Length contraction in Lorentzian relativity

• zenith8
In summary, the conversation discusses the differences between Lorentzian relativity and Einsteinian STR, specifically in regards to length contraction. In the Lorentz theory, there is a preferred frame and length contraction is a real physical effect due to motion in relation to absolute space. However, no experiment has been able to directly measure this effect. The conversation also addresses the potential dangers of traveling at high speeds in the Lorentzian theory, as well as the confusion between the Lorentzian and Einsteinian formulations.
zenith8
Hi,

I'm trying to understand Lorentzian relativity (Lorentz ether theory, whatever) which is empirically equivalent to the Einsteinian STR. I have, however, a problem in comprehending length contraction.

In the Lorentz theory we have a preferred frame and length contraction is a real physical effect. It has a causal explanation in terms of motion of the body with respect to this absolute space which causes distortions in the electromagnetic field and hence in the intermolecular forces holding rods and clocks together.

Of course no experiment has ever been performed which checks length contraction directly, as there is no known way to accelerate a macroscopic object to relativistic speeds.

However, why doesn't the following imply a difference between Einsteinian STR and Lorentz?

Imagine we can build a spaceship which will travel at 0.995c. In the frame of a stationary observer, everyone agrees that the spaceship looks squished as it flies past (because of a perspective effect in Minkowski spacetime for STR, or because it actually is squished for Lorentz).

However, if I am actually on the ship then other things inside either should look squished (because they are - Lorentz) or they do not look squished (because all inertial frames are equivalent - Einstein). Now whenever I have seen this discussed one just reads that in Lorentz theory measuring rods are distorted too so I can't measure the effect. But surely if I'm going at 0.995c then things will just look distorted (spheres not being spherical etc) and I can tell the damned measuring rod is a lot shorter than it used to be (because it's now square, rather than a long rectangular metre rule).

So maybe it's because my eyes are distorted, or whatever - but isn't this dangerous? Being compressed to the thickness of a piece of cardboard can't be good for the human body surely..

What's the flaw here? All opinions gratefully received.

Cheers,
Zenith

zenith8 said:
So maybe it's because my eyes are distorted, or whatever - but isn't this dangerous? Being compressed to the thickness of a piece of cardboard can't be good for the human body surely..

As long as everything in your body is equally compressed (including the chemical bonds), you would be ok.

zenith8 said:
Now whenever I have seen this discussed one just reads that in Lorentz theory measuring rods are distorted too so I can't measure the effect. But surely if I'm going at 0.995c then things will just look distorted (spheres not being spherical etc) and I can tell the damned measuring rod is a lot shorter than it used to be (because it's now square, rather than a long rectangular metre rule).
The part in bold is incorrect. What makes you think that?

zenith8 said:
So maybe it's because my eyes are distorted, or whatever - but isn't this dangerous? Being compressed to the thickness of a piece of cardboard can't be good for the human body surely..

High uniform velocity won't kill you. High accelerations even to relatively low velocities will.

DaleSpam said:
The part in bold is incorrect. What makes you think that?

I know it's incorrect in Einsteinian STR where every inertial frame is equivalent, but I'm trying to understand the Lorentzian viewpoint. There is a real physical length contraction, because I am going at 0.995c with respect to the fixed absolute space. Why can I not see the distortion if I am on board a ship going that fast with respect to the 'aether'?

atyy said:
As long as everything in your body is equally compressed (including the chemical bonds), you would be ok.

Why would I be OK? I'm only physically compressed in the direction of travel - that distorts my shape - and if I'm only an inch across in 1 dimension that is going to block some blood vessels.. There's go to be health issues.

