Is the gravitational time dilatation a real effect?

[Ich]

Great! Does that also mean that no event horizon will ever increase its size?

Classically and in principle, yes. In reality, however, we expect Hawking radiation.

I don't think there is a cap on how high energy can a photon have so if you could emit a single photon with energy of whole star it might have pretty reasonable wavelength after redshifting.

The point is, redshift is exponatial with time. You tell me the mass, say, mass of the observable universe, and I tell you the (finite, short,) time in seconds it takes until the photon's wavelength would be redshifted to the size of the observable universe.

Does infalling object have a way to know how much kinetic energy it gained?

No.

I think that annihilation of faster moving, free falling particles should result in higher energy photons otherwise there would be missing energy in that scenario.

If what I'm guessing is true, could you determine your speed in freefall while being completely blind to outside world by annihilating particle with its antiparticle and measuring wavelength of created photons?

You're missing that kinetic energy or photon energy are frame-dependent. Your first sentence is true, but if you change to the comoving frame, kinetic energy is zero and the photon energy is unchanged.

It's not obvious from the outside point of view, but you can imagine how gravitational shortening and time dilatation might forbid this in finite time.

Not so complicated. The object simply hits the singularity before the photon can catch up with it. Look at the http://casa.colorado.edu/~ajsh/schwp.html#freefall",

 

[Kamil Szot]

Classically and in principle, yes. In reality, however, we expect Hawking radiation.

Good. I'm not sure about Hawking radiation though. If pair production was used to explain Hawking radiation it would still take forever (in our time) for the particle created outside event horizon (no matter how close) to reach it. Particles would need to be produced exactly at event horizon, and since event horizon has zero volume I'm not sure how this could work.

The point is, redshift is exponatial with time. You tell me the mass, say, mass of the observable universe, and I tell you the (finite, short,) time in seconds it takes until the photon's wavelength would be redshifted to the size of the observable universe.

Ok. Great. How about photons shining at black hole that would due to blueshift in finite, short time get more energy then that of entire observable universe and after sliding near event horizon might come out with same wavelength as the had? Is that possible?

No.
You're missing that kinetic energy or photon energy are frame-dependent. Your first sentence is true, but if you change to the comoving frame, kinetic energy is zero and the photon energy is unchanged.

Thank you. That suits my common sense better. Because why would one freefalling frame of reference be discernible from some any other freefalling frame that just moves slower.

I think I know now what happens to energy in the case I presented. Photons produced by annihilation have normal wavelength in freefalling frame of reference. But if you observe them in stationary frame of reference you see that photons emitted towards black hole are heavily blueshifted and photons going back are heavily redshifted. This way even after annihilation almost all of the energy is still heading towards black hole. Photons that shined back are heavily redshifted even before they started their climb out of gravity well. Even if you happened to produce photons traveling in a plane exactly orthogonal to your speed you still have only the energy of your rest mass that is nothing compared to energy required to climb out of gravity well and you end up with very high wavelength.

So even if you got rid of your mass by converting it to energy traveling at exact speed of light you still couldn't get significant part of you out.

Not so complicated. The object simply hits the singularity before the photon can catch up with it. Look at the http://casa.colorado.edu/~ajsh/schwp.html#freefall",

Thank you for this. I especially like the Penrose diagram that brings all infinities into view.

This is indeed obvious by looking at this graph http://casa.colorado.edu/~ajsh/stff.gif and comparing green and yellow lines. Although drafting such graph is not trivial if you have never seen it. Standard graph http://casa.colorado.edu/~ajsh/st0big_gif.html does not allow to observe this effect.



I really don't like stating that "The Schwarzschild spacetime geometry appears ill-behaved at the horizon, the Schwarzschild radius. However, the pathology is an artefact of the Schwarzschild coordinate system. Spacetime itself is well-behaved at the Schwarzschild radius, as can be ascertained by computing the components of the Riemann curvature tensor, all of whose components remain finite at the Schwarzschild radius."


If you have simple problem like this: "You see remote object traveling with constant speed v1 and you yourself have speed v2 then at what direction you should point your speed vector to intercept this object?" You can formulate quadratic equation to solve this problem. If you get delta < 0 than right course is stating that this problem has no solutions not stating that this pathology is just result of using real numbers, the problem itself is well behaved and when doing calculations using complex numbers everything is still ok no matter how far you are from object that you want to intercept. It's good math but it's not the reality.

 

[nismaratwork]

Good. I'm not sure about Hawking radiation though. If pair production was used to explain Hawking radiation it would still take forever (in our time) for the particle created outside event horizon (no matter how close) to reach it. Particles would need to be produced exactly at event horizon, and since event horizon has zero volume I'm not sure how this could work.




Ok. Great. How about photons shining at black hole that would due to blueshift in finite, short time get more energy then that of entire observable universe and after sliding near event horizon might come out with same wavelength as the had? Is that possible?



Thank you. That suits my common sense better. Because why would one freefalling frame of reference be discernible from some any other freefalling frame that just moves slower.

I think I know now what happens to energy in the case I presented. Photons produced by annihilation have normal wavelength in freefalling frame of reference. But if you observe them in stationary frame of reference you see that photons emitted towards black hole are heavily blueshifted and photons going back are heavily redshifted. This way even after annihilation almost all of the energy is still heading towards black hole. Photons that shined back are heavily redshifted even before they started their climb out of gravity well. Even if you happened to produce photons traveling in a plane exactly orthogonal to your speed you still have only the energy of your rest mass that is nothing compared to energy required to climb out of gravity well and you end up with very high wavelength.

