# Time dilation reasoning

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1. Nov 20, 2015

### seb7

The video is pretty popular and being spread by science channels.
Is the last bit about the cause of time dilation correct?
I used to think like this, but came to the concoction its wrong, but seeing this video makes me wonder once again how could this be correct.

If the video is true then - wouldn't this mean everything isn't truly relative?
If the video is true then - wouldnt 50% of c would cause 50% of time? which does not match Einstein's equation on this.

2. Nov 20, 2015

### Staff: Mentor

Which last bit exactly do you mean? At which point in the movie?
No. That's not even well-defined without refering to another observer.

3. Nov 20, 2015

### seb7

When he talks about time dilation, 5min 15s, into the video. Is he correct?

4. Nov 20, 2015

### Mister T

The speed of light is absolute, not relative. That's what makes Einstein's relativity different from Galileo's. The notion that everything is relative was overturned by Einstein. That's what makes the theory revolutionary.

Nowhere in that movie is that claim made.

In the movie an error is made at about the 6-minute mark. The narrator speaks of the traveler being closer to the speed of light than people on Earth. That's just not true, and violates both postulates. If someone had a speed closer to the speed of light than someone else, that would constitute a way to distinguish between their inertial reference frames. And it would mean that they would measure different values for the speed of light. The explanation of time dilation that follows from that idea therefore has subtle flaws. You couldn't, for example, use that argument to explain why clocks on Earth run slow relative to the traveler.

Other than that, the movie accurately portrays the two postulates and the different aging of the traveler compared to the person left on Earth.

Last edited: Nov 20, 2015
5. Nov 21, 2015

### m4r35n357

No, but I'm not surprised you asked the "50%" question because he didn't give any relativistic equations at all, just d = s x t.

OK, if this guy has piqued your interest in the subject then search the internet for introductory SR material, and come back with more specific question when you are ready. That video has got you as far as you can get with words, but science in not done with words; you need equations to understand what is "really" happening.

6. Nov 21, 2015

### seb7

I understand Einstein's equations on time dilation, but this video talks about why, which doesn't seem correct to me.
Wouldn't his reasoning for the time dilation require a fixed ether frame?

yes, but only within its frame.

here's a question: Say we got on a ship traveling at 0.8c then while travelling we got on to its onboard shuttle and kicked it back to 0c, then the ship (still travelling at 0.8c), later went back to meet up with stationary shuttle.
When they compare clocks, which craft lost more time?

7. Nov 21, 2015

### jbriggs444

It would be more precise that the speed of light is both relative and invariant. "Invariant", meaning that the measured speed is the same, no matter what frame you use to measure it from. "Relative", meaning that the speed can only be measured relative to something else.

Since light has no frame, it is nonsense to say "within its frame".

8. Nov 21, 2015

### Staff: Mentor

It is right in some directions. Without further explanation, I think it is at least a bit misleading.
You can look up "light clock", where the same argument is made in a more formal way.

9. Nov 21, 2015

### stevendaryl

Staff Emeritus
No. What he's talking about when he talks about things slowing down because of speed is relative to ANY inertial rest frame. The simplest example to understand it is a light clock. A light clock consists of two parallel mirrors, with a pulse of light bouncing back and forth between the mirrors. The time for a complete circuit for the pulse of light is just $T = 2D/c$, where $D$ is the distance between the mirrors. Now, if you set the two mirrors in motion (or alternatively, switch to a different rest frame in which the mirrors are already moving), then the time required for a complete circuit is longer. If we assume that the motion is perpendicular to the line connecting the mirrors, and that the distance between the mirrors is still $D$ (a more thorough analysis is needed to conclude this, so for now, it's just an assumption), then for a pulse of light to travel from one mirror to the other and back at speed $c$ would take a time equal to:

$T' = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} 2D/c$

where $v$ is the speed of the mirrors.

To see this: let $\delta t$ be the time required to travel from one mirror to the other. During this time, the second mirror moves forward by an amount $v \delta t$. So the light, in traveling from one mirror to the other travels a distance $D$ in one direction, and a distance $v \delta t$ in the other. The total distance traveled, by Pythagoras, is: $D_{total} = \sqrt{D^2 + v^2 \delta t^2}$. If light always travels at speed $c$, then $D_{total} = c \delta t$. So we have: $c \delta t = \sqrt{D^2 + v^2 \delta t^2}$. Solving for $\delta t$ gives $\delta t = D/c \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. Double that for a round-trip.

So for a mirror in motion, the time for a complete circuit is longer, by a factor of $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. This is relative to the inertial reference frame in which $v$ is measured. So the amount of slowing is different for different frames. There is no absolute frame relative to which the slowing is to be measured--time dilation works in any frame.

