What's so paradoxical about the black hole information paradox?

[Linguofreak]

I've always been confused by the black hole information paradox. What I don't get is this: information is only potentially lost to the outside universe if infalling matter actually crosses the event horizon, but this takes an infinite amount of time to occur in any reference frame that does not itself cross the horizon. Meanwhile, if black holes radiate as described by Hawking (without which the whole paradox is moot), then a hole of finite mass will radiate away in finite time. As a result, we technically don't even see a black hole form: once neutron degeneracy pressure fails, a collapsing object's gravity well becomes arbitrarily, but finitely, deep before Hawking radiation begins to make it shallower. Eventually the mass becomes low enough that degeneracy pressure is able to halt the collapse, and I imagine there might even be a rebound (so that a significant amount of the infalling matter is actually ejected from the object, rather than that mass being radiated away as Hawking radiation). The whole process, as viewed from the outside, would take an incredibly long, but finite, time (as the time for a large collapsing object to decay by Hawking radiation is extremely long), but for the infalling matter it would all happen extremely quickly (less proper time than the proper time needed to cross the horizon in General Relativity without Hawking radiation until the collapse is halted, less than twice that for any rebound). In any case, the long and the short of it is that all the information contained in the infalling matter should be retrievable in finite time.

The fact that very smart physicists have been arguing about this for decades makes me think I must be missing something, but the premises my argument depends on (infalling matter takes an infinite time to cross the horizon for all external reference frames, and Hawking radiation takes a finite time to radiate the entire mass of a black hole as measured in those same frames) are, as far as I can tell, fairly uncontroversial, and I'm fairly confident that my logic from that point is sound, yet smarter people than me continue to argue about the issue. So what am I missing?

 

[Col_Klonk]

All theoretical theory's have been 'bunked' after a while, and even Hawking is looking 'bad'.
But this is the realm of Theoretical Physics.... lots of ideas, plenty of virulent gas (and $$$) until is fizzles out under the next 'load of gas'.

While GUT still seems far away, gravity will always be faster than light :hello:

 

[jangofett287]

gravity will always be faster than light :hello:

Umm, no. Gravity can carry information, therefore it can only travel AT the speed of light, it can never be faster than it. So long as relativity holds.

 

[Keithth G]

The 'speed of gravity' is always a controversial subject.

What is known, and has been known for a long time, that the standard elliptical motion of planets requires that gravity be based on where the primary body (e.g., the Sun) 'actually' is not where it appears to be taking into account the finite speed of light. For example, the light time from the Sun to Earth is around 8 and a half minutes. To calculate the gravitational force on the Earth correctly, you need to base your calculations on where the Sun is 'now' and not where it 'was' eight and a half minutes ago.

And the same is true if you wish to calculate the force of the Andromeda galaxy on the Sun. Even though the light time to the Andromeda Galaxy is around 2.5 million year, you need to base your calculations on where the Andromeda Galaxy is now - and not where it was 2.5 million years ago.

A violation of relativity? No, not really.

In General Relativity, bodies are viewed as moving on straight lines on a curved space-time manifold. Einstein's Field Equations - the set of equations you need to solve in order to work out how space-time is folded - must always be true. And, as it turns out, in the 'weak field' limit (e.g., in the neighbourhood of low mass objects like the Sun or the Earth as opposed to black holes), the solutions of Einsteins Field Equations simply reduce to classic Newtonian gravity (plus a few very small and largely ignorable relativistic corrections). And as we know, Newtonian gravity isn't constrained by speed of light limitations.

However, there is a special set of solutions to Einstein's Field Equations that describe gravitational waves. But these solutions are not the same as those that give rise to the weak field approximation of Newtonian gravity. As it turns out, gravitational waves do travel at the speed of light - which is just as well since (like all wave phenomena) they can be used (in principle) to convey information.

 

[Artlav]

In other words, it's not the gravity that propagates at the speed of light, it's the change in gravity that propagates at the speed of light.

