Speeds greater than the speed of light

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JesseM

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I have it now.

You cannot travel faster than the speed of light in this "coordinate system".
Let's put it this way: if you are inside an expanding light sphere, you can never outrun the light and escape the sphere, regardless of what coordinate system is used. Your own coordinate speed may be greater than the coordinate speed of light at some position, though (for example, in Schwarzschild coordinates the speed of light approaches zero at the event horizon, so observers far away from the horizon can certainly travel with a greater coordinate speed than light close to it).
 
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Let's put it this way: if you are inside an expanding light sphere, you can never outrun the light and escape the sphere, regardless of what coordinate system is used. Your own coordinate speed may be greater than the coordinate speed of light at some position, though (for example, in Schwarzschild coordinates the speed of light approaches zero at the event horizon, so observers far away from the horizon can certainly travel with a greater coordinate speed than light close to it).
Pretty funny.

You explain it in a way we are operating.
Yes, I get this.
 
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Love physics but had a bad teacher in math.
quick question: where to find: -If we go with speed of light we will be faster than any photon
 
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And how many ours have you thought about that? Or who proved it? Lets sacrifice him:)
 
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The limiting 'c' value is not proved 'per se'.
It was 'postulated' at SR, and as any other postulate it is not proved but assumed.

The Maxwell equations already have it.
Long before Einstein it was known that light and energy transfers (namely photons) can travel at most at a limiting value.

The first quantitavive measurement: "[URL [Broken] (1676)[/URL]

In any material this relation holds: c^2=1/( ε/μ ) where
μ is the magnetic constant or permeability
ε, permittivity or electric constant
ε0 and μ0 if related to vacuum.

All the measurements made in the past obtain a limiting value to 'c'.
But 'c' is not at all a 'constant'. It is dependent on the medium(*) and the gravitational field.

The permeability and the permittivity (and 'c') are 'properties' of space (or medium) that dictates the rate of change of energy transfers (and information exchange).

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If it is possible an 'infinite speed' of light then all 'causes' and 'effects' would existed at once, without a relation, and all past (and future) events would have existed in that single instant of 'no duration'.
A magical place where anything (or nothing ?) could exist.
If infinite speed brings un unlawfull universe then some limit must exist. 'c' its ok.
Frustating ? blame the 'space' or its creator ;) !
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(*) in a Bose-Einstein condensate (at extremely very low temps) the photons almost stop.
 
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The limiting 'c' value is not proved 'per se'.
It was 'postulated' at SR, and as any other postulate it is not proved but assumed.
That is not quite correct. SR postulates that c is the same in all reference frames (frame invariant). That a material object is limited to speeds < c is then a derived result from the postulates.
 
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If one is in inertial frame S and another inertial frame S' is moving to the right at just a "tad" below the speed of light and a third intertial frame S"" is moving relative to S' at a "tad" below the speed of light, the velocity of S" relative to S is still just a "tad" below the speed of light or c. This is by the Lorentz equations used by Einsteing to combine velocities:
(v1 + v2)/(1 + v1*v2/c^2) where v1 and v2 are speeds a "tad" below the speed of light.

If a Big Bang occured 13 billion years ago, then the advancing edge would be 13 billion years old and 13 Billion light years away. A second advancing edge on top of the first advancing edge would also be 13 billion light years away but the combined distance from the original center would still be only 13 billion light years away from the origin and also 13 billion light years from the other leading edge. We would thus have a circular universe as the path from the original center to the second "leading edge" would still be only 13 billion light years and could not go through the first leading edge.

Does anyone follow what the hell I am saying?
 
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Ich

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Does anyone follow what the hell I am saying?
Not really, but I'm familiar with the Milne model, and I think that's what you're talking about.
If a Big Bang occured 13 billion years ago, then the advancing edge would be 13 billion years old and 13 Billion light years away.
That's true if we neglect gravity and decribe the universe in standard minkowski coordinates instead of cosmological ones. The "edge" is the future light cone of the Big Bang event then, the position where the very first photons are.
A second advancing edge on top of the first advancing edge would also be 13 billion light years away but the combined distance from the original center would still be only 13 billion light years away from the origin and also 13 billion light years from the other leading edge.
No, there is no second edge. The details of "distance to the edge" are a bit tricky for different observers (because of simultaneity issues), but nonetheless it is one and only one light cone.
 
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To Ich...

I never said I was a genius.

I stated it backwards:

Imagine a point S at the theoretical beginning of time. Then BOOM! Along comes a Big Bang. Say point A flies out to the right at light speed, c.

Also, Point B flies to the left at light speed c. Now, what is the separation speed of points A and B?

Guess what! It is still c.

Now we are 13 billion years down stream and point A is 13 billion lightyears from S (although we never know what S is), and point B is 13 billion light years from point S the other way. A and B are still only 13 billion light years apart. You can't go through S to get from A to B because that would be bigger than 13 billlion light years hence, point S, A and B are on a great circle each 13 billion years from each other. There must be a fourth dimension to create this monstrosity.

I tell you, Hugo Lorentz and Albert Einstein made so many things uninterpretable...
 

Fredrik

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Imagine a point S at the theoretical beginning of time. Then BOOM! Along comes a Big Bang.
The big bang theory is the claim that the large-scale behavior of the universe is described by a solution with an intial singularity. All events have time coordinates t>0 in those solutions. There's no t=0 in them. So the big bang wasn't an event in spacetime, it's just a name for the limit t→0.

