The problem today is that the world is now one giant laboratory where a big enough mistake could end us all.

However sorry Otto, there are many colliders in the works and countries less safely conscious than Switzerland. Therefore earth life is finished if you are right, either something fast like you alone predict or in a few hundred years as less hysterical domesday prophets predict. or perhaps, if black holes are slower that cosmic rays, the sun winking out in a few thousand years or more.

Thus the only hope for humankind if you are somewhat right would be a dire warning at the last moment, I wonder what Otto or others can do to make such a warning more likely.

RichardKane
pa.blogspot.com

No it’s not. The equation you have given is simply wrong, it’s not Einstein’s, it’s empirically false, it’s in contradiction with the Schwarzschild metric, and even with your own verbal description of the situation. All this was pointed out to you repeatedly, and I hence assume you are aware of the problem, so what are you trying to pull here?

“Then you kindly out yourself as not believing in the gravitational twin paradox. ”

Sorry, you are delusional. Correcting your views about something is not the same as not believing in it.

“But for all practical purposes, the deviations between the times valid for different outside observers are negligible compared to the ratio of all those times to the horizon time. (I here for simplicity assiemed a stationary universe.) ”

No they aren’t negligible as is evident from the infiniteness of the outside observer’s time compared to the finite proper time of an infalling observer, which was the subject you just brought up. Also I wonder what you mean by “all practical purposes”. These “practical purposes” obviously exclude cricumstances in which these differences have been actually measured, which would rather make you the one not believing in the gravitational twin paradox. Finally, there is no “horizon time” any more than there is a “light ray time.”

“The exponents of the physics community for many decades lost awareness of this fact – that the infinite outside time in the Schwarzschild metric is not just something formal but the true ontological time in the cosmos (or at least in a simplified cosmos).”

That is a false alternative. The outside time is the “true ontological” time of an outside observer at rest. That doesn’t make it “something formal”, but it doesn’t make it the “time of the cosmos” either. There are lots of observers in the cosmos each with their own time.

Thank you for the concrete first question. I apologize for being unable to revise the equation which you point out because it is not mine but Einstein’s. It expresses his oldest and most important insight into the nature of gravity: the gravitational clock slowdown.

Neverthless I am very grateful for giving your own thought to this scandal which it still is (apart from its being right in my opinion).

Then you kindly out yourself as not believing in the gravitational twin paradox. This again is very meritful because you are the first physicist who does so openly. There may be another one — endowed with a Nobel medal perhaps — daring o come to your side now. For apparently the whole physics community is of the very same opinion as you expressed it.

Your third argument is equally deep and important again (all three only have an error of sign in them in my opinion — which in mathematics is not counted as a vice as you know). Again, the physics community is on your side: That different clock speeds are nothing ontological but can be “healed” by scale transformations. My dear friend David Finkelstein is co-responsible for the famous Eddington-Finkelstein scale transformation, for example. I am sure he forgives me if I here publicly declare that while I admire its mathematical beauty and rigor, it is not physical. He will come to your aid just as amiably as I here criticize him (I know he has more important work to do). Nevertheless I believe he could do our friendship and the world no greater service at the moment (I never dared approach him head-on on this so far).

Concretely: Your argument that there is no commmon time valid for the outside universe is numerically not false. Indeed only for infinitely far outside observers is there a common time. But for all practical purposes, the deviations between the times valid for different outside observers are negligible compared to the ratio of all those times to the horizon time. (I here for simplicity assiemed a stationary universe.)

Your argument nevertheless is very well taken. The exponents of the physics community for many decades lost awareness of this fact — that the infinite outside time in the Schwarzschild metric is not just something formal but the true ontological time in the cosmos (or at least in a simplified cosmos). You will be not alone if you contradict me here.

Please, accept my appreciation for your well-taken counterarguments. That I am of the opposite opinion in every single case I hope you can forgive me. I am waiting to learn more.

You are welcome. Speaking of which, have you corrected your Eq. (1) in http://lifeboat.com/blog/2011/05/osama-bin-cern already and reconsidered your conclusions accordingly?

“And forgive me if I find that the reference you kindly gave does not say anything about two clocks, one left on the outside, the other descending and then returning. In that case, it turns out that the returned twin clock finds the waiting twin clock grown infinitely old in the meantime.”

You are forgiven for not finding it there because it’s wrong. As long as the observer does not reach the horizon he may return in finite outside time. If he reaches the horizon he will never return. It is impossible for him to return *and* find his brother infinitely older.

“For the same reason, then, no black hole is ever finished and no horizon ever reached.”

Wrong too. Whether something can happen somewhere in spacetime is unrelated to the question of how long it would take for an outside observer to notice. If he has no way of knowing what is going on somewhere in finite time that’s exactly what makes “somewhere” a point on (or beyond) the horizon.

“Astronauts may think they can reach and cross the horizon in finite time. But this is a fairy tale told to them before their mission.
For before they reac the horizon, an infinite amount of time needs to have passed for the whole universe.”

