And that's not at all contradictory.
Then Sol is held up by the tension of the rope, and so is in an accelerated frame. Even in STR, acceleration gives a one-way horizon attempting to cross which will rip you apart. (Appropriately, near the horizon of a large Schwarzschild black hole locally looks exactly like an acceleration horizon of STR.)
If Sol has an idealized body that's both pointlike and lightlike, maybe. Being a static observer the event horizon is a mathematical impossibility. For any remotely realistic body, the tidal forces in this frame will rip him up long before that. But if he's falling inwards instead, then (relative to the stationary frame) he'll be approaching lightspeed near the horizon, so you can think of this as Lorentz contraction keeping the tidal forces on his body finite and small.
Ok, how about just taking the Schwarzschild geometry in different coordinates?
You're taking a statement that's true in a particular reference frame and treating as if it was absolute. It isn't. This is the same kind of mistake commonly made in STR, just in a different context.
So all processes slow and stop on the horizon. Everything is stopped. Light has stopped. Light isn't moving, it isn't going down any more, so neither are you.
It doesn't make any difference. Whether you're hanging on a rope or not, the light in your light clock isn't moving. It isn't moving between the mirrors, and it isn't moving downwards either.
The maths tells you that gravitational time dilation occurs, and that maths is backed up by experiment and observation. We allow for it in the GPS clock adjustment. But what the maths doesn't tell you that it isn't time that slows down, it's motion. Including the motion of light in your light clock that you use to determine the thing you call time t.
It isn't exactly the same maths. It's further maths that ignores the fact that both you and your clock are both stopped, and blunders on as if nothing unusual happens to conjure up a hop skip and a jump over the end of time. See the Schwarzschild chart on the left here. Look carefully at that conveniently truncated peak. Also see the wiki article which refers to the "coordinate artifact", and note this:
Look a bit further down on the wiki article. See the bit that says:
It doesn't matter ben. A reference frame isn't something that actually exists, it's isn't something that you're actually "in". It's just something we use to describe the uniformity or not of our measurements of space and time, sometimes when in motion, sometimes when not. We do these measurement using the motion of light, and at the event horizon the coordinate speed of light is zero.
No. I've already told you twice that the maths doesn't show you this. I've given you a good explanation, now deal with the argument instead of trying to play the inscrutable mathematics card.
Einstein thought the singularity at the Schwarzschild radius was physical. I'm with Einstein. You're not, and you're attempting to pooh-pooh Einstein by saying he didn't understand it? Come on sol, you can do better than that. Think this thing through.
But t isn't the thing I would call time if I was either suspended over a black hole or falling toward in. Actually, no one could naturally call the Schwarzschild t coordinate time except a stationary observer at infinity.
For those interested in a little historical diversion, as far as I'm aware of the first to seriously consider that "collapse goes on" in the formation of a black hole (rather than a "God-given" Schwarzschild geometry) were Oppenheimer and Snyder, also in 1939,
It's the same theory. The mathematics for studying its implications have greatly evolved (compared to today, differential geometry was barely in infacy when Einstein used to formulate GTR).
It's not inscrutable mathematics. It's basic calculus. Take Einstein's original paper for GTR, which tells you how to calculate geodesics, and the Schwarzschild metric. The radial freefall of an observer is very simple, and it doesn't stop at the horizon. (There's a neat little coincidence that's interesting in itself: for Schwarzschild r-coordinate vs proper time of an radially freefalling observer, the relationship between them is exactly the same as that of radius vs time in Newtonian gravity.)
And he was wrong. So what? Einstein made some mistakes, though even your own source (for whatever wiki's worth) even implied he wasn't even aware of Lemaître and Robertson's work.
In my view your first mistake: You seem ignorant of the actual topic of this thread.
Not practically, they won't be actually able to see it because the light can't escape. But that's where it will be. See post #25 above. A free falling observer would cross the r = rs singularity in a "finite amount of proper time", but this takes infinite coordinate time. So he never actually crosses the event horizon. Not in a million years. Not in a billion years. Not ever.
No, it isn't contradictory, it's crystal clear. All processes slow and stop on the horizon as viewed from outside. So a parallel-mirror light clock stops. And light stops. It stops moving back and forth between the mirrors. It stops moving, full stop. So it isn't moving down any more.
