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PTNLemay

Time dilation near a black hole caused by relativistic speed or extreme gravity?

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I was wondering which has a greater affect on time dilation, the extreme mass as you get closer to the black hole or the extreme speed that you build up as you fall into it. Also, at the extreme right before you hit the event horizon (or even when you move beyond it) how high can the time dilation get? Can the particles experience decades worth of time as they're falling in? More? I mean there must be a limit, on account of the fact that the particles do fall in eventually, but can the time dilation make the particles feel like they're standing still forever as they fall in?

Edited by PTNLemay

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but can the time dilation make the particles feel like they're standing still forever as they fall in?

The way I understand it, the particles will fall in just fine. BUT if you were watching it from far away, the closer they would be to the event horizon, the slower they would seem to move, since the information (light) would take longer to get to you.

EDIT: To answer your question, no, time dilatation doesn't have any limit.

Edited by theend3r

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Well... no, it's the other way around. Time dilation affects the particle. We see it falling towards the black hole faster and faster, but it's "aging" would slow down. We've seen experimental evidence of this at least in the relativistic speed time dilation. Particles created from high speed cosmic radiation impacts in our upper atmosphere have time to reach our detectors even though they should decay before they do so. Because they are travelling at near the speed of light they are time dilated, they "age" (or more properly they decay) much more slowly.

Actually... now that I think about it, if the particle would look out at the universe wouldn't time seem to speed up? Since it's slowing down, everything else would seem to accelerate in comparison. Wouldn't that mean that particles falling into a black hole would experience it in fast-forward? Please, someone who actually knows this stuff come in here and clear things up, because I'm confusing myself.

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Wouldn't that mean that particles falling into a black hole would experience it in fast-forward? Please, someone who actually knows this stuff come in here and clear things up, because I'm confusing myself.

AFAIK it would mean exactly that. Someone travelling into a black hole will experience it like time accelerating more and more. And someone observing it exactly the opposite.

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AFAIK it would mean exactly that. Someone travelling into a black hole will experience it like time accelerating more and more. And someone observing it exactly the opposite.

No, you have it backwards. Somebody orbiting a black hole would feel time slow down. It's the high speeds needed to orbit a black hole (they are massive + orbital mechanics) that slow time for the participant rather than the high gravity of the object. A simple way to think of it (to keep it straight, this is probably horribly inaccurate in reality, like most analogies involving physics) is that space and time in space-time are two perpendicular roads ( |_ ). The more you travel on one, the less you can on the other. When moving at relativistic speeds, one travels mainly on the space road, meaning that they can't be affected by time as much. This is why some believe that moving at superliminal speeds will make you travel backwards in time.

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I thought it was the high amount of acceleration (g-force) caused by the extreme gravity of the black hole that causes time dilation. Maybe I'm talking out of my buttocks here.

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I was wondering which has a greater affect on time dilation, the extreme mass as you get closer to the black hole or the extreme speed that you build up as you fall into it.

If you understand the concept of tau, you realize that these are one and the same... so the answer to your question is "neither has a greater effect, because they are the same thing".

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Actually... now that I think about it, if the particle would look out at the universe wouldn't time seem to speed up? Since it's slowing down, everything else would seem to accelerate in comparison. Wouldn't that mean that particles falling into a black hole would experience it in fast-forward? Please, someone who actually knows this stuff come in here and clear things up, because I'm confusing myself.

My understanding is that the effects of time dialation are relative to each observer - meaning that both the observer from outside the black hole, and the observer falling in, should observe each others time slow down.

Heres a great video by Eugene Khutoryansky explaining GR in laymans terms

Edited by mrfox

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To both individuals...nothing would change except the other person.

Near the black hole they'd see the other's time speeding up. Away from the black hole they'd see the other's time slow down.

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If you understand the concept of tau, you realize that these are one and the same... so the answer to your question is "neither has a greater effect, because they are the same thing".

Well... no, I'm pretty sure it's going to be one or the other. Do objects typically fall into the event horizon at speeds exceeding 90% SoL or is it usually much slower than this? I remember that the jets coming out of the poles usually blast off at something like... 70% C, I think... For relativistic effects to start matching the extreme gravity effects it would probably have to be as high as 99% SoL.

No, you have it backwards. Somebody orbiting a black hole would feel time slow down. It's the high speeds needed to orbit a black hole (they are massive + orbital mechanics) that slow time for the participant rather than the high gravity of the object.

