# Time Dilation question

1. Jan 20, 2009

### Charlie G

I was wondering if time dilation was simply a consequence of the speed of light being the same in all reference frames, or is it necessary for light to be a constant? Most books use the light clock on a train thought experiment to show time dilation, which makes it seem as if time dilation is just a consequence of lights constant speed, but I just want to make sure.

2. Jan 20, 2009

### JesseM

I don't understand the distinction you're making between "the speed of light being the same in all reference frames" and "light [being] a constant"--can you elaborate on what the second one means, if "constant" doesn't just mean "constant speed"?

3. Jan 20, 2009

### Charlie G

Yeah, I mean constant speed, sorry about that

4. Jan 20, 2009

### JesseM

But then what do you mean by asking if time dilation is "a consequence of the speed of light being the same in all reference frames, or is it necessary for light to be a constant"? It sounds like you're giving two options here, but I don't see how the option after the "or" is different from the option before it...are you just using "or" to mean a different way of phrasing the same question? If so, I would say the speed of light being constant is not quite sufficient, because the light clock derivation also depends on the assumption that in the frame where the clock is moving there is no length contraction (or length expansion!) along the vertical axis of the clock which is perpendicular to the direction of motion.

5. Jan 21, 2009

### Charlie G

I mean, do I need time dilation to explain lights constant speed. Like, if someone asked me how does light move at the same rate in all frames, would I have to say time slows down, and thats one thing that causes it to be the same speed in all frames. Or after explaining lights constant speed(which I can't do lol) would I then say, and because of lights constant speed, time will slow down for someone moving relative to you.

Sorry if my question is a bit vague. Im having trouble with wording it.

6. Jan 21, 2009

### Fredrik

Staff Emeritus
You don't need anything to explain that. The standard approach is to consider that a postulate. If you postulate a few more things, you can derive the whole theory, including time dilation. But you can probably drop the speed of light postulate and replace it with something else. The time dilation formula may be sufficient, but I haven't really thought that through.

The standard approach is to prove that if the speed of light is the same in all frames and the frames have the properties we expect them to, then there's time dilation and lots of other interesting stuff.

7. Jan 21, 2009

### thenewmans

The idea of time dialation came from the constant speed of light. So I wouldn't say one caused the other. They just are. But I would say that one idea caused the other idea. Does that help? Have you heard of the greatest failed experiment? The Michelson–Morley experiment? From that, people decided to think of the speed of light as constant. And that's when Lorentz came up with time dialation. Einstean combined the constant speed of light with the Principle of Relativity to come up with SR. The Principle of Relativity is that the laws of physics stay the same reguardless of speed.

8. Jan 21, 2009

### JesseM

As Fredrik says, the normal strategy is to derive time dilation and length contraction from the two postulates of relativity, the first of which says light has the same speed in all inertial frames, the second of which says all the laws of physics work the same in all inertial frames. It would be possible to derive the constant speed of light from the combination of time dilation and length contraction (along with Einstein's clock synchronization convention which results in the relativity of simultaneity), but not from time dilation alone. Here's an example I wrote up a while ago showing how time dilation, length contraction and the relativity of simultaneity work together to make sure two different observers both measure light to have the same speed in two directions:

To measure the speed of anything, you need to measure its position at one time and its position at another time, with the time of each measurement defined in terms of a local reading on a synchronized clock in the same local region as the measurement; then "speed" is just (change in position)/(change in time). So, time dilation, length contraction, and the relativity of simultaneity all come into play. From the stationary observer's perspective, the ruler which the moving observer used to measure the distance was shrunk by a factor of $$\sqrt{1 - v^2/c^2}$$, the time between ticks on the moving clocks is expanded by $$1 / \sqrt{1 - v^2/c^2}$$, and the two clocks are out-of-sync by $$vx/c^2$$ (where x is the distance between the clocks in their own rest frame, where they are synchronized). On another thread I posted an example of how these factors come together to ensure both observers measure the same light beam to move at c:

Say there's a ruler that's 50 light-seconds long in its own rest frame, moving at 0.6c in my frame. In this case the relativistic gamma-factor (which determines the amount of length contraction and time dilation) is 1.25, so in my frame its length is 50/1.25 = 40 light seconds long. At the front and back of the ruler are clocks which are synchronized in the ruler's rest frame; because of the relativity of simultaneity, this means that in my frame they are out-of-sync, with the front clock's time being behind the back clock's time by vx/c^2 = (0.6c)(50 light-seconds)/c^2 = 30 seconds.

