Terrell Revisited: The Invisibility of the Lorentz Contraction

[m4r35n357]

Wow, on reading this thread I'm glad I just did the calculations and let the computer deal with what things look like ;) However, I'm a bit puzzled at talk of weirdness in Galilean relativity. I was under the impression that Galilean relativity is characterized by infinite light speed, in which case there is no time dilation or length contraction, and no speed is sufficiently great to cause aberration effects.

What have I misunderstood??

 

[PAllen]

Wow, on reading this thread I'm glad I just did the calculations and let the computer deal with what things look like ;) However, I'm a bit puzzled at talk of weirdness in Galilean relativity. I was under the impression that Galilean relativity is characterized by infinite light speed, in which case there is no time dilation or length contraction, and no speed is sufficiently great to cause aberration effects.

What have I misunderstood??

Nonsense. Galilean relativity says nothing about lightspeed. In incorporates no theory of light. In the 1700s, the finite speed of light had already been determined. A sufficiently brilliant physicist at the time could have then computed there would be perverse visual effects for rapidly moving objects (a sphere would look like a long oval, and you would see the 'wrong' surface features compared to expectation from viewing angle). If you look at the website linked early in this thread (by AT, I believe), they have visualization of what would happen for finite light speed assuming Galilean spacetime. What is true of Galilean spacetime is that there is no way to have finite invariant speed. Thus, objects moving rapidly relative to you would depend on your frame dependent (and possibly non-isotropic) light speed. All in all, it would be much more weird and complex than SR.

[edit: as for aberration, Bradley originally derived this assuming Galilean relativity and finite light speed based on Newton's corpuscular model. For stars, so far as I know, it is still impossible to observe the high order corrections relativity makes to this formula (though the derivation in SR is obviously more sound, in that Bradley had to assume that source speed affected light speed is frame dependent.]

 

[m4r35n357]

I'm familiar with the history of light-speed measurement; I most certainly did not claim that the speed of light was thought to be infinite! Also some of us have recently discussed various parts of this article in other threads. I took from this chapter that most of the pre-relativity confusion regarding light was due to a fundamental mismatch between the properties of light (including very specifically aberration) and the Galilean transform, which was resolved only by SR in 1905. Or perhaps I'm just confusing the "top speed" and the speed of light.

 

[Ken G]

Yes, the Galilean transform can be achieved by taking the top speed to infinity, but keeping the speed of light the same. Perhaps you were not seeing that what we were talking about is what things look like, which includes the finite speed of light-- so using Galilean relativity and the finite speed of light, one could still figure out the illusions one would see (assuming you are in the ether frame). In what we might consider to be among the many great ironies of relativity (another being the constant wavelength shift of Compton scattering), the assumption of Galilean relativity, which might seem like an obvious form of relativity pre-Michelson-Morley, objects at speeds approaching c would look even weirder because they would combine rotation with stretching effects. The remarkable thing about Lorentzian relativity is that it removes any weird stretching-- so all you see is the apparent rotation. This points out something completely missing from the usual explanations about how bizarre Lorentzian relativity is! I can remember great hay being made of how relativity causes objects to look rotated, as if that was due to relativity and not just the finite speed of light. But actually, all relativity does is remove some of the distortions, it is certainly not the source of the rotation effect. That's my takeaway message from the "invisibility" of length contraction, a point that I believe PAllen was making much earlier in the thread and which is nicely demonstrated in JDoolin's final simulations.

 

[PAllen]

I'm familiar with the history of light-speed measurement; I most certainly did not claim that the speed of light was thought to be infinite! Also some of us have recently discussed various parts of this article in other threads. I took from this chapter that most of the pre-relativity confusion regarding light was due to a fundamental mismatch between the properties of light (including very specifically aberration) and the Galilean transform, which was resolved only by SR in 1905. Or perhaps I'm just confusing the "top speed" and the speed of light.

