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#1
07-02-2002, 03:45 PM
 JFMichael Guest Join Date: Apr 2000
General Relativity: Why does time run slower near a massive body?

From Stephen Hawking's A Brief History of Time:
Quote:
 Another prediction of general relativity is that time should appear to run slower near a massive body like the earth. This is because there is a relation between the energy of light and its frequency (that is, the number of waves of light per second): the greater the energy, the higher the frequency. As light travels upward in the earth's gravitational field, it loses energy, and so its frequency goes down. (This means that the length of time between one wave crest and the next goes up.) To someone high up, it would appear that everything down below was taking longer to happen.
I can understand how the light loses energy to the earth's gravitational pull, but how does this result in a slowdown of time? If the light's frequency goes down, or stretches out, it may look like everything below was taking longer to happen, but isn't that just a result of the stretched out light wave? Unless time is dependant on the frequency of light, then I don't see any difference in time. As the observer approaches the surface of the earth, shouldn't the people on earth appear to speed up and return to normal? I know that I am missing the point of relativity- that time is consistant for each observer, but I just don't see how longer wavelength of light = slowed down time. Is the wavelength of light the same thing as the speed of light? Thank you.
#2
07-02-2002, 04:56 PM
 Philster Guest Join Date: Aug 2000
Well, I have always heard it explained that gravity (large mass) warps time.

lots o' gravity slows time....but this is relative to the observer....to the one near the massive gravity....it's normal....to someone else near alot less gravity.....they look like slow mo.....and you can see how light wave frequency would have to fall victim to gravity too....for it all to make sense to an observer and remain relative.

Everything is warped, including light waves.

(crude explanation - i know)
#3
07-02-2002, 04:58 PM
 Philster Guest Join Date: Aug 2000
speed of light versus light wave freq: sound has various frequencies, but doesn't affect it's speed. Think along those lines.
#4
07-02-2002, 05:38 PM
 Whack-a-Mole Guest Join Date: Apr 2000
Remember, the speed of light is the same for all observers. Say I emit a light wave from a source that I know has a frequency of 1 wave per millisecond (just an example folks...don't nitpick that one) and I do this in a vacuum nowhere near a gravity source of any significance. My detector will register a light wave with a frequency of 1 wave per millisecond.

Now let's say I do the same experiment in a gravity well. I emit my light wave and my detector measures a wave with a pulse of...1 wave per millisecond!

How can that be? Someone standing outside my gravity well can clearly see the wave is arriving at my detector at 1 wave per 2 milliseconds (it's gotten stretched out). However, the people inside the gravity well are stuck in the same frame of reference as the light wave and they must measure 1 pulse every millisecond. The only way for this to happen is for the clocks in the gravity well to slow down so they measure the same rate for the light frequency.
#5
07-02-2002, 05:52 PM
 monstro Guest Join Date: Mar 2002
Would a person standing next to a black hole age at the same rate as a person standing a gazillion miles from a black hole? Help my ignorant mind understand.
#6
07-02-2002, 06:39 PM
 Whack-a-Mole Guest Join Date: Apr 2000
Quote:
 Originally posted by monstro Would a person standing next to a black hole age at the same rate as a person standing a gazillion miles from a black hole? Help my ignorant mind understand.
Yes and no. It depends whose viewpoint you care to take.

If you were very very close to the event horizon of a black hole (and lets assume it's a very small black hole and that you are somehow surviving this) time would be moving very slowly for you. From my perspective a million miles away you are barely moving at all. While I might die in 60 years it might appear to take 1,000 years for you to age and die. (And once again I am purely making up numbers here for the example to illustrate what's going on.)

However, from your perspective (the guy next to the black hole) it still takes 60 years for you to age and die. Frankly you don't notice a thing about time moving differently although if you could see the other guy a gazillion miles away he would seem to live a pretty short life as far as you were concerned.
#7
07-02-2002, 07:51 PM
 monstro Guest Join Date: Mar 2002
I'm still confused, Whack-a-Mole. Please have patience.

We have two syncronized clocks. We set one next to a black hole and set the other on Earth. After a while, we retrieve both clocks and compare them side-by-side. Will the black hole clock be behind the Earth clock?
#8
07-02-2002, 07:52 PM
 The Ryan BANNED Join Date: Aug 1999 Posts: 3,759
Something else to think about is that if you stay on the surface of the Earth, you age slowly because of the gravity well. If you were to get in a rocket, fly several thousand miles away, and come back, you would age more because of getting out of the gravity well, but less because of traveling at a high speed. To experience the greatest amount of time, a path involving no accleration (just fly up, then fall back under Earth's gravity) would give you a maxiimum.
#9
07-02-2002, 11:11 PM
 Ring Charter Member Join Date: Dec 2000 Location: South Carolina USA Posts: 1,561
Quote:
 Originally posted by monstro I'm still confused, Whack-a-Mole. Please have patience. We have two syncronized clocks. We set one next to a black hole and set the other on Earth. After a while, we retrieve both clocks and compare them side-by-side. Will the black hole clock be behind the Earth clock?
At one centimeter from a 10 solar mass black hole time will run 6 million times slower than it will far away. At the event horizon time comes to a complete stop with respect to a far away stationary observer.

