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The fastest you can age?

  1. Jul 4, 2011 #1
    It seems if one could travel at the speed of light, they would never age. Time stops. So if someone wants to slow down the aging process, say compared to their friends, they need to take a trip as close to the speed of light as possible. Contrary to that, many young children cant wait to get older. Does standing as still as possible make time pass the fastest, or is their a way to make someone age even quicker. Not sure how to state this, but is there something opposite the speed of light that would make one age instantly, or is standing perfectly still the fastest time can pass? Thanks for any help on another dumb question that interests me.
     
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  3. Jul 4, 2011 #2

    bcrowell

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    You can travel to a cosmological void, where the gravitational potential is higher than on Earth's surface. Due to gravitational time dilation you'll age somewhat more quickly, but I don't think the effect will be very large.

    If closed timelike curves existed in our universe, you could age yourself as rapidly as you liked. But CTCs probably don't exist in our universe.

    There is the question of whether there is some fundamental limit on the speed-up, and the thing about CTCs probably indicates that the answer depends on the cosmological structure of our universe. This may be related to the question of whether it is possible to perform an infinite computation, which is discussed in these references:

    Baez, J., 2004, "The End of the Universe.", http://math.ucr.edu/home/baez/end.html

    Dyson, Time without end: Physics and biology in an open universe, Reviews of Modern Physics 51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447.

    Krauss and Starkman, 1999, Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, http://arxiv.org/abs/astro-ph/9902189

    Katherine Freese and William Kinney, 2002, The ultimate fate of life in an accelerating universe, http://www.arxiv.org/abs/astro-ph/0205279
     
  4. Jul 5, 2011 #3

    ghwellsjr

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    I thought that the higher the gravitational potential, the slower you would age. I thought that if you were "standing still", you were in a gravitational potential. I thought if you got to a place where there was no gravity, ie, you were in free fall and therefore unable to "stand still" you would be aging at the maximum rate, relative to your friend back here on earth. But of course the difference is miniscule.

    Did I get this all wrong?
     
  5. Jul 5, 2011 #4
    No, it the other way around. A person on top of a very tall tower on the Earth's surface ages faster than a person in a deep mine.

    Standing still is not the definition of being in a gravitational potential, but if you are standing still on the surface of a gravitational body like the Earth, then you are subject to constant proper acceleration (as measured by your bathroom scales) so you would be ageing slower than someone in freefall or moving inertially in deep space.

    This last bit is sort of correct. As long as you are not moving relative to your friend on the surface of the Earth and as long as you are subject to zero proper acceleration then you would be be ageing faster than your friend.

    So all else being equal, if you attach accelerometers to two people, the one experiencing the least acceleration ages the most. While you are sitting at a desk reading this you are usually subject to 9.8m/s^2g of acceleration.
     
  6. Jul 5, 2011 #5
    Without considering gravitational fields, the best you can do to age faster is avoiding to accelerate. That seems not difficult to achieve.
    This not the same as "standing still" because you could as well be moving at any speed you like, even close to c, but you don't have to accelerate.
    But you cannot age faster than that because there is always the speed limit c.

    You can even consider gravitational fields, with the knowledge that standing still on the earth surface is being accelerated at 9,8m/s2, while not accelerating means free falling.
    The exact opposite of common experience.

    This is always only valid in your RF.
    Given you don't accelerate, you are the fastest aging object in your RF.
     
  7. Jul 5, 2011 #6

    Matterwave

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    Riding on a satellite in freefall orbit should make you age faster than people standing still on Earth. The amount, though...would probably be on the order of a few seconds over the course of a natural life-time (just my gut instinct on the size of the effect for Earth).
     
  8. Jul 5, 2011 #7

    pervect

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    Jumping up and down will help :-)

    Specifically, you want to move to a region of higher potential (away from massive bodies), without moving too quickly (to avoid relativistic time dilation).

    The path that accomplishes this will be a geodesic path. This was a question Feynman used to ask graduate students in GR to test their saavy.

    However, the effects of being in orbit aren't the optimal path to take - you're better off not orbiting, but getting as far away as you can.