That doesn't work though. Think back on the old example, you get aboard a rocketship that travels at 99.9% SoL and leave your twin behind. Your trip lasts 4 years, but for your twin 100 years will have passed and he'll have died. In the case of the particle falling into the black hole the singularity is analogous to the "stationary Earth". So while the particle would itself be slowed, it would see everything around it sped up as if in fast-forward.

I'm wondering all this because a friend of mine was telling me that near the singularity of a black hole relativistic effect (that being extreme speed) slows the absorbed matter until time stands still for them, and they don't ever actually hit it. That doesn't seem to work to me, though I don't know the math well enough to properly dispute it.

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Well... no, I'm pretty sure it's going to be one or the other.

Again, there is no "other".

You do not gain mass from the gravitation of the black hole. You may be confusing it with weight. Your mass increases from tau, which is the subjective effect of relativistic speeds. The time dilation and the increase in mass are caused together and in equal proportion, and so the increased mass cannot possibly "cause" time dilation - both are the product of relativistic speed.

Seems you are confusing weight for mass, and cause for effect.

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To answer your question, no, time dilatation doesn't have any limit.

Theoretically, an object travelling at c should have infinite time dilation... but there are two things that kind of punch holes in that theory:

1) The black hole has a finite size, therefore it has an upper limit on the amount of acceleration it can apply to an incoming object.

2) Light itself has a fixed speed, and therefore can only travel a finite distance in a finite period of time.

Edited by HeadHunter67

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Light itself has a fixed speed, and therefore can only travel a finite distance in a finite period of time.

The idea was, light has a fixed speed that applies to all observers, no matter their speed relative to each other.

If A was moving at .9c relative to B, and both observed that the speed of light is c, then it follows that A must perceive time as passing slower to him than it is to B by a factor of 2.294 (according to this). In other words, 1 second for A is perceived as 2.294 seconds by B.

If A was somehow moving at c relative to B, and the speed of light is still found to be the same for both observers, then A must experience time dilation by a factor of infinity, because to B, A is stationary relative to a photon particle/wave going in the same direction to himself, yet still perceives the photons as moving relative to him.

To answer the OP's question, the black hole's mass is likely to be the major contributor to the resulting time dilation effect.

Edited by shynung

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Isn't the effect of time dilation dependent on gravity and velocity?

I seem to remember reading that gravity caused dilation had the opposite but lesser effect than time dilated by velocity...

Theoretically, an object travelling at c should have infinite time dilation

Don't you get a divide by zero when travelling at c for time and mass dilation?

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No, you have it backwards. Somebody orbiting a black hole would feel time slow down. It's the high speeds needed to orbit a black hole (they are massive + orbital mechanics) that slow time for the participant rather than the high gravity of the object. A simple way to think of it (to keep it straight, this is probably horribly inaccurate in reality, like most analogies involving physics) is that space and time in space-time are two perpendicular roads ( |_ ). The more you travel on one, the less you can on the other. When moving at relativistic speeds, one travels mainly on the space road, meaning that they can't be affected by time as much. This is why some believe that moving at superliminal speeds will make you travel backwards in time.

I am pretty sure that what i posted before is right. Someone travelling at relativistic speeds will make a trip into the future. So he feels that time passed at a much faster rate then someone who is observing him. Because for the observer it seems he is standing still. You are confusing here what actually happens and what the observer/participant feels. So please read before you correcting someone.

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Theoretically, an object travelling at c should have infinite time dilation... but there are two things that kind of punch holes in that theory:

1) The black hole has a finite size, therefore it has an upper limit on the amount of acceleration it can apply to an incoming object.

2) Light itself has a fixed speed, and therefore can only travel a finite distance in a finite period of time.

ad 1) No and has nothing to do with time dilatation not having any limit

ad 2) Yes, although how "far" it travels in a fixed time depends on the observer.

None of your statements really dispute mine. Saying your limit is infinity doesn't mean you can reach it, just like in mathematics.

Edited by theend3r

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Don't you get a divide by zero when travelling at c for time and mass dilation?

From my understandings a divide by zero equals to infinite in physics. For example, the formula for kinetic energy(Newtonian for simplicity) is E=V/m2. From that formula we can derive that V=E/m2. Because a photon has no mass, this results in a divide by zero. This would give infinite as a result from my understandings, but due to relativistic effects the closest to infinite is c, causing photons to travel at the speed of light.

