Could life exist inside a black hole?

[ubavontuba]

Hello,

I'm new here and I have a question I hope you might help me with...

Might "dark energy" be a natural consequence of relativity?

It seems to me that if the matter at the edge of the "known universe" is moving away from us at nearly the speed of light... that relative to us it must have nearly infinite mass.

Or in other words, could the universe be apparently "falling" outward toward a black hole shell, rather than simply accelerating from some invisible internal force like "dark energy?"

The weird part about this idea is that from every observational point in the universe, you'd observe the same thing (meaning there is no real shell, only a relative shell).

I think this might account for the time lag from the first expansion to the current expansion too do to matters of scale. What do you think?

ubavontuba

 

[Ivan Seeking]

IIRC, the boundary conditions for the universe are, or can be described as that of a black hole. I know that Kaku says something close to this: "If you want to know what it looks like inside of a black hole, look around your room".

I'm in no position to vouch for this though, and it may be out of date.

 

[Garth]

The universe is like a BH only in that it is impossible to 'get out of' either.

The BH is one particlular solution of the spherically symmetric solution of Einstein's GR field equation, \rho = \rho(r), p = p(r), cosmology arises out of the cosmological solution \rho = \rho(t), p = p(t).

They are different and should not be confused. A BH is something within the universe, it is not the universe itself, even in the BB singularity - that expands whereas the BH solution does not.

Garth

 

[SpaceTiger]

This is a common enough question that we might want to consider putting it in a sticky (along some of the other common questions). Anyway, here's a link with more information:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html"

 

[ubavontuba]

Relating it more to "dark energy."

Hey guys,

Thanks for the responses.

I'm more intersted in how this relates to dark energy, rather than black holes.

My concept is that to the observer, the universe having seemingly been expanding at relativistic speed from any given point, the perceived black hole "shell" should not act inside like the interior gravitational effects of a normal gravitational sphere. This is because the mass is receding at near light speed in either perceived direction (sort of like shining two flashlights in opposite directions).

That is that from the standpoint of the observer, the energy and mass at the perceived edge of the universe on his left, let's say, is in a noncontiguos reference frame from the matter and energy on his right.

So, all the matter on his right, let's say, is going to be effected more and more by the matter at the perceived edge on his right, in a relationship to distance. The closer it is to the observer, the less it is thusly affected and conversely, the farther away it is, the faster it will seem to be accelerating outward (generally speaking).

As the universe expands, this effect should be perceived by the observer as an acceleration of the expansion of the universe. Ergo, as "dark energy." This is because the receding walls allow there to be more space for this effect to take place in, and therefore everything (including perceived motion) must seemingly get bigger (faster) too.

So, is dark energy an as yet unquantified force pushing outward? Or is dark energy merely a gravitational effect of relativity?

 

[pervect]

Hello,
I'm new here and I have a question I hope you might help me with...
Might "dark energy" be a natural consequence of relativity?
It seems to me that if the matter at the edge of the "known universe" is moving away from us at nearly the speed of light... that relative to us it must have nearly infinite mass.
Or in other words, could the universe be apparently "falling" outward toward a black hole shell, rather than simply accelerating from some invisible internal force like "dark energy?"
The weird part about this idea is that from every observational point in the universe, you'd observe the same thing (meaning there is no real shell, only a relative shell).
I think this might account for the time lag from the first expansion to the current expansion too do to matters of scale. What do you think?
ubavontuba

Some, but not all, of your issues are addressed in the FAQ

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html"

Basically the singularity of the big bang is just in the wrong place for the universe to be a black hole - it's possible the universe is a white hole, but this is not a standard model and it' not particularly likely.

For more detail, see the FAQ.

 

[SpaceTiger]

I'm more intersted in how this relates to dark energy, rather than black holes.
My concept is that to the observer, the universe having seemingly been expanding at relativistic speed from any given point, the perceived black hole "shell" should not act inside like the interior gravitational effects of a normal gravitational sphere.

Also, if I'm understanding you correctly, here you're relying on a common misconception about relativity:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html"

Our models of the universe already use general relativity, so it wouldn't make sense to say that dark energy is a "natural consequence of relativity" unless:

1) General relativity is modified at large scales
2) We use a distribution of matter different from that observed (i.e. reject the cosmological principle)
3) We add an extra component of "dark energy"

There are also some folks who speculate that the acceleration could be explained by a back-reaction from large-scale inhomogeneities, but that appears to be quite different from what you're suggesting.

 

[ubavontuba]

pervect and SpaceTiger:

Pervect, I guess I shouldn't have used the phrase "in a black hole," but rather; "Might that which is beyond our known universe be perceived by us as a sort of black hole?"

What I'm getting at is that it seems to me that the "edges" of the known universe should essentially behave (from our viewpoint) essentially the same as a black hole, only concave rather than convex/spherical. That is, that there is an event horizon, intense gravity and even Hawking radiation (we'd see this as the cosmic background radiation").

SpaceTiger,

I do not mean that we are a black hole because we are traveling at relativistic speeds as compared with other arbitrary masses.

In my concept, every observer notes that they are centrally located (as far as they can tell) and everything else is redshifting away from them (generally, as a matter of distance).

To us, an arbitrary point at the edge of the perceivable universe is moving at relativitic speeds and therefore any mass in that point will have relativistic properties (in the perspective of our reference frame). One of these properties being increased mass (relative to us).

Our mass doesn't increase because of this. And were we to move over to that far away point, we'd see that the matter there was normal and that the matter where we were (very far away now) has these same relativistic properties.

Wherever we are, the local reference frame seems normal. It's only in looking out and far away that we'd see the apparent effects (they're not local).

 

[SpaceTiger]

pervect and SpaceTiger:
Pervect, I guess I shouldn't have used the phrase "in a black hole," but rather; "Might that which is beyond our known universe be perceived by us as a sort of black hole?"

If you mean beyond the observable universe, then no, read the first link. Most models of the universe extend beyond the limits of our observational capabilities (i.e. beyond those points at which galaxies appear to be moving at relativistic speeds from us).