It doesn't matter. Make it a supermassive black hole so you don't have to worry about the tidal gradient. And take note: this is a place where light has stopped. The coordinate speed of light is zero. Aim a photon at the black hole and it doesn't get blue-shifted to some infinite frequency as it crosses th event horizon. Instead, it stops.
And what's lightspeed at the horizon? Remember what i said about the coordinate speed of light above. It's zero.
There is no time in that frame. In that frame, you're keeping time on a stopped clock. And you're stopped too. The two don't cancel each other out so that "you don't notice anything unusual". Everything has ground to a halt, light doesn't move, nor do nerve impulses in your head, so you don't notice anything.
I'm not making a mistake here Vorpal. In the STR scenario, it's like you travelling at the speed of light. We all know you can't actually do this, but think it through. If you were travelliung at c, you'd be totally time-dilated, you don't notice anything any more. You might imagine that "in your frame" everything is carrying on as normal, but it isn't. And in the real world, everybody sheds a tear, because poor old Vorpal is out there in space frozen and insensible, forever.
You write as if there are two worlds: the traveller's and the real world. As I understand it, they are both equally real. The traveller would see our world recede at the speed of light, and for him, our time will stop.
No, I'm saying you don't understand this.
Don't thump your "good book" at me, sol. Deal with the argument and the logic.
I've told you before, don't try hiding behind the maths, not with me. Look at this expression:
Are you being deliberately obtuse? Read post #25 again, and this time pay attention: what the maths doesn't tell you that it isn't time that slows down, it's motion. Including the motion of light in your light clock that you use to determine the thing you call time t. You've got a clock rate of zero. See what I told Vorpal. You're like the gedanken observer travelling at c. You observe nothing.
You know how you get all those cranks and crackpots who know b*ggar all physics and who insist that Einstein was wrong? Well, take a look at which side of the fence you're on.
According to distant observers. People who aren't falling into the black hole. Even if their measurements don't quite agree they can account for that from their knowledge of relativity - the coordinate speed of light is only constant in an inertial reference frame. In a non-inertial reference frame, such as the room you're in, it isn't constant. They can all see the black hole and the infalling observer, any differences in their measurements are miniscule and well-understood.
It isn't "collapsed", it's non-inertial.
Your local light speed is your measured speed of light. You always measure wave speed to be the same value because of the wave nature of matter. Remember pair production, and how you can create and electron (and a positron) from light? And how you can diffract electrons? And neutrons? And have you read what I've said about how the NIST caesium fountain clock works? In a nutshell, you calibrate your rods and clocks using the local motion of electromagnetic phenomena. Light in the wider sense. Then you use them to measure the local speed of light. That's why you always measure the same value. I'm not kidding you about this ben.
It isn't. Remember what sol said: all processes slow and stop on the horizon as viewed from outside. Now imagine that you're a light wave bouncing back and forth inside his parallel-mirror light clock. At the event horizon, you stop forever.
This isn't my idea, this is the original frozen star idea, in line with Schwarzschild and Einstein. Typical textbooks do that hop skip and a jump over the Schwarzschild event-horizon singularity and write it off as a coordinate artefact, missing the whole point that when light stops you don't have any coordinates any more. Again, see what I said to Vorpal. It's the GR equivalent of the SR case where you're travelling through flat space at c. You don't carry on observing as if nothing happened. You observe nothing.
If it's "straightforwardly wrong", try explaining it. Or try addressing my straightforward argument. When you can't do either, stop digging, and yield.
Oh, Farsight. I'm afraid that's completely wrong. The infalling observer's clock rate expressed as a fraction of the distant stationary observer's clock rate is:
You've not understood Einstein at all. You're just cherry-picking specific cases with no understanding of the bigger picture. Yes, the bigger picture Einstein himself explained.
No. It isn't relevant. The coordinate speed of light varies with gravitational potential. The tension in the rope is merely an indicator of the difference in gravitational potential between the bottom and the top. Whether the observer at the event horizon has fallen, or has been gently lowered on a gedanken rope doesn't make any difference. Either way, he is at a place where the coordinate speed of light is zero. Please don't clutch at straws to cling to something that you've been taught. Think for yourself instead.