Thus high speed space travel is dangerous in the Lorentzian case and not so in Einsteinian STR?

zenith8 said:
I know it's incorrect in Einsteinian STR where every inertial frame is equivalent, but I'm trying to understand the Lorentzian viewpoint. There is a real physical length contraction, because I am going at 0.995c with respect to the fixed absolute space. Why can I not see the distortion if I am on board a ship going that fast with respect to the 'aether'?
I understand that you are talking about Lorentzian aether theory. My question is why, using that theory, you would think there would be any visible distortion when you acknowledge that there is no measurable distortion. It seems like a strange assumption, particularly since so many of our measuring instruments use optics.

zenith8 said:
and if I'm only an inch across in 1 dimension that is going to block some blood vessels.
How so? Your blood cells and platelets would also be contracted so they would not block the vessel.

You are just making some rather strange assumptions that I don't understand.

atyy said:
High uniform velocity won't kill you. High accelerations even to relatively low velocities will.

How do you know that? Have you tried it? We can't accelerate macroscopic objects to anywhere near a speed where the contraction would even be noticeable.

And again, you're right in a spacetime where all inertial reference frames are equivalent. But in the Lorentzian theory where we have a privileged frame and a real physical contraction if we travel at high speeds with respect to that frame, I don't see why it is true.

Apologies if I'm being slow, but everyone seems to be answering my question using the Einsteinian formulation, not the Lorentz one.

zenith8 said:
Apologies if I'm being slow, but everyone seems to be answering my question using the Einsteinian formulation, not the Lorentz one.
No, we are not. It is just that the things that you are saying are not predictions of the Lorentz formulation.

DaleSpam said:
I understand that you are talking about Lorentzian aether theory. My question is why, using that theory, you would think there would be any visible distortion when you acknowledge that there is no measurable distortion. It seems like a strange assumption, particularly since so many of our measuring instruments use optics.

I didn't acknowledge that there is no measurable distortion. What I'm saying is roughly as follows:

In the Lorentz theory a physical object (a ball 1 metre across in absolute space, say) is contracted in the direction of travel. It is true that - as all the books say - a metre rule pointing along that direction will also be contracted. So if you use the metre rule to measure the diameter of the ball then it will still read '1m' because both objects have contracted.

But surely the ball will have distorted so that it is no longer spherical, and if I go to high enough speeds the length of the metre rule will be equal to its transverse width. These are distortions that I ought to be able to see with my eyes, no?

zenith8 said:
I didn't acknowledge that there is no measurable distortion.
Ahh, there is the problem. You either don't understand the motivation or the implication of Lorentz's aether theory (LAT). Allow me a brief historical digression that will hopefully clear things up.

Prior to Lorentz the prevailing aether theory (AT) essentially said that EM radiation propagated through a medium called the luminiferous aether and that Maxwell's equations, which predict a wave velocity of c, were only valid in the aether's frame. If you were moving through the aether then AT predicted that the speed of light would be some other value besides c, and this would lead to detectable optical effects (basically the opposite of what you were describing above, optically things would look stretched out in the direction of travel). Michelson and Morley built a very sensitive interferometer in order to detect precisely these kinds of optical effects. Although they couldn't accelerate a macroscopic object to a significant fraction of c, their interferometer was sensitive enough to detect the expected optical effects at speeds of about 8 km/s through the aether (Earth's speed around the sun is ~30 km/s).

As you know, they obtained a null result, which dealt a serious blow to AT. Lorentz' then proposed his LAT in order to explain the lack of any optical effect. Basically, he asserted that there was some physical length contraction and time dilation that exactly counteracted the changed speed of light so as to eliminate the optical effect. So, things got physically squished in such a way that, with the changed speed of light, they looked normal. Therefore, in LAT you have length contraction precisely in order to avoid any optical distortions of the type you are describing. That is why your suggestions seemed strange to me and why I mentioned that you were describing things that were not predictions of LAT.

DaleSpam said:
Ahh, there is the problem. You either don't understand the motivation or the implication of Lorentz's aether theory (LAT). Allow me a brief historical digression that will hopefully clear things up.

