Does pressure resist acceleration?

[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.

 

[AstroRoyale]

Unlike 1effect, I don't have any intuition as to why the pressure of an ideal gas should be an invariant, in doubt I'd take that stance on the safe side and suppose that it isn't an invariant. I haven't looked at the proof carefully yet, but I can and did offer the proof based on the stress/energy tensor that the pressure is not an invariant for an ideal gas.

\Lambda^{T} T \Lambda shows that p_xx does change during a boost. I think that when it comes to this, it really is best to discuss T^{\mu \nu} instead of 4 vectors. For instance, when talking about lorentz transforming the electric and magnetic fields, we need the field tensor F^{\mu \nu} to properly describe how the fields change, and how a pure electric field can become an electromagnetic field. The stress energy tensor is not just a General relativity object either, it applies in special relativity too of course, we can make a stress/energy tensor for the EM fields out out the field tensor for example. See Jackson for example. And the T^{\mu \nu} I gave is the same in general or special relativity anyway.

 

[1effect]

Unlike 1effect, I don't have any intuition as to why the pressure of an ideal gas should be an invariant, in doubt I'd take that stance on the safe side and suppose that it isn't an invariant. I haven't looked at the proof carefully yet,

Hi,

The proofs are all flawed, as pointed out earlier. We couldn't come to any agreement that any of the proofs are valid. Moreover, as you (and dharis before you), pointed out, the results contradict the way the stress-energy tensor transforms. So, we are hopelessly stuck.

 

[AstroRoyale]

Well, until someone shows me a proof that I can trust, I do believe that the pressure of an ideal gas is not a Lorentz invariant. For continuous media/fields (ie non point particles), the stress-energy tensor seems required if we want to talk about what happens when we boost these things. Is that a correct assumption?

I suppose that we could always use the stress-energy tensor in any case, but it takes the form of T_{00}=m and the other 15 components are zero for a point-like particle in the rest frame of the paticle so it can essentially be ignored.

 

[Xeinstein]

Well, until someone shows me a proof that I can trust, I do believe that the pressure of an ideal gas is not a Lorentz invariant. For continuous media/fields (ie non point particles), the stress-energy tensor seems required if we want to talk about what happens when we boost these things. Is that a correct assumption?

I suppose that we could always use the stress-energy tensor in any case, but it takes the form of T_{00}=m and the other 15 components are zero for a point-like particle in the rest frame of the paticle so it can essentially be ignored.

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. If the pressure of the box increase during acceleration in the observer's frame in which the box is moving, then eventually it could burst the box. But viewed from box own frame in which the box is at rest, the pressure will always be p since it's at rest, so it can't burst the box.
Since in relativity you cannot have something failing in one frame and being normal in another frame then you must come to the conclusion that Lorentz-contraction does not cause pressure to increase in general.

 

[matheinste]

Hello Xeinstein.

This is a scenario of the type used in many imagined paradoxes of SR. I think care must be taken in using it because on the face of it it may imply that nothing can happen to the contents of the box because, if anything did, any change is potentially detectable by the observer at rest in the frame of the box. The very fact that this discussion is happening implies that some effects are (or may be) detectable by an observer in a frame moving relative to the frame of the box. We know some things are detectable by the moving observer. The volume, as seen by the observer in the moving frame, changes because the length of one side contracts (in the standard configuration) and as nothing is detectable in the stationary observer's frame then this is obviously not detectable by a length measurement, or any other measurement, in the stationary observer's frame.

What i am really asking is "what is the nature of the effects that can be measured in the moving obsever's frame but not in the stationary observer's frame".

And as pointed out to me earlier in this thread, in the case of a gas the physics are a little more complicated than appears if you do not know, as i do not, all the mechanisms involved and take account of them.

The absolute fundamentals, even from a logical point of view, of what effects can and cannot be detected or seen by an observer in a frame moving with respect to a physical system may be worth discussion in another thread.

Matheinste.

 

[pervect]

Hi,

The proofs are all flawed, as pointed out earlier

I don't agree - I attempted to work the problem out myself, and got the same answer as Kev did and a different answer from 1effect. However I would say there is a lot of semantic confusion about what is being proved, and would agree that nobody has come up with any good papers or textbook references to address the point in question.

For the most part, people simple do not use the concept of "pressure" except in the rest frame of the fluid, so far as I'm aware. This makes it difficult to find said textbook references.

I also still think there is some confusion on 1effects part where he assumes that the stress-energy tensor is the same thing as pressure. This is again a semantic issue about what the term "pressure" really means. As nearly as I can tell, it probalby means what kev says, and not what 1effect says.

 

[1effect]

I don't agree - I attempted to work the problem out myself, and got the same answer as Kev did and a different answer from 1effect.

I did not get any answer,if we except this one. I just tried to help kev debug his many solutions. To date, they all have unresolved errors. I would be interested in seeing your solution.

However I would say there is a lot of semantic confusion about what is being proved, and would agree that nobody has come up with any good papers or textbook references to address the point in question.

This is the most important part, finding a good reference, there has to be one somewhere.

I also still think there is some confusion on 1effects part where he assumes that the stress-energy tensor is the same thing as pressure. This is again a semantic issue about what the term "pressure" really means. As nearly as I can tell, it probalby means what kev says, and not what 1effect says.

There are quite a few people that believe the same thing (dhris, AstroRoyale). What disturbs me are two things:

-all of the "published" solutions have errors
-we get disagreement with the only referenced solution, the one that uses the stress-energy tensor

You (pervect) cannot simply waive your magic wand and declare the discrepancy a "confusion" in terms of use of concepts. The reason is that there is no valid solution for the non-tensor treatment. Unless you have one :-) This is why, I'd like to see it.

 

[AstroRoyale]

Well, I think we've happened upon a conundrum. I've been looking around, and apparently there is still considerable discussion as to how even the temperature changes in a Lorentz transformation. Apparently, there are lines of reasoning that lead to increases, decreases and invariance of temperature as measured in the boosted frame. The paper below claims that the pressure IS invariant, but I'm still not convinced personally. I'm going to ask around though, this is really bugging me for some reason. Einstein and statistical thermodynamics. I. Relativistic thermodynamics

P T Landsberg 1981 Eur. J. Phys. 2 203-207

Not terribly recent, but I see some more very recent articles (2007) where the same inconsistencies are seen.

 

[AstroRoyale]

And I just found an article of astroph that claims that the pressure increases as

p=\gamma^{2}p

http://arxiv.org/abs/0712.3793

 

[1effect]

And I just found an article of astroph that claims that the pressure increases as

p=\gamma^{2}p

http://arxiv.org/abs/0712.3793

Interesting, thank you!