Light 'could' have had finite speed and been consistent with Galilean relativity in a different universe. Yes, I think the issue is that in Galilean relativity the only invariant speed is infinite. Thus light could have had frame dependent speed under an aether model, whence it would isotropic only in one frame, and you would have a preferred frame relative to the aether - but this need NOT be viewed as problematic any more than the speed of sound is isotropic only in a frame at rest relative to air. OR, light could have behaved per Newton's corpuscular model, when its speed would be both source speed dependent and frame dependent exactly as bullets are. The difficulties hit more and more in the 1800s was that some phenomena (e.g. aberration) seemed to fit much better with corpuscular model, while most others fit better with the aether model, and way to try to handle both were getting more and more baroque (aether drag, but then that wasn't enough). SR solved all these issues in a conceptually simple way.

 

[m4r35n357]

Yes, the Galilean transform can be achieved by taking the top speed to infinity, but keeping the speed of light the same.

That's where I lose it I think ;) I can't deal with the concept of a higher top/invariant speed than light because I don't have a mental model of physics that can handle frame dependent light speed. (OK let's not get all GR about this!).

 

[JDoolin]

I don't think you can really say there is any single Galilean construction. Once you throw out the idea of the Lorentzian model, you have to say something along the lines of what is preserved. If not an observer dependent speed of light, is it an infinite speed of light, as Galileo (I think) believed, or is it a source-dependent speed of light? Or do you wish to preserve the speed of light but remove length contraction?

If you try to have a non-finite but constant observer dependent speed of light, that not Galilean Relativity. You have to either have source-dependence, or infinite speed of light.

 

[JDoolin]

Thus light could have had frame dependent speed under an aether model, whence it would isotropic only in one frame, and you would have a preferred frame relative to the aether - but this need NOT be viewed as problematic any more than the speed of sound is isotropic only in a frame at rest relative to air.

Except it wouldn't be Galilean relativity...

 

[PAllen]

Except it wouldn't be Galilean relativity...

Do you believe the behavior of sound violates the POR? It is isotropic only in a frame without substantial motion relative to air. If an 1800s scientist viewed aether as strange form of matter (many did), they would (and did) think there was no issue with respect to the POR. For mechanics (or things not involving light) you had direct observance of POR. For light, there was a preferred frame only because of the presence of aether, just like the presence of air. Oh, and they even explored ideas of aether wind, and the the frame picked out be aether could vary from one place to another (due to motion of the aether).

 

[JDoolin]

Do you believe the behavior of sound violates the POR? It is isotropic only in a frame without substantial motion relative to air. If an 1800s scientist viewed aether as strange form of matter (many did), they would (and did) think there was no issue with respect to the POR. For mechanics (or things not involving light) you had direct observance of POR. For light, there was a preferred frame only because of the presence of aether, just like the presence of air. Oh, and they even explored ideas of aether wind, and the the frame picked out be aether could vary from one place to another (due to motion of the aether).

Okay... Good point. That would be another version of Galilean Relativity.

Once you throw out the idea of the Lorentzian model, you have to say something along the lines of what is preserved.

If not an observer dependent speed of light, is it

(1) an infinite speed of light, as Galileo (I think) believed, or

(2) is it a source-dependent speed of light?

(3) A constant speed of light embedded in luminiferous Aether.

So those would be three different models consistent with Galilean Relativity, right?

 

[PAllen]

Okay... Good point. That would be another version of Galilean Relativity.

Once you throw out the idea of the Lorentzian model, you have to say something along the lines of what is preserved.

If not an observer dependent speed of light, is it

(1) an infinite speed of light, as Galileo (I think) believed, or

(2) is it a source-dependent speed of light?

(3) A constant speed of light embedded in luminiferous Aether.

So those would be three different models consistent with Galilean Relativity, right?

Yup, those would be the variants with significant historical basis.

For the purposes talking about observability of length contraction, I therefore made explicit I was talking about a frame where light speed happened to be c and was isotropic, but that object's geometry was unaffected by motion. Thus (3), in the aether frame. (1) would be trivial, (2) would be more complex as would (3) in any frame other than the aether frame. In any case, what I proposed is the clearest way to contrast what you would see without length contraction.

