# Why are the effects of Time Dilation permanent but Length Contraction is Not?

1. Dec 20, 2011

### dfaullin

This question is in regard to special relativity.

From my rudimentary understanding, concerning the twin paradox, if one twin leaves traveling near the speed of light and returns, he will find himself younger than his twin who stayed behind. Hence, the effect of time dilation is permanent.

However, I have never read anywhere that the traveling twin's length will also be permanently adjusted due to length contraction.

How is it that one Lorentz transformed aspect remains while the other one vanishes upon the traveling twin's return?

I apologize if this question has been asked before. If so, and you know where to find the responses, please point me in the right direction.

Thank you!

~Dylan

2. Dec 20, 2011

### Staff: Mentor

Time and distance aren't the same type of dimensions and they work differently. You can walk down the street and come back to where you started, but you can't move forward in time, then go back to the time you started at. So time dilation's effects are cumulative.

3. Dec 20, 2011

### PAllen

Welcome to Physicsforums.

This question has been asked, but it is a good question. I don't know of an FAQ to point you to, but I am happy to answer this.

Note that accumulated time for one twin is less, but that once the twins are together, the rate of their clocks is immediately the same. Similarly, the twins height is immediately the same when they re-unite. Age is the sum of moment to moment 'passage of time'. What would be needed for distance would be a measure of moment to moment 'passage of space'. There is nothing as convenient as a clock to measure this. However, if the non-inertial twin measured the integrated distance traveled by the inertial twin, and vice versa, the non-inertial twin would conclude the inertial twin had traveled less distance (compared to what the inertial twin measures for the non-inertial twin). In this sense, there is an analogous 'permanent' length contraction effect for the twin scenario.

4. Dec 20, 2011

### dfaullin

Ah, very interesting. The traveling twin will have measured a smaller distance relative to the Earth-bound twin's measurement. That helps me feel better about it.

Because of this, will they both measure the same velocity for the traveling twin (since v=d/t)? In other words, does the smaller distance measured by the traveling twin occur in the same proportion as the smaller time measured by the traveling twin?

Also, thinking of time as accumulating (whereas length does not) helps me visualize the situation better too, so thank you for the prompt replies on the matter. I've been racking my brain on day on this stuff and it feels good to finally feel like I've accomplished something (a better understanding).

One last question: While the amount of time that passes for the traveling twin will be smaller than what is measured by the Earth-bound twin, each twin in his/her own frame does not feel time pass any differently. I guess I'm having trouble understanding how the clocks will show different times whereas the twins feel time pass at the same, normal rate in their own frames.

5. Dec 20, 2011

### PAllen

Yes.
If all processes (clocks, biological aging, chemical processes etc.) are all 'slower' by the same amount, everything seems normal. How can you detect anything out of the ordinary?

6. Dec 21, 2011

### ThomasT

Because it applies to different velocities (speeds). An oscillator's frequency is, apparently, dependent on its speed. So, when the travelling twin is reunited with the earthbound twin, then their clocks (and their biological oscillators) are 'keeping time' at the same rate. But while the travelling twin was travelling at a rate of speed exceeding the earthbound twin, then the periods of his clock and biological oscillators were increased. And that increase was cumulatively, and irreversibly, recorded as a slowing of time and aging.

7. Dec 21, 2011

### dfaullin

It just seems like 1 second for Twin A is the same as 1 second for Twin B. What is different is the time that Twin A sees passing for Twin B.

I think I just need to think some more about it. I need to reconsider how I view the situation in light of thinking about the distance of the traveling twin being literally less than what Earth-bound twin measures.

8. Dec 21, 2011

### Staff: Mentor

Actually, time dilation and length contraction are the same in this regard. A pair of ticks on a clock measures a uniform duration between the ticks. A pair of ticks on a rod measures a uniform distance between the ticks. While the twins are travelling both kinds of ticks are distorted. When they return to rest both kinds of ticks are undistorted.

The difference is simply that we typically keep a running total of the ticks for a clock but not for a ruler. The device which we use to keep a running total of ticks for a ruler is called an odometer. The device which we use to measure ticks of a clock without keeping a running total is called a metronome. So, the proper comparison is between clocks and odometers or between rulers and metronomes.

9. Dec 21, 2011

### harrylin

Actually a metronome produces a beat; we measure it with a frequency meter. But indeed, the comparison is between clocks and odometers as well as between rulers and frequency meters.

10. Dec 21, 2011

### dacruick

I like this explanation. I think it is useful to make a direct comparison from length contraction to time dilation. If we look at age as the sum of all of the ticks on a clock, then for our length contraction to show its effects in the same way, we would have to define height as the sum of the individual's length over time. It sounds absurd right? I agree...