So the black hole clock will be very behind the Earth clock.
#10
07-03-2002, 12:40 AM
 Ring Charter Member Join Date: Dec 2000 Location: South Carolina USA Posts: 1,561
Quote:
 Originally posted by Ring At one centimeter from a 10 solar mass black hole time will run 6 million times slower than it will far away. At the event horizon time comes to a complete stop with respect to a far away stationary observer. So the black hole clock will be very behind the Earth clock.
Of course if the clock is 1 cm from the the horizon your light cone would not have yet closed up so when you descend to retreive the clock you would be fried by the blueshifted radiation from the rest of the universe. So good luck and wear a lot of ice cubes around you heinie.
#11
07-03-2002, 10:22 AM
 Whack-a-Mole Guest Join Date: Apr 2000
Quote:
 Originally posted by Ring Of course if the clock is 1 cm from the the horizon your light cone would not have yet closed up so when you descend to retreive the clock you would be fried by the blueshifted radiation from the rest of the universe. So good luck and wear a lot of ice cubes around you heinie.
Here are some more tidbits to bake your noodle:

Gravity decreases the farther away you are from the gravitational source. So, standing here on earth, the gravity pulling down on your head is less than the gravitational pull on your feet. However, on earth, the effect is exceedingly small so it's no big deal. However, coming close to the event horizon of all but the largest black holes is a different matter entirely. The gravitational field there is so strong that the pull on your feet (assuming you are going in feet first) will be significantly stronger than the gravitational pull on your head only six feet or so further out. The effect of this will be to stretch you out like a piece of spaghetti.

As to the time thing when getting close to a black hole things go wonky real fast. If I am watching you go into a black hole from some safe distance I will never actually see you pass the event horizon. From my vantage point far away I will see you move right up to the event horizon and stop there where you will seem to stay forever (actually your image will fade over time as it gets redshifted beyond perception).

For you, the intrepid adventurer falling in to the black hole, things are even worse. Assuming you somehow avoid being turned into spaghetti and being cooked once you enter the event horizon the singularity will always lie in your future. This has two effects -- 1) You will never ever be able to get away from the singularity and 2) You will never actually reach the singularity...you will spend eternity falling towards it (if you reached the singularity it would be in your past and that can't happen).

As Stephen Hawking mentioned in his book it is appropriate to put the sign to the entrance to hell from Dante's Inferno near a black hole -- Abandon All Hope Ye Who Enter Here.
#12
07-03-2002, 10:55 AM
 DrMatrix Charter Member Charter Member Join Date: Nov 1999 Location: New York State of Mind Posts: 3,299
Quote:
 Originally posted by Whack-a-Mole Assuming you somehow avoid being turned into spaghetti and being cooked once you enter the event horizon the singularity will always lie in your future. This has two effects -- 1) You will never ever be able to get away from the singularity and 2) You will never actually reach the singularity...you will spend eternity falling towards it (if you reached the singularity it would be in your past and that can't happen).
Almost. A singularity can never be in the past light cone of any observer inside or outside the event horizon. It must be in the future light cone or the Absolute Elsewhere for an observer outside the horizon. And in the Absolute Future for an observer inside the horizon. However, this does not mean that you can never reach the singularity. Once inside the event horizon, you will reach the singularity and in a finite amout of time. It will be the end of time for you. Time ends at the singularity.
#13
07-03-2002, 11:18 AM
 Whack-a-Mole Guest Join Date: Apr 2000
Quote:
 Originally posted by DrMatrix However, this does not mean that you can never reach the singularity. Once inside the event horizon, you will reach the singularity and in a finite amout of time.
Don't take this as arguing with you because I realize you know more about this than I do. I'm just explaining my understanding so you can clarify where I'm going wrong.

I thought you never actually quite reached the singularity. the closer you got to it the slower time would move for you. You could get arbitrarily close but never quite get there (the way the universe will continue to expand forever but at an ever decreasing speed...you never quite reach zero). Eventually the universe will end or your black hole will boil away before you touched the singularity. Hence, the singularity is always in your future. If time stops for you upon reaching the singularity can it still be said the singularity always lies in your future? I realize that is somewhat meaningless since there is no longer a past or future for you but by that same token the statement that a singularity is always in your future would seem to go out the window as well.
#14
07-03-2002, 01:26 PM
 Ring Charter Member Join Date: Dec 2000 Location: South Carolina USA Posts: 1,561
From the Physics faq

http://antwrp.gsfc.nasa.gov/htmltest...h_pub_faq.html

Quote:
 If the black hole is mortal, you'll instead see those events happen closer and closer to the time the black hole evaporates. Extrapolating, you would calculate my time of passage through the event horizon as the exact moment the hole disappears! (Ofcourse, even if you could see me, the image would be drowned out by all the radiation from the evaporating hole.) I won't experience that cataclysm myself, though; I'll be through the horizon, leaving only my light behind. As far as I'm concerned, my grisly fate is unaffected by the evaporation.
If you want to delve deeper into this weird stuff do a search on the "Finkelstein FoR"

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