Wherever we are, the local reference frame seems normal. It's only in looking out and far away that we'd see the apparent effects (they're not local).

No, read the second link.

I feel like you're only reading the titles or something, since both of your questions are answered in the text of the links we provided. If you don't understand a particular point, please ask for clarification. Matter that is moving at relativistic speeds does not form a black hole, even "apparently". There are different kinds of cosmological horizons, beyond which our observational capabilities are limited in various ways, but there are no black holes involved. I'll be happy to elaborate if you're interested in horizons.

Again, models of the universe are fully general relativistic, so there is no room for the kind of error you're talking about.

 

[jhe1984]

On the horizons issue, can things (if they exist) beyond the universe's horizon have an effect on the way things inside the horizon (in our universe) behave?

I guess light effects are out the question, but are gravitational effects out of the question?

More generally, can our universe be connected (via what?) to areas beyond our horizon?

Eww, wasn't planning on getting into multiverse issues, but I guess just did...

 

[ubavontuba]

If you mean beyond the observable universe, then no, read the first link. Most models of the universe extend beyond the limits of our observational capabilities (i.e. beyond those points at which galaxies appear to be moving at relativistic speeds from us).

Right, I've read that. Referring to the portion that states:

The standard big bang models are the Friedmann-Robertson-Walker (FRW) solutions of the gravitational field equations of general relativity. These can describe open or closed universes. All these FRW universes have a singularity at the origin of time which represents the big bang. Black holes also have singularities. Furthermore, in the case of a closed universe no light can escape which is just the common definition of a black hole. So what is the difference?

The first clear difference is that the big bang singularity of the FRW models lies in the past of all events in the universe, whereas the singularity of a black hole lies in the future. The big bang is therefore more like a white hole which is the time reversal of a black hole. According to classical general relativity white holes should not exist since they cannot be created for the same (time-reversed) reasons that black holes cannot be destroyed. This might not apply if they always existed.

Doesn't the edge of the perceivable universe lie in the future? Isn't it in the future for mass to move toward it?

No, read the second link.

I feel like you're only reading the titles or something, since both of your questions are answered in the text of the links we provided. If you don't understand a particular point, please ask for clarification. Matter that is moving at relativistic speeds does not form a black hole, even "apparently". There are different kinds of cosmological horizons, beyond which our observational capabilities are limited in various ways, but there are no black holes involved. I'll be happy to elaborate if you're interested in horizons.

Again, models of the universe are fully general relativistic, so there is no room for the kind of error you're talking about.

I've read that too. Referring to:

In fact objects do not have any increased tendency to form black holes due to their extra energy of motion. In a frame of reference stationary with respect to the object, it has only rest mass energy and will not form a black hole unless its rest mass is sufficient. If it is not a black hole in one reference frame, then it cannot be a black hole in any other reference frame.

I am not stating that anything forms a black hole due to its relative kinetic energy/momentum. I am asking if objects receding away from us at relativistic speeds would appear to us as if they are entering a black hole horizon.

Like an object entering a black hole horizon, the object should appear compressed and highly red-shifted. In other words, the edges of the universe (if we could see them) would apppear to us like a concave black hole. Again, I'm not stating it is a black hole.
Eventually, mass moving away from us should appear infinitely red shifted (it disappears into the apparent event horizon).

So, supposing that any of this makes sense, isn't it possible to expect black hole behavior from the boundaries of the perceivable universe?

 

[Leonardo Sidis]

The universe is like a BH only in that it is impossible to 'get out of' either.
Garth

Just wondering, but have we proven that we can't escape from the universe? I think I read somewhere that if we created some massive amount of energy, we could rip a hole in the fabric of space-time. Also, we can't rule out wormholes.

 

[Garth]

Just wondering, but have we proven that we can't escape from the universe? I think I read somewhere that if we created some massive amount of energy, we could rip a hole in the fabric of space-time. Also, we can't rule out wormholes.

We will know that is possible when you do it, enjoy the trip!

Garth

 

[Mike2]

Both Black Holes and the Observable Universe have an Event Horizon. You already know about the Event Horizon of Black Holes. The Observable Universe has a Cosmological Event Horizon. This is the distance from us where the expansion of space has caused objects at that distance to recede away from us at the speed of light so that we can no longer see them. And just like a BH, galaxies that approach the Cosmological Event Horizon appear to red shift and slow down in their motion; they freeze just before they disappear.

Some have suggested that just as in the case of BH's, an entropy can be calculated for the area of the Cosmological Event Horizon with the same formula for calculating the entropy of a BH using the area of its event horizon. And they suggest that the area of the Cosmological Event Horizon constraines the entropy inside it just as in the case for a BH. The area is emmense for the Cosmological Event Horizon. But that suggests some interesting consequences for an accelerating universe.

If the expansion of the universe is accelerating, then the distance to the Cosmological Event Horizon is shrinking, and the area associated with the Cosmological Event Horizon is decreasing as well. That would mean that the entropy enclosed inside the Observable Universe is decreasing. And we should expect some form of structures to emerge to compensate for the decreasing entropy of the collapsing Cosmological Event Horizon. Not only that, but we are losing material behind the Cosmological Event Horizon as galaxies recede away from us. So there seems to be a need for more complex and stable structures required of ever decreasing amounts of material. I find it interesting that life arose on Earth at just about the same time that the universe started it accelerated expansion. But what can we expect of the future if this process continues? Will some people have to rise from the dead to make up for this decreasing entropy? I wonder.

 

[Leonardo Sidis]

We will know that is possible when you do it, enjoy the trip!
Garth

Thanks! Don't worry, I'll tell you how it went.

 

[Mike2]

So, is dark energy an as yet unquantified force pushing outward? Or is dark energy merely a gravitational effect of relativity?

Just had a thought. The Unruh effect assigns a temperature to acceleration, and points in space are accelerating away from each other - the farther away points of space get, the faster they move away from us. And there must be an energy density for a given temperature. So does someone want to do the calculation: What is the energy density associated with the expansion of space? Is it anywhere close to the dark energy density? If no one else wants to venture this question, I'll try to get to it when I get time. Thanks.