Prior to Lorentz the prevailing aether theory (AT) essentially said that EM radiation propagated through a medium called the luminiferous aether and that Maxwell's equations, which predict a wave velocity of c, were only valid in the aether's frame. If you were moving through the aether then AT predicted that the speed of light would be some other value besides c, and this would lead to detectable optical effects (basically the opposite of what you were describing above, optically things would look stretched out in the direction of travel). Michelson and Morley built a very sensitive interferometer in order to detect precisely these kinds of optical effects. Although they couldn't accelerate a macroscopic object to a significant fraction of c, their interferometer was sensitive enough to detect the expected optical effects at speeds of about 8 km/s through the aether (Earth's speed around the sun is ~30 km/s).

As you know, they obtained a null result, which dealt a serious blow to AT. Lorentz' then proposed his LAT in order to explain the lack of any optical effect. Basically, he asserted that there was some physical length contraction and time dilation that exactly counteracted the changed speed of light so as to eliminate the optical effect. So, things got physically squished in such a way that, with the changed speed of light, they looked normal. Therefore, in LAT you have length contraction precisely in order to avoid any optical distortions of the type you are describing. That is why your suggestions seemed strange to me and why I mentioned that you were describing things that were not predictions of LAT.

You're perfectly correct. Along one space dimension. The contraction (along the x-axis, say) is not measurable because the measuring device contracts in the same direction.

The point I'm trying to make is that I don't understand why the three-dimensional effects are not visible.
So if a ball that I am watching distorts into a flattened sphere, then the shape of the lens in my eye has to distort in such a precise way that the flattened sphere looks spherical again.

And there is the problem of physiological effects. Let's say I go to 0.9999999c. My body will be physically flattened to less than the width of a piece of paper. You and the other poster were trying to imply that this has no physical, biochemical effects. I don't see why not. As far as I can see I would die in short order.

Again, I'm perfectly happy to concede the point - but I haven't yet heard an argument which convinces me.
Sorry to be obtuse..

Zenith

Again, you are describing things that are simply not predicted by LAT. The Lorentz transform includes three spatial dimensions and the Michelson Morely interferometer worked along two spatial dimensions. The optical effects you are thinking of are simply not there, in fact, getting rid of them is the whole point of LAT.

DaleSpam said:
Again, you are describing things that are simply not predicted by LAT. The Lorentz transform includes three spatial dimensions and the Michelson Morely interferometer worked along two spatial dimensions. The optical effects you are thinking of are simply not there, in fact, getting rid of them is the whole point of LAT.

OK : Standard configuration (coord systems aligned; same origin; v along x-axis - Lorentz transformations are:

t' = gamma (t-vx/c^2)
x' = gamma (x-vt)
y' = y
z' = z

with the Lorentz factor gamma = 1 / sqrt{1-v^2/c^2}.

The three spatial dimensions are all there, as you state, but only one of them is changed. You're squashing a ball along the x-axis - it looks flattened. If you squash my eyeball lens the same way, the equations of geometrical optics don't imply that I see the ball as a perfectly sphere.

And what about the physiological effects. Is it really true that a body can still live when flattened to the thickness of a piece of paper? If not, then Lorentz and Einstein are not empirically equivalent.

I'm sorry - it's not obvious to me.

Hello zenith8.

Trying to paraphrase DaleSpam i think the point is that due to our relative motion through the aether a length increase was expected. The Lorentz contraction was "designed" to exactly balance out the expected increase. This was needed to explain the null result of MM. So nothing happens.

Matheinste

matheinste said:
Hello zenith8.

Trying to paraphrase DaleSpam i think the point is that due to our relative motion through the aether a length increase was expected. The Lorentz contraction was "designed" to exactly balance out the expected increase. This was needed to explain the null result of MM. So nothing happens.

Matheinste

Hello,

Hmmm.. Are you sure? I thought that due to our relative motion through the aether, no length contraction at all was expected. Hence the Galilean transformations used before MM. Then Lorentz/Fitzgerald came along and said there was actually a 1D length contraction, and that indeed explains the null result of MM.
I completely understand this point.

