Modern Physics view of Length Contraction?

[ghwellsjr]

People at the front of an accelerating spaceship age slower than those at the back.
If the equivalence principle is invoked, this is equivalent to gravitational reddening.

Those people are not accelerating identically.

 

[ghwellsjr]

I was talking about Special Relativity too.

What math of SR would you say is not simple?

 

[Agerhell]

Only a genius is smart in all things. so, happily, most people do understand what it is like not to be smart in some field (My problem area: QM).

Formally, a genius is someone who understands something of value that nobody have understood before.

 

[Agerhell]

I've been told several times that length contraction is not "real" in the sense of material or its space actually contracting. How does modern physics (by that I mean what is being taught currently) view Bell's spaceship paradox. Will the string break? Why, if length contraction is not real. I also have a hard time with the extended lifetimes of Muons in the atmosphere if, from their point of view, space had not contracted.

I would say that out of the three things, time dilation, mass increase and length contraction we normally attribute to relativity, length contraction is the least real.

Time dilation is, as the GPS system is living proof of, very real.

Mass increase (or relativistic momenta if you like) is very real in for instance accelerators.

Length contraction on the other hand is only used to explain some experimental findings, such as the Michelson-Morley experiment. Lifetimes of cosmic muons are also often explained using length contraction but could if you like be explained by the muons traveling with high speed compared to the Earth just like the GPS satellites are. There is one other example more closely related to classical electrodynamics where lengt contraction is used as an explanation but I do not at the moment know what it is.

Nobody has ever conducted any "Bell space-ship experiments", but you can of course speculate about it if you like.

 

[bobc2]

I would say that out of the three things, time dilation, mass increase and length contraction we normally attribute to relativity, length contraction is the least real.

Length contraction on the other hand is only used to explain some experimental findings, such as the Michelson-Morley experiment.

Experiments at the RHIC (Brookhaven Relativistic Heavy Ion Collider) have "seen" the nucleons inside gold nuclei contract to a thin disk configuration when moving at close-to-light speed. Gold nuclei, moving in opposite directions, are collided.

Hermann Weyl (Einstein's close friend and colleague) described the universe as 4-dimensional, populated by 4-dimensional objects, typically characterized by relatively short lengths in the X1, X2, and X3 dimensions while extending for billions and trillions of miles in the 4th dimension. He accounts for the "motion of observers" as the motion of consciousnesses moving along their 4th dimension world lines at the speed of light. After all, the 4-dimensional objects do not move at all, they are static--motionless as 4-dimensionl objects (as is the entire universe).

Using this model, the mechanism underlying length contraction is quite trivial: Observers moving at relativistic velocities with respect to each other simply "view" totally different 3-dimensional pieces of the same 4-dimensional objects. So, no--the objects don't really change--they don't really contract, shrink--they are static--unchangeable as 4-dimensional fixed objects. Observers are limited to a 3-dimensional view; their 4-D world lines are oriented at different angles, and their instantaneous world volumes cut across the 4-D objects at different angles (you can compute the cross-secton views using Lorentz transformations). Thus, different observers have different cross-section views of the same 4-D objects, which results in different "observed" lengths along their respective X1 axes, for example. This situation is shown in the sketches below.

Notice that the red and blue observer views along their respective X1 axes cut across the 4-dimensional beam at different angles, resulting in different "observed" lengths for each observer. The cross-section views shown for blue and red correspond to instaneous views peceived by red and blue consciousnesses at the instant the consciousnesses are located at those particular points along the respective 4th dimension world lines.

 

[Agerhell]

Experiments at the RHIC (Brookhaven Relativistic Heavy Ion Collider) have "seen" the nucleons inside gold nuclei contract to a thin disk configuration when moving at close-to-light speed. Gold nuclei, moving in opposite directions, are collided.

How have they seen that? Seems like a tricky measurment... Should I get that from the rest of your post? Could you provide a link to more information about this Brookhaven findings?

 

[bobc2]

How have they seen that? Seems like a tricky measurment... Should I get that from the rest of your post? Could you provide a link to more information about this Brookhaven findings?