 

[pervect]

pervect and SpaceTiger:
Pervect, I guess I shouldn't have used the phrase "in a black hole," but rather; "Might that which is beyond our known universe be perceived by us as a sort of black hole?"

What you can correctly say is that the universe has a cosmological event horizon, if that's what you're getting at.

Note that the the redshift and apparent disappearing of an object at the horiozn is what an outside observer sees.

An observer inside a black hole would not observe these effects, he would see light from the outside observer just fine - the horizon is a one way barrier. This barrier is "outside can't see inside" for a black hole, it's "inside can't see outside" for the universe.

Thus what's similar is the existence of a horizon in both cases, but it's not right to think of the universe as being a black hole.

As far as the gravity of rapidly moving objects go, it doesn't behave like you think it does.

For instance, take the following scenariospaceship1-------------->black hole
spaceship2

Spaceship1 heads directly towards a black hole at a high rate of speed, passig spaceship2 which is stationary with respect to the black hole.

Does the black hole appear heavier to spaceship 1 when it passes spaceship2, because of the relative motion? (Spaceship1 can consider that the black hole is moving directly towards it.)

The answer as to the black hole's apparent gravity depends on the coordinate system used, but a simple measurement that's easy to do on the two spaceships is to measure the difference in gravity along the length of the ship (the tidal force). If the black hole appeared heavier, we would expect that spaceship1 would experience more tidal force than spaceship2.

However, spaceship1 and spaceship2 will both measure the same tidal force in the above scenario.

If spaceship1 was moving away from the black hole we would have the same result.

If spaceship1 was moving up the page instead (with the black hole still to its right), it _would_ measure increased tidal forces as compared to spaceship 2.

 

[Mike2]

Just had a thought. The Unruh effect assigns a temperature to acceleration, and points in space are accelerating away from each other - the farther away points of space get, the faster they move away from us. And there must be an energy density for a given temperature. So does someone want to do the calculation: What is the energy density associated with the expansion of space? Is it anywhere close to the dark energy density? If no one else wants to venture this question, I'll try to get to it when I get time. Thanks.

If you could give me the expansion rate in units of meters and seconds and the dark energy density in SI units of Joules per meter cubed, I'll see what I can do. Thanks.

 

[SpaceTiger]

I've been trying to find the time to put together a good summary of cosmological horizons, but I'm afraid I'm still falling short. Start by taking a look at hellfire's brief review:

https://www.physicsforums.com/showthread.php?p=845204#post845204"

Doesn't the edge of the perceivable universe lie in the future?

The edge of the perceivable universe actually lies in the past. In theory, the maximally redshifted light would reach us from the moment of the Big Bang. In practice, we can't see anything before recombination (z ~ 1100).

Isn't it in the future for mass to move toward it?

There may exist an event horizon; that is, a comoving distance at which a light ray fired from Earth at the present time would never reach. I don't know if that's what you mean. It's not the same as a black hole event horizon, but is, in some ways, analogous to it.

Like an object entering a black hole horizon, the object should appear compressed and highly red-shifted. In other words, the edges of the universe (if we could see them) would apppear to us like a concave black hole. Again, I'm not stating it is a black hole.
Eventually, mass moving away from us should appear infinitely red shifted (it disappears into the apparent event horizon).
So, supposing that any of this makes sense, isn't it possible to expect black hole behavior from the boundaries of the perceivable universe?

In current theory, an infinitely redshifted "object" would sit at the particle horizon at t=0 (the Big Bang). The particle horizon is always growing with time, so nothing disappears behind it. The event horizon can shrink with time and objects can "disappear" behind it, but it doesn't represent a boundary of infinite redshift.

 

[Mike2]

The edge of the perceivable universe actually lies in the past. In theory, the maximally redshifted light would reach us from the moment of the Big Bang. In practice, we can't see anything before recombination (z ~ 1100).

So how far away is the Cosmological Event Horizon at present. I don't think this is the same as asking how far away the presently observeable horizon is because that is what it was in the past, right?

Would it be right to calculate the accelerataion of points in space from other points in space as the universe expanse as follows: Take the distance to the Cosmological Event Horizon (at present?) and say that there is a constant acceleration from zero to the speed of light over that distance over that time? Thanks.

 

[pervect]

I've been trying to find the time to put together a good summary of cosmological horizons, but I'm afraid I'm still falling short. Start by taking a look at hellfire's brief review:

"Horizons"[/URL]
[/quote]

I don't think this is the link you intended :-(

[quote]
There may exist an event horizon; that is, a comoving distance at which a light ray fired from Earth at the present time would never reach. I don't know if that's what you mean. It's not the same as a black hole event horizon, but is, in some ways, analogous to it.
[/quote]

They way I recall it is that such a horizon does in fact exist in FRW cosmologies [b]IF[/b] the expansion of the universe is acclerating. (Current data suggests that this is the case). I suppose I should go look for some references to support my recollections.

If the expansion of the universe is deaccelerating, we will (again IIRC) see all of it eventually.

 

[SpaceTiger]

I don't think this is the link you intended :-(

Oops, I typed the link name in place of the path (now edited)...no, I meant this link:

https://www.physicsforums.com/showthread.php?p=845204#post845204"

They way I recall it is that such a horizon does in fact exist in FRW cosmologies IF the expansion of the universe is acclerating. (Current data suggests that this is the case). I suppose I should go look for some references to support my recollections.

You're right, I hope I didn't give the wrong impression here...I don't have so much faith in the standard model that I would confidently extrapolate it to t->infinity.

There may be an event horizon. We are by no means confident that this is the case.

If the expansion of the universe is deaccelerating, we will (again IIRC) see all of it eventually.

Yup. And if it accelerates for a while, then decelerates (like the post-inflation universe), then an event horizon calculated assuming \Lambda CDM would be incorrect. It's for this reason (among others) that I view Mike2's entropy arguments with great suspicion.