 

[Ken G]

Yes, I think the natural "Galilean relativity" circa the Michelson-Morley experiment would just be what they expected when they did that experiment-- an infinite top speed, but a speed of light of c in the aether frame. That's what PAllen and I have been talking about, assuming our camera is in the aether frame where Maxwell's equations hold good. Remember, in 1900 they thought they were looking for the aether frame, it was quite a shock to essentially everyone that Maxwell's equations worked in all frames.

 

[JDoolin]

Yay!

I finally had a morning to work on my animations!

Changes:
(1) I made up an algorithm to give me a set of points in a circle.
(2) I switched to using Mathematica's "Sphere" instead of "Point" which renders a lot better. However, the sphere's here don't undergo the same transformationAnimation 1: A circle moving along within the plane of the fence at 0.866c

Animation 2: (Shown Above) The red circle is in the plane of the fence, the purple is in the plane normal to the direction of propagation. The blue is the flat plane. The perspective really plays tricks with you here, because it never really looks to the eye like the red plane is in the plane of the fence. It's much more clear in animation 1.Animation 3: Here is the animation without length contraction of the original figure. This is what you would expect to see in a Luminiferous Aether theory, where you were in the "Aether Frame" and the ball was passing through at 0.866c.

I think what's happening in animation 2, is that the figure is flattened in the direction

 

[PAllen]

Fantastic stuff, JDoolin!

 

[Ken G]

That's really cool, it totally shows that things look even weirder without length contraction. How ironic-- length contraction is invisible only if you are not expecting it!

 

[JDoolin]

Glad you liked those.

The sphere is obviously a special case. In ordinary rotation, a featureless smooth sphere looks identical regardless of how it is rotated. You could say, then, that "rotation of a smooth featureless sphere is 'INVISIBLE'" But the sphere is unique in that geometric quality. You couldn't say "rotation is invisible" in general. If there are any markings on the sphere, then the rotation can be detected by watching the markings. And the more the object differs from a perfect smooth sphere, the more obvious rotation would be.

I think, for Lorentz Contraction an analogous description could be made. If you have a spherical shape, it will appear to remain spherical, though the markings on that sphere may appear to be Lorentz Contracted, the overall shape of the sphere will remain spherical.

http://www.spoonfedrelativity.com/web_images/ViewFollowing14.gif (Animation 2, above)Since I had red blue and purple orthogonal circles all sharing a common center, I wondered what would happen if I spread out these circles so that they formed the walls of a cube, and produced two further animations.

http://www.spoonfedrelativity.com/web_images/ViewFollowing17.gif (6-sides)

and

http://www.spoonfedrelativity.com/web_images/ViewFollowing18.gif (3-sides)

I think these show that there is a noticeable distortion of shape for non-spherical objects.I also wanted to address Ken G's comment.

That's really cool, it totally shows that things look even weirder without length contraction. How ironic-- length contraction is invisible only if you are not expecting it!

I think it should also be noted that in this animation:

http://www.spoonfedrelativity.com/web_images/ViewFollowing13.gif (Animation 3, above)

... could happen in at least two different scenarios:
(1) A spherical shape passes by at 0.866c in a universe where the observer is stationary within a luminiferous ether.
(2) An oval shape (with length twice as great as its width and height) passes by at 0.866c in a Special Relativity universe (i.e. the real universe)

So if you have an oval shape, things would look exactly that weird. It's just that if you have a universe occupied almost wholly by perfectly spherical objects, (...which we do... such as stars and planets) they're not going to look as weird.

 

[JDoolin]

I had to ask, does it still work at 99% of the speed of light?

It looks like it does.
Sphere Animation at .99c
The spherical shape still looks spherical.

Cube Animation at .99c
The cube still doesn't look cubic.

 

[Ken G]

I think these show that there is a noticeable distortion of shape for non-spherical objects.