Logically, it could dismissed by those grounds, but there's indeed something pretty fishy and very questionable about all this attribution to Einstein in the first place, particularly in support of Farsight's rather strong misconceptions, such as
and especially statements such as
It does not make that Einstein, who derived such results as this in collaboration with Rosen: Phys. Rev. 48, 73–77 (1935), would now suddenly take the point of view that spacetime just gets cut off at the horizon of black hole, and then suddenly advance a solution that amounts to gluing two Schwarzschild exteriors together at the horizon.
Your view is wrong since what Banged was spacetime.
So in your world, a single qubit is able to generate zillions of qubits of information?
It isn't completely wrong. Yeah yeah, I should have said stationary observer, where his clock rate is a function of gravitational potential. But if you have that observer accelerating, his clock rate tends to zero even faster.
So come on then, run the numbers like I did. Let's see that clock rate.
I'm the one who's saying it's more than just some coordinate artefact. People who swallow Kruskal-Szekeres coordinates treat the event-horizon singularity like window dressing to be disregarded.
Baloney. What I'm saying is right, you're dodging.
Aw here we go, hiding behind inscrutable mathematics. If I say yes you sidetrack the discussion demanding that I support my claim, if I say no you say well there you go then. It isn't good enough Vorpal. Everybody can see you're ducking the argument. Let me take a look at the other posts, then I'll nail you to the floor. Hurry up and start backing down, because it's going to be embarrassing.
There's nothing "weird" about it all. The coordinate speed of light varies in a non-inertial reference frame, like the room you're in. Take a look at this report on a super-accurate optical clock. It's so precise that you can see two of these clocks losing synchronisation when they're separated by only a foot of vertical elevation. Now take a look at wiki re time dilation, and note the bit that says consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. When you simplify those optical clocks to parallel-mirror light clocks, when they lose synchronisation at different elevations this is what's happening:
See above. Don't dismiss this as uninteresting. This is physics ben. It's not what your good book tells you, but it's simple, and it's right.
I'm not ignoring the difference between clocks. I'm addressing it. Clocks clock up some kind of motion. All clocks do this. A light clock clocks up the motion of light. Nothing is weird, it's all very simple. When we see optical clocks at different elevations lose synchronisation, we say gravitational time dilation occurs. And if that goes infinite, the lower clock has stopped. And if light has stopped, it doesn't matter whether the light was falling into the black hole or bouncing back and forth between mirrors.
You haven't thought it through. If you had, you wouldn't be trying the you haven't taken a GR course defence. You'd address the argument. Now come on, give it a shot.
Pompous erudite flannel.
No, it hasn't, has it? It will.
But you think the coordinate speed of light is weird.
Is that the best you can do? A febrile accusation instead of addressing the point of issue? Here's an analogy for what you're doing: Huff, puff, waffle, the man doesn't understand Latin.
Not every physicist. Just those who thump your good book. Try emailing Steven Weinberg to see what he thinks.
No it isn't. I've said this and I'll say it again. Gravitational time dilation goes infinite at the event horizon, so your clock has stopped and you've stopped too. Light has stopped, so you can't measure anything, and there is no metric. Flat spacetime is irrelevant here because spacetime has gone. And you have in no way addressed the issue. The whole point of this discussion is the fallacy that a stopped clock carries on ticking. You said nothing unusual happens to observer. But everything has stopped, so nothing happens.
Oh yes? Now remind me, what did you say above? "Me, and every other physicist since the 1960s? Ooookaaay.... <backs away slowly>". You've been hoisted by your own petard sol.
I haven't presented Einstein quotes because the scientific evidence is more important than Einstein's view. I can if you wish, but I seem to recall that you dismissed them as "out of context". Look at what I said to ben about the coordinate speed of light. It varies. You and I know this, and we know about the Shapiro delay. We also know that if you were travelling at the speed of light, you wouldn't see anything. We know that as far as you're concerned, it isn't nothing unusual happens, it's nothing happens. And we understand the principle of equivalence.
Ah, the argument from authority again. I don't care what some expert declares to be right, I care about scientifc evidence, and logic, and sound argument. This is a discussion forum, not a scripture class.
Don't hide behind erudition sol. Instead just shoot a light beam between two stars. Slows down, doesn't it. And travels in a straight line. Now make the stars a bit more massive. Then repeat. You know where I'm going with this, so buck your ideas up, pull your finger out, and let's have a sincere discussion about a very interesting subject that takes us places.
