[Rian]

Who fell into black hole and sent back the information that yes, you will eventually reach the center/surface of whatever it is behind the event horizon?

*and rest of argument*

The text my relativity class used for the GR segment was Exploring Black Holes: An Introduction to General Relativity, by Taylor and Wheeler. According to that text, a mass falling into a black hole from just outside the event horizon will reach the central "crunch point" in a span of time that can vary from considerably less than a second (for a black hole of roughly the mass of the sun) to decades (for black holes massing "thousands of galaxies".) The river analogy I cited is also there.

What you’re doing is confusing the bookkeeper and free-fall coordinate systems. They can’t be treated in the same way – in the bookkeeper frame, which views the black hole from a distance, you observe the curved space-time and the Schwartszchild metric applies. This metric (which mathematically describes the space surrounding a massive object) actually makes no distinction between space inside and outside the event horizon. (meaning that I was slightly incorrect on that point in my first post. I took the class last semester; apparently I’m already forgetting things.) In the free-fall frame, space is presumed to be locally flat, and normal (inertial) physics applies in the immediate vicinity of the faller.

You have to be very careful to specify which frame you’re talking about when doing relativity, especially when considering effects like length contraction and time dilation. To make sense of why the different  frames are important, bear in mind that our tool for conducting these observations is light. It makes a difference where you’re measuring something because light takes a finite amount of time to reach the observer, and is itself affected by the curvature of space and so forth. It does make a great deal of sense when the math is there to back it up.

I will note that I am no kind of expert. This was an introductory class, though at a well-regarded university, and we dealt solely with the applications of GR, not its derivation.

[Herra Tohtori]

The text my relativity class used for the GR segment was Exploring Black Holes: An Introduction to General Relativity, by Taylor and Wheeler. According to that text, a mass falling into a black hole from just outside the event horizon will reach the central "crunch point" in a span of time that can vary from considerably less than a second (for a black hole of roughly the mass of the sun) to decades (for black holes massing "thousands of galaxies".) The river analogy I cited is also there.

What you’re doing is confusing the bookkeeper and free-fall coordinate systems. They can’t be treated in the same way – in the bookkeeper frame, which views the black hole from a distance, you observe the curved space-time and the Schwartszchild metric applies. This metric (which mathematically describes the space surrounding a massive object) actually makes no distinction between space inside and outside the event horizon. (meaning that I was slightly incorrect on that point in my first post. I took the class last semester; apparently I’m already forgetting things.) In the free-fall frame, space is presumed to be locally flat, and normal (inertial) physics applies in the immediate vicinity of the faller.

Okay, how about two book-keepers - one at orbit hundred kilometres from event horizon of relatively big black hole, and another orbiting the horizon significantly higher?

Both are free-falling; the only difference to freely falling observer would be that they would remain at static distance from the event horizon and thus offer more reliable observation platforms for comparing the effects to space and time relative to each position/altitude close to a horizon.

The way I see it, the observer further from the horizon would experience very close to eucleidean flat space-time. The observer lower on the gravity potential field would notice that the higher observers' clocks seem to run a lot faster, and that would be a very real effect directly analogous to the way the GPS satellite clocks need to be compensated for gravitational time dilatation. And if time dilatation is a real effect rather than based on observations getting clouded by limited signal speed (one thing I've always been annoyed of in special relativity was how the interpretations change a lot depending on how the signal delays are handled...), why would it be different with space dimensions?

The assumption that free-falling reference frames are locally flat is interesting, but not knowing the maths I can't see what leads to this assumption. Then again, the dilatation of time in itself obviously changes the metrics of space as well because the definition of a metre (length) is how far a photon travels at 1/299something seconds... which means that when time slows down and events are looked at from higher altitude, and a photon's distance per second is measured, thehigher observers' second would mean something less on lower observers' clocks, and that would mean that the distance travelled by the photon in that time would be less than a metre - but due to assumption of light's speed being constant for all observers, it would mean that the distance traveled by the photon in one measured second would be one metre... hmm, I'll have to think through this one rather carefully.

