Is Lorentz Contraction Specious for Photon Traversal Time?

[einswine]

bcrowell wrote:
"Lorentz contraction doesn't describe what we see. When we see things, that's an optical measurement. Relativistic optics is a whole separate subject. Lorentz contraction describes the results of the kind of elaborate surveying process that we have to undertake in order to lay out a coordinate system.

Lorentz contraction also doesn't describe the reduction in length of an accelerated object. To prove the equation for Lorentz contraction, we assume an inertial world-tube, which we then slice with a surface of simultaneity. The derivation doesn't hold if the world-tube is noninertial."

Please pardon my obtuseness but does that mean it is specious to use Lorentz contraction to explain the (non?) relation between "massless particles" and the concept of photon traversal time; or contrariwise?

My gratitude for any clarification,

einswine (the befuddled)

 

[PeterDonis]

does that mean it is specious to use Lorentz contraction to explain the (non?) relation between "massless particles" and the concept of photon traversal time

What do you mean by this? What is "the concept of photon traversal time"? And can you give an example of using Lorentz contraction to explain the relation between massless particles and this other concept?

 

[einswine]

Thank you for the reply. Elsewhere you wrote:

... Objects with zero rest mass, like photons, are fundamentally different, physically, from objects with nonzero rest mass, like us. The concepts of "elapsed time" and "simultaneous events" only make sense for the latter types of objects; they simply do not have any meaning for the former types of objects. The fact that you can do a mathematical process that looks like taking a limit as v approaches c does not mean that mathematical process necessarily tells you anything meaningful about physics.

Say, from my frame of reference, a photon is emitted at point `a and absorbed at point `b and the distance between `a and `b is `x. Can one take the view of the photon and say that the distance to be traveled, `x, is 0 because the length to be traversed is described by the Lorentz contraction and the photons velocity is c?

Again, thank you and I hope that is more intelligible.

einswine

 

[jtbell]

Can one take the view of the photon

No. In order to do so, there needs to exist a reference frame in which the photon is at rest, and there is no such frame:

https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/

 

[bcrowell]

I don't understand how the material quoted from me in #1 relates to the subject of the question.

 

[einswine]

bcrowell: I apologize but if you don't understand then I must be totally mistaken about the meaning and application of the Lorentz contraction. Still even knowing that is helpful. So thank you.

jtbell: And thank you for the answer.

If I may bother either of you and ask two related questions. Many years ago ( >45 ) I read a book that explained the Lorentz contraction as the result of a rotation of one Galilean frame with respect to another when modeled in Minkowski spacetime. At 90 degrees the rotated frame represented a velocity of c. Does that make any sense? And what do I need to read to really understand either case?

In any case my thanks for putting up with dumb questions.
.

 

[PeterDonis]

At 90 degrees the rotated frame represented a velocity of c.

First of all, if any angle is associated with a velocity of $c$, it would be 45 degrees (the angle that the worldlines of light rays are at on a spacetime diagram), not 90 degrees. But the "angles" involved in Lorentz transformations are hyperbolic angles, not ordinary angles, and they have infinite range (not 360 degrees).

Second, there is no Lorentz transformation that can "rotate" a timelike vector (something moving at less than $c$) into a null vector (something moving at $c$). As above, the rotation involved is hyperbolic rotation, not ordinary rotation; it "rotates" timelike vectors along a hyperbola. But null vectors--light rays--lie on the asymptotes of the hyperbola, and no amount of movement along a hyperbola will ever reach the asymptote.

In short, either you are misremembering what the book said, or the book wasn't a very good one.

 

[einswine]

PeterDonis, thank you.

 

[Herman Trivilino]

If I may bother either of you and ask two related questions. Many years ago ( >45 ) I read a book that explained the Lorentz contraction as the result of a rotation of one Galilean frame with respect to another when modeled in Minkowski spacetime. At 90 degrees the rotated frame represented a velocity of c. Does that make any sense? And what do I need to read to really understand either case?

Likely it was Spacetime Physics by Taylor and Wheeler. It's now available in a 2^nd edition, although I've read only the 1^st edition. You can pick up a copy of either on Amazon at very little cost. It's a short and excellent introduction to the topic, although it sounds like you remembered it a bit wrong. There's a pair of rotated frames, each consisting of two axes that are at right angles to each other. Observations in one frame are compared to the same observations made in the other frame.

The analogy is then made between that rotation in Euclidean two-dimensional space and the Lorentz transformation, presented as a hyperbolic rotation in Lorentzian two-dimensional spacetime.

That book, by the way, makes clear that what we see is different from what we observe. It treats the notion of observation in an unambiguous way that makes its meaning clear.

 

[PeterDonis]

There's a pair of rotated frames, each consisting of two axes that are at right angles to each other.

Yes, but, as you point out, this is only an analogy; it's a Euclidean rotation, not a hyperbolic rotation. And the two kinds of rotations don't have all of the same properties. That's why you always have to be very careful with analogies.

 

[einswine]

Likely it was Spacetime Physics by Taylor and Wheeler.

I now think the book might have been The Evolution of Scientific Thought by A. d'Abro. I've ordered a copy and am looking for a cheap used version of the Taylor book.

Many thanks,

einswine

 

[Herman Trivilino]

Yes, but, as you point out, this is only an analogy; it's a Euclidean rotation, not a hyperbolic rotation. And the two kinds of rotations don't have all of the same properties. That's why you always have to be very careful with analogies.

Yes, but Edwin Taylor and John Wheeler do a masterful job of being careful with the analogy. The book was published, I think, about 50 years ago, and it has withstood the test of time. It was one of two textbooks used in a course I took in the 1970's and just two years ago I worked my way through it thoroughly.

Interesting story, in and of itself, of the collaboration between the two co-authors. Taylor's account of it is easily found on the web.