Short question about length contraction

[Doc Al]

Should I read this book? Namely, It's About Time: Understanding Einstein's Relativity by N. David Merman who states on page 63

Despite that mysterious-sounding quote, the book is good and I recommend it. (Quote the entire paragraph and it will appear a bit less mysterious.) Laymen who want a good taste of relativity and who aren't afraid of a little algebra will get a lot out of it.

 

[losk]

Given that Michelson-Morley experiment lies at the heart of all this, does anyone know if it was every done while apparatus was in motion relative to Earth? As opposed to sitting in the lab.

 

[Simon Bridge]

Despite that mysterious-sounding quote, the book is good and I recommend it. (Quote the entire paragraph and it will appear a bit less mysterious.) Laymen who want a good taste of relativity and who aren't afraid of a little algebra will get a lot out of it.

Always remembering that anyone can be quoted out of context, even highly qualified people can write rubbish, and there is no cause so worthy there are no idiots supporting it

Given that Michelson-Morley experiment lies at the heart of all this, does anyone know if it was every done while apparatus was in motion relative to Earth? As opposed to sitting in the lab.

That would be hard to do - the apparatus is easily messed up by vibrations. What would you expect to be different?

Note: The MME is not "at the heart of this" in the sense that if the experiment were overturned somehow then relativity would be wrong. SR and GR are accepted on a preponderance of evidence from many clever and concerted disproof-attempts over many years. It was a key experiment, but not the only one.

 

[losk]

Always remembering that anyone can be quoted out of context, even highly qualified people can write rubbish, and there is no cause so worthy there are no idiots supporting it

That would be hard to do - the apparatus is easily messed up by vibrations. What would you expect to be different?

Note: The MME is not "at the heart of this" in the sense that if the experiment were overturned somehow then relativity would be wrong. SR and GR are accepted on a preponderance of evidence from many clever and concerted disproof-attempts over many years. It was a key experiment, but not the only one.

MM was designed to prove the stationary aether, and it succeeded in disproving it. However, it says nothing about the light medium that moves just like bodies do, attracted to them by gravity, just like satellites are. Performing MM in a motion relative to Earth surface would clear that up. Or could bring up something entirely unknown. And in general, performing experiments that we're sure have nothing to prove can be illuminating, as history suggests. Most theory-overturning events happened when people thought they were doing one thing, but they actually did another. MM being a perfect example of that. I guess I am just surprised that people conducted many stationary MM experiments, but none in motion. It seems like they were hitting the same nail on the head, instead of trying another one... That's all, just odd. It can be done. Satellites in orbit move at 3+ km/s relative to Earth without vibrations, so it should be no problem to do...

If MM were overturned, that would not mean SR and GR are dead, but it would certainly mean that they are not entirely correct, and that we have to look for a better theory. Much like Newton's physics isn't dead by means of SR and GR, but isn't entirely correct either.

 

[Simon Bridge]

The GPS system is like a continuous, world-wide Michelson-Morley experiment, much more precise than the original experiment, and uses satellites at different altitudes as well as ground stations also at different altitudes. If MM is wrong, then GPS navigation is also wrong.

It we got different results from some satellite measurement we'd look for some influence in orbit that is throwing the experiment off rather than look to modify SR and GR itself. That's how good the theory is. It's like if you dropped your pen and saw that it went sideways instead of down ... would you need to modify Newtonian gravity, or would you look for some additional effect knocking the pen to the side?

Anyway - this is off topic.
You are being copeously answered in another thread.
https://www.physicsforums.com/showthread.php?t=765235

 

[HALON]

I've started reading Mermin's It's About Time. Damn though...he doesn't cover rotations, which is what the ordinary clocks on the book's cover do. I suspect this may be my last post for a while.

Meanwhile, Brian Greene's book (which I haven't read in years) put this idea into my head "an object's motion is shared between the dimension of time and the dimension of space". So the diagonal path of light in the Michelson Morley experiment "dilates" by a factor of γ in the dimension of time. It "dilates" because γ=1/(1-v^2/{c^2})^{1/2} Therefore the photon's path in the dimension of space must "contract" by the reciprocal factor 1/γ. Well, knock me out. Because when I simplified the equation for the double diagonal path as 2/(c^2-v^2)^{1/2} (from Greene's end notes for the "mathematically inclined reader" LOL) and called it a radius, I found the "clock face" obeyed the same rules, because its circumference divided by the area equalled the length contraction factor 1/γ, and the area divided by the circumference equalled the "time dilation" factor γ. Try it out, it's fun.

