Can Anyone Answer These Black Hole Problems?

Honestly, the Lorentz factor is closely related to Pythagoras' theorem. Check it out on google. A version of it is used in the spacetime interval too.
I also derived the proper time using Pythagoras' Theorem, and it doesn't have anything to do with how long it takes for a clock to tick, only the amount of time they would have to measure in order to measure the same speed of light of a beam that traveled a certain distance.


My derivation of the proper time using the Pythagorean Theorem.
 
I don't see an alternative.

Is there something wrong with the alternative already given by General Relativity? In case you've never seen it, a Kruskal-like diagram for a gravitationally collapsing star looks like this:

figure_seven18.jpg

(copied from here).

That diagram isn't cropped on the left, by the way. The Kruskal u coordinate (horizontal axis) is a radial coordinate, and u < 0 simply doesn't exist (just like r < 0 doesn't exist in polar coordinates). The event horizon in particular doesn't extend into the infinite past. It simply starts exactly where it looks like it does on the diagram.
 
I didn't think he was being serious on the subject anymore.

In a nutshell, he'd be refuting the Big Bang model, and hence, not worth talking to.
 
No my friend, it's reasoning. For something "to have occurred" for an observer in a certain frame it must exist in that observer's past light cone. Mass crossing the event horizon will never exist in any outside observer's past light cone, therefore it has also never crossed the event horizon in the past for those observers, or else those observers would be able to identify such a future event prior to that time.

Inductive reasoning.

Of course, you could just as validly argue that for something "to have occurred" for an observer it must exist outside that observer's future light cone. As in no actions at this point can have any influence on that event, so it is effectively past. The observer just hasn't seen it yet.
 
Wow. The nonsense quotient in this thread really is quite unexpectedly high.

This thread gets longer and longer and duller and duller.

Here's an idea: if you're not interested in a thread you don't have to read it or post in it.

Because Einstein explained "time" in terms of "simultaneity". This "simultaneity" can not be observed in the Black-Hole. Neither can "gravitational collapse" of light itself.

This is meaningless mumbo-jumbo.

Presume a black hole "exists today" (of any arbitrary mass, etc). Now run time backwards to locate its creation event, and you will discover that it exists at "negative infinity" (i.e. prior to the big bang).

I presume this amounts to a claim that black holes do not exist.

That is not true. There is abundant evidence that black holes exist. Moreover, there is evidence of the formation of black holes ... after the big bang.

"Time Dilation" is slowing down of the "clock" and not "slowing down of time".

Time is what clocks measure. The distinction really isn't important.

Clocks don't literally measure "the flow of time". That's a figure of speech. What they actually do, is employ some kind of motion which is usually regular and cyclical, and show you a cumulative result that you call "the time".

Or, in other words, time is defined to be what clocks measure. Most useful definitions in physics are operational, and time is no exception.

For something "to have occurred" for an observer in a certain frame it must exist in that observer's past light cone. Mass crossing the event horizon will never exist in any outside observer's past light cone, therefore it has also never crossed the event horizon in the past for those observers, or else those observers would be able to identify such a future event prior to that time.

This does not show that a black hole does not exist.

It is true that when we observe black holes we see that no mass has crossed the event horizon. But then, we don't observe that mass directly; we can only infer things about it. Moreover, the gravitational field, or spacetime curvature, created by that mass is the field of a black hole.

It is true that the inside of a black hole is not within out past light cones, in the sense that no information can get out to us from inside the hole. In that sense, when we look at a black hole we are seeing a remnant field which tells us what happened there in the past (e.g. the collapse of a massive star).

There is no problem of there being a time after the big bang when a particular star underwent catastophic gravitational collapse and an event horizon formed. We can't see the star's mass disappear behind the event horizon, but we do see it disappear towards the horizon. The black hole is demonstrably there.
 
I didn't mean your bits James.
It's just that sometimes on this thread, I feel like I've seen posts before.
 
