Monday, June 28, 2010

Speed of light paradox

Just a simple question that probably has an answer I won't understand, but I am going to try and ask it anyway...

If speed is relative, then how is there supposed to be a universal speed limit? For example:

Two spaceships leave Earth.
One accelerates up to a high speed (doesn't matter what it is) relative to Earth.
The other spaceship is flying beside it matching its speed.

Now, let's say we forgot about Earth (cause it's so far behind us now) and all we have are the two spaceships and no other reference point. Wouldn't we just be back at where we started? The spaceships would have no speed relative to each other.

What's the point if speed is relative? Is it just impossible to go the speed of light relative to something and pass that something close by? Or is it just impossible to go the speed of light in relation to anything no matter how far away it is from you?


Matthew said...
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Matthew said...

"Or is it just impossible to go the speed of light in relation to anything no matter how far away it is from you?"

This. It's really messed up, but space and time start distorting once you approach the speed of light relative to something else. It's what Einstein's theory of relativity is all about, so look up that as a starting point.

It's called 'time dilation' for info on it -- basically if you're traveling near the speed of light compared to Earth, time will actually run slower for you than it will for stuff on earth, to keep the speed of light constant (for you and earth.) They proved it at one point using supersonic jets and super-accurate clocks, and showed that clocks on the jets were a few milliseconds slower than the clocks on earth.

Matthew said...

For more explanation (or maybe more confusion) of your original question (different things travelling relative to one another), consider this:

2 spaceships take off from earth in opposite directions going .75 times the speed of light. Since they're going in opposite directions, you might think they're going 1.5 times the speed of light relative to one another.

However, that's not allowed because of the speed of light limit. So what happens?

Both ships will travel .75 times the speed of light relative to Earth. However, relative to one another, time and space will dilate so that they are only going something like .96 times the speed of light relative to each other.

Dan said...

This goes a little bit into what Matthew said, but as I've understood it, yeah, time runs slower and I suppose you could say we age slower the faster we are moving.

Though I'm not sure if it's entirely correct, the analogy I've always thought of is, I suppose you could say, a little more down to earth (pun intended); I generally think of an vehicle that can fly faster than the earth spins. If it takes off and manages to circle all the way round the planet to it's starting point, then when it reaches that point, less time will have elapsed for the people in the ship than those who stayed back on earth in the same place, because literally they would have been lapped by those in the ship. In other words, the people who were traveling faster got there earlier, but since the destination was the same place they started and they were going so fast, literally less time went by for them, and they aged slower than those left behind. Mind you, they only aged a few hours slower than those left behind, which is miniscule compared to the length of a human life.

I've heard of this concept used in some sci-fi flicks before where people take off to go into space at unreal speeds, and they say good bye to loved ones hop into their ship for only a few months or years but when they come back everyone they said good-bye to is now much much older and it's like "oh man it's been so long for us, we haven't seen you for ages, but you haven't changed hardly a bit, it was only a short time for you but for us it was years and years..."

I've asked myself if there were any practical application for this, and while I suppose you could use it to fast forward into time and see the future farther than your normal life would naturally take you, couldn't think of much since you'd have to leave behind everything to make the trip. I guess you could buy some wine and then when you came back it would be well aged, without you having to wait so long, but that'd be a pretty silly way to use a scientific technological realization like this. Maybe something else will come to me later.

Mark said...

Thanks for the comments.

So yeah, I know about how all that works with time dilation and all. But my question is, even if you are going way too fast in relation to Earth, wouldn't you still be able to go faster than the spaceship beside you? Because in that reference, your speed is zero. Would the reference frame with Earth really even mean anything any more?

Also, another thing I wanna throw into the conversation...

There is a paradox I read about with time dilation. Both observers (one at "rest" in relation to the other and one accelerating in relation to the other) see each other's time as slowing down. But only the accelerating observer's time is the one that actually does slow down. The explanation I read was because the acceleration is the difference between the two and that's why only the accelerating observer's time slows down. But I can't find anything that says "why" this is true. Do they know why only the accelerating observer's time would slow down?

Matthew said...

Yes, you would still be able to go faster than the spaceship next to you -- but the increase in speed with respect to that would be different than the increase in speed with respect to Earth or another fixed point.

Also, the paradox you're talking about is the Twin Paradox ( -- from what I understand, it's the fact that the rocket-ship twin turns around and changes his inertial frame that causes him to return to Earth younger.

Mark said...

Thanks, Matthew.

So because of time dilation, they are both slowed down in relation to each other and perceive the speed as less than light speed. I see. But wouldn't that not really matter? Like, even if a space ship only perceives their own speed as less than light speed compared to Earth, wouldn't they still get to their destination faster since they are continuously accelerating?

Mark said...

Also, I hear people say "when matter gets closer to light speed it's mass increases and requires more energy to accelerate it".

Does this mean that mass is relative as well?