At any rate, I have let myself be told that time dimension is not the only one affected and that the space dimensions are stretched as well, but seeing how the time stretching in itself would change the length of a metre relative to space on different gravitation potential, I just don't know what to think of it. Like you said:

You have to be very careful to specify which frame you’re talking about when doing relativity, especially when considering effects like length contraction and time dilation. To make sense of why the different  frames are important, bear in mind that our tool for conducting these observations is light. It makes a difference where you’re measuring something because light takes a finite amount of time to reach the observer, and is itself affected by the curvature of space and so forth. It does make a great deal of sense when the math is there to back it up.

The question to me is, what makes the situation fundamentally different from the situation between observers at Earth's surface vicinity and satellites at orbit having different time propagation speed? Is the time actually the only thing affected by mass and energy, and the rest of the stuff comes from the metric changes caused by that? Or is the "stretching" of space and time evenly spread to all dimensions?

Or is it the time stretching-induced metric changes actually what constitutes as stretching of space axes?


Bah, I'll have to take soem time to look into it in the future...

[General Battuta]

I promise you that, no matter how good you think your conceptual grasp of the situation may be, exploration of the actual math will prove enlightening. You've probably already had this experience with the math of special relativity.

And I'll echo Rian's comment about the importance of reference frames. Most apparent paradoxes can be resolved by recognizing reference frame errors.

Lastly, it seems a bit odd to think that all the hundreds of physicists who've tried to overthrow relativity have failed to spot something that we might recognize with mere intuition.

[Rian]

Okay, how about two book-keepers - one at orbit hundred kilometres from event horizon of relatively big black hole, and another orbiting the horizon significantly higher?

Both are free-falling; the only difference to freely falling observer would be that they would remain at static distance from the event horizon and thus offer more reliable observation platforms for comparing the effects to space and time relative to each position/altitude close to a horizon.

The way I see it, the observer further from the horizon would experience very close to eucleidean flat space-time. The observer lower on the gravity potential field would notice that the higher observers' clocks seem to run a lot faster, and that would be a very real effect directly analogous to the way the GPS satellite clocks need to be compensated for gravitational time dilatation. And if time dilatation is a real effect rather than based on observations getting clouded by limited signal speed (one thing I've always been annoyed of in special relativity was how the interpretations change a lot depending on how the signal delays are handled...), why would it be different with space dimensions?

What you're talking about here is actually a third set of coordinates that’s often used in these calculations. The "bookkeeper" observer is actually assumed to be at infinity – that is, some appropriately large distance away, where space can be taken to be flat. If you’re talking about a stationary observer located somewhere closer to the black hole, that’s what’s called "shell" coordinates. (As if this observer were standing on some solid shell of fixed radius.)

A free-falling observer has to be actually falling in order for that system to apply. In fact, it’s sometimes useful to talk about a free-faller relative to a stationary shell observer – in this case, they’d be considered to be at the same radial position, and special relativistic relationships according to the momentary speed of the faller would be used to determine, for example, the time difference between them.

There is actually a very specific way that physicists resolve the way the light travel delay affects observation, and I believe it was used in deriving the special relativistic relationships when we did it in class. Time dilation and length contraction are both real effects: you can fit a long stick into a shorter box if they’re moving relative to each other at relativistic speeds, and time dilation must be factored into GPS calculations, as you’ve mentioned. (we did this calculation at one point – the difference in speed between clocks on a GPS satellite and on the earth’s surface adds up to about 40,000 nanoseconds every day.)

Space and time both interact to produce relativistic effects. The easiest way to describe the way they relate to each other in special relativity is with manipulation of Lorentz matrices and four-dimensional vectors, (time is usually multiplied by the speed of light to give it units of distance) and it's very difficult to describe in intuitive terms. As I recall, most of the calculations we did in GR worked directly with the Schwartzchild metric – the Lorentz transform only applies to inertial frames.

[CP5670]

I promise you that, no matter how good you think your conceptual grasp of the situation may be, exploration of the actual math will prove enlightening. You've probably already had this experience with the math of special relativity.

I'm in an odd situation in that I would probably be comfortable with the math behind the EFEs, but hardly know anything about the physical concepts involved.