    Ideally you'd jump up and "coast" into interstellar space, then land down right where you started. Depending on how much time you had, you'd want to optimize your jump to avoid the Earth's closeness (for small jumps), the Sun's closeness (for longer jumps), and eventually for really long jumps you'd be worrying about the galaxy's gravity, or the local cluster of galaxy's gravity, or the local supercluster - if you could live that long, which is rather unlikely.
     
  9. Jul 5, 2011 #8
    In GR, is the rate of time related to the gradient or the potential? I'm assuming the potential. So it's not the force of gravity that matters, but the depth in the well, yes? A lower depth in the well is considered a lower gravitational potential, yes?

    GrayGhost
     
  10. Jul 5, 2011 #9

    ghwellsjr

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    So a higher gravitational potential means less gravity? That seems backwards, what am I missing?
     
  11. Jul 5, 2011 #10
    Higher gravitational potential is linked to higher potential energy which has the potential to be converted to kinetic energy. Things generally move from high potential to low potential like a ball rolling down a hill goes from high to low. In Newtonian physics if you have an object at a given height (potential) and drop the object, it accelerates because potential energy is being converted to kinetic energy. Lower down the additional kinetic energy is compensated for the by the reduced potential energy of the object, preserving the conservation of energy principle.
     
  12. Jul 5, 2011 #11
    Yes to the last question and yes, time dilation is a function of gravitational potential rather than gradient.
     
  13. Jul 5, 2011 #12
    That depends on the radius of the satellite orbit. I will quote bcrowell here from an old thread:
    See https://www.physicsforums.com/showthread.php?t=507230

    So a person in low Earth orbit ages less than a person on the surface of the Earth and a person in high Earth orbit ages faster than a person on the surface.
     
  14. Jul 5, 2011 #13
    Imagine a hollow sphere. A gravity well surrounds it which attracts bodies toward it. One can imagine the slope (gradient) of the well increasing as one approaches the surface of the sphere. The higher the slope, the higher the G force. Inside the hollow sphere, the gravitational gradient becomes flat, and so there is no attraction at all. The gravitational potential is the lowest here, and is the same everywhere. You'd float freely w/o accelerating.

    Inside a solid sphere such as the earth, the slope of the well begins decreasing once inside the outer surface of the sphere (so less G force), and at the center of gravity the slope is zero (0-G). The gravitational potential is at its lowest at the center of gravity. No G-force there, but the potential is (I think) at its lowest point there ... which (I think) means time is the slowest.

    We'll see what the experts say.

    GrayGhost
     
    Last edited: Jul 5, 2011
  15. Jul 5, 2011 #14
    I am by no means an expert, but that I believe is essentially correct. It does however demonstrate that what I said earlier about the person experiencing the least proper acceleration ages the most is not always true, if we are talking about the interior of solid or hollow gravitational masses.
     
  16. Jul 5, 2011 #15
    OK, thanx. I did screw up the wording a little bit though. I've reworded the post since you saw it.

    GrayGhost
     
    Last edited: Jul 5, 2011
  17. Jul 5, 2011 #16

    ghwellsjr

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    But when we are talking about potentials, aren't we always talking about potential difference between two points? So doesn't this mean that in the absence of gravity or as pervect said, "away from massive bodies", there really is no number we can associate with this condition. Can't we call this gravitational potential zero if we want and as we move toward any massive body the gravitational potential is more negative?

    Or to put it another way, if we start on the survace of earth and move far away from massive bodies we will get one value for the gravitational potential but if we started on the surface of Jupiter and moved to the same place away from massive bodies we would get a larger value for the gravitational potential?
     
  18. Jul 5, 2011 #17
    First of all, think about what EXACTLY you mean by someone's "rate of ageing". You will probably be able to see that the phrase, without further qualification, actually has NO meaning at all.

    There's no way that any particular person can perceive his own rate of ageing as anything other than what it IS. It's somewhat analogous to a computer "perceiving" the passage of time only as how many cpu cycles have occurred since some previous "incident" ... if the computer's clock is slowed down, there's no way for the computer to "perceive" that occurred. Or, another analogy is that, to a surgical patient on an operating table, there is NO perceived time between when he loses consciousness from the anesthesia and when he wakes up.