10. Nov 21, 2015

### Mister T

I agree. I do not think the explanation is correct either. I explained why.

Part of it, yes. Part of the explanation is equivalent to the standard light clock analysis, which is correct.

0.8 c and 0 c relative to what? These speeds are relative, so you have to specify which frame of reference you're measuring the speed relative to. On the other hand, if you stated that a light beam was moving at speed c you wouldn't need to state which frame you're measuring the speed relative to, because every frame would measure it to be speed c. This is what I meant when I said that the speed of light is absolute.

You could analyze this situation in the following way. Let's choose a frame of reference where the shuttle is at rest after it leaves the ship, and measure every speed relative to this frame. Ignore the acceleration the shuttle must undergo to come to a stop. The ship departs from the shuttle at speed 0.8 c. It then turns around and comes back to meet up with the shuttle. The ship's clock would be behind the shuttle's.

11. Nov 21, 2015

### seb7

yep, understand the mirror concept, and the resulting equation.
(I got the 50% thing wrong, as I was thinking in 1 dimension, not 2).

Using the video reasoning, I don't understand why an object with velocity has the slower time.
If a ship leaves earth, travels around at 0.8c and comes back, in both reference frames, the ship apparently aged more slowly - who decides which object with the set of mirrors had the faster velocity? (since object speed is relative).

12. Nov 21, 2015

### Staff: Mentor

13. Nov 21, 2015

### Mister T

In Post #4 I explained that you couldn't use the argument given in the video to explain why clocks on Earth run slow relative to the traveler. That's the part they got wrong.

In a proper analysis you can either look at things only from only Earth's frame of reference because it's the only inertial frame. The traveler's frame is not inertial because he has to turn around. Or, if you want to also understand things from the frames of reference of the traveler you have to take into account the change in reference frames when he switches directions. When you do that you find consistency. The traveler's clock is behind Earth's clocks upon the traveler's return.

14. Nov 21, 2015

### seb7

Mister T, I would expect the clocks to be the same (or close), since the shuttle had to accelerate at relative velocity of 0.8c away from the ship, the ship then (later) would have to accelerate beyond 0.8c to catch the shuttle, thus the ship dilation was even slower, but had further to travel.

15. Nov 21, 2015

### seb7

thanks Mister T, and Nugatory for the explanation. I will ponder on this.

16. Nov 21, 2015

### Mister T

Read the details of the analysis in the link Nugatory posted in Post #12.

17. Nov 21, 2015

### stevendaryl

Staff Emeritus
A quantity such as "How old is the traveler in the ship when it gets back to earth?" is invariant, which means you can use any inertial frame you like to calculate the answer. If we use the inertial frame of the Earth, then we can reason that while the ship is traveling, its "light clock" is running slower, so the total number of complete circuits for a light pulse on the ship's light clock will be fewer than the number of complete circuits for the earth's light clock. So less time (as measured by light clocks) will have passed for the ship. If you assume that biological processes are affected in the same way as light clocks, then the traveler will have aged less.

You can use any inertial reference frame to compute this answer. If you have some inertial reference frame that is traveling at speed $v$ relative to the Earth in the same direction as the rocket, then according to this frame, the Earth's light clock is running slower than the rocket's during the outward journey, but the rocket's is running slower than the Earth's during the return journey. In this frame, the return journey takes longer, so the rocket ends up aging less.

18. Nov 21, 2015

### seb7

ok. got it. ship or earth might move apart at 0.8c, but ship actually needs 1.6c to return, still making it the faster object. 0.8c to decelerate to a stop, another 0.8c to return.

but ... if photos/atoms are actually working like this 'light clock', wouldn't there be a direction which has less velocity than our current frame? though, I cant see how it could ever possibly be measured, probably the same issues when trying to measure one-way light.

19. Nov 21, 2015

### Mister T

No! The ship's speed cannot exceed c in anyone's frame of refernece.

When you say "less velocity" what do you mean? Velocity is not something that ship has unless you specify in which frame of reference that's occurring.

You are retaining the notion of a "true rest frame" in which the velocity of the ship can be measured. This is the same mistake the narrator makes in the movie when he says the ship's speed is "closer to c".

20. Nov 21, 2015

### Mister T

It took me some effort to untangle that last sentence. In this frame, the rocket's clock will be observed to run slower during the return journey, so the rocket ends up aging less than Earth. In the observer's frame the return journey takes the same amount of time as the outbound journey.

I think I remember having seen this argument before, but I must have forgotten it somewhere along the way. Thanks for bringing it up.