 

[SpaceTiger]

So how far away is the Cosmological Event Horizon at present. I don't think this is the same as asking how far away the presently observeable horizon is because that is what it was in the past, right?

That depends on the model, but you should be able to get the result by just integrating:

\int_{a_0}^{\infty}\frac{dt}{a}

For that integral, you would need the time dependence of the scale factor and it will give you a result in comoving coordinates (it would diverge in physical coordinates). I have to run soon, so I don't have time to do the integral.

 

[ubavontuba]

I think I perceive the point of misundertanding

What you can correctly say is that the universe has a cosmological event horizon, if that's what you're getting at.

Note that the the redshift and apparent disappearing of an object at the horiozn is what an outside observer sees.

I'm thinking you mean in the case of observing a regular black hole (not an extra-universe observer, observing the universe).

An observer inside a black hole would not observe these effects, he would see light from the outside observer just fine - the horizon is a one way barrier. This barrier is "outside can't see inside" for a black hole, it's "inside can't see outside" for the universe.

Right, with an ordinary black hole. What I'm suggesting is to take all of these effects and turn them inside-out (the infinite density is beyond the sphere, not within the sphere).

Thus what's similar is the existence of a horizon in both cases, but it's not right to think of the universe as being a black hole.

Actually, I'm thinking of the extra-universe as a black hole (perceived, not real), not the universe itself.

As far as the gravity of rapidly moving objects go, it doesn't behave like you think it does.

For instance, take the following scenario


spaceship1-------------->black hole
spaceship2

Spaceship1 heads directly towards a black hole at a high rate of speed, passig spaceship2 which is stationary with respect to the black hole.

Does the black hole appear heavier to spaceship 1 when it passes spaceship2, because of the relative motion? (Spaceship1 can consider that the black hole is moving directly towards it.)

The answer as to the black hole's apparent gravity depends on the coordinate system used, but a simple measurement that's easy to do on the two spaceships is to measure the difference in gravity along the length of the ship (the tidal force). If the black hole appeared heavier, we would expect that spaceship1 would experience more tidal force than spaceship2.

However, spaceship1 and spaceship2 will both measure the same tidal force in the above scenario.

If spaceship1 was moving away from the black hole we would have the same result.

If spaceship1 was moving up the page instead (with the black hole still to its right), it _would_ measure increased tidal forces as compared to spaceship 2.

Sure, but spaceship 1's mass will appear to change (relative to spaceship 2) as it approaches the black hole. But, I'm not talking about black holes (in general) here anyway.

I will reiterate as delicately as I can. I am not talking about black holes. I am talking about an apparent effect of relativity. There is no real black hole in question to consider.

 

[ubavontuba]

Mike2

Both Black Holes and the Observable Universe have an Event Horizon. You already know about the Event Horizon of Black Holes. The Observable Universe has a Cosmological Event Horizon. This is the distance from us where the expansion of space has caused objects at that distance to recede away from us at the speed of light so that we can no longer see them. And just like a BH, galaxies that approach the Cosmological Event Horizon appear to red shift and slow down in their motion; they freeze just before they disappear.
Some have suggested that just as in the case of BH's, an entropy can be calculated for the area of the Cosmological Event Horizon with the same formula for calculating the entropy of a BH using the area of its event horizon. And they suggest that the area of the Cosmological Event Horizon constraines the entropy inside it just as in the case for a BH. The area is emmense for the Cosmological Event Horizon. But that suggests some interesting consequences for an accelerating universe.
If the expansion of the universe is accelerating, then the distance to the Cosmological Event Horizon is shrinking, and the area associated with the Cosmological Event Horizon is decreasing as well. That would mean that the entropy enclosed inside the Observable Universe is decreasing. And we should expect some form of structures to emerge to compensate for the decreasing entropy of the collapsing Cosmological Event Horizon. Not only that, but we are losing material behind the Cosmological Event Horizon as galaxies recede away from us. So there seems to be a need for more complex and stable structures required of ever decreasing amounts of material. I find it interesting that life arose on Earth at just about the same time that the universe started it accelerated expansion. But what can we expect of the future if this process continues? Will some people have to rise from the dead to make up for this decreasing entropy? I wonder.

It looks like you're getting it. I'm not too sure about the decreasing size of the cosmological event horizon though. I don't think the horizon is even real (in the sense that you can visit it). The size of the event horizon should always be determined by the relative speed of a lot of galaxies way out there. Where a large percentage of them approach c will determine the boundary (it needn't even be smooth).

 

[ubavontuba]

Unruh!

Mike2,

Just had a thought. The Unruh effect assigns a temperature to acceleration, and points in space are accelerating away from each other - the farther away points of space get, the faster they move away from us. And there must be an energy density for a given temperature. So does someone want to do the calculation: What is the energy density associated with the expansion of space? Is it anywhere close to the dark energy density? If no one else wants to venture this question, I'll try to get to it when I get time. Thanks.

I think this is a step in the right direction.

 

[hellfire]

That depends on the model, but you should be able to get the result by just integrating:
\int_{a_0}^{\infty}\frac{dt}{a}
For that integral, you would need the time dependence of the scale factor and it will give you a result in comoving coordinates (it would diverge in physical coordinates). I have to run soon, so I don't have time to do the integral.

I think one can get an estimation about this considering that the universe will end in a phase of exponential expansion due to the action of the dark energy which will become dominant. In such a case (considering that the scale factor today is a_0 = 1):

\int_{a_0}^{\infty} \frac{dt}{a} \quad = \quad \int_{a_0}^{\infty} \frac{dt}{e^{Ht}} \quad = \quad \frac{1}{H}

This means that the event horizon will be at same distance than the Hubble sphere. I guess that an exact calculation for \Omega_{\Lambda} = 0.73 and \Omega_M = 0.27 must be done numerically.

 

[pervect]

Sure, but spaceship 1's mass will appear to change (relative to spaceship 2) as it approaches the black hole. But, I'm not talking about black holes (in general) here anyway.
I will reiterate as delicately as I can. I am not talking about black holes. I am talking about an apparent effect of relativity. There is no real black hole in question to consider.

