So, in spite of many well-intentioned people's attempts to give honest and well thought answers in this thread, we are down to this level?
And thanks to Motor Daddy
Thanks for this tashja. I have to say that IMHO this "waterfall" answer is cargo-cult crap. A gravitational field alters the motion of light and matter through space, but it doesn't suck space in.Prof. Olum's reply to Farsight's gedanken:
The original poster is right that the light does not curve round and so is always going radially outward at the speed of light. But if it is emitted at the black hole horizon, it nevertheless makes no outward progress and is trapped in the horizon forever. The situation is somewhat similar to ripples on the surface of a river which is falling over a waterfall. Some of the ripples move upstream at their usual speed, but if they are too close to the brink, they don't make any upstream progress. If the light is emitted from inside the horizon, then it gets closer and closer to the singularity, even though it is always directed outward and moving at the speed of light.
Again, appreciate the professional replies tashja....
With the one from Prof Olum, though, while agreeing with the bulk of what he said, I was of the opnion that the light emitted just at the EH but outside, would actually arc or curve back to secumb to the EH, unless it is emitted directly radially away.
Then it will appear to hover forever just outside that EH [as the professor says] which in my understanding reinforces the "space falling in" and "water fall" analogy as I illustrated in my previous post.
My querie is with photons that are not emitted directly radially away.
I was always of the opinion that with that scenario, from a local FoR, they would indeed arc back and secumb to the BH's EH.
Not wanting you to wear out your welcome, but if that position could be clarified, I would appreciate it.
Thanks.
Prof. Olum:
Suppose you are slightly outside the event horizon of a black hole and
you sent out a flash of light in all directions. The photons emitted in
a narrow cone around the outward radial direction will travel outward
and escape. Outward-going photons outside this cone will start to make
outward progress, but curve back and fall in through the horizon. (Of
course an observer outside the horizon never actually sees the photon
pass through the horizon.)
Near the cone on the inside the photons will go around the black hole
many times before getting loose, whereas near the cone on the outside
they will circle many times before falling in. I think the photons that
lie on the cone will asymptotically approach the innermost stable photon
orbit from the inside.
The closer you are to the horizon, the narrower this cone becomes. On
the horizon, a single direction leads to neither falling in nor getting
out, but rather hanging forever, while all other directions fall in
without ever making any outward progress.
Ken Olum
Tashja, Prof. Begelman responce, except for reference to firewalls in the last paragraph seems limited to a description of spacetime as per GR.
At first glance, Prof. Hamilton's link also appears to be limiting its focus to GR...
I have no issues with the GR thought experiments. My comments were an attempt to at least reintroduce the general implications of the thread title and early posts... It seems that what happens within the event horizon, must involve both the affects of GR and QM... And the QM aspect has not yet been settled... but it seems to me from the neutron star reference, that the emission of photons is at least altered, if not, once again non existent.
The result is that a photon can travel outwards at c relative to local space inside the black hole, yet still be dragged inward so no escape is possible.
Thanks for this tashja. I have to say that IMHO this "waterfall" answer is cargo-cult crap. A gravitational field alters the motion of light and matter through space, but it doesn't suck space in.
We note the telling phrase "like to think". I "like to think" you don't - stalemate. Great science!!I like to think I understand gravity,
But, as I know to my cost, reading and understanding are quite different thingsI've read the original material.
Then you clearly have no idea what a 4-manifold is, specifically a semi Riemann 4-manifold that Minkowski called spacetme. This is absolutely the structure that the Field Equations are based on.Einstein thought of a gravitational field as "a state of space".
I do, and it just isn't what space is. Space is real, it's physical, it's what light moves through. There's no motion in spacetime, it's a static abstract "structure".Then you clearly have no idea what a 4-manifold is, specifically a semi Riemann 4-manifold that Minkowski called spacetime. This is absolutely the structure that the Field Equations are based on.
IMHO that's part of the problem. Einstein said spacetime in one sentence and space in another, and he was referring to two different things. But many people see no distinction between the two. I point to the Baez article which says this: Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial. But people like you just can't accept the distinction. NB: apologies for not responding to your post #548. I was tied up for a few days. The metric has 10 components because you're measuring motion through space.2 points you might like to consider: in mathematics (and I assume in mathematical physics) the term "space" is used to refer to the "playground" you are working in, not necessarily "physical space" (whatever that is) .
And there's no doubt that a gravitational field isn't curved space. So don't confuse space with spacetime.There is absolutely no doubt that the Field equations refer to spacetime.
Read and understood, but not derived.Have you read, understood and derived these equations?
