7 ms·

I thought the reason time flows differently on top of Mount Everest is because the top of the mountain travels faster through space-time than the base (because

by pbz 12y ago

I thought the reason time flows differently on top of Mount Everest is because the top of the mountain travels faster through space-time than the base (because of the rotation of the earth), not because of gravity...

deleted 12y ago
[deleted]
DennisP 12y ago
It's gravity. The mountaintop doesn't travel faster through space-time. There's no such thing as absolute speed, there's only the velocity compared to something else. Special relativity covers time dilation due to relative velocity, general relativity covers time dilation due to gravity.
- haberman 12y ago
  Even in relative terms, the top of Mt. Everest is traveling faster than objects at sea level, no? Wikipedia says: "Time dilation is caused by differences in either gravity or relative velocity. Both factors are at play in the case of ISS astronauts (and are actually opposing one another)." Why wouldn't the same apply to the top of Mt Everest. Sure, unlike the ISS, Everest is actually attached to the Earth, but still it is traveling a longer distance than the oceans over the same period, and therefore would be moving faster in relative terms AFAICS.
  - tedunangst 12y ago
    Is the top of Mt. Everest traveling faster? The distance between here and there is a constant, no? From my frame of reference it's not moving at all.
    - haberman 12y ago
      Mt. Everest is higher. Because of the Earth's rotation, every point on earth traces 360 degrees every day. However the radius of these arcs depends on elevation. Ergo the top of Mt. Everest travels farther every day due to rotation that any other place on earth. That is the same as saying it is moving faster. EDIT: I guess compared to a rotating reference frame this isn't true? Clearly this isn't my area of expertise.
      - tedunangst 12y ago
        I think a way to rephrase the question is to ask, is the light coming from the top of mt. everest red shifted or blue shifted or neither? (I'm not certain of the answer, either. Physics was a long time ago.)
        Smudge 12y ago
        It depends on the location of the observer. (coming towards you = blue, moving away from you = red)
      - Nursie 12y ago
        Not that I disagree with your point in any way, but I thought you might like to know - the top of Everest is not the furthest point from the centre of the earth. It is the highest point above sea level, but given the slightly ellipsoid nature of the planet, the spot with the largest radius value is actually in South America - http://en.m.wikipedia.org/wiki/Chimborazo http://en.m.wikipedia.org/wiki/Chimborazo
    - ithkuil 12y ago
      your scenario to the extreme: a spacecraft is traveling at 0.5c in an circular path around earth at 1/pi light days of distance. From your (non inertial) frame of reference it's not moving at all. Yet the spacecraft is experiencing time dilation of about 15%.
  - deleted 12y ago
    [deleted]
  - HCIdivision17 12y ago
    You're correct, and my napkin guess is that it's going about 1.5mph faster than sea level. But the ISS is going a whopping 16100 mph faster than sea level [0]. Popping that into MS Mathematics using the Lorentz equation, we see that gamma now is 0.2 billionths above unity. Which is super small, but definitely detectable. In contrast, 1.5mph doesn't yield anything - I'm guessing (1.5/670616629)^2 is nearing the floating point epsilon (I guess MS Math is using floats?) [1]. [0] http://www.wolframalpha.com/input/?i=orbital+velocity+of+ISS http://www.wolframalpha.com/input/?i=orbital+velocity+of+ISS [1] http://en.wikipedia.org/wiki/Machine_epsilon http://en.wikipedia.org/wiki/Machine_epsilon EDIT: Right, as noted elsewhere, this assumes Everest is at the equator. Which Wikipedia tells me is not a great approximation for where Nepal is. So assume that Nepal ended up in the wrong place for a little while, and the arguement holds. Otherwise, we've got a bit more calculating to do.
    - haberman 12y ago
      Thanks for the info! What's the right answer if someone makes this counterargument: in the inertial reference frame of the Earth the Earth is not rotating, so neither the sea nor Mt. Everest are moving at all, so there is no relative velocity difference and no time dilation from velocity difference. Btw, I'm not sure about the phrase "I'm guessing (1.5/670616629)^2 is nearing the floating point epsilon" (unlike physics, I do have a fair amount of expertise in floating point formats). The way you put it suggests that the "machine epsilon" represents the smallest increments that floating point can represent, and therefore suggests that (1.5/670616629)^2 represented as float will underflow to zero or be so inaccurate as to be meaningless (sorry if I'm misreading you). I find the definition of "machine epsilon" given on that page somewhat confusing. I think it's more intuitive to think of floating point error in terms of percentages. That page says the "machine epsilon" for float is ~1e-7; an equivalent and IMO more intuitive way to say it is that float is accurate to ~0.00001%. The range of float goes far smaller than 1e-7; FLT_MIN is ~1e-38, and that's not even considering subnormal numbers. So float can very easily represent the results of (1.5/670616629)^2 ≈ 5e-18, and like any other representable float this is accurate to no worse than ~0.00001%, which is pretty decent.