You've totally missed the point, partially because of my choice of example.

Spaceship 1 is approaching a planet or a black hole - it doesn't matter. (I said black hole in the first post, but it doesn't really matter, black holes are just convenient to calculate with - and the example in my textbook that this is drawn from involves a black hole).

From the frame of spaceship 1, the planet is more massive. (Not its invariant mass, which is invariant, but it has a greater energy, and hence a greater "relativistic mass".)

(Technical note: to define the mass at all, you need an asymptotically flat space-time.)

However, the gravity of the planet/black hole is not spherically uniform in the moving frame. Thus when spaceship1, directly approaching (or fleeing) the planet, fires up its Forward mass detector (a real device, which however measures tidal forces, and not mass directly), it finds that the gravity (specifically, tidal gravity) of the planet has not increased _even though_ the relativistic mass (energy) of the planet has increased.

The same thing happens if the spaceship is moving away from the planet. The same thing happens if the planet is moving away from the spaceship.

Motion towards or away from a planet (or black hole) does not affect tidal gravity.

The same thing does _not_ happen if the spaceship is moving perpendicularly to the line connecting it to the planet - in that case, the tidal gravity actually does incease.

This can be understood (in an approximate sense) by thinking of the gravitational field of a moving object being compressed, much like the electric field of a moving charge is. (The anology is not exact, mainly because gravity isn't really a field in GR).

The bottom line is your idea does not work - there is no "infinite mass" due to the expanding universe, even when the velocity of recession is very large. The velocity of recession is on a direct line, and thus it does not affect the gravitational forces.

There's another way of saying something similar that is more in the spirit of true GR and perhaps simpler. The net gravitational effect of a spherically symmemtric expanding shell of matter can be shown to be zero inside the shell.

The cosmological horizon (assuming it exists, which means assuming that the universe's expansion is accelerating and will continue to accelerte) is thus not due to the effects of the matter outside - it is due to the effects of the matter (and dark energy) inside the horizon.

[add]
Here's a reference (unfortunately it's in postscript - but with google you can view it as text, though it won't be quite as intelligible). The theorem is called Birkhoff's theorem.

www.ucolick.org/~burke/class/grclass.ps

What this means, roughly, is that spherical symmetry is enough to ensure that the spacetime is static, without separately requiring it. Another way to appreciate the content of the theorem is to consider any spherical object. If you go inside it and do anything you wish that does not disturb the spherical symmetry, then the external gravitational field cannot change. This is consistent with our earlier result that there is no monopole gravitational radiation. Yet another meaning for the theorem is than inside of a spherically symmetric distribution of mass there are no gravitational effects, just as in Newtonian theory, despite the nonlinearities.

 

[hellfire]

I think one can get an estimation about this considering that the universe will end in a phase of exponential expansion due to the action of the dark energy which will become dominant. In such a case (considering that the scale factor today is a_0 = 1):

\int_{a_0}^{\infty} \frac{dt}{a} \quad = \quad \int_{a_0}^{\infty} \frac{dt}{e^{Ht}} \quad = \quad \frac{1}{H}

This means that the event horizon will be at same distance than the Hubble sphere. I guess that an exact calculation for \Omega_{\Lambda} = 0.73 and \Omega_M = 0.27 must be done numerically.

So for the case \Omega_{\Lambda} = 1 the event horizon is located at the Hubble sphere. The Hubble radius for H = 71 km/s Mpc is equal to 13,7 Gly.

I have calculated the integral for the case \Omega_{\Lambda} = 0.73 and \Omega_M = 0.27. The event horizon should be located about 15,5 Gly away from us. I had some problems with the numerical integration, but nevertheless I think this should be a good estimation (I can provide details if someone is interested).

 

[George Jones]

So how far away is the Cosmological Event Horizon at present. I don't think this is the same as asking how far away the presently observeable horizon is because that is what it was in the past, right?

I think what you're calling the presently observable horizon is the following. A "galaxy" is on the presently observable horizon if, at t = 0, the worldline of the galaxy intersects the past lightcone for us at t = now. You colud also mean at t = photon decoupling. The distance to the presently observable horizon is then the distance between our worldline and the galaxy's worldline as the measured using the spatial scale at t = now.

A galaxy is on what (I think) you're calling the Cosmological Event Horizon if, at t = now, the worldline of the galaxy intersects the past lightcone for us at t = infinity. I think you're asking for the spatial distance between our worldline and the galaxy's worldline.

As Space Tiger says, the coodinate distance between these worldlines is

\int_{a_0}^{\infty}\frac{dt}{a}.

The physical distance between our wordline at the galaxy's worldline is the spatial scale multplied by the coordinate distance. At t = infinity, the scale is infinite, so the physical distance between the worldlines is infinite. But I think you're asking for the physical distance between the worldlines as measured along the spatial hypersurface t = now, i.e., the coordinate distance multiplied by the scale at t = now. With appropriate normalization, this physical distance is same as the coordinate distance.

Hellfire computed this physical distance to be 15.5 gigalightyears, and this also is what I calculate.

Regards,
George

 

[Mike2]

Thank you both: George Jones and hellfire,

It would seem as though there is a real difference in reference frames between us and distant objects. It is not objects moving in stationary space (with respect to us) that accounts for the recession and expansion of the universe. But their space (reference frame) itself is moving with respect to us.

As I understand it, that is exactly what is required to apply the Unruh effect - a frame of reference that is accelerating with respect to ours will feel a temperature whereas we would not. One question might be do these frames of reference have to be at the same physical location for the Unruh effect to apply? Or can they be separated by some distance?