I'll try to get a reference to one of the RHIC papers, but at this point I have the information mentioned based only on an e-mail sent to me some time ago from a friend at The University of Texas Physics Dept. who led a team working on the the STAR project (part of the RHIC experiment).

 

[meBigGuy]

Those people are not accelerating identically.

They sure think they are.
If, when you make your troll like statements, you would care to elaborate, then your posts would be useful. Other wise they are just noise and will be ignored for now on (at least by me).

 

[pervect]

They sure think they are.
If, when you make your troll like statements, you would care to elaborate, then your posts would be useful. Other wise they are just noise and will be ignored for now on (at least by me).

That would be a pity, because then you'd miss out on realizing that if you mount an accelerometer on the front and back of two spaceships, said spaceships maintaining a constant distance apart, the accelerometer readings on the front spaceship and the rear spaceship will be different.

Not only will their local accelerometers read different numbers, but an inertial observer measuring the accelerations of the front and rear spaceships will also get different numbers for the front and the rear spaceships.

You can also (if you're careful about definitions) apply the same analysis to a single long, "rigid" spaceship (rather than the pair of spaceships maintining a constant separation), though to carry out this analysis you need to define "rigid". The usual manner of defining "rigid" is due to Born, and called "Born rigidity".

This all ties into the "Bell spaceship paradox".

 

[ghwellsjr]

Aging occurs without regard to direction.

Pretty sure meBigGuy is referring to comparative aging. with the observations being symmetric how is this "regardless of direction"?

I'm not sure what you mean by "the observations being symmetric". Usually in SR a statement like that refers to the reciprocal nature of two observers in relative motion but I don't see how that applies here so I don't know what you mean.

His entire sentence was:

People age differenty in the direction of acceleration, so lengths change also.

It seemed to me that he is leveraging off the idea that a change in length occurs only in the direction of motion as a result of an acceleration and he's thinking that this also applies to aging, in what way, I don't know, but in any case, it is wrong. I really don't know what else to say about it because it doesn't make any sense. I was hoping he would elaborate and explain what he meant.

But when he did elaborate, he said:

I was saying that identically accelerated objects age differently in the direction of acceleration.

And this also makes no sense. Assuming that the objects were relatively at rest prior to the acceleration so that their aging was at the same rate, if they then accelerate identically, they will continue to be relatively at rest and both change their aging rates identically. What does "age differently in the direction of acceleration" even mean?

 

[ghwellsjr]

Those people are not accelerating identically.

They sure think they are.
If, when you make your troll like statements, you would care to elaborate, then your posts would be useful. Other wise they are just noise and will be ignored for now on (at least by me).

I elaborated on your subject matter in post #4 which you apparently ignored since you didn't learn what I said there. I pointed out the difference between accelerating a rigid object at one point and at multiple points. I pointed out that if you apply a force of acceleration to just one point, the object will contract. Isn't it obvious that this means that one end of the object is accelerating differently than the other end?

Now I have no idea if your response to my response to clem's post:

People at the front of an accelerating spaceship age slower than those at the back.
If the equivalence principle is invoked, this is equivalent to gravitational reddening.

had anything to do with your comment "People age differenty in the direction of acceleration" but whether it does or not, you are the one that needs to elaborate if you want me to go into more detail about why I disagreed. Let me start by asking you if your comment is related to the fact that length contraction is directional?

 

[Drakkith]

People at the front of an accelerating spaceship age slower than those at the back.
If the equivalence principle is invoked, this is equivalent to gravitational reddening.

Can you elaborate? Why would people in the front age slower? Aren't they all accelerating at the same rate?
Or does post #4 explain it completely?

 

[harrylin]

I would say that out of the three things, time dilation, mass increase and length contraction we normally attribute to relativity, length contraction is the least real.

Time dilation is, as the GPS system is living proof of, very real.

Mass increase (or relativistic momenta if you like) is very real in for instance accelerators.