I think that might just be because the solid angle of the image is not small, so we are seeing the kinds of distortions that can happen around the edges of conformal mappings. To strictly hold to the idea that the effects are "invisible", the objects need to occupy only a small solid angle.

I think it should also be noted that in this animation:

http://www.spoonfedrelativity.com/web_images/ViewFollowing13.gif (Animation 3, above)

... could happen in at least two different scenarios:
(1) A spherical shape passes by at 0.866c in a universe where the observer is stationary within a luminiferous ether.
(2) An oval shape (with length twice as great as its width and height) passes by at 0.866c in a Special Relativity universe (i.e. the real universe)[/qute]

So if you have an oval shape, things would look exactly that weird. It's just that if you have a universe occupied almost wholly by perfectly spherical objects, (...which we do... such as stars and planets) they're not going to look as weird.

Yes, I think you have a good point there, which gibes with PAllen's "anti-boost" idea. If you don't know the shape you are supposed to be seeing, you can't tell if it has been anti-boosted (as in a Galilean universe) or if it is just seen from some angle it would be seen from in a comoving reference frame. What all this means is that there is never any way to tell if you are in a Lorentzian or Galilean universe simply by visual inspection of small objects moving at constant speeds, without knowing the intrinsic shapes of the obects you are looking at. And if you do know those intrinsic shapes, it is the Galilean universe that will show distortions, not the Lorentzian universe. I think that's a remarkable fact, though we can agree that calling it "invisibility" of length contraction isn't a great way to carry this point across.

Now of course the key question is, what is it about length contraction that cancels out time-of-flight distortions, to produce an undistorted image? Is there some reason our universe works like that?

 

[Mentz114]

Yay!

I finally had a morning to work on my animations!Animation 2: (Shown Above) The red circle is in the plane of the fence, the purple is in the plane normal to the direction of propagation. The blue is the flat plane. The perspective really plays tricks with you here, because it never really looks to the eye like the red plane is in the plane of the fence. It's much more clear in animation 1.Animation 3: Here is the animation without length contraction of the original figure. This is what you would expect to see in a Luminiferous Aether theory, where you were in the "Aether Frame" and the ball was passing through at 0.866c.

I think what's happening in animation 2, is that the figure is flattened in the direction

Terrific !

Surely one could set up an experiment to see if measuring a moving object results in a contracted reading ? Your sim predicts something photographable.

 

[JDoolin]

I think that might just be because the solid angle of the image is not small, so we are seeing the kinds of distortions that can happen around the edges of conformal mappings. To strictly hold to the idea that the effects are "invisible", the objects need to occupy only a small solid angle.

Here's a stack three balls high, moving by at .866c

http://www.spoonfedrelativity.com/web_images/ViewFollowing21.gif

More noticeable distortion in the vertical line, but the balls still appear spherical.

 

[Ken G]

Here's a stack three balls high, moving by at .866c

http://www.spoonfedrelativity.com/web_images/ViewFollowing21.gif

More noticeable distortion in the vertical line, but the balls still appear spherical.

Yes, I think that shows pretty clearly the distortion is only on larger angular scales. In a Galilean universe, distortion would be apparent on all scales.

 

[PAllen]

Terrific !

Surely one could set up an experiment to see if measuring a moving object results in a contracted reading ? Your sim predicts something photographable.

The basic issue is getting macroscopic objects at significant fraction of c relative to observer. So far as I know, this basic thing has not been achieved. Even at speeds of the fastest meteorite ever detected, you would not be able to see any of the Galilean distortion, should it exist.

 

[JDoolin]

http://www.spoonfedrelativity.com/web_images/ViewFollowing25.gif
Now the whole figure is smaller than your fist held at arm's length, and the vertical distortion is hardly noticeable.