Now, when the back end of the moving ruler is lined up with the 0-light-seconds mark of my own ruler (with my own ruler at rest relative to me), I set up a light flash at that position. Let's say at this moment the clock at the back of the moving ruler reads a time of 0 seconds, and since the clock at the front is always behind it by 30 seconds in my frame, then in my frame the clock at the front must read -30 seconds at that moment. 100 seconds later in my frame, the back end will have moved (100 seconds)*(0.6c) = 60 light-seconds along my ruler, and since the ruler is 40 light-seconds long in my frame, this means the front end will be lined up with the 100-light-seconds mark on my ruler. Since 100 seconds have passed, if the light beam is moving at c in my frame it must have moved 100 light-seconds in that time, so it will also be at the 100-light-seconds mark on my ruler, just having caught up with the front end of the moving ruler.

Since 100 seconds passed in my frame, this means 100/1.25 = 80 seconds have passed on the clocks at the front and back of the moving ruler. Since the clock at the back read 0 seconds when the flash was set off, it now reads 80 seconds; and since the clock at the front read -30 seconds, it now reads 50 seconds. And remember, the ruler was 50 light-seconds long in its own rest frame! So in its frame, where the clock at the front is synchronized with the clock at the back, the light flash was set off at the back when the clock there read 0 seconds, and the light beam passed the clock at the front when its time read 50 seconds, so since the ruler is 50-light-seconds long, the beam must have been moving at 50 light-seconds/50 seconds = c as well! So you can see that everything works out--if I measure distances and times with rulers and clocks at rest in my frame, I conclude the light beam moved at 1 c, and if a moving observer measures distance and times with rulers and clocks at rest in his frame, he also concludes the same light beam moved at 1 c.

If you want to also consider what happens if, after reaching the front end of the moving ruler at 100 seconds in my frame, the light then bounces back towards the back in the opposite direction towards the back end, then at 125 seconds in my frame the light will be at a position of 75 light-seconds on my ruler, and the back end of the moving ruler will be at that position as well. Since 125 seconds have passed in my frame, 125/1.25 = 100 seconds will have passed on the clock at the back of the moving ruler. Now remember that on the clock at the front read 50 seconds when the light reached it, and the ruler is 50 light-seconds long in its own rest frame, so an observer on the moving ruler will have measured the light to take an additional 50 seconds to travel the 50 light-seconds from front end to back end.

9. Jan 21, 2009

### Naty1

and while I like Fredrik/ Jesse's answer:

because that's what Einstein did, remember it was originally an hypothesis...not a proof nor guarantee. He called it a "theory" himself. So don't let that necessarily constrain your thinking from other possibilites (which don't seem to apply here and now) because the one discussed here may not apply to all universes (if others exist). His own work originated with a 'simple' teenage thought experiment which he never let go...just one thing did not make sense to him and he revolutionized the understanding of space and time forever.

At the time Einstein decided to try the approach nobody knew (for sure) that light speed was the same in all inertial frames so one did not prove the others....rather they have been subsequently verified experimentally and we all pretty much take them for granted...likely you can see the logic Einstein used many places, Appendix I of his RELATIVITY is one place where a derivation of the Lorentz transformation is developed by Einstein himself for the general public...it's high school math.....
http://www.gutenberg.org/etext/5001 It was the idea, the concept, that rocked the world.

Last edited by a moderator: Apr 24, 2017
10. Jan 21, 2009

### Charlie G

Thx for the replies, Jesse and Fredrik, u guys really helped clear my problem up:)