      - 12y ago
- waqf 12y ago
  There is no absolute velocity, but there is absolute acceleration. And the mountaintop is accelerating more because it's in circular motion with a larger radius. However, the effect of gravity is much more significant (if it weren't, the mountaintop would be flying out into space due to centripetal force).
  - DennisP 12y ago
    But if I'm standing on the Earth's surface, it's not accelerating relative to me. It's always at the same distance and direction. Since acceleration is change in velocity, it's impossible to have absolute acceleration without absolute velocity. You can only say that it's accelerating compared to X.
    - HCIdivision17 12y ago
      It actually is accelerating relative to you, in exactly the same way that a kid on the outside of a spinny-go-round is accelerating harder than a kid on the inside. Of course, there's not a huge difference, as a couple km is spare change to the radius of the planet, but it's there. There's definitely a constant vector difference between you and Everest's peak, and that's likely what you're thinking of. But Everest itself is under a greater strain to maintain that vector compared to you. And that's actually a measurable difference (where measurable is on scales of stupefying precision not normally used in everyday life). And as another noted, it really should maintain that relative vector - if it didn't, the earth wouldn't be in steady-state and you'd have a changing position vector between you and it, and that'd imply one of you was moving... hopefully it's you. (Let's ignore all the techtonic complications, as that really ruins the simplicity of the argument :) EDIT: As noted elsewhere in the thread, Everest isn't on the equator, and - if I may be bold enough to presume - you likely aren't either. So it's not clear if you or Everest is on the outside of the spinny-go-round in the analogy. For the purposes of wondering if velocity or gravitational effects on spacetime are the dominant factors, this has no effect. If you're actually interested in the effective relative centrifugal forces between you and Everest, then it's damn near everything.
- AnimalMuppet 12y ago
  > Special relativity covers time dilation due to relative velocity, general relativity covers time dilation due to gravity. It's actually due to acceleration, whether from gravity or from motion. And, given earth's rotation, points on the surface accelerate (except for the poles). But, as I pointed out elsewhere in this discussion, it's distance from the axis that determines acceleration from rotation, not distance from the center of the earth. (Distance from the center does determine gravity, though).
HCIdivision17 12y ago
Probably not. You're looking at a height difference of about 9 km [1], at a radius of 6380 km from earth's core [0] versus about an equatorial 6371 km. Rotational velocity at the equator is about 1040 mph [5], while Everest is looking at about 6380 km / 6371 km * 1040 mph = 1041.5 mph, assuming we moved Everest to the equator and kept everything else the same. One or two mph is really small compared to c, so much so WA just sorta says gamma = 1 [4]. And so is a mere 0.15% increase in height. But compare the gravitational acceleration at these two heights: [2] Everest = 9.76322 m/s^2 [3] Sea Level = 9.831 m/s^2 Sea level is 0.69% stronger. That's somewhat more significant, and given that gravitational energy follows the inverse-square law, it makes some sense that it would amplify differences more than the linear effects of speed. [0] https://www.google.com/search?q=radius+of+earth https://www.google.com/search?q=radius+of+earth [1] https://www.google.com/search?q=height+of+everest https://www.google.com/search?q=height+of+everest [2] http://www.wolframalpha.com/input/?i=gravitational+acceleration+at+the+top+of+mount+everest http://www.wolframalpha.com/input/?i=gravitational+accelerat... [3] http://www.wolframalpha.com/input/?i=gravitational+acceleration+at+sea+level http://www.wolframalpha.com/input/?i=gravitational+accelerat... [4] http://www.wolframalpha.com/input/?i=lorentz+factor+at+1.5+mph http://www.wolframalpha.com/input/?i=lorentz+factor+at+1.5+m... [5] http://www.wolframalpha.com/input/?i=rotational+velocity+of+earth http://www.wolframalpha.com/input/?i=rotational+velocity+of+... EDIT: forgot the reference to rotational velocity (and spelling). Note that the point is scale here. Gravity is n^2 versus velocity's n. It'll have a stronger effect in most cases (and any where speed overcomes, well, we call them relativistic speeds, and they'll often be some appreciable fraction of c, like 1% or more). DOUBLE EDIT: 'AnimalMuppet makes a good point that the entire estimate for Everest's rotational velocity is flat out wrong. So I've changed my premise to match my initial incredibly incorrect assumption. If I were to attempt to be correct about the problem, we'd see that Everest is cos(27.9881 degrees [10]) = 0.8837 [11] as fast as the equator, which sorta blasts out any height changes by long shot. (Note I'm assuming the earth to be a perfect, frictionless sphere here, and definitely not a oblate spheroid.) [10] https://www.google.com/search?q=latitude+of+everest https://www.google.com/search?q=latitude+of+everest [11] https://www.google.com/search?q=cos(27.9+degrees) https://www.google.com/search?q=cos(27.9+degrees)
- AnimalMuppet 12y ago

