# Infinite time and SR

1. Mar 19, 2015

### james weaver

Alright i'm a noob to all this but I have been reading a really good book that talks about special relativity and had a question. Considering that light does not pass through time, it travels between any two points in zero time, correct? Does that mean that from the perspective of the light, it's rate of speed is infinite? A second part to this question, if a person were to hypothetically travel at the speed of light, let's say from the earth to the sun and back, would that imply that an infinite amount of time would have elapsed for an observer back on earth?

2. Mar 19, 2015

### Staff: Mentor

What is this "really good book"? If we don't know what is in it, it's hard for us to answer questions you have from reading it. However, I can say:

It is not true that "light does not pass through time", nor does light travel between any two points in zero time or with infinite speed. There is a concept called the space-time interval between any two events in space-time, and it is zero between the emission and absorption of a light signal - but a zero space-time interval implies neither zero time nor zero distance.

We have a FAQ (in the STEM learning materials section) about "the perspective of light".

The question about what would happen if hypothetically we could travel at the speed of light cannot be answered because if relativity is correct we cannot, even in principle, travel at the speed of light. Thus, the question comes down to "if relativity were not correct, what would it tell us?"

3. Mar 19, 2015

### Ibix

It isn't possible for a person (or any object with mass) to travel at the speed of light, and it isn't possible to build a clock that travels at the speed of light. This, in fact, means that "the perspective of something travelling at the speed of light" doesn't really make sense, so it isn't really possible to answer your questions.

The "light does not experience time" argument (popularised by Brian Greene) is the result of one way of looking at this. A slightly different approach will tell you that light experiences infinite time. This is the maths' way of telling you that you are asking a daft question - it gives you daft answers.

This doesn't stop some people talking about light experiencing zero time, but it's not really right.

4. Mar 19, 2015

### james weaver

yes the book is called the fabric of the cosmos by brian greene. I guess my question was "mathmatically speaking" would an observer on earth experience infinite time relative to someone traveling to the moon and back at light speed.

5. Mar 19, 2015

### Ibix

You can't travel at light speed, so the question has no meaning, I'm afraid. Time isn't defined along the paths that light follows - Greene notwithstanding.

6. Mar 19, 2015

### james weaver

the way he explained it was that the faster you travel through space, the slower you can travel through time and vice versa. Let me reword the question again without traveling at light speed. If I were to travel at a speed "approaching" light speed, then, to an observers standpoint on earth, would the passage of time before i returned begin to "approach" infinity?

7. Mar 19, 2015

### Ibix

No. The time recorded on Earth for your round trip would be exactly what you'd expect - it's 2.25 light seconds, or thereabouts, round trip to the moon, so Earth clocks would read slightly over 2.25s. Your clocks would record less and less time the faster you went - so given a brutal enough acceleration you could make the trip in arbitrarily low time by your clocks.

You might think you can extend the argument to light speed and get zero time. Stripped of the window dressing, that's what Greene is doing. However, you can also do a calculation based on the Lorentz transforms to calculate the time you would measure. For any speed below light speed you get the same answer. At light speed you get that you would record infinite time, not zero. Greene just doesn't do that version, so far as I am aware. :D

This contradiction arises because you are asking a question that doesn't make sense - like "what does green smell like?". You can approach the question by trying to assign a colour to a smell or by trying to assign a smell to a colour. You aren't likely to get helpful answers either way - although one may look superficially reasonable.

8. Mar 19, 2015

### Ibix

PS: Green/Greene was unintentional. I am not casting aspersions at Greene's personal hygeine.

9. Mar 19, 2015

### james weaver

alright, i think i get what you're talking about. If you don't mind, please bear with me through one final example. If I am traveling very close to the speed of light to the moon and back, whereas it may only feel like it's taking me a couple seconds to do so, everyone else on earth may experience hundreds or even thousands of years (depending on just how "close" i was to the speed of light). So, would it be accurate to conclude that the closer our hypothetical traveler got to the speed of light on his journey to the moon and back, the more time that would ultimately pass to an observer on earth? I'm just trying to understand the relationship here.

10. Mar 19, 2015

### Staff: Mentor

That is correct, but be aware that it only works this way because it is a trip to the moon and back. If your traveller were to just keep on going, we could just as well say that the traveller is at rest while the earth is the thing that's moving away from him at a constant speed, and that it's the earth-based clock that is running slow. This is the famous and much-discussed "Twin Paradox", and a good starting point would be http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

Brian Greene is fun to read, but not an especially good source if you want to understand what's going on.

11. Mar 19, 2015

### Ibix

From the Earth frame it'll take a couple of seconds - time taken is just distance divided by speed. The rocket clocks will record less time - a fraction of a millisecond if you have the magic technology to make and survive the accelerations you'd need.

Think about it - the Apollo missions made it to the moon in a few days. How could it take hundreds of years at higher speed?

Now, if you made a trip to the other side of the galaxy (call it 100,000 light years) then Earth clocks would measure a fraction over 100,000 years while yours can measure as little as you like (assuming magitech acceleration capabilities).

Basically, you have the ratio right but the baseline wrong.

I'll also warn you that there's a trap looming in front of you in the form of the Twin Paradox, which I'd suggest you have a read about.