Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox

[Shubee]

It's not clear to me why the Lorentz transformation can't be reduced to the Galilean transformation by resetting clocks, rescaling distance measures and fiddling with clock rates according to the recipe on page 11 of A Derivation of the Lorentz Transformation From a Simple Definition of Time and equations (48) to (58).

 

How do you answer this riddle?

[Klaynos]

Because you'd have to "resetting clocks, rescaling distance measures and fiddling with clock rates" for every single frame you wanted to measure something in.

 

You must remember everything is relative. It'd be far far far more time consuming to do that.

[Shubee]

Because you'd have to "resetting clocks, rescaling distance measures and fiddling with clock rates" for every single frame you wanted to measure something in.

 

You must remember everything is relative. It'd be far far far more time consuming to do that.

 

How does that answer the riddle? Aren't you saying that the Lorentz transformation is logically equivalent to the Galilean transformation if one is willing to do all the work necessary to bring about a conceptual equivalence?

[ajb]

Basically there is no global notion of synchronising the clocks.

 

One possible way to synchronise the clocks is to have a light bulb exactly half way between the two clocks. Then you turn the light bulb on and each clock starts as soon as the light reaches them. Thus they appear to be synchronised.

 

However, from the point of view of a third observer, the clocks are not synchronised by doing this. Remember he will see the light travel a c in his frame. Thus (generally) the flash will hit one of the clocks before the other one as he sees it. Thus they are not synchronised.

 

Thus, we have no global notion of how to synchronise the clocks. The best that can be done it between only two specified frames. Therefore any construction like this depends on the frames employed and cannot be a relativistic construction.

[Klaynos]

What ajb said.

 

To reiterate, if you wanted to be able to measure something in any frame, you'd have to have an infinite number of differently synchronised clocks.

[ajb]

Indeed Klaynos

[Shubee]

We have no global notion of how to synchronise the clocks. The best that can be done it between only two specified frames.

 

Einstein's special relativity begins with a global notion of how to synchronize clocks frame by frame for all frames of reference. It is clear that Einstein's special relativity has a clock assigned to each point in every frame of reference. To reset a clock simply means to add or subtract a fixed amount from the stated time. The recipe given by equation 54 of A Derivation of the Lorentz Transformation From a Simple Definition of Time and equations explains how to do that at every point for every velocity v. There is no law against resetting all clocks in all frames of reference according to the recipe given.

 

Shubee

[Sayonara]

Synchronise them with what?

[Shubee]

Synchronise them with what?

 

With light signals. In 1904 Poincaré illustrated the procedure in the following way: A sends a signal at time 0 to B. B also sends a signal at time 0 to A. If in both cases the signals arrive at the same time t the clocks are synchronous.

http://en.wikipedia.org/wiki/Einstein_synchronisation

[Klaynos]

But you'd still have to do it an infinite number of times :s

[Sayonara]

With light signals. In 1904 Poincaré illustrated the procedure in the following way: A sends a signal at time 0 to B. B also sends a signal at time 0 to A. If in both cases the signals arrive at the same time t the clocks are synchronous.

http://en.wikipedia.org/wiki/Einstein_synchronisation

 

I think there might be an element of practicality here which you are somehow overlooking.

[foodchain]

Basically there is no global notion of synchronising the clocks.

 

One possible way to synchronise the clocks is to have a light bulb exactly half way between the two clocks. Then you turn the light bulb on and each clock starts as soon as the light reaches them. Thus they appear to be synchronised.

 

However, from the point of view of a third observer, the clocks are not synchronised by doing this. Remember he will see the light travel a c in his frame. Thus (generally) the flash will hit one of the clocks before the other one as he sees it. Thus they are not synchronised.

 

Thus, we have no global notion of how to synchronise the clocks. The best that can be done it between only two specified frames. Therefore any construction like this depends on the frames employed and cannot be a relativistic construction.

 

Yes but how can you know when the light reached even the surface of the clock, how did it interact with this not only that but then the sensor would have to transmute such information I imagine electronically somehow for record.

 

I think maybe some quantum dots might be able to work but then how do you equate in uncertainty with that measurement being photons are being observed? It would seem you could never know that exact time of something in that if you want my opinion.

[Shubee]

But you'd still have to do it an infinite number of times :s

 

Sure, but relativists and mathematicians have no problem conceptualizing the process.

[swansont]

Yes but how can you know when the light reached even the surface of the clock, how did it interact with this not only that but then the sensor would have to transmute such information I imagine electronically somehow for record.

 

I think maybe some quantum dots might be able to work but then how do you equate in uncertainty with that measurement being photons are being observed? It would seem you could never know that exact time of something in that if you want my opinion.

 

That's detail that is assumed to be taken care of. One is assuming perfect clocks and detection, and only worrying about effect of the frames. One problem at a time.

 

———

 

 

I think what it boils down to is this: yes, you can mathematically figure out how to make clocks agree that are in different frames. If you compare time signals and know the relative velocity, you have the information necessary to do the calculation. Conceptually, this is not that much different than a "paper clock" where you keep track of difference between timekeeping devices rather than try and physically adjust the rate (e.g. my watch runs slow, 1 second per day. If it was synchronized a week ago, it is now 7 seconds slow. Taking that into account, I know what time it is in my frame)

 

However, this is not the same as saying that we've reduced the Lorentz transformation to a Galilean one.

 

The objection here would be one of practicality, as has already been noted. You have an infinite number of frames.

[alextwo]

I have a problem with relitive motion. If a light source is moving toward me a some high percent of c, the light will not reach me any sooner than if the light were stationary. The intantanious position of the light is the only thing that matters. Light is bound by a maximum propigation rate that is not determined by v. And if I am the one that is moving, position is still the only determining factor. I don't see how to determine the speed exclusive of position. I know this probably sounds dopey, but how does all this work?

[Klaynos]

I have a problem with relitive motion. If a light source is moving toward me a some high percent of c, the light will not reach me any sooner than if the light were stationary. The intantanious position of the light is the only thing that matters. Light is bound by a maximum propigation rate that is not determined by v. And if I am the one that is moving, position is still the only determining factor. I don't see how to determine the speed exclusive of position. I know this probably sounds dopey, but how does all this work?

 

Velocities are always measured relative to something else. So the light source is moving relative to you, but in it's rest frame it's stationary and you're moving...

 

There's no absolute velocity, you can't say "John has velocity x" you have to say "John has velocity x relative to me."

 

This is lost somewhat in classical mechanics because the assumption is always that you're velocity is measured relative to earth.

[booker]

You must remember everything is relative.

 

Everything is relative?

Edited August 17, 2008 by booker
multiple post merged

[Klaynos]

Everything is relative?

 

Well really, no, the Lorentz invariants arn't in SR... but lots and lots of things are...

[booker]

Well really, no, the Lorentz invariants arn't in SR... but lots and lots of things are...

 

For a minute I thought I'd been warped into a Star Trek convention.

 

Relative, or corvariant and invariant.