by pbz 12y ago

deleted 12y ago

[deleted]

DennisP 12y ago

It's gravity. The mountaintop doesn't travel faster through space-time. There's no such thing as absolute speed, there's only the velocity compared to something else. Special relativity covers time dilation due to relative velocity, general relativity covers time dilation due to gravity.

haberman 12y ago
Even in relative terms, the top of Mt. Everest is traveling faster than objects at sea level, no? Wikipedia says: "Time dilation is caused by differences in either gravity or relative velocity. Both factors are at play in the case of ISS astronauts (and are actually opposing one another)." Why wouldn't the same apply to the top of Mt Everest. Sure, unlike the ISS, Everest is actually attached to the Earth, but still it is traveling a longer distance than the oceans over the same period, and therefore would be moving faster in relative terms AFAICS.
- tedunangst 12y ago
  Is the top of Mt. Everest traveling faster? The distance between here and there is a constant, no? From my frame of reference it's not moving at all.
  - haberman 12y ago
    Mt. Everest is higher. Because of the Earth's rotation, every point on earth traces 360 degrees every day. However the radius of these arcs depends on elevation. Ergo the top of Mt. Everest travels farther every day due to rotation that any other place on earth. That is the same as saying it is moving faster. EDIT: I guess compared to a rotating reference frame this isn't true? Clearly this isn't my area of expertise.
    - tedunangst 12y ago
      I think a way to rephrase the question is to ask, is the light coming from the top of mt. everest red shifted or blue shifted or neither? (I'm not certain of the answer, either. Physics was a long time ago.)
      - Smudge 12y ago
        It depends on the location of the observer. (coming towards you = blue, moving away from you = red)
    - Nursie 12y ago
      Not that I disagree with your point in any way, but I thought you might like to know - the top of Everest is not the furthest point from the centre of the earth. It is the highest point above sea level, but given the slightly ellipsoid nature of the planet, the spot with the largest radius value is actually in South America - http://en.m.wikipedia.org/wiki/Chimborazo http://en.m.wikipedia.org/wiki/Chimborazo
  - ithkuil 12y ago
    your scenario to the extreme: a spacecraft is traveling at 0.5c in an circular path around earth at 1/pi light days of distance. From your (non inertial) frame of reference it's not moving at all. Yet the spacecraft is experiencing time dilation of about 15%.
- deleted 12y ago
  [deleted]
- HCIdivision17 12y ago
  You're correct, and my napkin guess is that it's going about 1.5mph faster than sea level. But the ISS is going a whopping 16100 mph faster than sea level [0]. Popping that into MS Mathematics using the Lorentz equation, we see that gamma now is 0.2 billionths above unity. Which is super small, but definitely detectable. In contrast, 1.5mph doesn't yield anything - I'm guessing (1.5/670616629)^2 is nearing the floating point epsilon (I guess MS Math is using floats?) [1]. [0] http://www.wolframalpha.com/input/?i=orbital+velocity+of+ISS http://www.wolframalpha.com/input/?i=orbital+velocity+of+ISS [1] http://en.wikipedia.org/wiki/Machine_epsilon http://en.wikipedia.org/wiki/Machine_epsilon EDIT: Right, as noted elsewhere, this assumes Everest is at the equator. Which Wikipedia tells me is not a great approximation for where Nepal is. So assume that Nepal ended up in the wrong place for a little while, and the arguement holds. Otherwise, we've got a bit more calculating to do.
  - haberman 12y ago