Move in closer (about halfway) and you can see noticeable vertical distortion.
http://www.spoonfedrelativity.com/web_images/ViewFollowing24.gif

Halve the distance again, and the vertical distortion is even more pronounced.
http://www.spoonfedrelativity.com/web_images/ViewFollowing23.gif

Here is the same, but the figure only shows the balls along the fence-row.
http://www.spoonfedrelativity.com/web_images/ViewFollowing22.gifFinally, here is the "plus sign" configuration back to the longest distance again.
http://www.spoonfedrelativity.com/web_images/ViewFollowing26.gif
You can see that the vertical distortion isn't noticeable, but if you realize that all the objects lie in the plane of the fence, then the Lorentz Contraction "distortion' is very noticeable, even though the vertical distortion is gone.

 

[Mentz114]

The basic issue is getting macroscopic objects at significant fraction of c relative to observer. So far as I know, this basic thing has not been achieved. Even at speeds of the fastest meteorite ever detected, you would not be able to see any of the Galilean distortion, should it exist.

Very true. My friend at CERN said there was no chance of me borrowing the LHC one weekend when they weren't using it.

 

[PAllen]

Actually I was curious about maximum speed observed or produced near Earth for a macroscopic object. So far as I can find, no such object has been observed or created with relative speed greater than .0003 c, way way too slow for visual effects from finite light speed.

That is actually a good thing. It is worth remembering that to get a 1 gram object up to .866c would require giving it a kinetic energy greater than the atomic bomb that blew up Nagasaki (21 kilotons of TNT worth of KE per gram is required for .866c). To get a baseball going at .866 c would require giving it the KE of a large H-bomb (3 megatons of TNT).

 

[Ken G]

Yes, it is remarkable how "slow" the universe usually is at the macro level. The universe has a fundamental speed limit that individual particles (especially light, but also electrons) routinely encounter, but it rarely produces encounters between macroscopic objects at anything close to that speed limit. You'd have to look near very strong gravitational sources like black holes and neutron stars to find encounters between macroscopic objects that probe anything close to the speed limit. The possible phase space is very sparsely populated at the macro level!

 

[PAllen]

Yes, it is remarkable how "slow" the universe usually is at the macro level. The universe has a fundamental speed limit that individual particles (especially light, but also electrons) routinely encounter, but it rarely produces encounters between macroscopic objects at anything close to that speed limit. You'd have to look near very strong gravitational sources like black holes and neutron stars to find encounters between macroscopic objects that probe anything close to the speed limit. The possible phase space is very sparsely populated at the macro level!

As I recall, even for an object free falling to a neutron star surface, the speed reached is at most .5 c. Speed of 1/3 c is considered more typical of neutron star escape velocity.

 

[Ken G]

Yes, and though presumably there is a range of masses for neutron stars that push the escape speed right up to c, these are still unusual environments for macroscopic objects to ever encounter. Most of the macro objects in our universe will never encounter any other macro objects at relative speeds larger than perhaps 0.001 c or less. That includes intelligent observers, who might never pass each other at any faster speeds than that, for all we know. So we have the odd situation of a theory built to talk about encounters like 0.999 c, yet it hasn't been tested (for macro object encounters) at speeds larger than maybe 0.0001 c. We have no reason to think what works for individual particles won't work for macro systems, but JDoolin's simulations here haven't been seen with our own eyes, if you will. That may be the real reason length contraction is "invisible"-- there just aren't situations where you can see it!

 

[JDoolin]

There's "superluminal jets":
The superluminal jets probably consist of particles--not individual macroscopic objects. And high redshift objects, such as distant supernova with z>7, and CMBR with z>1000.
The high redshift objects are traveling more than .866c but straight away from us.

 

[John F. Gogo]

Yup, those would be the variants with significant historical basis.

For the purposes talking about observability of length contraction, I therefore made explicit I was talking about a frame where light speed happened to be c and was isotropic, but that object's geometry was unaffected by motion. Thus (3), in the aether frame. (1) would be trivial, (2) would be more complex as would (3) in any frame other than the aether frame. In any case, what I proposed is the clearest way to contrast what you would see without length contraction.

I would go with the trivial.