It just seems to me that a distortion of a 3-dimensional object along one space dimension is visible and not compensated through a distortion of the eyeball or anything else. That is *not* what MM was designed to detect.

And squashing of your body to a significant extent *will* kill you, surely? We are talking about a real physical distortion in Lorentz theory where the atoms actually get closer together. Biochemistry with active sites on enzymes and all that will no longer function in the same way.

Zenith

Hello zenith8.

The MM experiment was designed to measure the speed of the Earth through the aether. A null result was not expected. The contraction was proposed to compensate for the expected effects and explain this null result. As nothing happens, even in LAT,due to the expected effect and the compensating Lorentz, contraction, the body has no problem.

Matheinste.

matheinste said:
Hello zenith8.

The MM experiment was designed to measure the speed of the Earth through the aether. A null result was not expected. The contraction was proposed to compensate for the expected effects and explain this null result. As nothing happens, even in LAT,due to the expected effect and the compensating Lorentz, contraction, the body has no problem.

Matheinste.

Er, really? I did not say that people expected a null result in the MM experiment - of course they didn't! You said, and I quote: "due to our relative motion through the aether a length increase was expected". What I said was that this is absolutey not true. No-one was talking about either length contraction or length increases before Michelson-Morley. People expected lengths to stay the same, hence they would be able to detect the motion of the Earth through the ether.

You seem to be misunderstanding my original question as well as misquoting what I said, no?

Zenith

Hello zenith8.

""The MM experiment was designed to measure the speed of the Earth through the aether. A null result was not expected."" This was meant as a statement of fact and i did not not mean to imply that you said or believed otherwise.

Matheinste

I just wanted to clear that up quickly before any further response.

matheinste said:
Hello zenith8.

""The MM experiment was designed to measure the speed of the Earth through the aether. A null result was not expected."" This was meant as a statement of fact and i did not not mean to imply that you said or believed otherwise.

Matheinste

I just wanted to clear that up quickly before any further response.

Ah sorry - my mistake.

Zenith.

zenith8 said:
OK : Standard configuration (coord systems aligned; same origin; v along x-axis - Lorentz transformations are:

t' = gamma (t-vx/c^2)
x' = gamma (x-vt)
y' = y
z' = z

with the Lorentz factor gamma = 1 / sqrt{1-v^2/c^2}.

The three spatial dimensions are all there, as you state, but only one of them is changed.
Yes, that is how the object is in the aether frame. That is not how the object looks in the moving frame.

zenith8 said:
You're squashing a ball along the x-axis - it looks flattened. If you squash my eyeball lens the same way, the equations of geometrical optics don't imply that I see the ball as a perfectly sphere.
No, actually they do. This is basic geometry; it is just similar triangles.

Let's say that you are at rest wrt the aether and you photograph a ball using a pinhole camera. The width of the image made on the film is determined by two similar triangles whose points meet at the pinhole. The height is also determined by two similar triangles and, since the height of the ball is equal to the width of the ball, by similar triangles you can tell that the height of the image is equal to the width of the image. Take two photos.

Now, let's say that the camera is moving forwards at relativistic speeds through the aether with the ball at rest wrt the camera and in front of the camera. Now, to determine if the ball looks any different we will double-expose the first film and see if the new image lines up with the old image. The images are still formed by similar triangles, but in this case the distance from the ball to the pinhole is shorter by a factor of γ. This makes the angle of the similar triangles greater. However, the distance from the pinhole to the film is also shorter by a factor of γ. Therefore, the new image lines up right on top of the old image.

Now, let's say the camera is moving sideways through the aether at relativistic speeds with the ball at rest wrt the camera and in front of the camera. To determine if the ball looks any different we will double-expose the second film and see if the new image lines up with the old image. Now, in this case the similar triangles for the height are unchanged from the resting condition. However, the width of the ball is reduced by a factor of γ and by similar traingles the width of the new image also reduced by a factor of γ. At the same time the width of the old image is reduced by the same factor of γ, so the new image again lines up right on top of the old image.