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Time is what clocks measure.
What 'clock measures' is the 'local time'. Clock does not measure 'Universal Time', which is uniform. This 'Universal Time' does not slow down.

The distinction really isn't important.

Distinction of what?

Is it distinction of 'local Time' and 'Universal Time' or distinction of 'time' and 'clock'?

'Time' can mean 'local time' or 'universal time'.
 
What 'clock measures' is the 'local time'. Clock does not measure 'Universal Time', which is uniform. This 'Universal Time' does not slow down.

What do you mean by universal time?
 
Is there something wrong with the alternative already given by General Relativity? In case you've never seen it, a Kruskal-like diagram for a gravitationally collapsing star looks like this:

figure_seven18.jpg

(copied from here).

That diagram isn't cropped on the left, by the way. The Kruskal u coordinate (horizontal axis) is a radial coordinate, and u < 0 simply doesn't exist (just like r < 0 doesn't exist in polar coordinates). The event horizon in particular doesn't extend into the infinite past. It simply starts exactly where it looks like it does on the diagram.
The time coordinate has a very specific meaning in this context for observers. You cannot replace t and r with U and V and then apply the original definitions to the new variables (which were derived to accommodate the math, not to describe reality). Specifically, restricting ourselves to the "region 1" (exterior), where

$$V^2 - U^2 < 0$$ and $$U > 0$$

the transformation between Schwarzschild t and Kruskal U, V is

$$tanh({{t}\over{4GM}}) = V/U$$

U has a lower bound of zero because that is simply what defines region 1; however, V can be negative, which is why $$-\infty <= t <= +\infty$$ for the exterior of any black hole.

Pete said:
Of course, you could just as validly argue that for something "to have occurred" for an observer it must exist outside that observer's future light cone. As in no actions at this point can have any influence on that event, so it is effectively past. The observer just hasn't seen it yet.
This may be valid if two events were space-like separated and determining which event occurred first were a matter of perspective, but that is not the case with black hole creation and/or growth: there is not a frame in which the creation occurred "after" negative infinity.
 
What do you mean by universal time?

"Universal Time" is the time, through which simultaneity between any two events in the universe can be made. When it is said that, "Two events are happening at the same time"; here this 'time' refers to 'universal time'.
 
"Universal Time" is the time, through which simultaneity between any two events in the universe can be made. When it is said that, "Two events are happening at the same time"; here this 'time' refers to 'universal time'.

Universal time as you define it does not exist except as an idealized concept.
 
I presume this amounts to a claim that black holes do not exist.

That is not true. There is abundant evidence that black holes exist. Moreover, there is evidence of the formation of black holes ... after the big bang.
...
This does not show that a black hole does not exist.

It is true that when we observe black holes we see that no mass has crossed the event horizon. But then, we don't observe that mass directly; we can only infer things about it. Moreover, the gravitational field, or spacetime curvature, created by that mass is the field of a black hole.
...or the gravitational field and spacetime curvature of a neutron star on the eternal brink of collapse. It would appear the same to us.
James R said:
There is no problem of there being a time after the big bang when a particular star underwent catastophic gravitational collapse and an event horizon formed. We can't see the star's mass disappear behind the event horizon, but we do see it disappear towards the horizon. The black hole is demonstrably there.
I'm afraid it isn't demonstrably there. It is mathematically predicted to be there, yet I'm questioning whether or not that mathematical analysis allows us to validly make the claim that a black hole "exists" today.

If it's true that black holes "spontaneously form" rather than grow from the center of mass (where pressure is highest), outward as was suggested by some in my exploration of hawking radiation, then I can name an observable difference between the two scenarios: gradation of collapse. A frozen star would 'freeze' from the center, out, and our ability to see it would vary over time; it would disappear from view in a dimming fashion. On the other hand, if the currently accepted model of black holes is accurate then a neutron star and a black hole are discrete and exclusive states, and there would be no intermediary states. I would be curious to know how visible neutron stars are to astrophysicists, and whether or not our ability to observe them varies over time.
 