Why then is the slowing of clocks called "time dilation"? Maybe because the clock, um, expands in time while its energy remains invariant? (Yep, the big hand can't go faster but the circumference is longer). So its mass expands in time too? Didn't I read that old fashioned relativistic mass increases ("dilates"?) by mγ with increasing speed? Isn't that...hmmmm... coincidental to the slowing of clocks when a body's mass increases in space? It's kind of "equivalent". What does that teach us about mass? For me, this is the missing chapter in every relativity book I've read.

 

[PeterDonis]

Brian Greene's book (which I haven't read in years) put this idea into my head "an object's motion is shared between the dimension of time and the dimension of space".

This is another of those Brian Greeneisms that, while it isn't wrong, causes a *lot* of misunderstandings. From the rest of your post, I think it is leading you in a direction that is going to increase your confusion, not decrease it.

(Btw, here's a suggested heuristic for spotting pop science things that, while not wrong, are likely to cause misunderstandings if you're actually trying to understand the science: does the author actually use the model he's presenting in the pop science book, in his research papers--the ones that get peer reviewed? If the answer is "no", which, AFAIK, it is for the Brian Greene model you refer to, that's a big red flag, IMO, that the pop science presentation is going to cause confusion. If the author himself isn't using it in his own research, why is he trying to pawn it off on lay readers?)

 

[HALON]

This is another of those Brian Greeneisms that, while it isn't wrong, causes a *lot* of misunderstandings.

In fairness to Brian Greene, the sharing of motion between dimensions was his "heuristic". The rest of the model was my take. The mathematics agreed neatly, so actually I'm not confused at all. It seems others are. So I'll retire from this thread to reflect.

 

[ghwellsjr]

I think you have come to a wrong conclusion. Are you thinking that time stops for a photon, so that the time of each tick of a clock (so to speak) propagates outward in all directions at the speed of light like an expanding soap bubble? Is that what you're thinking?

I'll put it in terms of the Doppler effect. When the distance between the signal emitter and the receiver widens, more wavelengths will fill the wider distance which causes the receiver to perceive them as a lower frequency as the signal is "stretched" over a longer distance. And the converse is true when the distance shortens.

It sounds to me like you're trying to describe how conventional non-relativistic Doppler works where the waves are traveling in a medium at a relatively slow speed and we can ignore any Time Dilation for the moving receiver.

But when it comes to light signals, in addition to the frequency shift due to the receiver encountering a differing number of waves, there is also an additional frequency shift due to Time Dilation that is dependent only on the speed of the receiver according to the rest frame of the signal emitter. It doesn't matter what direction the receiver is moving, it has the same Time Dilation independent of direction or any acceleration that causes just a change in direction.

But in the very different circumstance of one body rotating about another body, the radial distance between them is constant. Now the central body receives a lower frequency, while the rotating body receives a higher frequency. This is called the transverse Doppler effect.

Yes, in this case, there is no conventional Doppler but the rotating body is subject to Time Dilation according to Special Relativity. The slowing down of the clock of the rotating body is the reason why it detects a Doppler shift of a higher frequency and why it emits a lower frequency that is detected by the central body as a lower frequency. It's not any more complicated than that.

The rest of your post has nothing to do with Transverse Doppler.

So rather than the signal filling a longer or shorter distance, in this situation the signals fill a larger or smaller time volume. I don't know how else to picture it. (You can draw it quite simply using each clock "tick" as the radius of the time bubble, and the Lorentz transformation is the same). Anyway, Einstein said a body's acceleration is equivalent to a gravitational field- which is associated with mass. So if you use e=γmc^2 you can describe the bubble's increase in relativistic mass and come to an analogous conclusion regarding a body's relative increase in mass. Relative and relativistic mean different things. To illustrate the idea, see this image from Wikipedia

http://en.wikipedia.org/wiki/Gravitational_redshift#mediaviewer/File:Gravitational_red-shifting2.png

A body with greater relative mass receives a higher frequency of wavelengths, just as a body with greater relativistic mass does. You can re-imagine the larger sphere representing the rotating body compared to the central smaller sphere. But if you do so, the sphere's shown are now filled with relative time, not relative mass. (Or you can say each is composed of different relativistic mass, but not necessarily of different relative masses.).

Einstein introduced the equivalence principle. But equivalence does not mean identical. As I'm trying to convey, relativistic mass is not identical to relative mass. But as long as this distinction is clear, then it's OK to say a body's relativistic mass increases while its relative length contracts, although it's kind of using mixed terminology. Maybe that's why the term relativistic mass is avoided nowadays. In my early readings it was difficult to understand why writers would say the relativistic mass would increase, while elsewhere they would say it's length contracted. The distinction between relativistic and relative were not clear in the textbooks I read.