Other viewing angles constitute some combination of these two cases, so they also work out to the same conclusion that the relativistically moving ball looks perfectly undistorted despite the fact that it actually is length contracted.

zenith8 said:
And what about the physiological effects. Is it really true that a body can still live when flattened to the thickness of a piece of paper? If not, then Lorentz and Einstein are not empirically equivalent.
I will be glad to come back to this once we finish with the optics part.

Hello zenith8

With regards to length increase. Aether theory predicted that the time taken for the round trip of light in the arm of the apparatus parallel to the Earth's motion through the aether would be increased. This is equivalent in its effect to a lengthening of that arm. So in other words, if this path length were shortened, the transit time of light would remain the same and so explain the null result. The Lorentz contraction factor was meant to compensate for this.

So this non effect (Lorentz contraction) compenstaed for the original non effect (the change in light speed in the direction parallel to the Earth's motion through the aether)leading to a total non effect.

Matheinste

DaleSpam said:
No, actually they do. This is basic geometry; it is just similar triangles.

Excellent answer. Just what I was looking for - thank you!

Hmmm.. But just so I'm sure I understand this, let me think about a real lens rather than a pinhole.

Let the spacecraft move at relativistic speeds in the x direction. Camera, intervening convex lens, and ball are lined up inside the spacecraft on the y-axis perpendicular to this. Have a large distance between the lens and the ball so we have parallel wavefronts coming into the lens. The ball and lens are physically distorted into teardrop shapes'. The distortion of the lens changes its radius of curvature along all directions except the z axis so it apparently no longer focuses everything to the same image plane. Hmmm..how does this work?

(I'm sure you're right - but I'm having trouble visualizing this correctly).

I will be glad to come back to this once we finish with the optics part.

Still interested!

matheinste said:
Hello zenith8

With regards to length increase. Aether theory predicted that the time taken for the round trip of light in the arm of the apparatus parallel to the Earth's motion through the aether would be increased. This is equivalent in its effect to a lengthening of that arm. So in other words, if this path length were shortened, the transit time of light would remain the same and so explain the null result. The Lorentz contraction factor was meant to compensate for this.

So this non effect (Lorentz contraction) compenstaed for the original non effect (the change in light speed in the direction parallel to the Earth's motion through the aether)leading to a total non effect.

Matheinste

OK - now I understand you. Thanks for clarifying..

zenith8 said:
Hmmm.. But just so I'm sure I understand this, let me think about a real lens rather than a pinhole.
I would recommend using mirrors rather than lenses. Lenses work by slowing light, so not only do you have to consider the geometry, but you also have to consider speed of light effects. With mirrors you can just stick to geometry. In either case I will leave the derivation to someone with more interest (e.g. you). I am satisfied by a first-principles argument that LAT is observationally indistinguishable from SR and therefore the ball must look the same.
zenith8 said:
Let the spacecraft move at relativistic speeds in the x direction. Camera, intervening convex lens, and ball are lined up inside the spacecraft on the y-axis perpendicular to this. Have a large distance between the lens and the ball so we have parallel wavefronts coming into the lens. The ball and lens are physically distorted into teardrop shapes'.
No, they are ellipses, not teardrops.

DaleSpam said:
I would recommend using mirrors rather than lenses. Lenses work by slowing light, so not only do you have to consider the geometry, but you also have to consider speed of light effects. With mirrors you can just stick to geometry. In either case I will leave the derivation to someone with more interest (e.g. you). I am satisfied by a first-principles argument that LAT is observationally indistinguishable from SR and therefore the ball must look the same.

OK - fair enough. It's a bit boring to do it properly, I admit.

