View Full Version : What does the EFE predict about space-time dilation past the EH?

tommac

2010-Jun-08, 10:53 PM

Lets say I have 1space + 1 time dimensions

BH----3----EH(2)----1

At a point outside of the EH there would be some space-time dilation due to GR. At the EH(2) there is enough space-time dilation that time appears to be stopped and light can not escape ... Would the EFE mathmatically show that at point 3 ( a point inside of the EH ) that the curavture would cause a time-reversal of sorts?

I understand that the mainstream answer is that inside of the EH is undefined ... but in a simple mathmatical model based on the EFE would time be warped such that an external observer would ( if he could observe ) time going in reverse?

I understand that he can not observe anything inside of EH ... just wondering what the model would predict?

Hornblower

2010-Jun-08, 10:58 PM

What is EFE?

Please don't just assume that all of us know every acronym that pops up in your head.

tommac

2010-Jun-08, 11:13 PM

OK ... EFE stands for Einstein Field Equations

oh ... sorry ... I think OK stands for Old Kinderhook or something like that ... ;-)

What is EFE?

Please don't just assume that all of us know every acronym that pops up in your head.

tommac

2010-Jun-09, 12:29 AM

Can I assume something ( yes I know the Bad news bears quote ) .... but if the EFEs predict that there is time dilation that would result in the external observer theoretically observing time running in reverse. How would that work in a model?

korjik

2010-Jun-09, 03:23 AM

The EFEs say that past the event horizon, you are no longer in the same causal universe as outsode the event horizon, so time dilation gets kinda moot.

korjik

2010-Jun-09, 03:23 AM

Can I assume something ( yes I know the Bad news bears quote ) .... but if the EFEs predict that there is time dilation that would result in the external observer theoretically observing time running in reverse. How would that work in a model?

Dosent cause time to go in reverse. Causes time to become an imaginary number

DrRocket

2010-Jun-09, 03:57 AM

Lets say I have 1space + 1 time dimensions

BH----3----EH(2)----1

At a point outside of the EH there would be some space-time dilation due to GR. At the EH(2) there is enough space-time dilation that time appears to be stopped and light can not escape ... Would the EFE mathmatically show that at point 3 ( a point inside of the EH ) that the curavture would cause a time-reversal of sorts?

I understand that the mainstream answer is that inside of the EH is undefined ... but in a simple mathmatical model based on the EFE would time be warped such that an external observer would ( if he could observe ) time going in reverse?

I understand that he can not observe anything inside of EH ... just wondering what the model would predict?

The fundamental thing that you are missing is that in general relativity there is no such thing as time dilation.

Time dilation is a concept from special relativity and it very explicitly depends on the notion of a universal time coordinate in each inertial reference frame.

In general relativity, which is where the "EFE" apply, time and space are local concepts. There is no global time. Any comparison of clocks must occur at a single point in spacetime.

So, your confusion, as usual, stems from trying to apply ordinarly language (e.g. time) naively in a situation where it simply has no meaning. If you are going to ask subtle and sophisticated questions of general relativity you have to use the subtle and sophisticated language that is appropriate to that theory and the questions related to it -- mathematics.

tommac

2010-Jun-09, 10:43 AM

The EFEs say that past the event horizon, you are no longer in the same causal universe as outsode the event horizon, so time dilation gets kinda moot.

Yes ... I understand moot ... but ... what would it predict ... if it for some reason wasnt moot ... basically just looking for the mathmatical prediction

tommac

2010-Jun-09, 10:43 AM

Dosent cause time to go in reverse. Causes time to become an imaginary number

OK .. thanks ... this is what I thought.

tommac

2010-Jun-09, 10:53 AM

yes ... trying hard to break that habit. What I meant to say was ... if I were a wizard or had some mysterious way to see things faster than the speed of light ... or I was a mathematician ( equally not as likely ;-) ) and I dropped a clock into the EH and either watched or predicted ... what rate would that clock run when compared to my local watch. As I magically observe this clock fall into the EH ... I see that it slows relative to mine as an external observer ( this is what i am calling time dilation ... what is the proper term for this ? ) , I should be able to use the EFE to calculate how slow this clock is running compared to mine by determining the difference in gravity correct? .... As I watch the Clock come very close to the event horizon I see that it slows almost to a stop. As it hits the EH .. it can no longer be observed ... but from the post below ... based on the EFE any time comparisons to my clock produces an imaginary number right ?

The fundamental thing that you are missing is that in general relativity there is no such thing as time dilation.

Time dilation is a concept from special relativity and it very explicitly depends on the notion of a universal time coordinate in each inertial reference frame.