    Thanks for the info! What's the right answer if someone makes this counterargument: in the inertial reference frame of the Earth the Earth is not rotating, so neither the sea nor Mt. Everest are moving at all, so there is no relative velocity difference and no time dilation from velocity difference. Btw, I'm not sure about the phrase "I'm guessing (1.5/670616629)^2 is nearing the floating point epsilon" (unlike physics, I do have a fair amount of expertise in floating point formats). The way you put it suggests that the "machine epsilon" represents the smallest increments that floating point can represent, and therefore suggests that (1.5/670616629)^2 represented as float will underflow to zero or be so inaccurate as to be meaningless (sorry if I'm misreading you). I find the definition of "machine epsilon" given on that page somewhat confusing. I think it's more intuitive to think of floating point error in terms of percentages. That page says the "machine epsilon" for float is ~1e-7; an equivalent and IMO more intuitive way to say it is that float is accurate to ~0.00001%. The range of float goes far smaller than 1e-7; FLT_MIN is ~1e-38, and that's not even considering subnormal numbers. So float can very easily represent the results of (1.5/670616629)^2 ≈ 5e-18, and like any other representable float this is accurate to no worse than ~0.00001%, which is pretty decent.
    - 12y ago
waqf 12y ago
There is no absolute velocity, but there is absolute acceleration. And the mountaintop is accelerating more because it's in circular motion with a larger radius. However, the effect of gravity is much more significant (if it weren't, the mountaintop would be flying out into space due to centripetal force).
- DennisP 12y ago
  But if I'm standing on the Earth's surface, it's not accelerating relative to me. It's always at the same distance and direction. Since acceleration is change in velocity, it's impossible to have absolute acceleration without absolute velocity. You can only say that it's accelerating compared to X.
  - HCIdivision17 12y ago
    It actually is accelerating relative to you, in exactly the same way that a kid on the outside of a spinny-go-round is accelerating harder than a kid on the inside. Of course, there's not a huge difference, as a couple km is spare change to the radius of the planet, but it's there. There's definitely a constant vector difference between you and Everest's peak, and that's likely what you're thinking of. But Everest itself is under a greater strain to maintain that vector compared to you. And that's actually a measurable difference (where measurable is on scales of stupefying precision not normally used in everyday life). And as another noted, it really should maintain that relative vector - if it didn't, the earth wouldn't be in steady-state and you'd have a changing position vector between you and it, and that'd imply one of you was moving... hopefully it's you. (Let's ignore all the techtonic complications, as that really ruins the simplicity of the argument :) EDIT: As noted elsewhere in the thread, Everest isn't on the equator, and - if I may be bold enough to presume - you likely aren't either. So it's not clear if you or Everest is on the outside of the spinny-go-round in the analogy. For the purposes of wondering if velocity or gravitational effects on spacetime are the dominant factors, this has no effect. If you're actually interested in the effective relative centrifugal forces between you and Everest, then it's damn near everything.
AnimalMuppet 12y ago
> Special relativity covers time dilation due to relative velocity, general relativity covers time dilation due to gravity. It's actually due to acceleration, whether from gravity or from motion. And, given earth's rotation, points on the surface accelerate (except for the poles). But, as I pointed out elsewhere in this discussion, it's distance from the axis that determines acceleration from rotation, not distance from the center of the earth. (Distance from the center does determine gravity, though).

