Monday, January 24, 2005

In some of the shows I see about time travel (and there aren’t that many), the claim is made that if you travel faster than light, you will go back in time.

I don’t see why this would happen.

If you read the laws of special relativity, you will find the formulas relating time and space. One of them (Lorentz contraction) tells you the rate at which you travel through time is sqrt(1 - (v/c)2), where v is the rate at which you travel through space. The quicker you go through space, the slower you go through time. But what happens when v > c? You get the square root of a negative number. You do not get a negative number; you get an imaginary number.

Alternatively, you can think of it as the Pythagorean theorem, where one leg of the triangle is speed through space, one leg is speed through time, and the hypotenuse is the speed of light. (Is this Minkowski space?) In this model, it makes no sense to go faster than light. You can’t have a triangle where one leg is longer than the hypotenuse.

So it’s not at all obvious to me how going faster than light makes you go backwards in time.

Another thing that bothers me is the talk of wormholes. Oh sure, if you could bend the entire universe in half, you might be able to go back in time. Bending the universe seems like a harder problem than time travel.

I do think backwards time travel could be possible. However, I think the only reasonable way to make it would be to travel from one universe to another. You have to believe in the many-worlds theory first. I don’t believe backwards time travel into the same universe can work.

5 comments:

Tom Zhang wrote at Tuesday, February 1, 2005 at 10:49:00 PM PST

Maybe string theory -- the 10-dimensional universe? I'm not an expert, but I kinda believe in it now.

--Xiaohu

BTW, the webblog is very interesting!

Swaroop C H wrote at Sunday, February 6, 2005 at 1:22:00 AM PST

Its kinda eerie to know that there could be replicas of me out there... ;)

Interesting post though.

- Swaroop
www.swaroopch.info

Anonymous wrote at Thursday, March 3, 2005 at 12:54:00 AM PST

Amit, I've been a googler for a month or so, and every day I walk past the whiteboard near the piano in 42, and I see the drawing for "Talk like a Pirate Day" (which one of my former co-workers at EA celebrated), and this blog address.

So after about a month of walking by it a few times a day to go to the kitchen, I visited your blog. Funny how impression advertising works. :)

I haven't thought about relativity since college, but I think I have a good answer for why going faster than the speed of light is thought of as going back in time.

OK, suppose you're watching a movie in a theatre. You see a new image 24 times a second. Suppose for simplicity that the speed of light is 10 mph.

Now say the theatre is 10 miles long, and your seat is in the back. You will be watching the movie at normal pace, but effectively an hour delayed, since it takes any frame 1 hour to get to you.

Now suppose you run backwards at 5 mph at the very beginning of the movie. When you depart, you will see the first frame. Now, after one hour, you will be 5 miles away. Light is travelling at 10 miles an hour, so when you arrive, you will see the frame that departed a 1/2 hour ago. But wait, that is only a half hour into the movie? So you have been running for one hour, but you have only seen a half hour of the movie. If you're not convinced, move on, the next part is the time travel part.

Now suppose you're back at the front of the theatre watching another movie (say 2 hours long), and halfway through you run away from the screen at 20 mph. So you're going twice the speed of light. After one hour you'll be 20 miles away. The frame of the movie you saw when you left (halfway through at the one hour point) will _only_ _have_ _travelled_ 10 miles at that point. It will take another hour to travel the next 10 miles to catch up with you, at which point you will see it again.

Wait, so you saw one frame of the movie, and then ran twice the speed of light for an hour, and then waited for an hour and saw the same exact frame?!

Also notice when you get there after 1 hour of running, you will be looking at the frame that left 2 hours ago. So you will be looking at the first frame of the movie! That is, you watch the first hour of the movie, then run at twice the speed of light away from the screen. When you arrive, you will see the beginning of the movie again.

Now forget the movie altogether. Just suppose you're running away from a lamp. Say you put on your shoes when you start running 20 mph away from the lamp. So you will run for an hour, be 20 miles away, and then wait one hour there, and then you'll see yourself putting on your shoes to leave! Make sense?

It is easier to think of running in a straight line, but you can work out what happens if you run 20 mph away and then 20 mph back to the same spot.

There are probably dozens of other paradoxes you can come up with, but that is one that's relatively simple to get.

Andy Chu

Anonymous wrote at Friday, September 23, 2005 at 9:03:00 AM PDT

crazy stuff!

Anonymous wrote at Monday, May 14, 2007 at 12:38:00 AM PDT

Faster than light is a popular concept, there is no science for that!

sqrt(1-(v/c)**2)**-1

You are already in a LOT of trouble if you are AT the speed of light.
If you could blink your eyes ever so short you'd still see the entire history of the universe!

That famous one who build the theory around Lorentz's formula did it by intuitively postulating that the speed of light is the maximum.

Hence, traveling faster than light a person might get a tap on the shoulder from an amazed famous one saying:

you're on your own, you have to invent your own theory.


Apart from that, physically speaking, just under the speed of light there is a speed where you would have consumed all the energy in the universe to reach it. You're in trouble even sooner.

The reason that light can travel with the speed of light is that it has no mass. So my five cent advise would be: loose weight!

As to bending space. You'll need gravity for that. Not time or speed.

To aid you in your time traveling aspirations. Around the beginning of this millenium scientist(See Alain Aspect or Anton Zeilinger) have succeeded in proving instantanious effect over a distance. Relativistic world vision dictates at least an intermediate effect traveling not faster than light. Quantum physics comes into play here.
Finally, making a Quantum leap here, I would agree with you wishing some sort of Many World theory included in my own Back to the Future traveling kit.