h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Sorry to ressurect and old thread, but...

It has been proven experiment that everyone in the Universe, not matter what their acceleration or velocity, measures the speed of light to be precisely c. What about someone moving at the speed of light?

Exactly. What about it. Who can explain. Not me

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Well, to start with it's impossible to go at the speed of light (see post 13). But assuming you could go at, say, 99.99% of C relative to something else, then you would still measure the speed of light to be precisely C.

Has the original twins question been answered yet? The answer is because one twin underwent acceleration while the other didn't. The one that undergoes acceleration (and deceleration) is the one that ages less.

I prefer to express Einstein's famous equation as:

E = m

(with an appropriate choice of units)

It only confuses things to introduce c².

I agree Gnomon.

In particle physics, the units of mass are often given as GeV/c^2

The page that was linked to with the answer specifically cited that it was not the acceleration, but rather the change in reference frame that was important.

Is acceleration not relative as well?

Generally...

Acceleration is not relative, because you can feel it. If you are hanging in space and I am a hundred kilometers away facing you, and I accelerate towards you, I will feel myself being pushed into the pilot's chair of my space ship. You'll feel nothing. Then when I slow down so that I can pull up beside you, I'll feel the deceleration as I press against the straps of my seat belt. Again you'll feel nothing. If we now compare clocks, we'll find that mine will be slower than yours.

Acceleration seems to be a factor, but it is not explanation. Both the "stationary" twin and the accelerating one would both see each other's clocks slowing down, as you would expect since they are both moving equally fast relative to each other. It is only when they return to the same inertial frame that the differences become apparent.

Imagine an observer in Earth orbit or in free-fall. He/she is undergoing constant acceleration due to Earth's gravity, but will not "feel" it. An observer on the surface is also undergoing constant acceleration. These are not inertial frames, so there is no apparent reason why an Earthbound observer should always have the fast clock. In fact you could imagine a scenario whereby the travelling twin actually experiences lower accelerations than the Earth-bound one.

Despite having read and re-read that link, I still don't really understand, so all opinions welcome...

The clock in orbit and the clock on the Earth's surface are subject to a different effect: the effect of gravity on time. Time slows down in a gravitational field. That's why I chose the example of two people in space.

This seems to disprove acceleration as the explanation in itself:

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

And the whole series of explanations:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

There doesn't seem to be a simple one. Hence the paradox I guess.

That first article is confused, because it assumes the existence of absolute time. It says that the clock on one space ship can be advancing at a rate compared with the rate it advances on a different space ship. This isn't true. The times on the two space ships are independent.

All we can do is put an observer on one observing the clock on the other. If the two spaceships are moving relative to each other, each will see the clock on the other as having slowed down. But when the spaceships acclerate/decelerate so that they are both doing the same speed, the clock on the one that has done more acceleration/deceleration will have a clock that has slowed down more than the other.

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I don't believe it assumes anything of the sort. It refers to the second clock as relative to the first, but this doesn't imply any concept of absolute time.

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OK, it appears to be the case that the one doing the accelerating is the one with the slower clock when they return to the same interial frame. But only because he needs to accelerate to change his frame in the first place; the time dilation factor is not related to the acceleration itself and the acceleration does not come into the maths. And there are evidently scenarios that don't require accelerations at all. This doesn't actually explain *why* it happens.

My point is that the clock on the stationary ship goes faster than the one in the moving ship. And the clock on the moving ship goes faster than the one on the stationary ship as well.

I'm not sure this is correct (or even relevant), but doesn't the Mach principle come into play here?

'In his book The Science of Mechanics (1893), Ernst Mach put forth the idea that it did not make sense to speak of the acceleration of a mass relative to absolute space. Rather, one would do better to speak of acceleration relative to the distant stars. What this implies is that the inertia of a body here is influenced by matter far distant. This had a great influence on Einstein and in the development of his theory of general relativity.'

This would mean that even though there isn't absolute spacetime, locally there might as well be, in terms of the two frames of reference being differentiated. From the POV of the distant universe, it would be obvious which astronaut would be acceleratin.

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As you would expect, as their relative velocities are exactly the same regardless of who accelerated. But something very odd happens when they meet up again - why?

Hussassan, you must be right, but I can't understand a word you're saying. This business of c being constant must also be true, but its one of those that boggles your mind unless you've had several years of college physics classes (Someday I WILL understand)

Anyway, is all motion reletive? LIke the earth rotates around the sun. But if the earth is your reference point, the sun is the thing that is moving, and the planets all have really strange orbits. Or, along the same lines, how do we know that the galaxy is spinning? Spinning reletive to what? I think it is because of centrifugal force (or centripital, if you prefer) There is a gravitational force between the stars in the galaxy, or between the earth and the sun. Gravity should pull the earth straight into the sun, but the force of the Earth's rotation counteracts that and keeps us in orbit. So rotational motion isn't completely reletive, right?

Secondly, what about a ship (A) that is moving at, say, 98% c. I am guessing that he would probably experience some reletivistic effects (i.e. time slows down and mass increases) But reletive to what is he travelling? C is equal to 2.99x10^8 m/s ( I think). So ship A is travelling almost 299 billion m/s; now what about a second ship travelling at 200 billion m/s. Reletive to that ship, ship A would only be going 99 billion m/s, nowhere near the speed of light. From spaceship B's vantage point, ship A has 200 billion m/s to go before mass and energy required increase to infinity, but reletive to the earth, he is going 98% c and so can't speed up very much due to the laws of reletivity. So is there an absolute standard for speed, reletive to the universe itself? Or what is the deal here?

Ugn. No wonder DNA just said "forty-two" and left it at that

I believe centrifugal force doesn't actually exist, but is an illusion caused by inertia.

So if we have for simplicity object A being pulled by object B, and object A orbits in a circle. Object A's motion relative to B is always perpendicular to the force line AB, and that's enough. Rotational motion doesn't have to be absolute I don't think.