It is useful to treat time in this way (cumulatively), and it is not useful to treat height like this. Yet I do not think that they intrinsically differ. Hmm...well, those are just my thoughts.

11. Dec 21, 2011

### Elroch

There's another way to look at it, as well. With time dilation what happens is that two people keep a record of time and their record differs in the end. The same would happen with distance if it was performed in a certain way. Suppose A goes to Alpha Centauri and back, and B stays on Earth. Both measure the apparent distance they travel relative to each other.

When they compare distances at the end, B says the total distance was just over 8 light years, but A says it was actually a lot less. Of course we know the reason that for A the distance to his destination was contracted when he was going fast.

12. Dec 21, 2011

### dacruick

I have a question about this. Is it the distance between the planets that is contracted or the length of the spaceship that's contracted? I always assumed that both were possible, it just depended on the frame of reference. In the case that the distance between the planets is contracted, that then implies that the spaceship was stationary, and that both Earth and Alpha Centauri were moving with respect to the spaceship. This then also implies that the observer on Earth was experiencing time dilation to a greater degree than the observer on the spaceship.

Is my recollection of the events accurate?

13. Dec 21, 2011

### ghwellsjr

Remember, length contraction occurs only along the direction of motion, so unless the traveler is laying down, it's not his height that is contracted but his thickness front to back.

14. Dec 21, 2011

### ghwellsjr

Yes.

Just remember that in any Frame of Reference, nothing is unusual for stationary observers/objects/clocks--it's only those things that are moving in that FoR.

So in the spaceship's FoR, the spaceship is normal but the distance between planets is contracted. In the planet's RoR, the spaceship is contracted.

Also, remember that two observers in constant relative motion directly towards or away from each other will always measure that relative speed to be the same, independent of any FoR and independent of any means by which they make the measurement.

15. Dec 21, 2011

### dfaullin

Ah, I just made a connection (in my mind)!

Light takes the shortest path through space-time. Thus, the closer you are traveling at the speed of light, the shorter your distance will be.

But now I don't understand this: You say that the distance measured by Earth-bound twin will be greater than the distance measured by traveling twin. How does Earth-bound twin measure that distance? Using a photon? Then shouldn't that measurement give the shortest possible distance, since light is taking the shortest path to the star and back?

Thanks for the great responses.

It also helps to think that the stationary observers will notice nothing unusual ever, only those things which are moving that will exhibit strange behavior. I wish I would have used this forum sooner. I bet I would have done better in Physics when I was in college. :)

16. Dec 21, 2011

### dacruick

So if the person travelling to the other planet measures the distance to be quite small due to length contraction, and the person on earth measures that distance to be large, how can they both measure the same speed relative to each other? Is this reconciled using time dilation?

I can understand how the spaceship travelling at lets say 0.9c has it's length contraction balanced out by the time dilation, but in what way does the spaceship observe a person standing on earth.

17. Dec 21, 2011

### ghwellsjr

The Earth-bound twin can use light to measure the distance to the planet. He starts a timer when he sends a flash of light (it might actually be a radio signal as used in radar) which reflects off the planet and stops the timer when he receives the return signal. The distance is one half of the time interval times the speed of light. Even though the light take the shortest path, it still takes time for it to make the trip.

18. Dec 21, 2011

### ghwellsjr

The spaceship can measure the speed that the person standing on earth is traveling away from him by observing the Relativistic Doppler of a signal coming from earth and calculating the speed. It will be the same Doppler and therefor the same speed that the earth observer will measure of the spaceship.

19. Dec 21, 2011

### dfaullin

Okay, imagine this scenario.

An observer on Earth is going to measure the distance to Alpha Centauri in two ways. First, he will send a photon and calculate the distance as 1/2 ct.

Then, he will send an odometer to Alpha Centauri traveling near the speed of light (say .9c) and have it return and will take 1/2 of the odometer reading.

Which distance will be shorter?

~Dylan

20. Dec 21, 2011

### PAllen

Well, there really is no such thing as an odometer to measure travel through empty space. This is why, in my initial answer, what I posed for each twin to measure is the travel distance of the other, as they measure it. So let's say the twin A remains on earth and measures B traveling 4 lightyears away (to some star) and back - total distance 8 ly. Assume B has traveled there at .9c. B measures A traveling away and back to B. The distance B measures for A's trip will be approx 3.5 light years (assuming 'instant turnaround'). However, as soon as B stops at earth again and measures the distance to the star, they get 4 light years. So they say 'whoa, this relativity can be really strange'. Yes, it can.

As to how B can measure A (and the sun) distance as A travel's away and back (per B), any valid method will do (in our situation of constant speed). For example, they could use parallax with the aid of companion traveling along with them at some distance away. This modest distance (to the companion) could also be measured any convenient way (rulers, light travel time, it doesn't matter).