Length contraction on the other hand is only used to explain some experimental findings, such as the Michelson-Morley experiment. Lifetimes of cosmic muons are also often explained using length contraction but could if you like be explained by the muons traveling with high speed compared to the Earth just like the GPS satellites are. There is one other example more closely related to classical electrodynamics where lengt contraction is used as an explanation but I do not at the moment know what it is.

Nobody has ever conducted any "Bell space-ship experiments", but you can of course speculate about it if you like.

That would perhaps be a "Machian" interpretation of "real" (as well as of length contraction): as long as you don't directly measure it, it doesn't exist.

However, it is a fact that evidence for length contraction is only indirect, or perhaps I should say, less direct than for the other phenomena.

 

[Meir Achuz]

"People at the front of an accelerating spaceship age slower than those at the back.
If the equivalence principle is invoked, this is equivalent to gravitational reddening."

Can you elaborate? Why would people in the front age slower? Aren't they all accelerating at the same rate?
Or does post #4 explain it completely?

I got it backwards because I did it quickly off the top of my head. It should be that
people at the front of an accelerating spaceship age faster than those at the back.
The equation is \tau_{\rm back}=\tau_{\rm front}(1+aL/c).
A simple derivation is in Tolman 'Relativity Thermodynmics and Cosmology'.
Another way to look at it is that people in the ship would feel an equivalent gravitational field a, and interpret this difference as gravitational reddening.

 

[Meir Achuz]

Bobc2:
"Experiments at the RHIC (Brookhaven Relativistic Heavy Ion Collider) have "seen" the nucleons inside gold nuclei contract to a thin disk configuration when moving at close-to-light speed. Gold nuclei, moving in opposite directions, are collided."
A lot of theory has to be included before they "see" that.
Terrell J 1959 Phys. Rev. 116 1041 and Penrose have shown that if they looked, they would 'see' a sphere.
Doesn't your later statement "So, no--the objects don't really change--they don't really contract" imply that RHIC 'sees' an illusion?

 

[bobc2]

Bobc2:
"Experiments at the RHIC (Brookhaven Relativistic Heavy Ion Collider) have "seen" the nucleons inside gold nuclei contract to a thin disk configuration when moving at close-to-light speed. Gold nuclei, moving in opposite directions, are collided."
A lot of theory has to be included before they "see" that.
Terrell J 1959 Phys. Rev. 116 1041 and Penrose have shown that if they looked, they would 'see' a sphere.
Doesn't your later statement "So, no--the objects don't really change--they don't really contract" imply that RHIC 'sees' an illusion?

The length contractions are not illusions. These are the actual differing lengths as "viewed" in the various frames. This is explained in post #35.

 

[harrylin]

-the objects don't really change--they don't really contract
[..]
The length contractions are not illusions. These are the actual differing lengths as "viewed" in the various frames. This is explained in post #35.

In fact, that statement is based on a different (4D) definition of such things as "objects" and "contraction" - it corresponds to a different "view" of the world that we live in than the view that corresponds to the common definitions.
And it appears to me that objects can't change at all in that view, as with time as a dimension everything is "frozen" in Spacetime - is that a correct understanding of that view?

 

[bobc2]

In fact, that statement is based on a different (4D) definition of such things as "objects" and "contraction" - it corresponds to a different "view" of the world that we live in than the view that corresponds to the common definitions.
And it appears to me that objects can't change at all in that view, as with time as a dimension everything is "frozen" in Spacetime - is that a correct understanding of that view?

Yes. Nice summary, harrylin.

 

[PAllen]

A few points worked out in similar threads on this topic in the past are relevant here.

Just as you can over-interpret length contraction, you can over-interpret Penrose-Terrell rotation. The strongest statement it makes is for spheres photographed. However, in another thread on this, several of us cooperated on ray tracing and space time diagrams to demonstrate that in the barn-pole paradox (say, a 100 meter rod passing at near c through a 30 meter cubical barn), a photograph taken from the center of barn at the right moment would show the rod completely inside the barn with both doors closed. In this case, photo and simultaneity definitions of length agree on the existence of length contraction. Obviously, this experiment hasn't been done - but if it were - and because a photograph is an objective, frame invariant prediction, if this experiment did not come out as SR predicted, SR would have to be abandoned.