So even if you got rid of your mass by converting it to energy traveling at exact speed of light you still couldn't get significant part of you out.


Thank you for this. I especially like the Penrose diagram that brings all infinities into view.

This is indeed obvious by looking at this graph http://casa.colorado.edu/~ajsh/stff.gif and comparing green and yellow lines. Although drafting such graph is not trivial if you have never seen it. Standard graph http://casa.colorado.edu/~ajsh/st0big_gif.html does not allow to observe this effect.



I really don't like stating that "The Schwarzschild spacetime geometry appears ill-behaved at the horizon, the Schwarzschild radius. However, the pathology is an artefact of the Schwarzschild coordinate system. Spacetime itself is well-behaved at the Schwarzschild radius, as can be ascertained by computing the components of the Riemann curvature tensor, all of whose components remain finite at the Schwarzschild radius."


If you have simple problem like this: "You see remote object traveling with constant speed v1 and you yourself have speed v2 then at what direction you should point your speed vector to intercept this object?" You can formulate quadratic equation to solve this problem. If you get delta < 0 than right course is stating that this problem has no solutions not stating that this pathology is just result of using real numbers, the problem itself is well behaved and when doing calculations using complex numbers everything is still ok no matter how far you are from object that you want to intercept. It's good math but it's not the reality.

You keep saying "our time", which is frame dependent again. The event horizon does not have zero volume, that would be the singularity. The event horizon probably fluctuates as the BH gains mass from infalling matter, or (in some huge amount of time as the universe cools) loses mass to HR. The whole point of HR is that the pair-production DOES occur "exactly at the event horizon", wherever and whenever that is. I don't see a problem with that, although any non-mathematical treatment of HR is necessarily somewhat misleading.

It seems to me, from reading this thread that you believe, or are asking how we can never toss a ball into a black hole and observe it passing the event horizon. If we remain in our earthbound coordinate system, then you are left with what Ich is saying, and you can be confident that you've received your final signal from the ball, but in a classical sense you never see that finally .00000000000001...% fall in. if you managed to glue the ball to your hand, and then you went on the one-way journey with the ball, there would be no problem; you would fall in with the ball in, as Ich said, a very short interval.

You just cannot ask this question while thinking of two different frames of reference, unless you accept that it is a matter of your coordinates which defines whether or not you get to see the infalling matter complete its journey. So, event horizons do grow, and eventually shrink at some future time. I think DaleSpam gave you the best answers that had technical content that you are going to get.

 

[Kamil Szot]

You keep saying "our time", which is frame dependent again.

I know. When I say "our time" I mean time in frame of reference associated with Earth. I didn't expect that this would be that confusing.

The event horizon does not have zero volume, that would be the singularity.

Singularity is a point and as such has no volume. In 3d space also lines and surfaces have no volume (unless they are fractal). Since event horizon is very precisely defined smooth surface so I guessed it has no volume. And that implied for me that probability of anything occurring exactly at event horizon is zero.

The event horizon probably fluctuates as the BH gains mass from infalling matter,

I think that ICH agreed with me on the first line of his post that this does not happen.

or (in some huge amount of time as the universe cools) loses mass to HR.

I fail to see how shrinking of event horizon could lead to absorption of one of the particles created.

The whole point of HR is that the pair-production DOES occur "exactly at the event horizon", wherever and whenever that is. I don't see a problem with that, although any non-mathematical treatment of HR is necessarily somewhat misleading.

I see it like this. Virtual pair production is a random event. Each point of space has some nonzero probability density of such event. You may calculate probability of such event occurring in some volume by calculating integral over this volume of that probability of density function.

Integral over zero volume equals zero so the event cannot happen exactly at event horizon.

The only way I can imagine particle getting inside is that by uncertainty principle. Probability of finding this exact particle behind event horizon is nonzero. But because on the other side of event horizon there is nothing (except singularity far away from event horizon), I don't see what observation could cause wave function to collapse to actual particle there.

It seems to me, from reading this thread that you believe, or are asking how we can never toss a ball into a black hole and observe it passing the event horizon. If we remain in our earthbound coordinate system, then you are left with what Ich is saying, and you can be confident that you've received your final signal from the ball, but in a classical sense you never see that finally .00000000000001...% fall in.

I'm not asking about what I can see. I'm interested in what actually happens in there in sense of the diagrams that Ich directed me to.

And what I got from this thread so far is confirmation of my own concerns:
If you are far from event horizon no matter how long you wait no falling object ever passes any event horizon.

Don't you agree with the above statement?

if you managed to glue the ball to your hand, and then you went on the one-way journey with the ball, there would be no problem; you would fall in with the ball in, as Ich said, a very short interval.

If I'm hovering millimeter from the horizon it will still take forever for the ball to fall in (as ball can have arbitrarily slower time pace than my own because of being closer), but if I'm co-moving with the ball (even not exactly glued to it but some distance after it) this 'forever' changes to short finite time. This means that when two objects fall into a black hole difference of time paces of the frame of references associated with them must be always finite and for two objects near event horizon quite small. Right?

You just cannot ask this question while thinking of two different frames of reference, unless you accept that it is a matter of your coordinates which defines whether or not you get to see the infalling matter complete its journey. So, event horizons do grow, and eventually shrink at some future time.

