Hypothetically breaking the speed of light

[Person012345]

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.

Yeah. With closing speed, at no point does anything move faster than light and nothing can be transferred ftl. But two things can be observed to close (or put distance between each other) at 1.5c from a third reference point. Of course, at no point is anything observed to move ftl in such a circumstance.

Edited May 2, 2013 by Person012345

[K^2]

Third reference point always results in weird stuff in SR. You can have events appear to happen in the wrong order, things instantly jumping from one location to another, duplicates of objects... It's a mess. A fun mess, but a mess.

[Person012345]

Well, I'm not even sure it is "weird" in this case. I mean, it seems perfectly fine and logical to me. It doesn't result in any actual faster than light motion, all it means is that if two ships started 5 light years away from each other they could deliver a message to each other in ~2.5 years as measured from earth, but the message has only traveled 2.5 light years for the observer, and the receiver has also traveled 2.5LY. That's not weird it's just normal. the same way if two people walked at each other at 5 mph and they started out 10 miles apart one could deliver a message to the other within 1 hour. I think that's what I'm talking about.

When measured from the point of view of a ship traveling at .75c, although the apparent speed is only 0.96c, taking time dilation and length contraction into account I think makes it all work out. Of course at 5mph you aren't experiencing significant length contraction and the speed is merely additive so the analogy fails from that point of view, but of course that point of view was not my point so it doesn't matter.

[K^2]

From perspective of the two ships, the message was delivered across a span of 3.3 light years at the speed of 0.96c in 3.4 years. It has absolutely no correspondence to what the 3rd observer has witnessed.

[Person012345]

From perspective of the two ships, the message was delivered across a span of 3.3 light years at the speed of 0.96c in 3.4 years. It has absolutely no correspondence to what the 3rd observer has witnessed.

Well, I can't do math, but the fact that the 3rd observers sees what he sees is what I was getting at.

[ROFLCopter64bit]

But what would happen if the two spaceships travelling at 75% of c collided? Would it be similar if you collided into a brick wall at 150% of c? And what would be the energy result?

[K^2]

But what would happen if the two spaceships travelling at 75% of c collided? Would it be similar if you collided into a brick wall at 150% of c? And what would be the energy result?

And how do you picture collision with a wall at 1.5c when you can't be moving relative to wall faster than c? But it's nothing like .96c into the wall, either. In fact, it's the same result as in classical mechanics. You get twice the energy of one ship hitting a wall at .75c. Same damage to both ships. What I mean is that both ships will evaporate, but if you measure the hard radiation released...

Edited May 2, 2013 by K^2

[Holo]

Due to time dilation, from your viewpoint, you will be moving at 150%c. Remeber, though you aren't actaully travelling FTL, your perceptions are slowed so you will travel 1.5 ly every percieved year.

[Person012345]

Due to time dilation, from your viewpoint, you will be moving at 150%c. Remeber, though you aren't actaully travelling FTL, your perceptions are slowed so you will travel 1.5 ly every percieved year.

No. You won't measure yourself (or anything) to be moving at ftl. You'll travel an outside lightyear + 1/2 in an inside year, but that's taking measurements from two different frames of reference, which makes no sense. Due to length contraction, you won't measure yourself to have gone 1.5 lightyears, I think.

Edited May 4, 2013 by Person012345

[Stochasty]

Due to time dilation, from your viewpoint, you will be moving at 150%c.

Sigh.

No. This is a complete misunderstanding of relativity. From your own perspective, you will be stopped, and everything else will be moving relative to you. Even so, nothing will be moving faster than c; the hypothetical other ship will be moving at .96c.

[Extemporary]

Good thing we're talking about the intuitive stuff. Imagine if this discussion got into quantum effects.

[Holo]

No. You won't measure yourself (or anything) to be moving at ftl. You'll travel an outside lightyear + 1/2 in an inside year, but that's taking measurements from two different frames of reference, which makes no sense. Due to length contraction, you won't measure yourself to have gone 1.5 lightyears, I think.

It makes perfect sense if you want to visit the next star without aging severely.

Sigh.

No. This is a complete misunderstanding of relativity. From your own perspective, you will be stopped, and everything else will be moving relative to you. Even so, nothing will be moving faster than c; the hypothetical other ship will be moving at .96c.

But, due to time dilation, won't your brain slow down, making everything look like it's moving ~50% faster?

[Brenok]

But, due to time dilation, won't your brain slow down, making everything look like it's moving ~50% faster?

It will slow your brain down from an outsider perspective. To you, it will look like everything around you is slower.

[Holo]

It will slow your brain down from an outsider perspective. To you, it will look like everything around you is slower.