Secondly, if you don't interpret distances changing a frame dependent way, then you have radically frame dependent light speed, and also the ability for stars to move many times the speed of light. Consider the simple example of near c (relative to earth) travel to a star 10 light years a way. When traveler reaches the star they are one year older. If you insist distance didn't really contract, you conclude the star approached you 10 time c. And if distances do contract, how not length?

Basically, I found Clem's reference extremely shallow, ignoring precisely all the well known examples that conflicted with its thesis.

 

[Histspec]

Try http://arxiv.org/abs/0906.1919

There are some problematic statements in this paper. Bell's spaceship paradox is based on the assumption, that the acceleration is always simultaneous in the laboratory frame. As correctly pointed out by Franklin, this acceleration cannot be simultaneous in the new rest frame of the rockets. Thus the distance between the rockets increases and the rope, whose rest length is of course unchanged, must break. However, he writes:

Bell’s paradox was that his intuition told him the cable would
break, yet there was no change in the distance between the ships in system S.
He suggested resolving the paradox by stating that a cable between the ships
would shorten due to the contraction of a physical object proposed by Fitzgerald
and Lorentz, while the distance between the ships would not change. This
resolution however contradicts special relativity which allows no such difference
in any measurement of these two equal lengths.

No, Bell's solution is in agreement with the basic principles of special relativity, which requires the equivalence of all inertial frames of reference, that is, all IS are equally valid for the description of any phenomenon.

a Franklin) In their rest frame, the rest length of both rockets as well as the rope are unchanged, and since the distance between the rockets increases due to non-simultaneous acceleration, the rope breaks.

b Bell) In the lab-frame, both rockets as well as the rope are contracted, while the the distance between the rockets stays the same due to simultaneous acceleration , thus also in this frame the rope breaks.

There is no need to declare the "rest length" as the only meaningful length, as suggested in Franklin's paper.

This reminds me somehow on the attempts of Rohrlich and many others since 1960, to allow synchronous force and equilibrium conditions only in the rest frame of the measured object, and then create Lorentz covariant expressions leading to "asynchronous" force and equilibrium conditions in all other frames. At the end, all 3D quantities are replaced by 4D's. Though, since the experimental predictions are the same in both versions – that was also misinterpreted in that paper – that doesn't seem to be problematic.

Regards,

 

[pervect]

I thought I'd expand on some of my earlier remarks, with a bit more sophistication this go-around, with respect to the original questions about interpretation.

As far as interpretation goes, it's convenient and widespread (though perhaps not universal) to regard tensor quantities as fundamental.

Tensors are defined by their transformation properties. Rank 0 tensors, or scalars, have the simplest transformation possible. They have the same value for all observers.

Pre-relativity, distance was a tensor - if you measure it in one reference frame, it has the same value in all. This is obviously the simplest possible transform law for a scalar - something that doesn't change. Post relativity, distance is no longer a tensor - it's dependent on the reference frame. Instead, the Lorentz interval becomes the candidate for the fundamental quantity of interest, because of its tensor nature.

Rank 1 and higher tensors are important to relativity as well, but I'm going to skip over all the mathematical details. I'd like to encourage people to find out more about tensors, but I'm not quite sure where to point them, alas.

How did the tensor nature of distance get lost? Well, the manner in which we transform between frames changed When you have a moving frame with coordiantes (t',x') and a stationary frame with coordinates (t,x), there's some mapping from (t,x) to (t', x').

Pre-relativity, the mapping was defined by the Gallilean transform, t'=t, x'=x-vt v being the relative velocity between frames. Post relativity, the mapping is the Lorentz transform, t' = \gamma(t - vx/c^2), x' = \gamma((x - vt).

Changing the the way in which we transform between frames, changed distance from a fundamental tensor quantity independent of the observer, to a less fundamental non-tensor quantity that is observer-dependent.

The reason for choosing the more complex and less intuitive Lorentz transform as the way to switch between frames boils down to agreement with experiment.