I've looked into what might be the acceleration of space itself as the universe expands. The Hubble constant(?) is (71km/s +/- 4km/s)/Mpc. So to get the velocity that their reference frame (space) is moving wrt to us, just multipy the distance between us by the Hubble constant. OK, since this velocity is changing with distance (not time?), it would appear that this can be interpreted as an acceleration. But what is that accleration? So far we have:
r' = r*H
Then:
r'' = r'*H + r*H' But H'=0 (?)
substituting for r' with the above, then:
r'' = r*H²

There is no acceleration or velocity for points of space very near are own, but there is an acceleration for points at some distance from us, right? So the question is whether there would be an Unruh temperature associated with that acceleration. Thanks.

 

[George Jones]

Thank you both: George Jones and hellfire,

I was just following Space Tiger's lead.

As I understand it, that is exactly what is required to apply the Unruh effect

.

There is a similar effect associated with the expansion of the universe. As I understand it, this was first anticipated by Schrodinger. (?)

But what is that accleration? So far we have:
r' = r*H
Then:
r'' = r'*H + r*H' But H'=0 (?)
substituting for r' with the above, then:
r'' = r*H²

As I said, (in a universe with flat spatial sections like ours appears to have),

r(t) = a(t)R

where: r is the physical distance between worldlines of comoving observers; R is the (constant) coordinate distance between comoving observers; and a is the scale factor.

Thus,

r' = a'R = a'r/a = Hr,

where H = a'/a. Note that both a' and a depend on time, so that the Hubble "constant" is also a function of time. Then,

r'' = a''R = H'r + r'H,

and H' = a''/a - (a'/a)^2.

In our universe, H' < 0 and a''>0.

Regards,
George

 

[SpaceTiger]

As I understand it, that is exactly what is required to apply the Unruh effect - a frame of reference that is accelerating with respect to ours will feel a temperature whereas we would not.

I don't know much about the Unruh Effect, but it seems to be an effect that occurs for observers in non-inertial frames. In SR, an accelerating observer is in such a frame. In GR, however, inertial observers can have a coordinate acceleration (free-fall towards the earth, for example). In the case of the expanding universe, the galaxies are treated as following geodesics -- that is, they're treated as being an inertial frame. Were the accelerating expansion of the universe to cause an Unruh effect, I should think it would be a violation of the equivalence principle.

 

[pervect]

Unruh radiation is really confusing.

According to Baez

http://groups.google.com/group/sci.physics.research/msg/dceb3e4ad300a9e2?dmode=source&hl=en

1) An atom sitting on the Earth will not be excited by acceleration
radiation.
2) An atom freely falling near the Earth will (with some very small
probability) be excited by acceleration radiation.
3) An atom at constant distance from a black hole will (with some
small probability) be excited by acceleration radiation.
4) An atom freely falling near the horizon of a black hole will not
be excited be acceleration radiation (in the approximation where it's
right at the horizon).
5) An atom freely falling or at rest far from a black hole will
(with some small probability) be excited by acceleration radiation.

Why is the atom freely falling near the Earth excited by Unruh radiation? Because of the presence of a very distant Rindler horizon. If you think about the presence or absence of an event horizion, the existence/nonexistence of Unruh radiation becomes simpler. The existence of Unruh radiation depends on the existence of a horizon. If a horizon exists, so does Unruh radiation. If no horizon exists, then neither does Unruh radiation.

 

[Mike2]

Why is the atom freely falling near the Earth excited by Unruh radiation? Because of the presence of a very distant Rindler horizon. If you think about the presence or absence of an event horizion, the existence/nonexistence of Unruh radiation becomes simpler. The existence of Unruh radiation depends on the existence of a horizon. If a horizon exists, so does Unruh radiation. If no horizon exists, then neither does Unruh radiation.

I'm thinking that where there is an acceleration there will always also be an horizon. Black holes exist inside gravity wells where particles in the gravitational field experience an acceleration towards the singularity, and they also have event horizons. Particles that accelerate have an instantaneous particle horizon where, if the acceleration were to continue, at some distance behind them no light could ever reach them. And then, like wise, the existence of the cosmological event horizon would seem to prove that an acceleration exist. If the Unruh effect applies the black holes and accelerating particles, does it also apply to any acceleration due to the expansion of the universe?

ST: could you tell us why you think that this would violate the equivalence principle? Thanks.

 

[George Jones]

If a horizon exists, so does Unruh radiation. If no horizon exists, then neither does Unruh radiation.

And there is an effect associated with cosmological horizons. This effect exists in expanding universes even when the expansion is not accelerating. I can't remember who sees what.

Regards,
George

 

[pervect]

Here's a relevant quote from Baez, again

http://math.ucr.edu/home/baez/end.html

Why does the temperature approach a particular nonzero value, and what is this value? Well, in a universe whose expansion keeps accelerating, each pair of freely falling observers will eventually no longer be able to see each other, because they get redshifted out of sight. This effect is very much like the horizon of a black hole - it's called a "cosmological horizon". And, like the horizon of a black hole, a cosmological horizon emits thermal radiation at a specific temperature. This radiation is called Hawking radiation. Its temperature depends on the value of the cosmological constant. If we make a rough guess at the cosmological constant, the temperature we get is about 10-30 Kelvin.

So there is an Unruh effect from the cosmological horizon but it is very very very small. (Far too small to explain the 3k cosmic microwave background radiation, for instance, by about thirty orders of magnitude).

Unfortunately I'm not sure exactly how this number was calculated (I'm basically just taking Baez's word for the details.)

One of many things I'm puzzled about now that I think about the problem - if the universe stops expanding at some future date, then there is no horizon - is there still an Unruh radiation "now"?

[add]I think I may have at least part of an answer to this question. \Delta \mathrm{E} \Delta \mathrm{t} is constant, where E is energy and t is time. So it takes long time to observe the very low energies involved, it's not something you can observe quickly.

 

[Mike2]

Here's a relevant quote from Baez, again

http://math.ucr.edu/home/baez/end.html



So there is an Unruh effect from the cosmological horizon but it is very very very small. (Far too small to explain the 3k cosmic microwave background radiation, for instance, by about thirty orders of magnitude).

Unfortunately I'm not sure exactly how this number was calculated (I'm basically just taking Baez's word for the details.)

I followed the reference back to the book by R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chapter 5, page 105.