HCIdivision17 12y ago

Probably not. You're looking at a height difference of about 9 km [1], at a radius of 6380 km from earth's core [0] versus about an equatorial 6371 km. Rotational velocity at the equator is about 1040 mph [5], while Everest is looking at about 6380 km / 6371 km * 1040 mph = 1041.5 mph, assuming we moved Everest to the equator and kept everything else the same. One or two mph is really small compared to c, so much so WA just sorta says gamma = 1 [4]. And so is a mere 0.15% increase in height. But compare the gravitational acceleration at these two heights: [2] Everest = 9.76322 m/s^2 [3] Sea Level = 9.831 m/s^2 Sea level is 0.69% stronger. That's somewhat more significant, and given that gravitational energy follows the inverse-square law, it makes some sense that it would amplify differences more than the linear effects of speed. [0] https://www.google.com/search?q=radius+of+earth https://www.google.com/search?q=radius+of+earth [1] https://www.google.com/search?q=height+of+everest https://www.google.com/search?q=height+of+everest [2] http://www.wolframalpha.com/input/?i=gravitational+acceleration+at+the+top+of+mount+everest http://www.wolframalpha.com/input/?i=gravitational+accelerat... [3] http://www.wolframalpha.com/input/?i=gravitational+acceleration+at+sea+level http://www.wolframalpha.com/input/?i=gravitational+accelerat... [4] http://www.wolframalpha.com/input/?i=lorentz+factor+at+1.5+mph http://www.wolframalpha.com/input/?i=lorentz+factor+at+1.5+m... [5] http://www.wolframalpha.com/input/?i=rotational+velocity+of+earth http://www.wolframalpha.com/input/?i=rotational+velocity+of+... EDIT: forgot the reference to rotational velocity (and spelling). Note that the point is scale here. Gravity is n^2 versus velocity's n. It'll have a stronger effect in most cases (and any where speed overcomes, well, we call them relativistic speeds, and they'll often be some appreciable fraction of c, like 1% or more). DOUBLE EDIT: 'AnimalMuppet makes a good point that the entire estimate for Everest's rotational velocity is flat out wrong. So I've changed my premise to match my initial incredibly incorrect assumption. If I were to attempt to be correct about the problem, we'd see that Everest is cos(27.9881 degrees [10]) = 0.8837 [11] as fast as the equator, which sorta blasts out any height changes by long shot. (Note I'm assuming the earth to be a perfect, frictionless sphere here, and definitely not a oblate spheroid.) [10] https://www.google.com/search?q=latitude+of+everest https://www.google.com/search?q=latitude+of+everest [11] https://www.google.com/search?q=cos(27.9+degrees) https://www.google.com/search?q=cos(27.9+degrees)

AnimalMuppet 12y ago