 

[Lisias]

In other words, it's not the gravity that propagates at the speed of light, it's the change in gravity that propagates at the speed of light.

I'm confused. As usual.

You are saying that if by some miraculous act of Gord =P the Sun suddenly disappears, the Earth would be ejected out of the orbit only 8 minutes later?

Or, better yet, if a Sun sized star, travelling at 99.9999% of the speed of the light, crosses our Solar System, we would be kicked out of our orbit just moments before being fried by the heat?

 

[Col_Klonk]

I think the problem with gravity is that people are think in terms of Einsteins theories and max speed = speed of light, then formulate their theories around this = stunted progression.

It's the same as Big Bang.. a really crazy idea and the maths that were derived to prove it... square box hammered into a round hole .. then the next theory String.. more maths... and then Super Strings.. How many dimensions must one go to before you say... 'This is ridiculous, it should be simple'

 

[jedidia]

miraculous act of Gord

That came out very wrong :rofl:

 

[Urwumpe]

That came out very wrong :rofl:

You have never heard of Gørd, the norse warrior god of spacetime? Son of Thor?

 

[Lisias]

That came out very wrong :rofl:

You must read this.

 

[Urwumpe]

You are saying that if by some miraculous act of Gord =P the Sun suddenly disappears, the Earth would be ejected out of the orbit only 8 minutes later?

Yes. And much more exotic things would happen, which are called "gravitational waves". Instead of simply getting ejected out of the orbit, we would experience variations between sun gravity and almost anti-sun-gravity.

Unless gørd decides that he also hammers the spacetime flat.

 

[Artlav]

I'm confused. As usual.

Imagine the good old image of a heavy ball sitting on a stretched piece of rubber film:

Now, a thing in orbit would follow that curved surface, going around the ball.

This curvature just is here, it does not have anything propagating.

Now, imagine what would happen if a heavy ball got dropped onto that rubber.
Neither youtube nor the guy i ordered a high speed camera from delivered, so that's the closest thing i found:

See how the curvature does not happen instantly.
It propagated, taking it's time to reach out to a distance.

Same with gravity - if the sun was to vanish, the Earth would keep going for some minutes before the space containing it stretches back into near-flatness and the planet would start moving in a straight line.

It's the change of stretching of space that propagates, instead of the force of gravity constantly asking the sun where it is at light speed..

 

[Lisias]

It's the change of stretching of space that propagates, instead of the force of gravity constantly asking the sun where it is at light speed..

If I understand correctly, the space-time behave as a tissue or as a superficial tension on a fluid.

So, going on on that my second example of that Sun sized star crossing our Solar System nearly the speed of light. Let's suppose such star would cross the Solar System through the center, almost (but not) hitting the Sun physically.

Since the gravity waves will not travel faster than light, and since the Star is itself travelling near the speed of light, I would be correct by saying that this would form something as the shockwave formed by a moving ship?

And then the bodies on our Solar System would be hit by such shockwave in a similar manner little boats and swimmers would be hit by that moving ship shockwave?

 

[Urwumpe]

And then the bodies on our Solar System would be hit by such shockwave in a similar manner little boats and swimmers would be hit by that moving ship shockwave?

Exactly. That is what we expect to observe for example when two black holes rapidly orbit each other.

But for the gravitational waves, that we could observe in our solar system, we still lack the tools to measure such weak variations of space time. But we are getting closer.

 

[Linguofreak]

http://d1068036.site.myhosting.com/chemGraphics2/wake.jpg[/IMG]

Actually, not quite. First of all, the shockwave from a moving ship is created by waves piling up because the ship is moving faster than the waves can travel. This would not be the case for a relativistic star. Also, the star would only be accompanied by gravitational waves if it had been accelerated up to speed in the relatively recent past. Otherwise, its gravitational field would look normal, except for being modified by relativistic length contraction and time dilation.