No, only for the outside observer. There is no such thing as a “time for the whole universe.” Time is relative.

And forgive me if I find that the reference you kindly gave does not say anything about two clocks, one left on the outside, the other descending and then returning. In that case, it turns out that the returned twin clock finds the waiting twin clock grown infinitely old in the meantime.

For the same reason, then, no black hole is ever finished and no horizon ever reached. Astronauts may think they can reach and cross the horizon in finite time. But this is a fairy tale told to them before their mission. For before they reac the horizon, an infinite amount of time needs to have passed for the whole universe. In an infinitely long time, there is a good chance, however, that something will intervene.

For example, another black holemay have come close to the one in question. Any particle still on its way towards the former will then have to “decide” whether to continue approaching its own black hole or to change course toward the winning (bigger) black hole. This is a neat mathematical situation: a separatrix forms. Even though it is only an almost-asymptotic trajectory that we are talking about, the latter is very close to a genuine separatrix. That is, one can predict that before the smaller black hole is finished, any of its in-falling objects will be forced onto a separatrix-type trajectory — and therefore leave the gravitational field of both. This insight if correct allows for an eternal recycling of matter between 50 percent of the universe’s mass in the form of black-hole matter and cosmic ray particles that eventially condense into gas clouds etc. — an eternal perpetual motion machine.

You will say that the big bang guarantees finiteness at least in one time direction (the past). But there is a recent series of papers which proves that the universe is at least as likely to be nonexpanding and infinitely old. If you wish, I send you the corresponding review paper. But of course, cosmology is not our main topic. So please forgive me. It is just too rewarding to discuss normal science that is not beset by a hysterical tone owing to time’s running out.

Are you serious? Use google or consult Wikipedia about black holes.

Ok, here you are! From http://en.wikipedia.org/wiki/Black_hole#Event_horizon :

“To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole.[44] Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it.[45] ”

Unless you hold that wikipedia is largely unavailable in the western hemisphere your claim seems quite untenable to me.

“Second, your claim that quantum tunneling covers infinite distances, which you implicitly make, is most important. I would like to quote you on that. Please, tell me where I can find the evidence. ”

You can quote what I said, but not what you, based on your misconceptions, think I might have meant. Neither did I say anything about “quantum tunneling” nor about “infinite distances” (other than that your infinite distance argument is stupid, but you can quote me on that.)

For what may be wrong with the account of virtual particles tunneling an infinite distance see: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html
(and continue with the references cited therein)

From the content:
“In fact this argument also does not correspond in any clear way to the actual computation. Or at least I’ve never seen how the standard computation can be transmuted into one involving virtual particles sneaking over the horizon, and in the last talk I was at on this it was emphasized that nobody has ever worked out a “local” description of Hawking radiation in terms of stuff like this happening at the horizon. […] Note: I wouldn’t be surprised if this heuristic picture turned out to be accurate, but I don’t see how you get that picture from the usual computation.”

Even if there was such a description in local terms it would be hard to see how it could be invalidated by an infinite distance to the horizon, because there are *equivalent* descriptions already known, that do not in any way depend on that distance or its being finite. (Although, the distance in fact *is* finite, because your argument is nonsense as shown previously.)

Second, your claim that quantum tunneling covers infinite distances, which you implicitly make, is most important. I would like to quote you on that. Please, tell me where I can find the evidence.

Note that in effect this is saying that Hawking radiation cannot exist because classically nothing can escape the horizon. Rössler seems completely unaware that this is but the very *definition* of the black hole’s event horizon, and that its apparent contradiction with the principles of quantum mechanics was the major point to which Hawking radiation owes its fame. But Rössler’s “theorems” never even touch quantum mechanics at all, which means it misses the point completely.

It’s is a lot like arguing that the Schrödinger equation must be false, because from classical electrodynamics it follows that atoms can’t be stable, due to the electron’s radiation.

“This infinite travel time – the infinite gravitational twins paradox – is virtually unknown in the (Western) scientific community. ”

Please, could this get any more ludicrous? You seem to get increasingly disconnected from reality.

This infinite travel time — the infinite gravitational twins paradox — is virtually unknown in the (Western) scientific community. I thought I had found it in Frolov and Novikov, and it is there, but not very explicit. So it is fair to say (unless you correct me) that it is unknown.

The laughing question above is appreciated because it reflects the false assumption that black holes would eat matter only after having gulped it behind the horizon. This latter event indeed never happens in finite outside time. So if you wish, not a single balck hole exists in the universe (strictly speaking). Nevertheless it would be a big mistake to think that they would therefore not exist. They are merely unfinished. But FAPP — for all practical purposes — they do exist. This is because viewed from the outside, the matter in question has very soon reached what amounts to 99.999999… percent of the distance toward the horizon, measured in terms of the outside world’s meter sticks, that is, in percent of the remaining radius of the sphere surrounding the black hole in the outer world.

I am grateful that this question came up. It forces the scientific community to “think along” so that hiding behind wrong dogmas becomes impossible.