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Gravitational Time Dilation

  1. May 2, 2014 #1
    Hi people, please could someone enlighten me on gravitational time dilation. I have read online that some places, such as neutrons stars, warp time so much that time can pass 100 times slower than it does on Earth. I was just thinking about a human heart beating. If a healthy heart rate on Earth is 70bpm, does this mean that (hypothetically of course) in such a place your heart would beat 0.7bpm (70/100) but you would still be alive?
     
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  3. May 2, 2014 #2

    Matterwave

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    You certainly would not be alive if you were on the surface of a neutron star, but that's because you'd be crushed to a thin layer of atoms by the gravity of the neutron star, not because of time-dilation effects.

    Time runs slower deeper in a gravitational well, as observed by an observer in a higher part of that gravitational well. You cannot observe "your own" time dilation.

    Say here I am sitting on the surface of the Earth, and you are on the international space station, looking down at me. If you see my watch tick, you'd notice that my watch was ticking slightly slower than your watch. This is what we call gravitational time dilation. But it's not like I can tell, sitting here on Earth by myself, that my "time is running slow". I'm perfectly fine. I think time passes normally.
     
  4. May 2, 2014 #3

    Nugatory

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    No. Your heart would still beat at 70 beats per minute.

    However, your minutes would be "longer" than the minutes of the person far removed from the surface of the neutron star. That doesn't affect you at all; the anomaly will only show up if you compare times with the other person.

    You will look at your wristwatch and see that it reads noon. One minute later your wristwatch will read 12:01 and your heart will have beaten seventy times; there's no problem here.

    Meanwhile, the distant person has set his wristwatch so that it reads noon at the same time that your watch reads noon (this phrase "at the same time" is slippery and dangerous, but we don't need to go there now). After one minute has passed for you and your heart has beaten seventy times, your wristwatch will read 12:01 - but his wristwatch will read 12:10 and his heart will have beaten seven hundred times. You're both getting seventy beats per minute, and nothing weird is happening at all, unless you compare your wristwatches.
     
  5. May 3, 2014 #4
    Thanks that makes sense now. Why then, do people say that the effects of general relativity are irreversible. An example is if someone moves relative to someone else at constant velocity then each person argues about who is younger and this situation is like two sides of the same coin. However if you were to accelerate to near the speed of light and travel at this speed for 20 years and then come back then something like 38,000 years would have gone by on Earth and this is not like special relativity because it is not reversible, i.e. 38,000 years really would have gone by and the Earth may no longer be there. So what do people mean because this notion of considering general relativity and it no longer being two sides of the same coin always crops up when reading about GR and I don't quite know what people mean?
     
  6. May 3, 2014 #5

    Nugatory

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    If you're hearing that, it's because you're listening to someone who understands neither general relativity nor special relativity (although to be fair, this is a very widespread misunderstanding).

    The differential aging effect that you're describing (two people separate, then find that one of them has experienced more time and aged more than the other when they reunite) is a phenomenon of special relativity, not just general relativity. The Twin Paradox FAQ at http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html is a good introduction to what's really going on.

    The only thing that I will add is that aging is never "reversible". Your heart beat seventy times while your wristwatch ticked off one minute, and that's a minute of your life that is in your past forever. Likewise, the other person outside of the gravity well has aged ten minutes and experienced seven hundred heartbeats and there's no way of reversing that process either. It's always a one-way street from cradle to grave.
     
  7. May 3, 2014 #6
    Thanks again, and thank you for giving me a reliable link! So for the person who's watch has ticked 10 minutes and 700 heart beats have occurred then can you say that for the person near the neutron star, he will live 100 times longer relative to that person but in his own frame he just lives a normal life as far as he is concerned, is that right? What would be the equivalent case in SR, i.e. if I move relative to you in an inertial reference frame and the factor of time dilation is 100 then is it the exact same situation as for GR that we have been discussing?
     
  8. May 3, 2014 #7

    Matterwave

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    Yes, with some caveats. It's dangerous to compare times not at the same place. This is one of the fundamental results of relativity in general. It's best to compare times only at the same place.

    Let's call the person on the Neutron star person A, and the person far away from the neutron star person B. Person A and person B both will live their average life spans according to their own watch. So they both live their normal lives as far as they are concerned, that is correct. And in this case, because gravitational time dilation is not symmetric, person A will indeed see person B live longer, and person B will see person A live shorter.

    But this is not so in the case of the twin paradox! If person A is the person staying on Earth, and person B is the person flying away from Earth at very high speeds. During the trip out, person A will see that person B is aging slower, and person B will see that person A is aging slower! This is the twin paradox. Who is right? Who's clock is actually going slower? Well, according to relativity, they are both right! There is no objective way to tell who's clock is actually ticking slower (this would amount equivalently to an objective way to say who is actually moving, while relativity says that this determination cannot be made) until person B comes back to person A and they can compare their watches.

    When person B comes back to person A, and they can compare watches, THEN, one will see that person B aged less and person A aged more. Why is that? Well, because it's person B that made the reverse journey. Person B switched reference frames on his journey back (he had to slow down, stop, and reverse), and this switch in reference frames accounts for all the differential aging that will be seen when he actually gets back (contrary to some explanations, the switching reference frames part is the important part, and not necessarily the acceleration part, we can make the acceleration as quick as possible and still get the same effect).

    This example should illustrate why it's dangerous to say things like "A actually aged 100 times slower than B" if the comparison is NOT made in the same place (in the same reference frame).
     
    Last edited: May 3, 2014
  9. May 3, 2014 #8
    Thanks for your time guys, that makes much more sense now!
     
  10. May 4, 2014 #9
    If I am understanding what you mean here then are you saying that if I let my stop watch tick for 1 minute on Earth and then go near a neutron star and do the same thing then that minute would appear to last for the same amount of time? So I wouldn't be like "hey, the minute hand on my stop clock is going around much slower than it did on Earth". How can that be true! That seems really weird. How can you go into a really strong gravitational field (which distorts time) and not notice time dilation yourself as measured from your own watch? Why is this?
     
  11. May 4, 2014 #10

    Matterwave

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    Yes. If you go to the surface of a neutron star, other than the dying horribly due to the intense gravity, you would not be able to tell something weird was going on with the time. You can never observe YOUR OWN time move at anything other than 1 second every second.

    Why is this? Think about it the other way. How could you ever tell that your watch was ticking slowly? Think this through. If your stop watch ticks slowly (as seen from afar), so does EVERYTHING. So does your brain, so does your biological clock. So does every clock you have with you. How can you ever tell that something was wrong with the time?
     
  12. May 4, 2014 #11

    A.T.

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    Because to notice stuff you use your brain, which also runs slower in the gravitational field.
     
  13. May 4, 2014 #12
    Wow, so your brain processing ability slows down by the same factor which means you can't perceive it? That's so weird. Is it true that the equations of general relativity have to be applied to GPS systems in order for them to work correctly? So would the computer system driving them have to actually use Einsteins's field equations to pinpoint your location using GPS?
     
  14. May 4, 2014 #13

    A.T.

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    Everything slows down by the same factor. That's why it is called "time dilation", and not just "clock dilation" or "brain dilation".
     
  15. May 4, 2014 #14

    Matterwave

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    1) Yes, everything slows down (as viewed from afar). Why would your brain be an exception?

    2) Yes, GPS requires general relativity to pinpoint your location. But I am no expert on GPS technology so I can't tell you offhand the predicted effects. This link seems to suggest that the total effect from SR and GR combined would amount to 10km of deviation from true position every day (accumulated). http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
     
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