org/wiki/Stress-energy_tensor

Perhaps you can point out some flaws in the arguments I presented in the tread I linked to in my previous post?

 

[1effect]

I have no idea what the p in the stess energy tensor is as I am no expert on tensors. Pervect knows more about these things and he tends to agree in the tread I linked to that that stress energy tensor pressure and ideal gas pressure may not be the same thing. Pervect points out that engineers and physicists have different definitions of pressure and that may be the root of the disagreement. As far as I know, Pervect is the main author of thie article on the stress-energy tensor in Wikipedia. http://en.wikipedia.org/wiki/Stress-energy_tensor

Perhaps you can point out some flaws in the arguments I presented in the tread I linked to in my previous post?

kev,

You already know the flaws, they range from:
-incorrect modelling of the pressure (via springs or rods)

to

-incorrect physics (attributting the speed of the box wall to the molecules of gas)

to

-use of incomplete or conveniently modified formulas for relativistic force transformation in the calculation of momentum

All thse problems are evident in the thread, I have highlighted them as we moved from approach to approach. You are a very creative person but all the solutions have flaws. This is why we haven't managed to reach a conclusion in the calculation of the relativistic transformation for pressure. We have the intuition[/] that pressure might be invariant (intuition contradicted by the way the stress-energy tensor transforms) but we have no valid proof. Does someone have a correct proof? One way or another, I don't care about the outcome (invariant or non-invariant). Isn't there a published paper on this subject?

 

[yuiop]

kev,

You already know the flaws, they range from:
-incorrect modelling of the pressure (via springs or rods)

to

-incorrect physics (attributting the speed of the box wall to the molecules of gas)

to

-use of incomplete or conveniently modified formulas for relativistic force transformation in the calculation of momentum

All thse problems are evident in the thread, I have highlighted them as we moved from approach to approach. You are a very creative person but all the solutions have flaws. This is why we haven't managed to reach a conclusion in the calculation of the relativistic transformation for pressure. We have the intuition[/] that pressure might be invariant (intuition contradicted by the way the stress-energy tensor transforms) but we have no valid proof. Does someone have a correct proof? One way or another, I don't care about the outcome (invariant or non-invariant). Isn't there a published paper on this subject?

Well, you I know I disagree with your objections, so yes, some independent opinions would be welcome ;)

Also, IF the pressure of an enclosed ideal gas in not a Lorentz invariant THEN I can show you a whole host of unresolvable paradoxes that would be created.