The time coordinate has a very specific meaning in this context for observers.

Really? What meaning?

Incidentally, for a spherically symmetric collapsing star, the event horizon also starts at a finite value of the t coordinate even in a Schwarzschild-like coordinate system. This is not a feature of just Kruskal-like coordinates.


You cannot replace t and r with U and V and then apply the original definitions to the new variables

I didn't. I'm only drawing on two facts: 1) the event horizon forms at a finite value of the timelike (v) coordinate, and 2) in the Kruskal-like coordinates, the metric is finite everywhere except the singularity (i.e. there are no coordinate singularities), so finite distances on the diagram correspond to e.g. finite space-time intervals.

If you're going to say that the event horizon forms at "negative infinity", the burden of proof is really on you to explain where you're getting that from and to explain why it is a physical result and not an artefact of some coordinate system or other.


(which were derived to accommodate the math, not to describe reality).

You say that as if Schwarzschild-like coordinates did "describe reality" in some way that Kruskal-like coordinates don't. You shouldn't presume that. In general you shouldn't presume any coordinate system has any special significance except what you can explicitly justify from the metric. For the Schwarzschild black hole solution, Kruskal coordinates have the mathematical convenience that the metric is conformally flat in the v and u coordinates, so (the radial sections of) light cones look the same way on a Kruskal diagram as they do on a Minkowski diagram, which makes them convenient for answering questions related to causal relations and structure. Schwarzschild coordinates are defined differently and are more convenient in different respects, the most notable one being that the Schwarzschild metric is static in the Schwarzschild t coordinate (so for example for two objects at different but constant Schwarzchild radii, the metric components are related in a simple way to the Doppler shifts between them).


Specifically, restricting ourselves to the "region 1" (exterior), where

$$V^2 - U^2 < 0$$ and $$U > 0$$

the transformation between Schwarzschild t and Kruskal U, V is

$$tanh({{t}\over{4GM}}) = V/U$$

U has a lower bound of zero because that is simply what defines region 1; however, V can be negative, which is why $$-\infty <= t <= +\infty$$ for the exterior of any black hole.

You are copying what Wikipedia says about the Schwarzschild eternal black hole solution and naively applying it to a black hole that has formed by stellar collapse. In this and my previous post, there is a reason I've been referring to "Schwarzschild-like" and "Kruskal-like" coordinates rather than just "Schwarzshild" and "Kruskal" coordinates. The reason is that the latter are really defined in terms of the Schwarzschild eternal black hole metric taking a particular form in terms of those coordinates. For a black hole forming by stellar collapse, the spacetime metric takes the form of the Schwarzschild metric only outside the outer surface of the star, and it is only outside that region that you really have Schwarzchild and Kruskal coordinates that have the same significance and which are related in the same way as in the eternal black hole solution. In particular, inside the star, the Kruskal-like coordinates used in the diagram I gave in post #102 are not defined by the equations given here.

In fact, in any region of weak spacetime curvature, such as in and around a star before its gravitational collapse like in the bottom part of the diagram in post #102, Kruskal-like and Schwarzschild-like coordinates are very nearly the same thing. In flat (Minkowski) spacetime, they are identical.


This may be valid if two events were space-like separated and determining which event occurred first were a matter of perspective, but that is not the case with black hole creation and/or growth: there is not a frame in which the creation occurred "after" negative infinity.

I just gave you one! Even the stellar collapse solution in Schwarzchild-like coordinates has the event horizon forming at some finite t coordinate.

If you mean something different by "frame" than just "coordinate system", please define what you mean by that.
 
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Capt. Kremmen said:
If you have smashed a window with a football, how likely is it that the window will re-form and the ball appear at your feet.
That's why time goes forward rather than backwards.