So from your quote, may I take it that the cosmological event horizon and the cosmological constant itself are both derived from the acceleration radiation due to expansion alone? So do the existence of the horizon and the CC now serve as formal proof of the ZPE from which the acceleration radiation comes from? And has it yet been proven that the temperature associated with this CC is consistent with the energy density of Dark Energy? Have we solved the dark energy mystery now?

 

[pervect]

I followed the reference back to the book by R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chapter 5, page 105.
So from your quote, may I take it that the cosmological event horizon and the cosmological constant itself are both derived from the acceleration radiation due to expansion alone? So do the existence of the horizon and the CC now serve as formal proof of the ZPE from which the acceleration radiation comes from? And has it yet been proven that the temperature associated with this CC is consistent with the energy density of Dark Energy? Have we solved the dark energy mystery now?

I think you're leaping ahead too much.

The cosmological constant indicates that there is a cosmological event horizon, at least according to standard models. (But see Space Tiger's reservations - it's possible to construct models in which there is no cosmological event horizon, for instance if the expansion deaccelerates again. We don't expect that to happen, but dark energy is not well understood, and we may not have all the details totally correct.)

If a cosmological event horizon exists. we expect that there is a very tiny amount of unruh radiation associated with it's existence.

I would not call this proof of "ZPE", because that term isn't very well defined, and there's too much nonsense written under that name. Rather I'd stick with what Baez said, that if the current expansion continues to accelerate, we'd expect the universe to reach a minimum but positive temperature due to the Unruh radiation associated with the cosmological horizon.

 

[ubavontuba]

Cool stuff guys. Keep running with it.

Keep in mind though that the cosmological event horizon (CEH) I am referring to is not real in the sense that it's in a place that can be quantified. Think of it like a rainbow. It's there and it can be observed and it has an effect on your locality, but you cannot approach it.

It looks to me like this is simply a logical deduction of relativity. As a rainbow's position is relative to the observer, so is the CEH.

 

[ubavontuba]

Pervect,

There's another way of saying something similar that is more in the spirit of true GR and perhaps simpler. The net gravitational effect of a spherically symmemtric expanding shell of matter can be shown to be zero inside the shell.

The cosmological horizon (assuming it exists, which means assuming that the universe's expansion is accelerating and will continue to accelerte) is thus not due to the effects of the matter outside - it is due to the effects of the matter (and dark energy) inside the horizon.

Aparrently you may have missed this point:

My concept is that to the observer, the universe having seemingly been expanding at relativistic speed from any given point, the perceived black hole "shell" should not act inside like the interior gravitational effects of a normal gravitational sphere. This is because the mass is receding at near light speed in either perceived direction (sort of like shining two flashlights in opposite directions).

That is that from the standpoint of the observer, the energy and mass at the perceived edge of the universe on his left, let's say, is in a noncontiguos reference frame from the matter and energy on his right.

So, all the matter on his right, let's say, is going to be effected more and more by the matter at the perceived edge on his right, in a relationship to distance. The closer it is to the observer, the less it is thusly affected and conversely, the farther away it is, the faster it will seem to be accelerating outward (generally speaking).

As the universe expands, this effect should be perceived by the observer as an acceleration of the expansion of the universe. Ergo, as "dark energy." This is because the receding walls allow there to be more space for this effect to take place in, and therefore everything (including perceived motion) must seemingly get bigger (faster) too.

Do you see? We're not in a normal gravitational sphere in this case. All radii are noncontiguos (increasingly so with distance). In the normal gravitational sphere to which you refer, it's all in a single/contiguous reference frame. (Of course this is assuming that gravity truly propagates at the speed of light.)

 

[hellfire]

I am happy to see a discussion about horizons, because this will give me the oportunity to ask some questions that bother me a long time ago...

The cosmological event horizon is actually an observer dependent horizon, same as the Rindler horizon. What bothers me, specially in case of the Unruh radiation, is the following: You can get the result of an observer dependent horizon considering only the action of some field (a scalar field for example) in flat spacetime viewed by an accelerated observer. This observer will detect a thermal bath of particles. Calculations and qualitative discussions I am aware of stop at that point. However, a thermal bath of particles should create a gravitational field that should pertub the curvature making it non-vanishing. But, does this make sense? The inertial observer and the accelerated observer, both in the "same" spacetime, would measure different curvatures.

There are other things that bother me, like the fact that everywhere it is mentioned that the thermal radiation is "emitted" by the horizon. The thermal radiation from horizons is a mathematical consequence of the Bogolyubov transformations between two different vacua. In general, these lead to particle creation when evaluating the number operators in different vacua and I would expect that this is a homogeneous and isotropic and non-localized phenomenon of particle creation. These particles do not form a thermal distribution in the general case and thermal distributions appear only in case of horizons. Thus I would expect the thermal case to be a special case of the general case of particle creation between two different vacua. However, everywhere one can read that "horizons radiate", meaning that they produce the thermal distribution of particles. According to the more general case I would expect the thermal radiation in case of horizons to be also a bath of particles, a kind of "diffuse" radiation, isotropic and homogeneous, but not a radiation coming from the horizon.

 

[George Jones]

Sorry hellfire, I intended to make some comments this morning on your latest post in this thread, but I used up all my free time working on a post for the SR & GR forum, and I can procastinate no longer. To work!

I can say that many of your questions are answered in Quantum Fields in Curved Space by Birrell and Davies.

I hope come back to these issues.

Regards,
George

 

[hellfire]

I can say that many of your questions are answered in Quantum Fields in Curved Space by Birrell and Davies.
I hope come back to these issues.

Thanks George, it would be nice if you could summarize it, because I don't have any possibility to check this book.

 

[SpaceTiger]

Sorry hellfire, I intended to make some comments this morning on your latest post in this thread, but I used up all my free time working on a post for the SR & GR forum, and I can procastinate no longer.

I too should apologize for my rushed contributions to this thread. I'm in the middle of finals period (we have them after break here ), so I haven't been able to keep up with everything. When time permits, I have quite a bit to say, though I'm afraid it will contain more questions than answers, not being an expert on Hawking or Unruh radiation.