If you toss a star at a black hole and start a clock when see it disappear how long in your opinion will take the event horizon to grow? Less than 10¹⁰⁰⁰ years? Would you be able to detect this growth by seeing that black-hole now occludes larger portion of your view?

I think DaleSpam gave you the best answers that had technical content that you are going to get.

I liked answers from Ich better better because he understood what I meant.

 

[nismaratwork]

OK... I don't think I teach well enough to help you here, and if you feel that Ich is doing a better job, I won't interfere.

 

[Ich]

If pair production was used to explain Hawking radiation

It isn't. It's something to do with positive and negative frequencies going to future null infinity, the latter not cancelling the former as they should in the presence of an event horizon. Or something like that, I didn't understand the derivation.
HR can't be a process happening exactly at the EH, because the local spacetime at the EH is not different from the spacetime somewhere else.

How about photons shining at black hole that would due to blueshift in finite, short time get more energy then that of entire observable universe and after sliding near event horizon might come out with same wavelength as the had? Is that possible?

Of course, if you have a reflector ten times thes mass of the observable universe somehow hovering there, within <<1 attometer from the horizon.

I think I know now what happens to energy in the case I presented.
[...]
So even if you got rid of your mass by converting it to energy traveling at exact speed of light you still couldn't get significant part of you out.

Yes.

If you have simple problem like this: "You see remote object traveling with constant speed v1 and you yourself have speed v2 then at what direction you should point your speed vector to intercept this object?" You can formulate quadratic equation to solve this problem. If you get delta < 0 than right course is stating that this problem has no solutions not stating that this pathology is just result of using real numbers

it's exactly the same with Schwarzschild coordinates. These are supposed to be static coordinates. You'd like to place static observers (with r=const.) everywhere, and the solution blows up and then gets imaginary for r<=2M. So it tells you that there's no solution to the problem, just like in your example.
Also like in your example, that doesn't mean that spacetime is broken. You just can't place a static observer there. If you allow non-static observers, you can place them everywhere (the singularity remains a problem of course). That's reflected in the presence or absence of coordinate failures in the coordinarte systems that are based on the respective observers.
If you allow for arbitrary v2 in your example, you'll get it fixed the same way.


From your answers to nismaratwork:

The event horizon probably fluctuates as the BH gains mass from infalling matter,

I think that ICH agreed with me on the first line of his post that this does not happen.

I'm usually talking about infalling test particles, which do not affect the horizon. If you'd throw in a significant mass, the EH would expand. But it would do so before the mass actually reaches it, so it still wouldn't cross it.

I'm not asking about what I can see. I'm interested in what actually happens in there in sense of the diagrams that Ich directed me to.

And what I got from this thread so far is confirmation of my own concerns:
If you are far from event horizon no matter how long you wait no falling object ever passes any event horizon.

Contrary to what you can see, there are different diagrams showing different things "actually happening". There are some where there is no horizon at all*, and others, where the horizon cannot be crossed in finite time.

*: as far as the specific class of observers is concerned.
The interior of a black hole is defined in a coordinate independent way, so I think you should say that in these coordinate systems, particles "actually" cross the horizon in a finite time.

 

[Kamil Szot]

It isn't. It's something to do with positive and negative frequencies going to future null infinity, the latter not cancelling the former as they should in the presence of an event horizon. Or something like that, I didn't understand the derivation.
HR can't be a process happening exactly at the EH, because the local spacetime at the EH is not different from the spacetime somewhere else.

Ok. Let's leave HR for now. It's way too complicated subject for my current understanding.

How about photons shining at black hole that would due to blueshift in finite, short time get more energy then that of entire observable universe and after sliding near event horizon might come out with same wavelength as the had? Is that possible?

Of course, if you have a reflector ten times thes mass of the observable universe somehow hovering there, within <<1 attometer from the horizon.

That's not what I meant. I thought about hovering at a safe distance from event horizon, having normal reasonably powered reflector (or laser) and aiming it so the beam would slide as close to event horizon as possible, wait and observe if anything got out. I think that photons of the beam should blue shift as they go down the gravity well possibly gaining arbitrarily high energy (in my frame of reference) and then redshift as they are getting out returning to wavelength I sent them with. If my aim is precise I might have to wait billions of years for it to get out. If I have computing power high enough maybe I could even get to know what was near event horizon as light passed there.

Yes.

I hope you confirm not only my final conclusion but also the way I reached it. ;-)

[...], that doesn't mean that spacetime is broken. You just can't place a static observer there. If you allow non-static observers, you can place them everywhere

That's an interesting thought but I don't think that this is all that is to it. From the point of view of remote static observer something very peculiar happens with non-static objects that travel near event horizon. In the frame of reference of remote static observer not only static clocks at event horizon have infinitely slower time pace. Same thing goes for clocks freefalling there.

I'm usually talking about infalling test particles, which do not affect the horizon. If you'd throw in a significant mass, the EH would expand. But it would do so before the mass actually reaches it, so it still wouldn't cross it.

That's interesting. Could you please point me to some explanation how this works that I might understand?

Contrary to what you can see, there are different diagrams showing different things "actually happening". There are some where there is no horizon at all*, and others, where the horizon cannot be crossed in finite time.

