The edge of the universe

[Enola Straight]

Edwin Hubble discovered that the universe is expanding; the farther away, the faster the rate of expansion away from us.

At a certain distance from us, the rate of expansion is the speed of light.

From what I remember from Special Relativity, there are a number of apparent changes to an object accelerated to near the speed of light; flattening out in the direction of travel, mass goes to infinity, time slows to nothing, and radiant frequencies/wavelengths are red-shifted to zero.

Does this imply that, at the edge of the universe, we are surrounded by a spherical shell of quantum singularity?

[Rahvin]

No. There is no "edge" to the Universe.

Objects do not "speed up" as they move farther away - the distance, the actual spacial dimensions, grow larger. There is no actual motion on the part of distant objects.

The Universe, by all appearances, is finite yet unbounded, somewhat like the surface of a sphere (not topologically, but just to carry what "finite yet unbounded" means). There is no boundary, no "edge," and yet there is only so much space as opposed to an infinite expanse.

Objects sufficiently distant from each other will for all practical purposes be separated by the expansionof the Universe for the reasons you mentioned - when the distance between two locations is growing at a sufficient rate that one would have to travel faster than light to close that distance, neither location can "see" or travel to the other. However, this is not an "edge;" any two locations a sufficient distance apart will experience the same thing.

As an analogy, let's pretend that the Universe is the surface of a globe, and the distance between which the expansion approaches the speed of light is only 1000 miles. It will be impossible to travel to or even receive information from New York in Los Angeles, and equally impossible to travel to or receive information from Tokyo in Chicago. None of the cities are moving, there is no "edge" or boundary of any sort, but the surface area of the globe is expanding at a rate that prevents information or objects traveling to locations more than 1000 miles away at the moment of transmission.

Eventually, this also means that (within our analogy) the distance between Chicago and its own suburbs will exceed 1000 miles, and information transfer and travel will become impossible.

In the real Universe, of course, gravity will hold many structures together even as the expansion of space eventually causes more distant objects to gradually redshift and then disappear forever. If the rate of expansion were to significantly increase, gravity could no longer be sufficient to bind objects, and the matter of the Universe would be destroyed in a "Big Rip."

[Kuroneko]

Does this imply that, at the edge of the universe, we are surrounded by a spherical shell of quantum singularity?

Recall that the universe is not only isotropic, but also homogeneous on the large scale, so that there cannot be a spherical singularity anyhere--because if there was, it would be everywhere.

You're also thinking of event horizons a bit backwards. Nothing special happens when particles fall into the event horizon of a black hole. The trouble starts when they try not to, and discover that as they get closer to the horizon, the force required to keep them from falling in diverges to infinity, and the speed they're required to attain to escape it tends to the speed of light.

Similarly, there is a horizon caused by the expansion of space, but nothing particularly interesting happens to the particles (galaxies) themselves. They cross it completely unaffected, even though to you, gravitational redshift makes them appear to smear on the horizon, growing ever fainter. But of course to them, you're the one getting smeared on the horizon!

What can also be confusing about a dynamical universe is that the Hubble radius need not be the cosmological horizon, and it is in fact possible to observe objects with superluminal recession velocity. One thing to keep in mind here is that the speed of light limit is local, whereas here we're talking about very distant objects.

Objects do not "speed up" as they move farther away - the distance, the actual spacial dimensions, grow larger. There is no actual motion on the part of distant objects.

With the understanding that we're talking about motion in the comoving frame of reference, yes. But then the frame is defined that way... but yes, even consistently defining "relative velocity" is tricky in general relativity for distant objects, and sometimes even impossible.

[bz249]

"The trouble starts when they try not to, and discover that as they get closer to the horizon, the force required to keep them from falling in diverges to infinity, and the speed they're required to attain to escape it tends to the speed of light."

Isn't "centrifugal force" (the stuff coming from the conservation of angular momentum) overcomes gravity after a certain distance? Classically it should but i honestly do not know how this works in relativity...

[Sriad]

As an analogy, let's pretend that the Universe is the surface of a globe, and the distance between which the expansion approaches the speed of light is only 1000 miles. It will be impossible to travel to or even receive information from New York in Los Angeles, and equally impossible to travel to or receive information from Tokyo in Chicago. None of the cities are moving, there is no "edge" or boundary of any sort, but the surface area of the globe is expanding at a rate that prevents information or objects traveling to locations more than 1000 miles away at the moment of transmission.

Eventually, this also means that (within our analogy) the distance between Chicago and its own suburbs will exceed 1000 miles, and information transfer and travel will become impossible.

In the real Universe, of course, gravity will hold many structures together even as the expansion of space eventually causes more distant objects to gradually redshift and then disappear forever. If the rate of expansion were to significantly increase, gravity could no longer be sufficient to bind objects, and the matter of the Universe would be destroyed in a "Big Rip."

But wait a sec.

If we were in a spaceship jetting across the universe at .999etc C the expansion of space would carry us with it as we moved along. Sure the horizon we can see now seems to be moving away from us at ~C, but after 10 billion light-years of travel we'd be in a different region of the universe, the old horizon would be receding at a lesser relative speed so we could eventually get there. At that point the Milky Way would appear to be receding near the speed of light, and there would be X-billion light years of universe ahead of us still, but over the cosmic horizon as seen from Earth.

[Simon_Jester]

"The trouble starts when they try not to, and discover that as they get closer to the horizon, the force required to keep them from falling in diverges to infinity, and the speed they're required to attain to escape it tends to the speed of light."

Isn't "centrifugal force" (the stuff coming from the conservation of angular momentum) overcomes gravity after a certain distance? Classically it should but i honestly do not know how this works in relativity...

I think I could answer this question if I understood it a little better. Spinning will not save you from falling into a black hole, empirically, but I doubt that's your question. Could you try to phrase it a bit more formally?

[bz249]

So let´s make a system from the particle and the black hole. This system has an angular momentum, which should be conserved, the closer the particle gets to the black hole, the faster it has to be to conserve the momentum, sooner or later the particle will find a stable orbit around the black hole... if the momentum was large enough that orbit is farther away than the event horizon. At least this is the case classically.

[Surlethe]

What about the black hole's tides torquing the particle, if it has nonzero width? That will exchange L between the hole and the particle, which will either spin it away from the hole or spiral it in. Once it's in the event horizon, you can think of space itself as moving toward the singularity: it's like a conveyor belt, so anything on it gets dumped in no matter how fast it's orbiting or trying to escape. Maybe another way of thinking about it is that once it's inside the event horizon, tidal forces are strong enough that the black hole always leeches angular moment off the particle, no matter how small it is?

[Kuroneko]

So let´s make a system from the particle and the black hole. This system has an angular momentum, which should be conserved, the closer the particle gets to the black hole, the faster it has to be to conserve the momentum, sooner or later the particle will find a stable orbit around the black hole... if the momentum was large enough that orbit is farther away than the event horizon. At least this is the case classically.

In Schwarzschild spacetime, the effective gravitational potential for a test particle of specific angular momentum l, is (in units of c = 1)
[1] Veff = -GM[1/r + l²/r³] + l²/2r²,
where this r is the Schwarzschild radial coordinate. Under Newtonian gravity, the ~1/r³ term is not present (and r is ordinary distance from origin), so that the positive angular momentum (~1/r²) dominates when r<<1, making the effective potential repulsive (increasing with r) there. But in GTR, it's the relativistic correction of the negative ~1/r³ that dominates instead. So no, angular momentum does not 'overcome gravity', and if you come close enough to the black hole, it will not save you.

[bz249]

Thanks