Hypothetically breaking the speed of light

[GoldenShadowGS]

Let say we have two hypothetical spacecraft capable of reaching a high fraction of the speed of light. They both accelerate in opposite directions from their starting point each other and reach 75% of c. To observers at the starting point, each ship is traveling at 75% c. but to observers on the ship, the other ship is traveling away from them at 150% c.

Is this possible, and if so, what implications does this have for the light speed barrier?

[maltesh]

The two spacecraft don't see each other receding at 150% of lightspeed. When things are moving at an appreciable fraction of light speed, you have to use the relativistic velocity-addition formula.

The result is that each of the ships see the other ship receding at 96% of lightspeed.

[GoldenShadowGS]

I understand that they wouldn't be able to perceive each other, but they would still be physically moving at 150% of c, right?

[Nikolai]

I understand that they wouldn't be able to perceive each other, but they would still be physically moving at 150% of c, right?

They'd be able to perceive each other. And they wouldn't be physically moving at 150% of c.

That's because shifting coordinate axes from one velocity's frame of reference to the other has to be done in a way that's a bit more complicated than mere addition/subtraction. If you were on ship A, your definition of "meter" and "second" would be different from that of ship B. More to the point, what you would report about ship B would be different from what ship B would report about itself.

Edited May 1, 2013 by Nikolai
misspelled "frame"

[Kryten]

No. The main point of relativity is relative speeds above C are impossible. One ship sees the other ship moving at 96% of C because it genuinely is, relative to that ship.

[maltesh]

No, they're not physically moving at 150% of the speed of light relative to one another. Length contraction, time dilation, and the fact that the speed of light is constant in all reference frames means that the observer on the planet doesn't measure either spacecraft moving away from him at greater than the speed of light, nor do either spacecraft measure the other moving away at greater than the speed of light.

[Nikolai]

One ship sees the other ship moving at 96% of C because it genuinely is, relative to that ship.

Right. Your example involves ship A and ship B as seen from a third reference frame, and then implying that that third reference frame is the "right" one. According to relativity, there is no "right" frame.

So ship A would see the third reference frame receding from it at 0.75c, and ship B receding from it at 0.96c. And yes, the relative velocities of things will change depending on what your chosen reference frame is. But no one can claim that their preferred reference frame is "correct", or that it represents in a singular way how things are "physically moving".

[Person012345]

No, they're not physically moving at 150% of the speed of light relative to one another.

An observer on say, earth, would measure the two ships moving away from each other at 1.5 c, but obviously that doesn't require either of them to be moving ftl relative to that observer. I don't think you meant otherwise, but just to say.

To the OP, the short answer is they would not measure the other spacecraft moving away from them at 1.5 c It would just be... a higher fraction of c I think?

Edit: 96% apparently.

[Nikolai]

The two spacecraft don't see each other receding at 150% of lightspeed. When things are moving at an appreciable fraction of light speed, you have to use the relativistic velocity-addition formula.

If it helps, GoldenShadowGS, this relativistic velocity-addition formula works for objects moving much more slowly, too. It's just that it will give you results that are really, really close to simple addition/subtraction; it's not that the rules governing things suddenly and magically know to shift over to a different set of equations once things start getting "fast enough".

[iamaphazael]

An observer on say, earth, would measure the two ships moving away from each other at 1.5 c...

Actually, I don't even think that's the case. It's been a while since I took modern physics, but I believe that any experiment that actually measures the relative speeds of the two craft, even if performed in Earth's reference frame, would result in the correct value of .96c

[GoldenShadowGS]

What about this:

Each ship was traveling to another star exactly one light year away. At 75% of c, they would reach the star in 1.334~ years. They broadcast a signal when they arrive(and keep on going, no stopping) and the signal traveling at the speed of light takes one year to reach the starting point. It will take an extra year to reach the star the other ship was going. But after two years, when the signal finally reaches the 2nd star, the other ship will be 1.5~ light years beyond the point where the signal reached the 2nd star.

I guess I just don't understand your value of 96% c, that means the second ship would be receiving the signal before it reached the 2nd star, as it wouldn't have gotten there yet. But this doesn't make sense to me.

[Nikolai]

What about this:

In which reference frame are you measuring the distance to these stars?

[maltesh]

Yeah, here's where things get complicated. From the reference frame of the first ship, both stars are moving relative to it at 0.75c. Which means that, in that ship's reference frame, the distance between the stars experiences length-contraction, and so by the first ship's measurement, the distance between the two stars shrinks from 2 light years down to 1.32 light-years.