This diagrams are distorted in clever way to allow you to see things that are not visible on plain diagram. They allow you to discern between different ways (speeds) of asymptotically going to infinity. It allows you to see that (even in remote static frame of reference) light won't catch up freefalling object if it was shined too late. But as these diagrams expose some aspects they hide others. It's much harder to see from such deformed diagram that freefalling to event horizon as well as travel of light chasing frefalling object will both take infinite time (in remote static frame of reference).

What's actually happening might depend on chosen frame of reference (to some degree) but it shouldn't depend on how you illustrate it with a diagram.

About the things that shouldn't depend on the frame of reference: I think whether it is possible for two objects to meet should not depend on frame of reference from which you observe them so it's very good that light won't catch up falling object if it was sent to late after it no matter what frame of reference you pick. Other thing I think should be independent of frame of reference is the difference between how much two clocks meeting clocks aged since their previous meet up.

 

[Dale]

About the things that shouldn't depend on the frame of reference: I think whether it is possible for two objects to meet should not depend on frame of reference from which you observe them ... Other thing I think should be independent of frame of reference is the difference between how much two clocks meeting clocks aged since their previous meet up.

Those are both invariant. What is not invariant above is your question about whether or not something has crossed "yet", which requires a synchronization convention and is therefore coordinate-dependent.

 

[Kamil Szot]

Those are both invariant. What is not invariant above is your question about whether or not something has crossed "yet", which requires a synchronization convention and is therefore coordinate-dependent.

I know that and that's why I specified that I'm interested in "yet" in frame of reference associated with Earth.

 

[Dale]

Did I understood right that answer to my question in Schwarzschild coordinates (also in radar coordinates) is "You can never be sure that something you tossed at black hole won't come back out, no matter how long you wait, because from your point of view, as well as from point of view of anyone located farther from event horizon then the object you tossed, fall of this object towards even horizon will take forever" ?

Distance from the event horizon is not relevant, only that Schwarzschild coordinates are used to define the "point of view" (which is reasonable for any stationary observer).

If that is the answer in one set of coordinates valid for given situation then this is sufficient for me because transformation to any other valid set of coordinates can't change physical reality of my situation.

If this is your assertion then you cannot consider any coordinate dependent things to be "physical reality" (I agree). Whether or not something has crossed the horizon "yet" or "already" is therefore clearly not a question about "physical reality".

 

[Kamil Szot]

If this is your assertion then you cannot consider any coordinate dependent things to be "physical reality" (I agree). Whether or not something has crossed the horizon "yet" or "already" is therefore clearly not a question about "physical reality".

You say that there is a frame of reference in which something "already" crossed event horizon? And what time is on Earth then if you are looking from that frame of reference?

 

[Ich]

I thought about hovering at a safe distance from event horizon, having normal reasonably powered reflector (or laser) and aiming it so the beam would slide as close to event horizon as possible

As close as possible means the photosphere at r=3M. Any light ray entering it will end up in the singularity. Your scenario is not possible.

I hope you confirm not only my final conclusion but also the way I reached it. ;-)

Yes.

[...], that doesn't mean that spacetime is broken. You just can't place a static observer there. If you allow non-static observers, you can place them everywhere

That's an interesting thought but I don't think that this is all that is to it.

Yes, these non-stationary observers all will move towards the singularity inside the EH.

In the frame of reference of remote static observer not only static clocks at event horizon have infinitely slower time pace. Same thing goes for clocks freefalling there.

Tell me, what is going wrong with freefalling observers there except that remote static observers attribute some crazy numbers to them? These numbers refer to a class of observers that cannot possibly extend beyond the horizon, and it's this impossibility that you see in the infinities.

Could you please point me to some explanation how this works that I might understand?

I keep forgetting the source where I read about it, and it wouldn't be too helpful either. Simply put, the EH is defined as the boundary of the regio from which nothing can escape to infinity. If you bring another mass close to the one already existing, escaping to infinity becomes harder because you'd have to run from the combined potential of those masses. That why the EH becomes larger.

What's actually happening might depend on chosen frame of reference (to some degree) but it shouldn't depend on how you illustrate it with a diagram.

These diagrams are actually expressions of different frames of reference, i.e. coordinate systems. "distorted diagram" == different coordinate system. Are you aware that coordiates in GR can be defined quite arbitrarily?

I think whether it is possible for two objects to meet should not depend on frame of reference [...] Other thing I think should be independent of frame of reference is the difference between how much two clocks meeting clocks aged since their previous meet up.

Yes.
Whether something goes through the horizon in finite or infinite coordinate time is not something you can measure. It does not pertain to "what's actually happening". The other things do.

 

[Kamil Szot]

As close as possible means the photosphere at r=3M. Any light ray entering it will end up in the singularity. Your scenario is not possible.

Could you please elaborate bit on that? Is there area outside event horizon that light can't escape from? What r=3M mean? Does it exist for non-rotating uncharged black-holes?

Tell me, what is going wrong with freefalling observers there except that remote static observers attribute some crazy numbers to them? These numbers refer to a class of observers that cannot possibly extend beyond the horizon, and it's this impossibility that you see in the infinities.

It's not that you can't extend beyond event horizon, you can't even extend to it. I see infinities as I'm getting close to event horizon not when I've passed it.

As for what's wrong with free falling observers: Theoretically they can pass information back. They can pass back what their clock indicates so these crazy numbers are not an unobservable math trick to get calculations in line with reality. These crazy numbers show what's actually happening, at least as far as we in our frame of reference are concerned.