Now we are 13 billion years down stream and point A is 13 billion lightyears from S (although we never know what S is), and point B is 13 billion light years from point S the other way. A and B are still only 13 billion light years apart. You can't go through S to get from A to B because that would be bigger than 13 billlion light years hence, point S, A and B are on a great circle each 13 billion years from each other. There must be a fourth dimension to create this monstrosity.
In order to determine how far apart they are now, you need to specify how far apart they were at some early time t>0, and what their coordinate velocities were back then. Even if they were very close back then, and both had zero coordinate velocity, they could be unimaginably far apart now (much more than 13.7 billion light-years), because of the expansion of the universe.
 
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You're right... t>0 but can be infinitely close to zero (no minimul required... open interval ... you know all that Dedekind BS.

But, if this all happened, say, 13 billion years ago, no way can the universe we are in be greater than 13 billion light years, at least not in these three dimensions.

Who's to say there aren't other universes and who gives a sh-t what the Pope says that you can't discuss what occurred before t = 0. What the hell does he know about physics? At least he (John-Paul II was the pope who said this) had a handle on evolution and he believed it, much to the chagrin of our Christian and Muslim Fundamentalists.
 

JesseM

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You're right... t>0 but can be infinitely close to zero (no minimul required... open interval ... you know all that Dedekind BS.

But, if this all happened, say, 13 billion years ago, no way can the universe we are in be greater than 13 billion light years, at least not in these three dimensions.
But the Big Bang isn't an explosion from a central point in a preexisting space--the traditional GR models based on the FLRW metric suppose that every point in space (whether space is treated as finite or infinite) was filled with a uniform density of matter at every moment after the Big Bang. Imagine a universe with only two spatial dimensions (like Flatland), and then imagine those two dimensions curved into the surface of a sphere, with every point on the surface containing some matter. Then the Big Bang and the subsequent expansion of the universe could be thought of in terms of the sphere itself expanding from zero radius, with 2D matter evenly distributed on the surface at all times. Bump up the number of dimensions by 1 and you have something like the model of a Big Bang in a closed universe (for an open universe with infinite size, you can imagine something like an infinite chessboard where all the squares are growing simultaneously, but the amount of matter on each square stays constant so the density is continuously decreasing)
 
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Ich

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Hi Fredrik, JesseM,

as I read it, stevmg is talking about SR only. SR doesn't know cosmological coordinates and the FRW model.
So one could say: SR is not applicable to cosmology, and that's ok.
But, I think, to answer his SR questions, it's ok to neglect gravity and do the cosmology of an empty spacetime in SR coordinates. There, the Big Bang is an explosion, and things are moving away from that explosion with different speeds. That whole model is quite contrived, but it works well enough. So I'm discussing that special explosion, not actual cosmology.

Hi stevmg,
Imagine a point S at the theoretical beginning of time. Then BOOM! Along comes a Big Bang. Say point A flies out to the right at light speed, c.
S is an event, not a point. If you're familiar with spacetime diagrams, you know the difference. If not, I think you best start studying them before doing cosmology.

Also, Point B flies to the left at light speed c. Now, what is the separation speed of points A and B?

Guess what! It is still c.
Ok, but better stay below c. If it were c exactly, there'd be no reference frame of A or B to support such a statement.
Now we are 13 billion years down stream and point A is 13 billion lightyears from S (although we never know what S is), and point B is 13 billion light years from point S the other way.
No. S is not a point, it's an event in the common past of A and B. There is no such thing as a distance A-S or B-S.
If you imagine a point M such that A and B are moving away from it with equal but opposite v<c: There'd be a time when, in M's frame, the distance to A and to B is 13 Gly. At that time, A is 26 Gly away from B - again in M's frame.
At that time, A and B are, say, 10 My old. And they will measure their relative distance to be a tad less than 10 Gly, and their distance to M to be even less.

It's just when you try to calculate in a fram at light speed when it all becomes really weird. That's because such frames don't exist.

what the Pope says that you can't discuss what occurred before t = 0
I don't remember the Pope saying that.
 
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I'm not sure if my answer would fall under this category. I want to introduce an idea of transmitting information at a speed faster than the speed of light. I am sure somebody has already thought of this...? Basically all you need is a rod which would exceed the distance of the speed that the light travels, say in an hour (just for practical applications). Pushing that rod at one end will result in the rod being moved at the other end instantly, with zero delay. A principal of a Morse code can be applied - a rod can be pushing a button on the other end, thus transmitting information at a speed faster than the speed of light. Obviously there can be a number of problems with this - the rod can simply be pulled by a gravity of a passing planet, or be hit by a meteorite, etc... But the fact of the matter is that, information can be transmitted at a speed greater than the speed of light.
 
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No, it can't. Pushing on a rod transmits information at the speed of sound in that material, which is always much less than the speed of light. And yes, your idea has been thought of many many many times on this forum already.
 

JesseM

Science Advisor
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I'm not sure if my answer would fall under this category. I want to introduce an idea of transmitting information at a speed faster than the speed of light. I am sure somebody has already thought of this...? Basically all you need is a rod which would exceed the distance of the speed that the light travels, say in an hour (just for practical applications). Pushing that rod at one end will result in the rod being moved at the other end instantly, with zero delay. A principal of a Morse code can be applied - a rod can be pushing a button on the other end, thus transmitting information at a speed faster than the speed of light. Obviously there can be a number of problems with this - the rod can simply be pulled by a gravity of a passing planet, or be hit by a meteorite, etc... But the fact of the matter is that, information can be transmitted at a speed greater than the speed of light.
Turns out this idea doesn't work because there are no perfectly rigid objects in relativity (solid objects are just collections of atoms held together be the electromagnetic force, and electromagnetic interactions travel at light speed). If you push one end, it creates a compression wave that travels along the rod at the speed of sound in the material, the other end doesn't move until the wave reaches it. See here for more info:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#4
 

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