# I Time dilation

1. Oct 7, 2016

### Shayne T

How close to the speed of light would you have to travel to be able to traverse the entire span of the known universe(94 billion light years i think?) in a persons 80 year lifetime?

2. Oct 7, 2016

### Brian E

.If you travel with the speed of light, for 80 years you will move a distance of 80 light years. So your question does not make any sense

3. Oct 7, 2016

### sophiecentaur

Hello Shane and welcome to PF
I see you have put an I prefix against this question. That implies you have some familiarity with fairly straightforward maths. If you look at this link or this link, there are lists of formulae that involve the Lorentz transformation. Have a go at applying them to your problem. The Hyperphysics site is aimed at 'your' level, I think.

Sorry for not just giving you a numerical answer. PF wants people to learn about this stuff and we don't tend to spoonfeed questioners.

4. Oct 7, 2016

5. Oct 7, 2016

### Simon Bridge

The problem is fairly loosely phrased but it seems reasonable to suppose that the distance is measured in one frame and the time in another.
I agree the math is pretty straight forward, and clear once the problem is phrased more carefully.

6. Oct 7, 2016

### Brian E

I think you are trying to tell me, that I should not reply to questions, when I am not able to give correct answers. I know about the Lorentz transformation, but did not take that into account, my bad :-) I will be more careful in the future :-)

7. Oct 7, 2016

### Simon Bridge

... and here I thought you were cleverly pointing the OP down the path to realizing the solution! Your post was correct: as phrased the problem does not make sense. Pointing this out could lead to OP phrasing the problem better and then coming to a realization :)

8. Oct 7, 2016

### sophiecentaur

Never let that get in the way. Your initial answer was 'reasonable' as a first stab; before Einstein, it would have been everyone's answer. And people will always enjoy putting you right.
Relativity certainly introduced a load of new concepts. The 'frame of a photon' is now a nonsense concept, in many ways.

9. Oct 7, 2016

### Shayne T

From what ive gathered, this would be true for any outside observer who were not travelling at near light speeds. I guess a better way to put it, would be how close to the speed of light would you need to go in order to acheive a time dilation factor of 94billion:80 (traveller experiences time at a decelerated rate of 1.175 billion times less than a stationary observer left home at earth)

10. Oct 7, 2016

### Shayne T

Regarding your comment on the frame of a photon, ive always had trouble wrapping my brain around the following. If special relativity states that time approaches 0 as velocity approaches c, and photons are the only thing able to actually reach c, do photons not experience time? And if something that is moving, which does not experience time, wouldnt it, from its own frame of reference, instantaneously exist everywhere in the universe?

11. Oct 7, 2016

### Simon Bridge

Formally - you have proper distance d in frame S, and you want observer in frame S' travelling with relative speed v (wrt S) to traverse that distance in S in coordinate time t' or less. The time in S to traverse d is going to be $t=d/v = \gamma t'$ so solve for v.

This question is meaningless in special relativity.
Everything is stationary in their own reference frame. So to which observer do you think something could be considered "everywhere in the Universe"? Surely all observers agree that the photon exists in only one place at a time?

... consider that the length contraction in this limit is 100%, so the "photon" does not exist everywhere in space, but everywhere in the "direction of travel" is the same place - so there is only one place for the photon to be.

But like I said before - the question is actually meaningless. The confusion above is due to this.
To see why, try constructing the usually time-dilation derivation using light-clocks but putting v=c in at the start ... then add the postulate that all observers measure the same value for c. You should see a logical contradiction pretty much right away. Therefore, the equation you were taking the limit in before cannot even be constructed.

You can get at the contradiction much quicker by considering the reducto ad absurdum: pre-suppose an observer that is stationary in the frame of a photon, the photon has v=0 in this frame. Now apply Einsteins postulates to bring the physics into SR: all frames/observers measure the same speed for the photon.
Then we note that not all observers measure v=0 for the photon ... which is a logical contradiction. Either the initial presupposition is untrue or special relativity is untrue.
It follows that a photon cannot be an observer.

There's probably a more rigorous way to put this but you get the idea.

12. Oct 7, 2016

### Staff: Mentor

Photons don't have a frame of reference. When someone says "the frame of reference of <something>", that's a convenient shortcut for the more precise "a frame of reference in which that something is at rest"... But a photon is moving at speed c in all frames, so there can be no frame in which it is at rest.

It is tempting to look at the time dilation and length contraction formulas, set $v=c$, and watch the elapsed time and length go to zero. However, the mathematical derivation of these formulas starts with an assumption that is equivalent to $v$ never being equal to $c$ so they cannot be used when $v=c$.

13. Oct 8, 2016

### sophiecentaur

To put the question in context and to show that there is an answer (however impractical), it's worth while mentioning the 'Muon' experiment, which dramatically demonstrates how a fast travelling 'observer' perceives time differently.
Muons are produced by cosmic rays high in the earth's atmosphere, and travel at about 0.98c. Their rest half life is around 1.6μs. Measuring the muon flux at a height of 10km and at sea level, you would expect only 0.3 per million to make it before they disintegrate - ignoring the relativistic effect on 'their' rate of passage of time. But, in their frame of reference, they will travelled a much shorter distance than 10km by virtue of the fact that their local clock is running at about one fifth of an Earthbound clock. So many more of them will survive the 10km journey - about 49,000 per million.
This hyper physics link shows it very well - pictures and everything!!
Put your own values into the formulae and you will get a (sort of) valid answer. Once you have an answer then you need to calculate just how much energy would be needed to take a space ship to that sort of speed.