In order for it to be possible to reverse time,
you have to reverse probability.
Is that possible?
Newton's laws of motion relate forces to acceleration, which has units of m.s[sup]-2[/sup]. Now units of time squared can be positive or negative, so the laws of motion are time-symmetric in the sense it's irrelevant if acceleration occurs in positive or negative time.
However, (the process of) smashing a window introduces nonlinear friction, which is a function of atomic motion and electric charges; Newtonian mechanics accounts for this with a linear 'damping' coefficient. So the laws remain time-symmetric--although friction is accounted for it isn't 'explained'. But we know that friction results in dissipation of energy to the environment, and that there are many ways a window can be smashed, but only one way it isn't (i.e. remains unsmashed).
So there is a low probability that a smashed window will reassemble into an unsmashed one, and time therefore appears to be unidirectional--it 'follows' the direction of greatest probability, type of thing.
 
What 'clock measures' is the 'local time'. Clock does not measure 'Universal Time', which is uniform. This 'Universal Time' does not slow down.

There is no universal time because there are no preferred reference frames.

Is it distinction of 'local Time' and 'Universal Time' or distinction of 'time' and 'clock'?

I meant that distinguishing between time and what clocks measure is a pointless exercise.

"Universal Time" is the time, through which simultaneity between any two events in the universe can be made. When it is said that, "Two events are happening at the same time"; here this 'time' refers to 'universal time'.

Simultaneity is relative. Einstein showed that in 1905.
 
Universal time as you define it does not exist...

Why?

Two events can exist anywhere in the universe. Two events anywhere in the universe, can happen simultaneously. So, 'simultaneity' can exist between any two events in the universe. If 'simultaneity' can exist between any two events, why 'universal time' can not exist?

... except as an idealized concept.

It is true, it is difficult to measure 'universal time' because no clock can be designed to measure it. All the clocks measures 'local time' which is gravity depended. 'Universal Time' is gravity independent. Though 'atomic clocks' are being designed to measure 'universal time' as per wiki.
 
I'm afraid it isn't demonstrably there. It is mathematically predicted to be there

How is that any different from any other observation that might lead you to say something is 'there'?


On the other hand, if the currently accepted model of black holes is accurate then a neutron star and a black hole are discrete and exclusive states, and there would be no intermediary states.

No. According to currently accepted models of black holes (i.e. the sort of black hole predicted by general relativity), black hole formation is a continuous process. An outside observer watching the gravitational collapse of a star is predicted to see the outer surface of the star shrink to what will eventually become the black hole's Schwarzschild radius, while appearing increasingly dim and redshifted. From memory, the dimming is predicted to occur something like exponentially over time, so it would look quite rapid and the collapsing stellar material would quickly become practically unobservable.

Incidentally, the frozen star "interpretation" of black holes doesn't hold in the context of general relativity. The currently accepted model of black holes is the one predicted by general relativity. GR predicts full black hole solutions, singularity and event horizon and all, and disregarding that or simply cutting off the solution on one side of the event horizon because you don't like it is arbitrary at best.
 
There is no universal time because there are no preferred reference frames.

Here is one paper which claims "Indications for a preferred reference frame
from an ether-drift experiment"



I meant that distinguishing between time and what clocks measure is a pointless exercise.

Clock just measure local time. 'Simultaneity' can be used to explain 'universal time'.



Simultaneity is relative.

Relative to what?

Einstein showed that in 1905.

Einstein used 'simultaneity' to explain 'time'. In this explanation he considered 'clock' as an event and not as time.
 
hansda said:
Relative to what?
Relative to observers in uniform motion.
Einstein used 'simultaneity' to explain 'time'. In this explanation he considered 'clock' as an event and not as time.
Clocks are demonstrably a sequence of events, the sequence is again (due to) uniform motion.
A spacetime event always has a time coordinate measured by referring to a local clock.
 
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