[Mika]

Just one note, Schwarzschild metric is applicable just outside of the event horizon. The Eddington-Finkelstein metric will show that the singularity at Schwarzschild's radius caused by Schwarzschild metric is only apparent and depends on how the metric was derived. Schwarzschild's solution is a trial solution, with the simple justification that it fulfils the Einstein field equations. Note that he figured out the solution in the trenches of WWI!

So, if one wants to study properties of space time beyond the event horizon, one should use some other metric, Eddington-Finkelstein being the most common one to describe it.

More of Eddington-Finkelstein metric here:
http:  //en.wikipedia.org/wiki/Eddington-Finkelstein_coordinates
http:  //casa.colorado.edu/~ajsh/phys5770_08/bh.pdf
http:  //www.sron.nl/~jheise/lectures/kruskal.pdf

The proper falling time for an observer inside the event horizon can be calculated using this metric.

Let's see if I was smarter than the system with the links

Mika

[Jeff Vader]

http://en.wikipedia.org/wiki/Eddington-Finkelstein_coordinates
http://casa.colorado.edu/~ajsh/phys5770_08/bh.pdf
http://www.sron.nl/~jheise/lectures/kruskal.pdf

The proper falling time for an observer inside the event horizon can be calculated using this metric.

Let's see if I was smarter than the system with the links

Typing the links directly to the post actually works. That way it is possible to just select and copy-paste them. The url tags are the ones that cause pain and misery Rick Astley.

[Mika]

Typing the links directly to the post actually works. That way it is possible to just select and copy-paste them. The url tags are the ones that cause pain and misery Rick Astley.

For some reason I don't believe that. Firefox is a handy tool. But I clicked the link anyways to keep up the April Fools spirit. You can listen that song once/year, but actually watching it causes my eyes to melt.

Mika

[Jeff Vader]

Typing the links directly to the post actually works. That way it is possible to just select and copy-paste them. The url tags are the ones that cause pain and misery Rick Astley.

For some reason I don't believe that. Firefox is a handy tool. But I clicked the link anyways to keep up the April Fools spirit. You can listen that song once/year, but actually watching it causes my eyes to melt.

Mika

Lähinnä meinasin siis, että jos klikkaa linkkiä, niin tulee Rick Astleyä. Mutta jos maalaa tuommoisen asianmukaisesti typotetun linkin ja copypastettaa osoitekenttään ja lyö entteriä, niin tulee asianmukaista settiä. Trust me.

In Engrish, for great justice: I was merely saying, that if you just click a link, Rick Astley happens. But if you "paint" the link and copypaste it to the address bar and hit Enter, you'll get what you're supposed to get.

[Mika]

Jeps, olispahan pitäny tajuta, että tuosta siinä oli kyse. Hyvä idea muuten kirjotella tänne kerrankin suomeksi, kun on sentään aprillipäivä. Rädyn kuolemattomia sanoja lainatakseni ****uillakseni kirjotin. Saas nährä millanen kaaos tästä vie'ä saadaan aikaseks.

EDIT: What the hell? What did it do now??!!

EDIT^2: This is hilarious if you are shown as Mobius!

[Mars]

What the ****?

[Jeff Vader]

A forumwide identity crisis.

[Mika]

I was thinking to write something of LHC, but since I'm drunken I think I drop it. Too bad, the only justification to stay on topic.

Anyways, I have not too much trouble to figure out General Relativity, but the quantum stuff really starts to make me think if the given explanations are the correct ones. Obviously, the maths seems to model the phenomenom quite well, but the explanations simply make you wonder what the hell is really going on. Many worlds, photons scanning every possible path, etc. etc. This would make one think that a photon has to spend infinite amount of energy in finding out the shortest possible route from A to B. But again, I never read too much of quantum mechanics in the university. If someone could provide an explanation what actually happens when a photon passes a double slit, I would appreciate it. Especially because I'm quite fond of photons in any case.

Mika

[General Battuta]

I don't believe that the many-worlds interpretation of quantum mechanics is the prevalent or accepted one.

[WMCoolmon]

Somewhat relevant - smallest black hole to date found