I keep forgetting the source where I read about it, and it wouldn't be too helpful either.

If you ever recall that please share it with me.

Simply put, the EH is defined as the boundary of the regio from which nothing can escape to infinity. If you bring another mass close to the one already existing, escaping to infinity becomes harder because you'd have to run from the combined potential of those masses. That why the EH becomes larger.

Potential at EH is infinite. Potential outside of EH is finite. As you bring new mass close you add finite potential to finite potential. There is no way that sum of two finite numbers gave you infinity.

I'm not saying it's not happening. Maybe you just put it too simple.

These diagrams are actually expressions of different frames of reference, i.e. coordinate systems. "distorted diagram" == different coordinate system.

Yes. I noticed that.

Are you aware that coordiates in GR can be defined quite arbitrarily?

If you mean that you can consider any physical situation from any frame of reference (also non-inertial) using not necessarily Cartesian set of coordinates but also any other set of coordinates you can transform them to (keeping some physical invariants like two things I gave example of), and draw right diagrams and write right equations to properly describe this situation in these coordinates, then yes I'm aware of that.

Whether something goes through the horizon in finite or infinite coordinate time is not something you can measure.

But you can discern between short finite time and waiting billions of years for something to happen.


Can you answer the question how long will I have to wait after feeding a star to a black-hole to observe it EH grow?

 

[Ich]

Could you please elaborate bit on that? Is there area outside event horizon that light can't escape from? What r=3M mean? Does it exist for non-rotating uncharged black-holes?

I always try to supply key words to look up in Wikipedia, for example. But here my own elaboration:
There's a minimum radius from which light can escape when it's moving tangentially - like an incoming beam grazing that region. That radius is 3M in geometric units, it's 1.5 times the Schwarzschild radius. Time dilation there is very finite. Worst thing that could happen is that you shoot the light in a long-lasting orbit, but that's arbitrarily unlikely.

Theoretically they can pass information back. They can pass back what their clock indicates so these crazy numbers are not an unobservable math trick to get calculations in line with reality.

What crazy numbers? 12:47:05 PM? There's nothing wrong with the numbers such a probe could relay. The problem is that you'll receive the updates less and less freequently, until they finally cease.

These crazy numbers show what's actually happening, at least as far as we in our frame of reference are concerned.

Yeah, that it was 12:47:05 PM when the probe sent the signal. And your clock shows that it was, say, 3:00 am the next day when you picked up the signal. So what?

Potential at EH is infinite. Potential outside of EH is finite. As you bring new mass close you add finite potential to finite potential. There is no way that sum of two finite numbers gave you infinity.

I'm not saying it's not happening. Maybe you just put it too simple.

Yes, I put it too simple. Just wanted to explain that the definition of an EH is highly nonlocal (you have to wait for an eternity to be sure which photon escaped and which not), and make plausible that it can grow before the matter actually falls in.
Doesn't matter, I remembered thathttps://www.physicsforums.com/showthread.php?p=2370131#post2370131". (The review paper).

But you can discern between short finite time and waiting billions of years for something to happen.

Yes. But what's going to happen to you when something crosses the horizon? (Hint: nothing.)

 

[Kamil Szot]

I always try to supply key words to look up in Wikipedia, for example. But here my own elaboration:
There's a minimum radius from which light can escape when it's moving tangentially - like an incoming beam grazing that region. That radius is 3M in geometric units, it's 1.5 times the Schwarzschild radius. Time dilation there is very finite. Worst thing that could happen is that you shoot the light in a long-lasting orbit, but that's arbitrarily unlikely.

Thank you. I think that's sufficient amount of keywords for me and also an interesting information that I was not aware of.

What crazy numbers? 12:47:05 PM? There's nothing wrong with the numbers such a probe could relay. The problem is that you'll receive the updates less and less freequently, until they finally cease.

Yeah, that it was 12:47:05 PM when the probe sent the signal. And your clock shows that it was, say, 3:00 am the next day when you picked up the signal. So what?

I mean that in probes message there is 12:47:05 PM year 13.7 bilionth since big bang while on Earth there is 12:01:03 PM year 18 billionth.

Being unable to detect signal because it has too huge wavelength doesn't mean that it is impossible to receive the message. Maybe in a billion year humanity will discover how to pump this photons back with energy and blue shift them enough to read the message?

Also you'll never cease to receive the updates. You'll just have to wait longer and longer for each one, but that might be actually good because this gives you time to upgrade your technology so you could capture next update with even higher wavelength.

Doesn't matter, I remembered thathttps://www.physicsforums.com/showthread.php?p=2370131#post2370131". (The review paper).

Thank you!

Yes. But what's going to happen to you when something crosses the horizon? (Hint: nothing.)

How about end of universe if it will have an end?

 

[Ich]

I mean that in probes message there is 12:47:05 PM year 13.7 bilionth since big bang while on Earth there is 12:01:03 PM year 18 billionth.
[...]
Also you'll never cease to receive the updates. You'll just have to wait longer and longer for each one, but that might be actually good because this gives you time to upgrade your technology so you could capture next update with even higher wavelength.

