Relativity and pressure

[bojan]

I am reading the book "Gravity from the bottom up", by Bernard Schutz.

I always thought that Lorentz transformations are about space geometry..
The below didn't (and still doesn't really) make sense to me (quotation is from the book):

The Lorentz–Fitzgerald contraction is inevitable: the faster the box goes, the
shorter it gets. But this shortening 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)
than 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.
In fact, the formula for the extra inertia is simple. If the box has a mass-density
ρ (which, in relativity, includes the mass associated with all the different forms of
energy in the gas) and pressure p, then the density of inertial mass is
inertial mass density = ρ + p/c2. (15.10)

Could anybody throw some more light on the above?
Is it about geometry or not? (well, if it was about geometry, there would be no increase in pressure, because the atoms would become proportionally flatter in the direction of movement (the same transformation applies both for atoms and its constituents and/or box) and therefore there would be no reason for pressure to change)
How and why they came up with this?

[CraigS]

Boy a brain bender right there, Bojan !



Seems to me there's space between the atoms. Wouldn't this get reduced as the volume decreases ? If so, then the atoms get closer together hence the pressure and temperature (energy) goes up ?

I dunno .. very interesting …

Cheers

[bojan]

Originally Posted by CraigS

Boy a brain bender right there, Bojan !



Seems to me there's space between the atoms. Wouldn't this get reduced as the volume decreases ? If so, then the atoms get closer together hence the pressure and temperature (energy) goes up ?

I dunno .. very interesting …

Cheers

According to this citation, the Lorentz transformation does not apply for atoms... or does it?

[DavidU (Dave)]

"The fact that the one-way velocity of light equal to c is only apparent, has been explained (5, 6, 7) previously. This illusion is due to a phenomenon involving the increase of kinetic energy needed to carry (the atoms of) the clock from the rest frame to the moving frame. Using quantum mechanics, it has been shown (5, 6, 7) that using the principle of mass-energy conservation, the increase of velocity (kinetic energy) produces a change of energy (quantum levels) to the electrons in atoms, which is responsible for a shift of quantum levels of all atoms in the moving frame."

A quote from Newtonphysics.

[CraigS]

Hmmm … interesting …

Wouldn't the gas contents and the box take up the energy at different rates because there is a mass-density difference between the gas and the box to start with ?

This would result in a volume difference and hence a pressure difference as well ?

Cheers

[Robh (Rob)]

I would have thought that to an observer travelling on the box there is no actual change in the box's volume. It only appears shorter to an observer watching the box moving at high velocity.

Regards, Rob

[bojan]

Originally Posted by Robh

I would have thought that to an observer travelling on the box there is no actual change in the box's volume. It only appears shorter to an observer watching the box moving at high velocity.
Regards, Rob

Exactly.
Just like time passing slower, it can't be noticed by that observer.
When he is back, however, the comparison between watches will show time did go slower.
But pressure of air in the box (cabin)? How to account for this effect when he is back?

[CraigS]

Ok .. now I get the issue.

So, I'll have a guess and say that where Schutz is coming from, is the observer's perspective (as opposed to the travelling box's perspective).

The observer (in an external frame of reference) would see the length contraction. If he sees this, then wouldn't he also expect (or predict) a pressure change in the gas ?

So, the pressure change could be used to calculate the inertial mass density as as he shows ?

However as the box approaches c, doesn't the mass also increase towards infinite ?

(I'm not trying to answer this from knowledge, guys … I have no direct knowledge about Lorentz transformations !! ... just trying to reason out a possible answer).

Interesting topic .. thanks Bojan, and everyone !

Cheers

[CraigS]

So, where this thought exercise comes together and makes sense, is in verifying observations from particle collision (and other) experiments.

There some more info in Wiki of this.

Cheers

[cwjohn (Chris)]

Hi

First if all - Lorentz contraction is geometric but not in Euclid space, but rather it is a rotation in Minkowski space time. Whilst this may seem a subtle difference it is huge in reality. Like many mind concepts like baloons in cosmology and strings for GUTs, the concept of contraction in Euclid geometry is flawed and will lead on up the wrong path conceptually. If you want to think about changes in a box then it is better to imagine a rotation in Euclid space and the corresponding contraction you would see, but of course this is ultimately misleading as well.

You do not mention the context in which the reference is made, but it will definitely be in some context associated with an observer at rest observing relativistic particles. Examples could be observing fast moving boson gas clouds or superconducting particles in a wire. In this instance there has to be adjustments for the perceived particle density for the observer at rest. Here we are talking about the perceived reduction in volume and therefore the perceived increase in density.

I have not read the book but would be interested as to how this relates to gravity.

I hope that helps.

Chris

[CraigS]

Hmm;

I wonder what effect would be observed if you were sitting on one of the atoms ?

I guess you could say that the outsides of the box might be the thing that's contracting (not you, & your atom vehicle), and you'd measure an increase in pressure, also. The box could be perceived as thing that's squashing you and the surrounding atoms. This would depend on the size and mass difference between you & your atom, and the box, I guess.

There's also some words on this in the next paragraph in Wiki.


Cheers

[CraigS]

Ok .. so then there's Lorentz Covariance that says:

Experimental results are independent of the orientation or the boost velocity of the laboratory through space … In particular, a scalar (e.g. the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant

and the key property of a Lorentz covariant equation is that:

if they hold in one inertial frame, then they hold in any inertial frame. This condition is a requirement according to the principle of relativity, i.e. all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference.

So, if there's a pressure change seen from one inertial frame then it should be seen in any other inertial frame, if it can be written as either Lorentz invariant or covariant (which I guess it is, in Bojan's post #1).

Interesting .. do I have this right ?

Cheers

[Robh (Rob)]

To an observer traveling on the box, its mass, temperature and internal pressure should appear constant. To a second observer "watching" the box as it nears light speed, the mass, internal pressure and temperature is rising. At some point, to this second observer, the box's contents should initiate nuclear fusion and destroy the box itself. So, the box is there and not there to two different observers.

Rob

[CraigS]

Originally Posted by Robh

To an observer traveling on the box, its mass, temperature and internal pressure should appear constant. To a second observer "watching" the box as it nears light speed, the mass, internal pressure and temperature is rising. At some point, to this second observer, the box's contents should initiate nuclear fusion and destroy the box itself. So, the box is there and not there to two different observers.

Rob

What a classic, Rob !
(Good to see you back).

Cheers

[CraigS]

Then there's Ehrenfest paradox

Another famous paradox is the Ehrenfest paradox, which proves that the concept of rigid bodies is not compatible with relativity. It also shows that for a co-rotating observer the geometry is in fact non-euclidean.

(As per Chris' post previously, about non-euclidean geometry being involved).

It also suggests that the box would have to be a bit 'wobbly' (non-rigid).

Also interestingly, (from the perspective of our recent discussions on rotating neutron stars), the box would have to be made from neutronium (at least !) …

Any rigid object made from real materials, which is rotating with the transverse velocity close to the speed of sound in this material, must exceed the point of rupture due to centrifugal force. Thus, in the case of speed of light, it is only a thought experiment (The neutron-degenerate matter allows velocities close to speed of light, because e.g. the speed of neutron-star oscillations is relativistic).

Boy this on really is a mixed bag of interpretations.

Better change the thought experiment model there, Mr Schutz !

Cheers

[The_Cat (Jeremy)]

Originally Posted by cwjohn

Hi

... Here we are talking about the perceived reduction in volume and therefore the perceived increase in density.

...

Chris

Question: Is the reduction perceived or is there an adiabatic compression of the gas ? Can I make an estimate of the enthropy ?

Jeremy.