And so when he fires his light-speed signal, he sees it cross that 1.32 light-years at the speed of light, and reach the other ship at the appropriate time.

Edit: Going further, an observer stationary relative to the two stars also measures the radio beam crossing the distance, which is 2 light-years in his reference frame, at the appropriate time: 2 years after it left . However, if he asks the ship about how long it took the light beam to cross the distance between the two stars, the ship will give him a different answer: 1.32 years. Odd, but consistency is maintained (after a fashion) because, relative to the star observer, the spacecraft is moving at 0.75c, and experiencing time dilation. The star observer sees all clocks moving abord the spacecraft ticking at 0.66 ship seconds per star second.

Edited May 1, 2013 by maltesh

[andrewas]

Actually, I don't even think that's the case. It's been a while since I took modern physics, but I believe that any experiment that actually measures the relative speeds of the two craft, even if performed in Earth's reference frame, would result in the correct value of .96c

Nope, the Earth observer measures each ship at 0.75c. The distance between them, in Earth's reference frame, increases at 1.5Ly/year.

[Person012345]

Actually, I don't even think that's the case. It's been a while since I took modern physics, but I believe that any experiment that actually measures the relative speeds of the two craft, even if performed in Earth's reference frame, would result in the correct value of .96c

http://en.wikipedia.org/wiki/Faster-than-light#Closing_speeds

[iamaphazael]

http://en.wikipedia.org/wiki/Faster-than-light#Closing_speeds

Yes. Look at the formula at the end of that section.

[iGame97]

If you are faster than light, you travel back in time.

So it is impossible.

[Person012345]

Yes. Look at the formula at the end of that section.

I dislike math, so if you could explain to me what it says that would be great.

I am, however, capable of reading the paragraphs before it which apparently state that the closing speed can be ~2c. Is that not what it says?

Edit: Also, what is it talking about? Because I'm not sure what it's applying to? If it's talking about the relative velocity to the other particle then yes, it won't be 2c, to make sure we're clear. I'm only talking about the closing speed as measured by earth.

Edited May 1, 2013 by Person012345

[drakesdoom]

I think what you are missing is that "speed" is a derived formula of distance traveled over time. Since an observer on board a ship traveling at significant fractions of c measures both of these things with significantly different results than an observer who is relative to the ship standing still, they will not agree on closing "speed." So when two approaching ships arrived at your station and you told the captains they were approaching each other at 1.5c they will laugh at you and show you video from inside their ship of them approaching each other at .96c.

[lobsterbark]

Reading this thread, I think part of my brain exploded.

[Drunken Hobo]

Yes. Look at the formula at the end of that section.

Think about it in the simplest terms possible; instead of spaceships, use something like electricity or light.

Imagine you have a single button that controls a lightbulb at one end of a room. Press it, and a signal will travel along the wire at the speed of light and turn on the bulb.

Now a second bulb at the other end of the room is connected to the same button. The signal will still travel at the speed of light to both bulbs, giving a relative speed of ~2c according to the stationary observer. Adding the second bulb can't change the speed of the signal - imagine how complicated electronics would be if it did!

(I think I've explained that properly... maybe).

[K^2]

I am, however, capable of reading the paragraphs before it which apparently state that the closing speed can be ~2c. Is that not what it says?

You are confusing closing speed and relative speed.

[Person012345]

You are confusing closing speed and relative speed.

No I'm not. I'm talking about closing speed not relative speed.

[Person012345]

I think what you are missing is that "speed" is a derived formula of distance traveled over time. Since an observer on board a ship traveling at significant fractions of c measures both of these things with significantly different results than an observer who is relative to the ship standing still, they will not agree on closing "speed." So when two approaching ships arrived at your station and you told the captains they were approaching each other at 1.5c they will laugh at you and show you video from inside their ship of them approaching each other at .96c.

That's not what I'm missing because that's totally irrelevant to the point.

I'm talking specifically about what an observer on earth measures.

[K^2]

No I'm not. I'm talking about closing speed not relative speed.

Fair enough. But that's the source of confusion, at any rate. People were talking about relative speed in the beginning.

Anyhow, closing speed is not really "physically relevant". E.g., you cannot use closing speed to send information from point A to point B at 2c. That's really the proper test of speed limit violation.

Of course, speed of light is a local limit. Hence the warp drive, etc. But we had a lengthy discussion of that in another thread. I think it's safe to assume that in this thread we're talking about local violations.