You're talking about "classically and in principle" again. There will still be a last signal, the one shortly before the probe enters the horizon. From then on, there will be no more updates.
If you like to imagine a continuous stream, you get the notion of an "frozen and redshifted" image of the probe. But usually it is not appreciated just hoz frozen and redshifted that image really is.
Rest assured that, even classically, after a day or so there is absolutely nothing to receive, no matter how advanced your technology is.

How about end of universe if it will have an end?

Maybe. I was rather thinking about something that makes the "crossing event" relevant one way or another. Like the obsever hearing the EH crack when the probe runs into it.

 

[Dale]

I know that and that's why I specified that I'm interested in "yet" in frame of reference associated with Earth.

We have discussed this over and over. Please see above.

You say that there is a frame of reference in which something "already" crossed event horizon? And what time is on Earth then if you are looking from that frame of reference?

That is completely arbitrary. You don't seem to understand that in GR the whole concept of simultaneity is up to the whim of whoever specifies the coordinate system. It is only a label attached to a set of events, with no significance other than to identify the events. You are free to re-label as desired.

 

[nismaratwork]

Is it wrong to just say that he doesn't understand GR or its underpinnings, and leave it at that?

 

[Kamil Szot]

You're talking about "classically and in principle" again. There will still be a last signal, the one shortly before the probe enters the horizon. From then on, there will be no more updates.

But won't this last signal arrive to Earth after infinite Earth time? - "classically and in principle" whatever you mean by that

Rest assured that, even classically, after a day or so there is absolutely nothing to receive, no matter how advanced your technology is.

So you are saying that in Earth frame of reference travel to event horizon of a black hole takes less than a day? That's completely opposite to what I understood from your previous answers.

I think you rather mean that signal will just be undetectable because of its wavelength and delay between each two consecutive photons. I don't know on what basis do you dismiss technical possibility of receiving such signal.

I can think of one way how detecting such signal might be possible. You might put precisely designed set of moving masses on the way of the signal and pump it up with energy, same way passing near Jupiter pumped energy into Voyager probe.

Maybe. I was rather thinking about something that makes the "crossing event" relevant one way or another. Like the obsever hearing the EH crack when the probe runs into it.

Now you are just pulling my leg. ;-)

What I wanted to say is that universe might end before you receive last signal no matter how long finite time of existence universe has ahead of itself. Maybe not if universe final fate is big crunch.


One thing again about reality of last signal: When I ask you if function y=1/x as you approach zero from the right has some last non-negative point, if you look at plot of this function in normal coordinates you may say 'no'. But if you never knew of normal coordinates and used coordinates labeled x and 1/y and plotted this function in those coordinates your answer might be 'yes'.

Of course that's not the same situation because the answer to the above is always 'no' and I just erroneously extended domain of function y=1/x with point x=0 while plotting it in hyperbolic coordinates.

In case of EH changing plots is not just simple coordinate transformation. It is changing the frame of reference, and I think that existence of 'last signal' might be frame dependent.

 

[Kamil Szot]

Is it wrong to just say that he doesn't understand GR or its underpinnings, and leave it at that?

If I understood it to the extent you do I wouldn't be asking questions about it here.

Purpose of my questions is broadening my understanding. And I already understand few things I have not understood before so from my point of view your responses are far from being pointless, and I'm very thankful to members of this forum that respond to this thread.

 

[Kamil Szot]

That is completely arbitrary. You don't seem to understand that in GR the whole concept of simultaneity is up to the whim of whoever specifies the coordinate system. It is only a label attached to a set of events, with no significance other than to identify the events. You are free to re-label as desired.

In SR what is simultaneous depends on frame of reference.

You say that in GR what is simultaneous is not only dependent on frame of reference but also on which set from equivalent sets of coordinates you pick to describe events that you are interested in?

Does frame of reference and set of coordinates in GR precisely imply how you should define what it means to be 'simultaneous'?

If so then my question is still valid:

Do you know any frame of reference and any set of coordinates that imply simultaneity by which 12:00:00 PM 06.17.2010 Earth is after the event of some freefalling object passing some EH?


I think that you can't have full freedom in choosing how do you define simultaneity in GR. If that was the case I could use GR instead of Newton mechanics to describe my neighborhood and declare such simultaneity that event of me sitting at my computer now an event of my neighbors house being built (hundred years ago by Newtonian coordinates) are exactly simultaneous.


I find it very strange that GR might not have notion of simultaneity.

If you use simpler, less precise theory to describe reality some new qualities might crop up, like absolute time in Newton mechanics if you use it instead of SR. But this qualities are always (?) derived from similar qualities in more precise theory. Newtons absolute time is just SR time that is shared by all slowly moving inertial systems. Same way SR notion of simultaneity becomes Newtons absolute notion of simultaneity.

Can you explain how arbitrary simultaneity of GR can transform into very precisely defined notion of simultaneity in SR when you are using SR instead GR to describe world around you?




I want to apologize to you all for my poor quality English. Unfortunately I'm not a native English speaker and I'm always afraid that this might be the cause of me not being able to convey what I'm meaning. If you spot language barrier between us please ask me questions and I'll try to rephrase what I wrote somehow.

 

[Dale]

In SR what is simultaneous depends on frame of reference.

You say that in GR what is simultaneous is not only dependent on frame of reference but also on which set from equivalent sets of coordinates you pick to describe events that you are interested in?

Does frame of reference and set of coordinates in GR precisely imply how you should define what it means to be 'simultaneous'?

