I Speed > C: Does Einstein's Theory Allow It?

[kent davidge]

(I'm sorry for my poor English.) I read a text that says the speed of recession of a distant galaxy can be greater than c, and it does not violate the special theory of relativity because that speed is not caused by the motion of the object (galaxy) relative to some coordinate system. Would it mean that when the coordinate system is moving (in this case it would be the space itself) the speed can be greater than c?

In which cases Einstein's theory allows a speed greater than c? I remember I read something about it in Feynman's book.

 

[Chronos]

It does not violate SR because distant galaxies are not actually moving with respect to any inertial reference frame. The empty space between them and us is expanding. GR does not constrain the 'speed' of any such expansion.

 

[kent davidge]

distant galaxies are not actually moving with respect to any inertial reference frame

Is it the same as "distant galaxies does not move relative to some coordinate system" or "the coordinate system is moving along with these galaxies"?

 

[Nugatory]

Is it the same as "distant galaxies does not move relative to some coordinate system" or "the coordinate system is moving along with these galaxies"?

The latter is closer to what is going on, but it may be better not to think in terms of coordinates at all. A coordinate grid laid on top of a curved and expanding spacetime doesn't do what you expect a coordinate grid to so, so can be misleading.

For an analogy, you could imagine a snail crawling around on a large and infinitely stretchable rubber sheet. The laws of physics biology determine the speed of light the snail, but if some distant part of the sheet is being continually stretched away from the snail, the speed of the snail relative to a dot on that distant piece of sheet may be something completely different.

 

[hsdrop]

For an analogy, you could imagine a snail crawling around on a large and infinitely stretchable rubber sheet. The laws of physics biology determine the speed of light the snail, but if some distant part of the sheet is being continually stretched away from the snail, the speed of the snail relative to a dot on that distant piece of sheet may be something completely different.

how far a way does the "snail" and the "dot" before it is considered different spaces

 

[Nugatory]

how far a way does the "snail" and the "dot" before it is considered different spaces

That question is like asking how far apart on the curved surface of the Earth two people both walking due south have to be before we don't consider their paths to be parallel - it depends on how small of an effect you're worried about. When I'm laying out the foundations for a house that is 10 meters by 20 meters, I assume that it's a perfect rectangle with two 10 meter sides and two 20 meters sides and all the angles are exactly 90 degrees, even though the curvature of the Earth means that none of that is correct. If I needed accuracy to fractions of a nanometer, as opposed to the centimeter or so that homebuilders work to, I'd care a lot more about the curvature effects.

 

[hsdrop]

so in theory the dot and the snail could be 2 subatomic particles but we just don't have any means to measure the difference in the space between the two and may never have the means to. also the difference is so little it does not matter unless we are looking at very large spaces between the snail and the dot. so we just do the best we can with what we have and know that the discrepancy is still there. thank you i believe I'm getting what you're saying

 

[PAllen]

It does not violate SR because distant galaxies are not actually moving with respect to any inertial reference frame. The empty space between them and us is expanding. GR does not constrain the 'speed' of any such expansion.

And neither does SR, as shown by super luminal recession rates in zero density limit of Friedman solutions, which are pure SR. In this case, a true relative velocity is also uniquely defined, and it is subluminal. A better statement is that recession rate is not in the same category as relative velocity, and is not precluded from being super luminal in SR or GR.

 

[RandyD123]

As a novice I really don't understand this whole concept. If distant galaxies are (apparently) moving away from us at speeds greater than light, then the same can be said about someone viewing our galaxy from some other distant galaxy. If it is actually "space" that is expanding FTL then where exactly does that happen? I mean, we can't feel it or observe it from anywhere in our own galaxy. So I ask, is this real? or is it some equation that makes sense on paper but not in the real universe?

 

[A.T.]

If it is actually "space" that is expanding FTL then where exactly does that happen?

Between the galaxies.

 

[RandyD123]

so what happens to an object that is in between galaxies? what is "viewed" from a planet that sits in such a space?

 

[PeterDonis]

If it is actually "space" that is expanding FTL then where exactly does that happen?

I would say the question is not well posed, because "space expanding FTL" is something that depends on the coordinates you choose. The only thing that is actually happening physically is that galaxies, and any other objects that are not gravitationally bound to each other, are moving apart--and even that, strictly speaking, is an inference from the fact that they see each other's light redshifted, which is the actual observable.

so what happens to an object that is in between galaxies? what is "viewed" from a planet that sits in such a space?

If the planet is not gravitationally bound to any galaxy, then it will see light from all the galaxies redshifted, much as we do on Earth for light from galaxies other than our own (and a few others that are gravitationally bound to ours, like the Andromeda galaxy).

 

[PAllen]

I

If the planet is not gravitationally bound to any galaxy, then it will see light from all the galaxies redshifted, much as we do on Earth for light from galaxies other than our own (and a few others that are gravitationally bound to ours, like the Andromeda galaxy).

..and if its motion is such that it sees isotropy. For some other inertial state of motions, it will see a skewed pattern of red shift and possibly blue shift, the more its motion differs from the specific motion that sees isotropy. I know you know this well, just wanted to dot this 'i'.

 

[MattRob]

As a novice I really don't understand this whole concept. If distant galaxies are (apparently) moving away from us at speeds greater than light, then the same can be said about someone viewing our galaxy from some other distant galaxy. If it is actually "space" that is expanding FTL then where exactly does that happen? I mean, we can't feel it or observe it from anywhere in our own galaxy. So I ask, is this real? or is it some equation that makes sense on paper but not in the real universe?

The classic example is to imagine taking a black marker and marking a few points on a balloon, then inflating the balloon further. The black dots aren't actually moving against the skin of the balloon, but are getting further apart. This is a very simplified, but somewhat useful way to picture it.

There are plenty of shortcomings to the analogy, and it leads to a lot of misconceptions, but it's better than nothing and a good starting point to try imagining how this works - there's no single point that's expanding faster than any other, and where "space is expanding faster than light" depends on where you're looking at it from, since every black dot is holding still, locally.

There's a PF article on this analogy, and one of the user/mentors/advisors here, Phinds, has a link in his signature that goes to this page.