 

[George Jones]

I'm in the middle of finals period

Good luck Space Tiger!

I suspect, though, that with your intellect, you won't need much luck.

Regards,
George

 

[pervect]

Pervect,
Aparrently you may have missed this point:
Do you see? We're not in a normal gravitational sphere in this case. All radii are noncontiguos (increasingly so with distance). In the normal gravitational sphere to which you refer, it's all in a single/contiguous reference frame. (Of course this is assuming that gravity truly propagates at the speed of light.)

The problem is, that the universe appears to us to be isotropic and homogeneous around any specific point, at least as long as that point is at rest relative to the CMB frame.

That's the standard assumption, and it fits well with observations. Of course we can only directly observe the universe from one particular point of view, though we can construct what we think other people should see based on our observations.

This symmetry of the universe isn't obvious if you chose some other frame. For instance, in some frame moving relative to the CMB frame, the symmetry that was present in the stationary frame becomes non-obvious, the universe appears anisotropic.

But that doesn't mean that the symmetry still isn't there, the solution in the moving frame must still appear symmetrical when viewed from the frame in which the universe is symmetrical. And we know how to switch points of view via the Lorentz transform (in SR), or generalized coordinate changes (in GR).

I don't think I can say much more without resorting to writing down equations.

 

[pervect]

I am happy to see a discussion about horizons, because this will give me the oportunity to ask some questions that bother me a long time ago...

The cosmological event horizon is actually an observer dependent horizon, same as the Rindler horizon. What bothers me, specially in case of the Unruh radiation, is the following: You can get the result of an observer dependent horizon considering only the action of some field (a scalar field for example) in flat spacetime viewed by an accelerated observer. This observer will detect a thermal bath of particles. Calculations and qualitative discussions I am aware of stop at that point. However, a thermal bath of particles should create a gravitational field that should pertub the curvature making it non-vanishing.

Here is the way I look at it. The stress-energy tensor is, and must be, the same according to both descriptions. You can actually get the stress-energy tensor when you write down the Lagrangian of your field, for instance from the Lagrangian. So we expect it to be the same.

The more "intuitive" way I look at it is this. Real particles contribute to the stress energy tensor, but so do "virtual" particles. For instance, the electric field between two charges is due entirely to virtual particles, however the electric field contributes to the stress-energy tensor as is well-known.

What happens in accelerated frames of reference as nearly as I can make out is that the booga-booga (oops, I mean Bogoliubov :-)) transforms turn some real particles into virtual particles, and some virtual particles into real particles, and that's all they do. (This comes from the fact that some postive frequences w get mapped to negative frequences w', and vica-versa, the postive frequencies corresponding to 'real' particles and the negative frequencies correspoinding to 'virtual' particles.) So the particles that you see from acceleration are not appearing from nowhere, they appear because virtual particles are being turned into real ones.

Unfortunately, it's possible I could be full of **** here, but that's the way I look at it at the moment. I haven't done any extensive calculations with quantum mechanics in curved space-time, and I find that doing detailed calculations is one of the few ways of discovering "bad" mental models.

 

[Mike2]

I think you're leaping ahead too much.
The cosmological constant indicates that there is a cosmological event horizon, at least according to standard models. (But see Space Tiger's reservations - it's possible to construct models in which there is no cosmological event horizon, for instance if the expansion deaccelerates again. We don't expect that to happen, but dark energy is not well understood, and we may not have all the details totally correct.)
If a cosmological event horizon exists. we expect that there is a very tiny amount of unruh radiation associated with it's existence.
I would not call this proof of "ZPE", because that term isn't very well defined, and there's too much nonsense written under that name. Rather I'd stick with what Baez said, that if the current expansion continues to accelerate, we'd expect the universe to reach a minimum but positive temperature due to the Unruh radiation associated with the cosmological horizon.

I wonder how they calculated that temperature. Aren't they assuming that dark energy is the same as the cosmological constant, and aren't they using that energy density to come up with an equivalent temperature? If not, can't we just do this and see if it is equal to these other calculations? If we are at least in the same order of magnitude, then isn't that encouragement to make more precise calculations?

My calculations tell me that a temperature of 10^-30K corresponds to an energy density of 7*10^-136(J/m³), which is about 128*10^-51eV/Mpc³. I'm sure this is too small to be the dark energy density, right?

 

[ubavontuba]

isotropic-anisotropic

Pervect,

The problem is, that the universe appears to us to be isotropic and homogeneous around any specific point, at least as long as that point is at rest relative to the CMB frame.

Right. I'm saying the same thing. Every reference point would view the effect the same way. There is no assymetry (to speak of) in my concept.

That's the standard assumption, and it fits well with observations. Of course we can only directly observe the universe from one particular point of view, though we can construct what we think other people should see based on our observations.

Right. Again, I'm saying the same thing as in the current model, that being that any observer anywhere will perceive themselves as being in the middle of an expanding universe. I've just built upon this a little.

This symmetry of the universe isn't obvious if you chose some other frame. For instance, in some frame moving relative to the CMB frame, the symmetry that was present in the stationary frame becomes non-obvious, the universe appears anisotropic.

Exactly. This is my point concerning noncontiguous frames of reference. To us, a point a few billion light years away seems anisotropic in respect to the rest of the universe. However, would we to be where that point is, we'd see that it is isotropic and apparently at the center of an expanding universe (just like what we see here).

But that doesn't mean that the symmetry still isn't there, the solution in the moving frame must still appear symmetrical when viewed from the frame in which the universe is symmetrical. And we know how to switch points of view via the Lorentz transform (in SR), or generalized coordinate changes (in GR).

That's what I'm saying. Everything in regards to this still applies. The difference is that I feel I have taken it a step further (not refuted it).

I don't think I can say much more without resorting to writing down equations.

Yeah, those pesky equations. I wish I knew a couple of good physicists looking to publish. I think a heck of a good paper could come out of this...