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cfrogue
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JesseM said:
I must ask the experimental basis for this conclusion.
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JesseM said:Sorry, I didn't notice that, it had been free for a long time...anyway I found a free PDF copy on an MIT page here:
http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf
The problem is that to deal with cosmological scenarios we have to deal with non-inertial coordinate systems, while the restriction that nothing can travel faster than c is only intended to apply in inertial frames, the way that we can define a non-inertial coordinate system in GR is totally arbitrary (you could define a coordinate system where you were moving faster than c relative to some object in your own room, for example, although presumably light itself would move even faster in such a coordinate system). In general relativity all large-scale coordinate systems are non-inertial, one can only define "local" inertial frames in very small neighborhoods around freefalling observers, a consequence of the "equivalence principle" which is discussed in http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html .
A coordinate system isn't defined by experiment, it's just a way we choose to label events in spacetime, we can define it however we want. And purely as a theoretical matter, it's possible to show that if the tensor equations of GR work in one coordinate system in a given spacetime (say, Schwarzschild coordinates in a black hole spacetime), they will be unchanged under a totally arbitrary coordinate system (such an arbitrary transformation is called a diffeomorphism, and the equations of GR are 'diffeomorphism invariant').cfrogue said:I must ask the experimental basis for this conclusion.
JesseM said:A coordinate system isn't defined by experiment, it's just a way we choose to label events in spacetime, we can define it however we want. And purely as a theoretical matter, it's possible to show that if the tensor equations of GR work in one coordinate system in a given spacetime (say, Schwarzschild coordinates in a black hole spacetime), they will be unchanged under a totally arbitrary coordinate system (such an arbitrary transformation is called a diffeomorphism, and the equations of GR are 'diffeomorphism invariant').
What assertion? Do you want an experiment to verify the assertion that we humans are free to label events with whatever coordinates you want (which isn't a physical claim so it would make no sense to demand experimental evidence for it), or do you want an experiment to verify that the equations of GR is diffeomorphism-invariant? (which is a purely mathematical matter so it doesn't require experiments either, any more so than the claim the Maxwell's laws of electromagnetism are Lorentz-invariant...the only thing you might test experimentally are whether the equations of GR or Maxwell's equations are actually the correct ones to describe the physical world, but even if they turned out to be incorrect, it wouldn't change the fact that the equations of GR are diffeomorphism-invariant and Maxwell's equations are Lorentz-invariant)cfrogue said:Yea, you can do whatever you want.
I would like to see an experiment to verify this assertion.
JesseM said:A coordinate system isn't defined by experiment, it's just a way we choose to label events in spacetime, we can define it however we want. And purely as a theoretical matter, it's possible to show that if the tensor equations of GR work in one coordinate system in a given spacetime (say, Schwarzschild coordinates in a black hole spacetime), they will be unchanged under a totally arbitrary coordinate system (such an arbitrary transformation is called a diffeomorphism, and the equations of GR are 'diffeomorphism invariant').
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).cfrogue said:I have it now.
You cannot travel faster than the speed of light in this "coordinate system".
JesseM said: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).
In the science fiction section of your local library.Mihael@@/& said:where to find: -If we go with speed of light we will be faster than any photon
I believe it was either Einstein or Minkowski, but I don't have a reference.Mihael@@/& said:Or who proved it?
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.heldervelez said: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.
Not really, but I'm familiar with the Milne model, and I think that's what you're talking about.Does anyone follow what the hell I am saying?
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.If a Big Bang occurred 13 billion years ago, then the advancing edge would be 13 billion years old and 13 Billion light years away.
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.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.
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.stevmg said:Imagine a point S at the theoretical beginning of time. Then BOOM! Along comes a Big Bang.
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.stevmg said: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.
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)stevmg said: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.
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.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.
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.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.
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.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.
I don't remember the Pope saying that.what the Pope says that you can't discuss what occurred before t = 0
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:escogido said: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.