The distance-dependent nature behind lorentz time-transformation

1. Oct 4, 2005

Twukwuw

The distance-dependent nature behind lorentz "time-transformation"...

The Lorentz transformation give sush an equation:
t = y(T-ux/c^2).

t = "time-point" where an eventZ happens in a moving frame
T = "time-point" where the event Z happens in a stationary frame.
u = relative velocity.

I am wondering that why the t is dependent on x. Somebody tell me that the distance-dependent is an outcome of the Lorentz transformation (i.e. we have derived it, and we accept it, EVEN THOUGH we really dont understand the MECHANISM in the PROCESS in which nature work( or how Lorentz transformation work))
In my opinion, the answer given by that guy is somehow make me uncomfortable, it is just like when we apply a programming language( let's say C++), we just need to KNOW THE RULES, but no need to UNDERSTAND how the mechine language (or the computer) operate. In other words, we use it and treatit as a "black box."
How can we learn and understand nature in this way?

Can anybody tell me HOW TO INTERPRET the distance-dependence nature in the Lorentz transformation, for t = y(T-ux/c^2) ?

Twukwuw

2. Oct 4, 2005

Staff: Mentor

This is the "relativity of simultaneity." Two events at different locations, that are simultaneous in one inertial reference frame, are not simultaneous in other inertial reference frames.

Or, to put it another way, two clocks at different locations, that are synchronized in one inertial reference frame, are not synchronized in other inertial reference frames.

3. Oct 4, 2005

Sherlock

I'm just a hobbyist with a superficial knowledge of relativity. With that in mind, here's how I'd make sense of your considerations.

To learn and understand the *deeper* (that is assuming that there are phenonemological levels or scales of behavior fundamental to and hidden from our normal sensory experience) nature of reality, it's first necessary to observe. catalog, and relate what can be dealt with directly.

Science progresses along those lines. For now there's just no comprehensive, *qualitative* understanding of the deep nature of gravity fields, em fields, etc. In a hundred, or a thousand years, assuming continued technological progress, who knows. It's with the hope that the spaces between the macroscopic dots will be filled that scientists proceed with basic research.

That the "t is dependent on x", and that relativistic theories make correct predictions suggests that there is something physically correct about the Lorentz contraction. Systems change, and the periods of their oscillators change, as their states of motion change.

If you have systems A (eg.,earthbound twin) and B (eg.,travelling twin) which are both part of system C (earth), then as, eg., B moves relative to C while A doesn't, then during this motion B has undergone some changes that A hasn't undergone. One aspect of this is that the values of B's time and distance units are different (in a way defined, at least on one level, by the Lorentz transformations) as it moves relative to A wrt C.

On reformation of the original ABC system (eg., when the traveller lands back on earth), then A and B's time and distance units return to their original state (we're assuming that A and B's 'clock periods' are synchronized, or equal, when A and B are co-moving wrt each other and C). So, the physical changes (eg., length contraction) due to relative motion aren't cumulative. However, the indexing of some aspect of those physical changes (eg., counting the periods of some oscillator in B that was previously synchronized or equal to a similar oscillator in A) is cumulative.

A continual (and symmetric from a purely kinematic view of A from B, or B from A), but not necessarily permanent, effect of increased relative velocity are time dilation proportional to length contraction (and mass increase?), etc. A permanent effect (eg., on twin B landing back on earth, or the reformation of the original ABC system) of B's relative motion is that his oscillators will have oscillated fewer times than A's did during the period of B's relative motion.

The distance-dependent nature of Lorentz contractions has to do with the fact that distance units are defined wrt a certain (more or less arbitrarily chosen convention) number of oscillations of some (as regular and rapid as technology allows) oscillator. So, it follows that if an oscillator's period increases (wrt a previous state) as it accelerates (and is therefore different for different velocities relative to a previous state), then the value of the distance unit that the oscillations define will also change and be different for different relative states of motion.

Last edited: Oct 4, 2005
4. Oct 4, 2005

pervect

Staff Emeritus
There was another long thread on this somewhere recently. Anyway, it's fairly easy to see that given that the speed of light is the same for all observers, the relativity of simultaneity is necessary.

This observation doesn't establish the exact form of the Lorentz equations without more analsyis, but it does show that some such term is needed, because events that are simultaneous in one frame are NOT simultaneous in another frame.

Note that the constancy of the speed of light ultimately came from experiment, and was a surprise, not something that people expected to happen.

Anyway, one of the usual examples is that you have a railroad car moving east-west at a large velocity. In the railroad care frame, at some time T=0, a flashbulb exactly in the middle of the railroad car goes off.

Meanwhile, you have an observer, standing outside the railroad car, who has a flashbulb that goes off at the same time and the same place.

Because the speed of light is constant to all observers and independent of the motion of the source, the light from these two flashbulbs travel exactly the same path.

In the railroad car frame they strike the walls of the car simultaneously - i.e. the two events (light strikes left wall) and (light strikes right wall) occur at the same time.

In the stationary frame, these two events cannot be simultaneous given that the speed of light is constant, because the walls of the train are moving in that frame.

For diagrams see "Experiments and the relativity of simultaneity"

http://www.iop.org/EJ/article/-ffissn=0143-0807/-ff30=all/0143-0807/26/6/017/ejp5_6_017.pdf

or here on PF,

https://www.physicsforums.com/showpost.php?p=767151&postcount=42

(the rest of the thread might be relevant too, but it's _VERY _ long and rambles a lot).

There are a couple of different ways of setting up the thought experiment - the one I mentioned was from the paper (and is supposed, according to the authors of the paper, be easier to grasp) - the PF articles chose the other approach. If you read the first link above, you'll see both approaches described.

5. Oct 5, 2005

Mortimer

Although not mainstream physics, Euclidean relativity gives an intuitive and visual explanation for the distance dependent nature of t. See the section "Length in space and length in time" at this page.

6. Oct 7, 2005

Perspicacious

The person who told you that there is no known MECHANISM for the Lorentz transformation and time dilation told you the truth.

But physics is a black box. Do you really expect to learn universe engineering from physicists and be able to understand everything, from a few childish principles?

If you can't comprehend what is known, how on earth are you going to be able to comprehend what isn't known?

http://www.everythingimportant.org/relativity/