For practical purposes "reference frame" is synonymous with "coordinate system" (there are subtle differences that are not relevant here). So, simultaneity is simply the set of events whose time coordinate is the same. I don't know what distinction you are trying to make between "reference frame" and "coordinate system".

If so then my question is still valid:

Do you know any frame of reference and any set of coordinates that imply simultaneity by which 12:00:00 PM 06.17.2010 Earth is after the event of some freefalling object passing some EH?

Yes, I have already answered this question multiple times. You should read this paper: http://arxiv.org/abs/gr-qc/0311038 Note that you can specify B so as to make any given pair of events simultaneous.

I think that you can't have full freedom in choosing how do you define simultaneity in GR. If that was the case I could use GR instead of Newton mechanics to describe my neighborhood and declare such simultaneity that event of me sitting at my computer now an event of my neighbors house being built (hundred years ago by Newtonian coordinates) are exactly simultaneous.

Yes, you could do that in GR. All predictions of physics would remain unchanged under such a coordinate transformation.

I find it very strange that GR might not have notion of simultaneity.

If you use simpler, less precise theory to describe reality some new qualities might crop up, like absolute time in Newton mechanics if you use it instead of SR. But this qualities are always (?) derived from similar qualities in more precise theory. Newtons absolute time is just SR time that is shared by all slowly moving inertial systems. Same way SR notion of simultaneity becomes Newtons absolute notion of simultaneity.

Can you explain how arbitrary simultaneity of GR can transform into very precisely defined notion of simultaneity in SR when you are using SR instead GR to describe world around you?

Locally you can always construct an SR inertial frame which is valid only over a small region of spacetime without significant curvature. Just as the Newtonian concept becomes limited to objects that are moving slowly, so the SR concept becomes limited to objects that are nearby.

I want to apologize to you all for my poor quality English. Unfortunately I'm not a native English speaker and I'm always afraid that this might be the cause of me not being able to convey what I'm meaning. If you spot language barrier between us please ask me questions and I'll try to rephrase what I wrote somehow.

Your English is fine, your physics is what is lacking. The problem is that you are asking the same questions over and over and rejecting the answers instead of trying to learn the new concepts. Perhaps you are assuming that your difficulty in understanding is due to your perceived language barrier, but to me it seems that what is foreign here is not so much the language as the physics.

I am really trying to be helpful, but frankly going in circles like this is extremely frustrating. Please stop asking the same questions and making the same assertions that I have already told you are wrong. If you don't understand an explanation then let's examine that in more detail by asking new questions that get at the root of your confusion, but if your only goal is to listen to yourself talk then you don't need me for that.

 

[nismaratwork]

If I understood it to the extent you do I wouldn't be asking questions about it here.

Purpose of my questions is broadening my understanding. And I already understand few things I have not understood before so from my point of view your responses are far from being pointless, and I'm very thankful to members of this forum that respond to this thread.

You're not listening, I'm not insulting your level of knowledge, I'm saying you need more basic study first, or to listen to the answers to your questions. In short I'm questioning your approach, not your mind, I want to make that clear. I don't mean to be insulting, I just think some time spent reading the papers DaleSpam referenced would do you a lot of good. Then, you can ask specific questions about that paper, and we can answer them, from which we can work back to this point.

 

[Kamil Szot]

For practical purposes "reference frame" is synonymous with "coordinate system" (there are subtle differences that are not relevant here). So, simultaneity is simply the set of events whose time coordinate is the same. I don't know what distinction you are trying to make between "reference frame" and "coordinate system".

Sorry. I didn't notice that coordinate system and frame of reference are used interchangeably so I thought that these are two different things. I thought coordinate system was just that (Cartesian, polar, hyperbolic, etc.) and frame of reference was some set of coordinates moving with some speed and acceleration.

Yes, I have already answered this question multiple times. You should read this paper: http://arxiv.org/abs/gr-qc/0311038 Note that you can specify B so as to make any given pair of events simultaneous.

Thank you. I promise not to ask anyone any question about simultaneity in GR before reading that.

Yes, you could do that in GR. All predictions of physics would remain unchanged under such a coordinate transformation.

That's very strange. If me sitting here now and event of my neighbors house being built 100 years ago can be simultaneous events that I could affect how this house was built.

I still can't get my head around the simultaneity being completely arbitrary. I guess I'll have to see some math to believe it. I hope I'll find it in paper you recommended.

Locally you can always construct an SR inertial frame which is valid only over a small region of spacetime without significant curvature. Just as the Newtonian concept becomes limited to objects that are moving slowly, so the SR concept becomes limited to objects that are nearby.

I though SR doesn't require locality. Just flat space and only inertial movement. As long as these things are true I can draw simultaneity line on the diagram and precisely decide if something on the other end of universe already happen or is yet to happen. It depends on my speed and direction of movement but that's all. Simultaneity in SR is precisely defined and quite limited, for example event lying inside my light cone can never be simultaneous with event of me being now, here.

Your English is fine, your physics is what is lacking.

Great to hear that.

The problem is that you are asking the same questions over and over and rejecting the answers instead of trying to learn the new concepts.

I'm trying. For example now I am trying to understand concept of simultaneity being completely arbitrary in GR and how it fits observable relations like gravitational time dilatation. It's not easy so I'm trying to rephrase my questions to get additional answers. I'm also asking new questions. I can't just learn concepts by heart. I need to understand them, how they are possible, how they work.