No, Einstein doesn't often say space when he means spacetime. Au contraire, he uses both words in one paragraph and there's a clear distinction between them.Second, for just this reason, and others, in English translation E. often says "space" when he means spacetime. Just as he often says "velocity" when he means "speed" (according to Google translate, these are the same words in German)
No it doesn't. I will pass judgement on the basis of whether they agree with Einstein, and with each other. And if they don't, then Houston, we have a problem.As for passing judgement on qualified university faculty on the basis of whether or not they agree with the omniscient (and unqualified) Farsight, it quite literally beggars belief
"People like you"??? In the UK this is considered as an offensive generalization across race, gender, sexual preference, class etc.And in the present case knowledge of differential geometry And have I not just demonstrated I understand the distinction? - . and yet in an earlier post I find thisspace, but of spacetime. The distinction is crucial.[/I] But people like you just can't accept the distinction
What is THAT supposed to mean in the context of this discussion?Farsight said:]Einstein thought of a gravitational field as "a state of space".
Ha ha. Is this the best you can do? Your response is "not even wrong", it's nonsensicalThe metric has 10 components because you're measuring motion through space.
This is a strawman- nobody suggested the field "is" curved space. I promise you I am not confusedAnd there's no doubt that a gravitational field isn't curved space. So don't confuse space with spacetime.
Well assuming E.was not a god, it still begs the question as to whether you understand his original work (and I don't mean his popularizing) and whether thinking in the "gravity" community may have moved on in , what, 99 years.I will pass judgement on the basis of whether they agree with Einstein
Sure, up to the point that the original authors start being exact with their statements through the use of mathematics. That way, you are free to interpret whatever vague things they say as you see fit, ignorant of any requirements to actually get physics done.I like to think I understand gravity, tashja, because I've read the original material.
Except where he worked out the details.Einstein thought of a gravitational field as "a state of space".
Yes, they can, because of the way that GR works and the freedom one has in choosing coordinate systems.I think the differences in the responses are interesting. To summarise, Moore gave what I thought was the right answer, S Shapiro didn't answer the question, Baez gave what I thought was the right answer, Olum's answer started off OK but then turned into the waterfall analogy, which I think is junk, and Begelman's answer seemed partially correct. Obviously they can't all be correct.
As above. Space is not the same thing as spacetime. Curved spacetime is the map. Inhomogeneous space is the territory. And the map is not the territory."People like you"??? In the UK this is considered as an offensive generalization across race, gender, sexual preference, class etc. And in the present case knowledge of differential geometry And have I not just demonstrated I understand the distinction? - . and yet in an earlier post I find this: Einstein thought of a gravitational field as "a state of space". What is THAT supposed to mean in the context of this discussion?
Huh? You measure distance and time using the motion of light through space. The metric is an abstract thing derived from what you measure. Space isn't curved, instead your plot of measurements is curved. For example you place parallel-mirror light-clocks throughout an equatorial slice of space, and when you plot clock rates, what you get is this:Ha ha. Is this the best you can do? Your response is "not even wrong", it's nonsensical
Then describe the state of space in the room you're in. In your own words. You do not really understand something unless you can explain it to your grandmother. How about you start a thread explaining why your pencil falls down?"This is a strawman- nobody suggested the field "is" curved space. I promise you I am not confused.
See the answers to my black-hole gedankenexperiment. The majority gave what I consider to be the right answer in line with Einstein and the evidence, wherein light doesn't get out because it's stopped. However one answer referred to "infalling space". That's wrong. The space in the room you're in isn't falling towards the floor. If you think of that as the gravity community moving on, you're in for a rude awakening.[/URL]Well assuming E.was not a god, it still begs the question as to whether you understand his original work (and I don't mean his popularizing) and whether thinking in the "gravity" community may have moved on in , what, 99 years.
This whole "explain to your grandmother" thing is just an excuse for cranks to omit details. Nobody should expect everything to be explainable to everybody.
I like to think I understand gravity, tashja, because I've read the original material.
. Obviously they can't all be correct.
what can be done to ascertain what is happening here?
In 1960 there were discovered more suitable coordinates for describing Schwarzschild spacetime, called Kruskal-Szekeres coordinates… …Although the metric does break down at r = 0, the more serious problem at r = 2M has vanished.
if we did not have a good set of coordinates ( such as Kruskal-Szekeres ) how could we tell if the horizon was real or not?
My underline in above quotes.So with this time-space swap incorporated, the normalised Riemann components don’t diverge at r = 2M, and we know for certain that spacetime is perfectly well behaved there.