My brain hurts, enough relativity for today

[Stochasty]

But, due to time dilation, won't your brain slow down, making everything look like it's moving ~50% faster?

Exactly backwards. From your own perspective, you are always stopped. Time dilation is something that happens to someone else*, never to you. That's the point of relativity. Velocity is not an intrinsic property of the Universe: you yourself are never moving from your own frame of reference; it's always everything else that is moving in relation to you. Until you internalize this concept, your intuition regarding relativity will be wrong - even if you understand the details of the math behind the concepts of time dilation and length contraction, if you don't understand the fundamental idea that all inertial frames are equivalent and all observations are observer dependent you won't come to the right conclusion about who sees what when.

*This is true for unaccelerated observers. Observers undergoing acceleration will experience time dilation even from their own frame of reference, but that's because acceleration (unlike velocity) is an intrinsic property of the Universe.

[Holo]

Exactly backwards. From your own perspective, you are always stopped. Time dilation is something that happens to someone else*, never to you. That's the point of relativity. Velocity is not an intrinsic property of the Universe: you yourself are never moving from your own frame of reference; it's always everything else that is moving in relation to you. Until you internalize this concept, your intuition regarding relativity will be wrong - even if you understand the details of the math behind the concepts of time dilation and length contraction, if you don't understand the fundamental idea that all inertial frames are equivalent and all observations are observer dependent you won't come to the right conclusion about who sees what when.

*This is true for unaccelerated observers. Observers undergoing acceleration will experience time dilation even from their own frame of reference, but that's because acceleration (unlike velocity) is an intrinsic property of the Universe.

This makes my brain hurt, so I'm just going to believe this guy instead:

Speed of light? More like speed of waves travelling through the luminiferous ether!

(reading through some relativity stuff, it looks like acceleration makes distances shorter ? or something like that so I dunno)

Edited May 6, 2013 by Holo

[WestAir]

Acceleration makes distances shorter, yes. I think it's called length contraction. The faster you go, the shorter the distances between you and objects in-front of you become. When you reach the speed of light, the distance to infinity reaches zero - in essence you're everywhere at once relative to you because the universe will have contracted into an infinitely small point before you. That's, apparently, how photons see the Universe.

[Holo]

Acceleration makes distances shorter, yes. I think it's called length contraction. The faster you go, the shorter the distances between you and objects in-front of you become. When you reach the speed of light, the distance to infinity reaches zero - in essence you're everywhere at once relative to you because the universe will have contracted into an infinitely small point before you. That's, apparently, how photons see the Universe.

And since the distance is shorter, does that mean that from your point of view you have reached your destination more rapidly?

[Tada]

Vicious aerobraking I say!

[Extemporary]

Vicious aerobraking I say!

>Discussion of effects at relativistic speeds

>Proposes aerobraking

Only KSP...

[WestAir]

And since the distance is shorter, does that mean that from your point of view you have reached your destination more rapidly?

Yes and no.

Yes, if you don't plan to decelerate. Once you begin to decelerate, the distance to your destination gets further as lengths expand, as opposed to contracting.

[Nikolai]

But, due to time dilation, won't your brain slow down, making everything look like it's moving ~50% faster?

Maybe it would help to realize that the same event occurs at different times in different frames of reference.

Perhaps this paradox will clarify. Consider a train that is 1000 meters long at rest that can travel at 0.999c relative to its track. It passes through a tunnel with (flimsy) doors that can close instantly on both ends. The tunnel is 100 meters long (as measured by someone stationary relative to it).

Because measured length changes for an object in motion, the tunnel's operator, who happens to be somewhat disgruntled this morning, sees the train as being about 44.7 meters long. Feeling a bit punchy, he closes the doors simultaneously with the train inside. Since the train is shorter than the tunnel, he can do so; a split second before the train smashes through the far door, there is some measurable time during which the train fit completely inside the tunnel.

The train's conductor, on the other hand, sees the tunnel as a mere 4.47 meters long. He, too, sees the doors close on either side of the train. This would be a contradiction except that the conductor and the tunnel operator disagree on the timing of the door closings. From the tunnel operator's point of view, the doors closed simultaneously. From the conductor's point of view, the front (far) tunnel door closed long before the back tunnel door did.

If you give up your ideas of a universal clock that everyone is measuring velocity with, and allow that distance and time are pliable in order to keep the speed of light constant in all reference frames, the fact that no one will ever see something appear to break c falls right out of the coordinate transformations from one frame of reference to another.

Edited May 7, 2013 by Nikolai
Clarified source of 100 meter measurement

[Person012345]

http://en.wikipedia.org/wiki/Ladder_paradox

More info on that.

[Nikolai]

More info on that.

Oh, that's great! I especially like the "man falling into grate" paradox.