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ad 1) No and has nothing to do with time dilatation not having any limit

ad 2) Yes, although how "far" it travels in a fixed time depends on the observer.

Focus on the topic, please. We are talking about time dilation as an object is accelerated toward a fixed point. Therefore, at some point well before infinity, the object will have reached that fixed point and thus, its maximum speed.

Yes, the time it appears to take light to travel depends on the observer - but if you are trying to contend that time dilation can truly become infinite for the subject, then you need to consider this:

At infinite time dilation, the subject could travel an infinite distance instantly. Since any measurable distance is not infinite, and any measurable unit of time is not instant, this of course cannot truly happen - it is only in the perception of the subject relative to the reference frame of the universe - and (by definition) without an external reference frame, there can be no measure of distance. The subject is still limited by the speed of light.

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Focus on the topic, please. We are talking about time dilation as an object is accelerated toward a fixed point. Therefore, at some point well before infinity, the object will have reached that fixed point and thus, its maximum speed.

Yes, the time it appears to take light to travel depends on the observer - but if you are trying to contend that time dilation can truly become infinite for the subject, then you need to consider this:

At infinite time dilation, the subject could travel an infinite distance instantly. Since any measurable distance is not infinite, and any measurable unit of time is not instant, this of course cannot truly happen - it is only in the perception of the subject relative to the reference frame of the universe - and (by definition) without an external reference frame, there can be no measure of distance. The subject is still limited by the speed of light.

There is no such thing as infinite time dilatation and I never said so, I just said it doesn't have any limit. It's like if I said lim(infinity) for y=x/1 is 0 and you said that y=1/x will never be 0. YES.

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If it doesn't have a limit, it's infinite. If it has any limit, no matter how large, then it is a finite limit. Words mean things.

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In regards to the original question, the time dilation is caused by the extreme gravity, since if you hover just above the event horizon using an amazing rocket engine you will still be slowed down (that is, your friend far away from the black hole will see you slow down). You will see the outside universe go faster, but not infinitely fast.

Source: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

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You do get both contributions, though. And this doesn't just work this way for black holes. You have the same effect on satellites in Earth's orbit, and it has to be taken into account by GPS satellites, or any other means of precise radio tracking/positioning. Person standing on the surface is affected the most by gravitational time dilation, but only very little by Earth's relatively slow rotation. An astronaut on the ISS is affected by gravity almost as much, but also by high orbital velocity, so his clock runs slower than that of any person on Earth. On the other hand, a GPS satellite is on high enough orbit that its clock runs faster than that on the GPS receiver on Earth, because gravitational time dilation is much weaker up there, and it's not moving fast enough to compensate. The altitude at which time flows at the same rate for a person on Earth as it does for a satellite is about 3,000km.

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Look, I wrote a program to figure this out, so here's how time dilation works:

If you were traveling at 75% lightspeed, over a distance of 42 light-years, it would take you 56 years to get there. That is, that is how long Mission Control would record. Your ship's clocks, and your biological clocks, would only advance 37.04 years.

Now, if you went at 99% c, this is the result:

Mission Control records a time of 42.42 years.

Your ship records 5.985 years.

At 99.999% c:

Mission Control: 42 years

Ship: 0.1878 years, or 68.5 days.

So yeah, it's exponential. And it proves that time is relative.

EDIT:

Here's the program:


#Time Dilation Calculator

import math


c = 299792458 #Speed of light (m/s)

velMessage = "Input Ship Velocity (Percent of c): "
disMessage = "Input Distance (Light-Years): "
timeMessage = "Observer Time: "
shipMessage = "Ship Time: "


while True:

print(velMessage,end = "")
v = float(input())

print(disMessage,end = "")
d = float(input())

sTime = d / v
oTime = sTime * ((1-(((v*c)**2)/(c**2)))**(1/2))

print(timeMessage + str(sTime))
print(shipMessage + str(oTime))

ifQuit = input().lower()
if ifQuit == "q":
break

EDIT TWO:

Another odd thing: at the speed of light (100% c) time stops. As in, Mission Control registers 42 years, and you register zero. Now, the danger is the physics on the ship also register zero, so the computer cannot decelerate you. Only interstellar drag (or a stray planet :wink:) could stop you at that point.

NOT THAT YOU COULD GO 100% LIGHTSPEED, ANYWAY, BUT AN INTERESTING CONCEPT.

Edited by Starwhip

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