In general relativity, which is where the "EFE" apply, time and space are local concepts. There is no global time. Any comparison of clocks must occur at a single point in spacetime.

So, your confusion, as usual, stems from trying to apply ordinarly language (e.g. time) naively in a situation where it simply has no meaning. If you are going to ask subtle and sophisticated questions of general relativity you have to use the subtle and sophisticated language that is appropriate to that theory and the questions related to it -- mathematics.

Andrew D

2010-Jun-09, 01:35 PM

.... As I watch the Clock come very close to the event horizon I see that it slows almost to a stop. As it hits the EH .. it can no longer be observed ... but from the post below ... based on the EFE any time comparisons to my clock produces an imaginary number right ?

No. The outsider never sees the clock "hit" the EH at any rate, and unless his recording equipment is infinitely precise, he will lose the ability to observe the clock before it even gets 'close'. I think what you're missing is that describing "the other side of the EH" from the perspective of someone outside the EH is quite literally impossible; in terms of the coordinate system he is defined within, there simply is no other side.

I don't expect you to accept this...

tommac

2010-Jun-09, 02:21 PM

I don't expect you to accept this...

Huh ? why ... this is fairly basic stuff. It is not like you are saying anything mind bending. I agree fully with your statement as well as most people on the board. Not sure what you think is controversial about it?

Please note above where I state:

if I were a wizard or had some mysterious way to see things faster than the speed of light ... or I was a mathematician

All I am looking for is what does the EFE predict happens to the relationship between my clock and the clock inside the EH.

Andrew D

2010-Jun-09, 07:37 PM

All I am looking for is what does the EFE predict happens to the relationship between my clock and the clock inside the EH.

They predict that as the falling clock approaches the horizon, the wavelength of the signal sent from the falling clock increases until you are no longer able to interpret it. Then, at some point in time after you lose contact, the relationship no longer exists.

WayneFrancis

2010-Jun-10, 02:36 AM

yes ... trying hard to break that habit. What I meant to say was ... if I were a wizard or had some mysterious way to see things faster than the speed of light ... or I was a mathematician ( equally not as likely ;-) ) and I dropped a clock into the EH and either watched or predicted ... what rate would that clock run when compared to my local watch. As I magically observe this clock fall into the EH ... I see that it slows relative to mine as an external observer ( this is what i am calling time dilation ... what is the proper term for this ? ) , I should be able to use the EFE to calculate how slow this clock is running compared to mine by determining the difference in gravity correct? .... As I watch the Clock come very close to the event horizon I see that it slows almost to a stop. As it hits the EH .. it can no longer be observed ... but from the post below ... based on the EFE any time comparisons to my clock produces an imaginary number right ?

As you watch the clock fall it it appears to run slower. The faller watches your clock speed up. You don't have to wait an infinite amount of time for the faller to disappear. Once they are closer to the EH then the wavelengths of light you normally observe them at then they effectively disappear because they can no longer emit a full photon.

WayneFrancis

2010-Jun-10, 02:38 AM

...

All I am looking for is what does the EFE predict happens to the relationship between my clock and the clock inside the EH.

Its beyond an event horizon. By definition there IS NO relationship between the 2.

tommac

2010-Jun-10, 03:10 AM

Its beyond an event horizon. By definition there IS NO relationship between the 2.

OK so can you explain why you disagree with korjik in post #6 ?

WayneFrancis

2010-Jun-10, 05:43 AM

Its beyond an event horizon. By definition there IS NO relationship between the 2.

OK so can you explain why you disagree with korjik in post #6 ?

Honestly tommac I don't see how you read stuff into what people say. How am I disagreeing with korjik in post number #6?

A clock that falls into the EH of a BH is causally disconnected from the clock outside of the EH. Period. About as good of a connection as you are going to get from that point on is HR that you could very loosely try to claim is attributed to the in falling clock.

I'm talking about the relationship that an external clock has with an clock past the EH of a black hole and korjik is pointing out that there is no travelling back in time via the formulas because you don't get a negative number but an imaginary one when you try to get the square root of a negative number.

The we are talking apples and fried chicken livers here. Sure both are food but me saying apples are sweet doesn't constitute me disagreeing with korjik that chicken livers are a bit gritty if over cooked. We are talking about 2 different things.

Shaula

2010-Jun-10, 08:24 AM

So, tommac. What predictions does Ohm's Law make about the composition of Lunar soils?

Andrew D

2010-Jun-10, 05:55 PM

The we are talking apples and fried chicken livers here. Sure both are food but me saying apples are sweet doesn't constitute me disagreeing with korjik that chicken livers are a bit gritty if over cooked. We are talking about 2 different things.

Can we please start a "BAUTforum quotes that bear repeating" thread?

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