I am very grateful for each new piece of information that you give me by answering, what it for you seems to be, same question over and over again.

Perhaps you are assuming that your difficulty in understanding is due to your perceived language barrier, but to me it seems that what is foreign here is not so much the language as the physics.

Physics is definitely less foreign to me than English language. I was one of the laureates of national level of eliminations for IPhO at age 18. Unfortunately wasn't chosen for the international competition because there was enough laureates better than me that year. My country has population about 38 mln people. I'm also member of mensa, and firm believer in experiment, mathematical reasoning and science as a whole, so I think that I might have some capacity of understanding concepts that are new to me, especially in area of physics.

I am really trying to be helpful, but frankly going in circles like this is extremely frustrating.

I know how it's like, and I apologize for that. I once again want to thank you. All of you already helped me broaden my understanding of GR more than anyone I talked to before. I must admit I majored in CS not physics.

 

[Kamil Szot]

You're not listening, I'm not insulting your level of knowledge, I'm saying you need more basic study first, or to listen to the answers to your questions. In short I'm questioning your approach, not your mind, I want to make that clear.

Good that you clarify because I didn't get that from what you wrote. What I understood was more like 'Is it morally wrong to ignore him until he goes away, because he obviously doesn't know or get anything?' :-)

I don't mean to be insulting, I just think some time spent reading the papers DaleSpam referenced would do you a lot of good. Then, you can ask specific questions about that paper, and we can answer them, from which we can work back to this point.

I think you are right and I am going to do just that. If you can think of some other materials that might help me with understanding of GR, time dilatation, deformation of space, simultaneity and how EH works as long as objects in remote stationary frame of reference are concerned, please direct me to them.

Also if you could address any questions that I asked in this thread by answering them or pointing out why there is no answer to them I'll also be grateful.

I'm very sorry if for you this thread was more of a drudgery than a thing of interest.

 

[yuiop]

I though SR doesn't require locality. Just flat space and only inertial movement. As long as these things are true I can draw simultaneity line on the diagram and precisely decide if something on the other end of universe already happen or is yet to happen. It depends on my speed and direction of movement but that's all. can never be simultaneous with event of me being now, here.

SR does not require locality, but SR applied in GR does. In GR the spacetime very near a particle is like SR but further you move away from it, the greater the distortion due to curvature and SR can not be applied non-locally in GR. You have to be careful talking about the other end of the universe in SR because as long as there is significant mass etc in the universe, you can not safely just assume flatness. SR does not require locality in an idealised hypothetical empty universe. This "locality" for a particle in GR need not be a single point, but can be worldline of a free falling particle.

 

[yuiop]

I have not read all this thread, but I think I can shed some light on the question posed in the title of this thread, "Is the gravitational time dilation a real effect?".

Gravitational twins paradox thought experiment:

Twins A and B are r1. Twin A slowly descends to r2 and waits there. A network of stationary observers monitor the descent rate of A. After about 50 years by B's clock, B descends slowly to r2 and stops alongside twin A. The network of observers confirm that B descended at the same rate as A.

Two solutions.

1) If it is agreed that twin A is now younger than twin B (assuming they were the same age at the start) then gravitational time dilation is a real effect.

2) If it is agreed that twin A and twin B are biologically the same age after the experiment then gravitational time dilation is just an illusion or artifact of using coordinate measurements.

My intuition is with answer (1) but others may have a different physical interpretation.

 

[starthaus]

I have not read all this thread, but I think I can shed some light on the question posed in the title of this thread, "Is the gravitational time dilation a real effect?".

Gravitational twins paradox thought experiment:

Twins A and B are r1. Twin A slowly descends to r2 and waits there. A network of stationary observers monitor the descent rate of A. After about 50 years by B's clock, B descends slowly to r2 and stops alongside twin A. The netwrok of observers confirm that B descended at the same rate as A.

Two solutions.

1) If it is agreed that twin A is now younger than twin B (assuming they were the same age at the start) then gravitational time dilation is a real effect.

2) If it is agreed that twin A and twin B are biologically the same age after the experiment then gravitational time dilation is just an illusion or artifact of using coordinate measurements.

My intuition is with answer (1) but others may have a different physical interpretation.

You need to do the calculations, you can't simply list two possibilities only (ther are more) since the result depends on the radial distance between A and B and on the angular speed. You really need to calculate the proper time as a function of the radial distance and of the angular speed. I'll give you a hint, you know the integrand:

\sqrt{1-r_s/r}\sqrt{1-(\omega r/c)^2/(1-r_s/r)}

 

[yuiop]

You need to do the calculations, you can't simply list only the two possibilities since the result depends on the radial distance between A and B. You really need to calculate the proper time as a function of the radial distance. I'll give you a hint, you know the integrand.

Keep it simple for now and assume r1>r2>2m and purely radial motion in Schwarzschild coordinates.

The proper time is easy to calculate. For a stationary clock ds = dt\sqrt{(1-2m/r)}. The twin that spends the most time at r2 experiences the least proper time when they meet. Therefore answer (1) is the correct solution and gravitational time dilation is a real effect. The journey downwards is identical for both twins so we can ignore that.

 

[starthaus]

Keep it simple for now and assume r1>r2>2m.

The proper time is easy to calculate. For a stationary clock ds = dt\sqrt{(1-2m/r)}.

Umm, no. I gave you the correct expression. Look above.