1. ## Special relativity question

It is obvious from Einsteins postulate (light travels at c no matter what the velocity of a frame of reference is) that in order for all observers to measure the speed of light as c, then time must slow down on a frame moving with respect to the observers frame. Thats fairly intuitive when you accept that the value c is independent of velocity.

What has always troubled me about relativity is that why is there a need for length contraction at all if time dilation is enough to explain it? Teachers often say that time dilation accounts for most of the reconcilitation between frames but not all of it and that the remainder is accounted for by length contraction.

Can somebody explain (preferably with as little mathematics as possible), why length should contract as well as time dilate when the latter should be enough? Fair enough we now know that contraction does occur experimentally but from where is this concept derived in the theory?

2. Because either viewpoint is valid, you always need both length contraction and time dilation, especially when you look at two observers in relative motion to each other.

Muons from space fall to earth as viewed by Earth observer. They travel much further than their speed (near c) times their laboratory-measured lifetime, so they clock instead of taking $\tau$ per half-life takes $\gamma \tau > \tau$.

Muons are born in the upper atmosphere of Earth as seen by themselves. Of course they measure the speed of the Earth at close to c and won't reach the distance if the distance was as their Earth friend thinks, L. But the muons measure $\gamma^{-1} L < L$ and they expect that distance to pass them by at close to c before their time $\tau$ is up.

The relative speed $|v| = \frac{\gamma^{-1} L}{\tau} = \frac{L}{\gamma \tau } \approx c$ is the same, but different observers see different lengths and times.

3. Here's another way to explain it.

Consider the classical Light clock experiment: The light bounces back and forth between two mirrors in a path that is perpendicular to the Relative motion.

Time dilation is all that is needed to explain this situation.

However, what if we add a second set of mirrors, so the that the light bounces back and forth parallel to the relative motion, like this:

Something's wrong, the up and down light makes a complete circuit in the moving clock, but the parallel light doesn't.

However, if the the light clock length contracts we get this:

and all is right with the world again.

You will also note that the parallel light takes longer going in one direction for the moving clock than in the other.

What his means is that you also have to include the Relativity of Simultaneity to make sure that the speed of light in constant for all observers.

4. Nice animation! Can this situation be explained by the number of parameters we need to tune to get everything in order (i.e., number of parameters in the coordinate transformation between frames)? For instance, time dilation alone is not enough because there are more than one parameter etc.

5. I copied much of your post to

Its a thread that I started to teach beginners the basics of special relativity.

I hope there isnt any trouble with copyright or anything.

6. Originally Posted by John Connellan
It is obvious from Einsteins postulate (light travels at c no matter what the velocity of a frame of reference is) that in order for all observers to measure the speed of light as c, then time must slow down on a frame moving with respect to the observers frame. Thats fairly intuitive when you accept that the value c is independent of velocity.

What has always troubled me about relativity is that why is there a need for length contraction at all if time dilation is enough to explain it? Teachers often say that time dilation accounts for most of the reconcilitation between frames but not all of it and that the remainder is accounted for by length contraction.

Can somebody explain (preferably with as little mathematics as possible), why length should contract as well as time dilate when the latter should be enough? Fair enough we now know that contraction does occur experimentally but from where is this concept derived in the theory?

Lets get something clear here. Do you think or does anyone here think that in length a physical object actually becomes physically shorter, or is it just an appearance?

7. Originally Posted by mark 8
Lets get something clear here. Do you think or does anyone here think that in length a physical object actually becomes physically shorter, or is it just an appearance?
It's relative. To the outside observer, it physically gets shorter.

8. Originally Posted by mark 8
Lets get something clear here. Do you think or does anyone here think that in length a physical object actually becomes physically shorter, or is it just an appearance?
Tricky to answer. "Becomes" might be the wrong word. "Is" might be better.

It's not just the motion of the object that affects the measured length, but also the motion of your measuring device as well.

So, if you measure the length of an apparently stationary object by ataching a ruler to it, you'll get the object's proper length.
If that same object is measured by someone flying past at high speed, they will measure a shorter length*.
And if you measure the object against a ruler flying past at high speed, you will measure a longer length*.

(The difference between these two cases is in how you decide when to look at each end of the object as the ruler flies past.
The flying-past observer seems to be using unsynchronized clocks. They seem to compare the trailing end of the ruler to that end of the object before they check the other end of the ruler against the object.
The funny thing about this is that you can't tell or sure which clocks are synchronized and which are not.)

One thing is certain:
Measuring the length of moving objects is tricksy, and needs clocks as well as rulers.

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