Which leaves only the survivability of being squashed to the thickness of a piece of paper. Given the incredibly delicately balanced nature of biochemical interactions - does physically changing the distance between all the molecules in this way *really* leave one not even feeling slightly queasy?

zenith8 said:
Given the incredibly delicately balanced nature of biochemical interactions - does physically changing the distance between all the molecules in this way *really* leave one not even feeling slightly queasy?
*Really, really*

Let's take an example of a sodium channel. As you know, sodium channels are size-selective. So let's say that a sodium channel is traveling sideways at a relativistic velocity such that γ = 100. That means that the sodium channel is distorted so that it is the normal height and length, but only 1% of its normal width. So, your argument is that because the sodium channel is size selective it should no longer function. However, a sodium ion is also normal height and length but 1% of its normal width, so it will still fit.

There are many other more complicated biochemical "lock and key" reactions. Since both the "locks" and the "keys" are flattened in exactly the same way they all still fit just as precisely.

Expand that same concept up from the molecular level to the organ level and you realize that everything still fits exactly how it should.

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DaleSpam said:
*Really, really*

Let's take an example of a sodium channel. As you know, sodium channels are size-selective. So let's say that a sodium channel is traveling sideways at a relativistic velocity such that γ = 100. That means that the sodium channel is distorted so that it is the normal height and length, but only 1% of its normal width. So, your argument is that because the sodium channel is size selective it should no longer function. However, a sodium ion is also normal height and length but 1% of its normal width, so it will still fit.

There are many other more complicated biochemical "lock and key" reactions. Since both the "locks" and the "keys" are flattened in exactly the same way they all still fit just as precisely.

Expand that same concept up from the molecular level to the organ level and you realize that everything still fits exactly how it should.

OK - I hear what you're saying - I can see how you could be right...

What about at 0.99999999999999999c when you get squashed to the width of an atom? Still no change in the biochemistry?

Let me check - for you does the rope break in a Bell-type spaceship paradox?

Zenith

zenith8 said:
What about at 0.99999999999999999c when you get squashed to the width of an atom?
The point is that you never get squished to the width of an atom since your atoms all get squished exactly proportionally.

zenith8 said:
What about at 0.99999999999999999c when you get squashed to the width of an atom? Still no change in the biochemistry?
You cannot get squashed to the width of an atom, because the atom will also get squashed by the same factor, so the width ratio between you and atom will remain the same. And of course, the atom will no longer be spherical (although you will not be able to see it, because your eyes will also get squashed), the potential V(x,y,z) determining the shape of the hydrogen atom will no longer be isotropic, etc. Everything will conspire so that the biochemistry will remain the same.

zenith8 said:
Let me check - for you does the rope break in a Bell-type spaceship paradox?
Yes it does.

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People in this thread might benefit from
http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v2.pdf

Last edited by a moderator:

1. What is length contraction in Lorentzian relativity?

Length contraction is a phenomenon that occurs in Lorentzian relativity, which is a theory of special relativity. It refers to the shortening of an object's length as it moves at high speeds relative to an observer.

2. How does length contraction occur?

According to Lorentzian relativity, as an object moves at high speeds, its length in the direction of motion appears to decrease from the perspective of an observer. This is due to the fact that time and space are relative and change depending on the observer's frame of reference.

3. What is the formula for calculating length contraction?

The formula for calculating length contraction is L = L0 * √(1 - v2/c2), where L is the contracted length, L0 is the rest length of the object, v is the velocity of the object, and c is the speed of light.

4. Can length contraction be observed in everyday life?

No, length contraction can only be observed at extremely high speeds, close to the speed of light. In everyday life, the effects of length contraction are negligible and cannot be perceived by humans.

5. What is the significance of length contraction in Lorentzian relativity?

Length contraction is one of the fundamental principles of Lorentzian relativity and helps to explain the observed phenomena of time dilation and the constancy of the speed of light. It also plays a crucial role in our understanding of the universe and its physical laws.

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