    The ONLY way the phrase "the rate of someone's ageing" has any meaning is when his ageing is compared with someone else's ageing. There IS meaning to the question, "Is person A ageing faster than person B, at some given instant in person A's life?". But, in special relativity, there is NOT just one answer to that question ... person A will generally come to a different conclusion about the answer to that question than person B will. And they are BOTH correct.

    Once you have asked the question properly, the answer is that, according to person A, it is possible for person B to be ageing at an arbitrarily greater rate, or at an arbitrarily lesser rate, then person A. It is even possible for person A to conclude that person B is getting YOUNGER at an arbitrarily large rate, as person A is getting older.

    If you want to pursue these issues further, I recommend that you start with these links:

    https://www.physicsforums.com/showpost.php?p=2934906&postcount=7

    https://www.physicsforums.com/showpost.php?p=2923277&postcount=1

    Mike Fontenot
     
  19. Jul 5, 2011 #18

    bcrowell

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    A free-falling world-line has extremal aging compared to world-lines that differ from it infinitesimally and that start and end at the same events P and Q. Extremal doesn't necessarily mean maximal. It could be a minimum or a saddle point. Even if it is a maximum, it's not necessarily a global maximum. I think the world-line of someone floating weightless at the center of the earth has locally maximal aging, but not globally maximal aging.

    It's the same as in Newtonian mechanics. Yes, gravitational potentials are only defined up to an additive constant. The gravitational time-dilation ratio relates to the difference in gravitational potential.

    This is partly right and partly wrong. You're right that the question is meaningless unless you pose it correctly. I would distinguish three cases:

    (1) In a general, non-static spacetime, the only well-defined comparison is to compare the proper time along two world-lines A and B, each of which starts at the same event P and each of which ends at the same event Q. If you pose the question in this way, then there is always a well-defined answer; A and B will not come to different conclusions.

    (2) In a static spacetime with no additional symmetries beyond staticity (i.e., no additional Killing vectors besides the timelike one), there is a preferred rest frame at any given point. For example, in a Schwarzschild spacetime, the preferred rest frame is the one at rest relative to the source of the field. In this case, the gravitational potential is well defined, and there is a sensible way of defining a gravitational time dilation factor, without worrying about the technicalities referred to in #1. For example, the Pound-Rebka experiment http://en.wikipedia.org/wiki/Pound–Rebka_experiment measured the gravitational time dilation between the top and bottom of a tower in this way.

    (3) In SR, which you were referring to, the spacetime is static, but there are additional symmetries beyond staticity, and therefore there is no preferred rest frame. The only meaningful comparison is the kind described in #1. You get maximal aging by not accelerating, and there is no meaningful way of making comparisons except when observers A and B are reunited at event Q.

    In SR, it's only meaningful to compare proper times for world-lines that intersect at P and Q. With that restriction, you don't get results like this.
     
  20. Jul 5, 2011 #19

    PAllen

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    A further comment on orbiting versus sitting on the ground. As noted in an earlier post, there is kinematic effect of orbital speed versus the gravitational potential difference. However (even ignoring comparison to sitting on the ground), the reason that an orbit is not necessarily the 'fastest aging between two given spacetime points' is because there is a family of geodesics between these points. The global maximum aging rate is for the most extremal of this family of geodesics. That one (assuming only one massive body in the universe) is always the free fall path going radially outword and falling back.

    Thus, if your chosen events are one orbit apart in time, then radial free fall path that meets after one orbit will be the globally maximum aging between those events. If you consider events two orbits apart in time, then there is a longer radial path that will be at its furthest position after one orbit, meeting up after two orbits, etc.

    In general, in GR, in physically plausible situations, you have to specify two specific events, and then state there exists a most extremal geodesic between them that constitutes the global maximum age between them. Further, for any other geodesic, there are non-inertial paths that age faster than one of the other geodesics that are only locally extremal (meaning faster than small perturbations of the path).
     
  21. Jul 5, 2011 #20
    Yes, you can do that and people often do, but the higher point still has the greatest potential and least gravitational time dilation.
     
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