# Question on lightspeed

1. Apr 5, 2014

### Amygdala

Hey all,

I've been reading my fair share on physics and I would like to find a solution to a question that has been eating away at me. Look at the following extract from a book I read a while ago.

"If we managed to travel at 99.99999999 percent of light speed, then we could travel out of the Milky Way and all the way to the neighboring Andromeda galaxy, almost 3 million light-years away, in a mere ﬁfty years."

The above is based on a hypothetical situation that we could build a spaceship to reach such speeds.

Is the the above situation true? I'm assuming it's to do with space-time warping and objects/spaces becoming smaller at fast speeds.

Finally, a thought experiment:

If you got a stopwatch [on the spaceship] and timed the time it took to get to Andromeda. It would read 50 years.

If you then got a hypothetical stopwatch to attach it to a photon and timed the same route to Andromeda it would equally read 3 million light years. - It appears as if the spaceship travelled faster than the photon.

^Could you explain where I have gone wrong in that thought experiment as clearly relatively cannot be violated.

Sorry for the long post, I'm excited to of found a forum to discuss such ideas.

2. Apr 5, 2014

### The_Duck

Yes.

Let's stop right there. You can't attach a stopwatch to a photon. This is not a pedantic point about the practical capabilities of known adhesives; it is a fundamental limitation. Nothing with mass can travel at the speed of light, and indeed nothing that could be considered a clock can travel at the speed of light.

3. Apr 5, 2014

### homeomorphic

Should be relativity forum.

Yes, that's time-dilation. From a certain point of view, it is related to length-contraction. From the point of view space-ship, the distance to the neighboring galaxy will be contracted, so it won't take as long to get there. But usually, the way relativity is taught is the other way around. Time dilates (for stationary observer), so lengths contract in the direction of motion contract (from spaceship point of view).

The thing you have to get used to in relativity is the coexistence of two seemingly inconsistent points of view that are both correct.

Time doesn't seem to make much sense to a photon. Poetically, I guess you could say the photon's stopwatch would read 0. You shouldn't really use a photon, though. You can't put a stopwatch on the photon because the watch has mass and therefore would take infinite energy to accelerate to light speed. So, that's impossible, even in theory. Use something that's going very close to the speed of light. Then the stopwatch would read some very small amount of time only, like a millisecond.

Highly recommended new online course on special relativity for these things:

http://www.worldscienceu.com/

Last edited: Apr 5, 2014
4. Apr 5, 2014

### Amygdala

I thought somebody would pull me up on that. How about simply thinking about it in a different way; its 3 million light years to Andromeda, how could a spaceship get there in 50 years without breaking relativity.

To repeat, I know this doesn't violate it, I'm trying to wrap my head around this.

5. Apr 5, 2014

### Amygdala

Thanks everyone!

6. Apr 5, 2014

### homeomorphic

That is from OUR point of view. From the space-ship's point of view, it is less than 50-light years. To the space-ship, the rest of the stars, galaxies and other stuff will be in motion. All that stuff will be shrunk in the direction of motion.

7. Apr 5, 2014

### Amygdala

Thank you, for some reason it was 50 regular years not light years. That world science u looks great!

8. Apr 5, 2014

### Staff: Mentor

The earthbound observer sees the spaceship cover the three million light years in slightly more than three million years, for a speed that's (just barely) less than light-speed, so no problem there.

The spaceship observer sees himself at rest, the earth behind him and rushing away at that same speed, and the Andromeda galaxy in front of him and rushing towards him... And the Andromeda galaxy is only fifty light-years away, so it reaches the ship in slightly more than fifty years. Again, nothing is moving faster than light, so there's no problem with relativity.

The key here is length contraction and time dilation, both of which have been carried to extremes in this case.

9. Apr 5, 2014

### homeomorphic

Yes, the spaceship is going less than light speed. So, the distance will be a little less than 50 light-years, but it will take the spaceship a little longer than light, so it's 50 years for the spaceship.

10. Apr 6, 2014

### andromeda

How "All that stuff will be shrunk" when Lorentz transformation from stationary to the moving tell us that the only thing that shrinks is the moving spaceship and its meter yardstick?

In this case I presume all world around it grows relatively rather then shrinks. Do I make a logical or mathematical error here?

11. Apr 6, 2014

### ghwellsjr

No, the moving spaceship and its meter yardstick shrink before you apply the Lorentz transformation, that is, in the earth/andromeda rest frame.

When you transform from the earth/andromeda rest frame to the spaceship rest frame, the spaceship and its meter yardstick are their Proper Length (just like they were when at rest in the earth/andromeda rest frame) and everything else shrinks along the direction of motion. The distance between the earth and andromeda shrinks as well as their thicknesses.

12. Apr 6, 2014

### andromeda

Thank you all of you for the response. Need to think for a while on this such that we progress a step closer in resolving my questions. Will get back in a day or two.