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Speed of light and acceleration in general relativity

  1. Jan 24, 2016 #1
    Mentor note: this discussion was split out of a different thread.

    The speed of light in a vacuum is constant, but what I would like some information regarding is Black Holes. Does a Black Hole increase the speed of a light photon as it is being pulled into the Event Horizon?
    Last edited by a moderator: Jan 25, 2016
  2. jcsd
  3. Jan 25, 2016 #2


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    In order to model a black hole, one must be using general relativity. But in general relativity, gravity is not a pull. It is curved space-time. Objects that are freely falling under the influence of gravity are not accelerated. They are following "straight line" trajectories -- geodesics.

    If one calculated the speed of light against a locally inertial reference frame (i.e. a reference frame that is freely falling), the result would always be c. That is to say that the speed of light is unchanged by the presence of a black hole. [In general relativity the curvature of space-time can be ignored and the rules of special relativity and inertial frames applied as long as one considers a sufficiently small local region]

    If one calculates the speed of light using a global frame of reference then the speed of light can be determined to be greater than c. But the speed you calculate depends on the coordinate system you choose. There is no such thing as a global inertial frame in general relativity, no preferred notion of simultaneity at a distance and, accordingly, no unambiguously correct way to specify how the speed of light should be calculated.
  4. Jan 25, 2016 #3
    What on Earth (or in space) is all this about the constancy of speed (such as c) implying constancy of velocity (v)?
    Denial of that idea can't be just my ignorance; others already have pointed it out, apparently casting their pearls futilely.
    That there are frames of reference according to which a given photon does not change its velocity is irrelevant to the extent that it might be true in any given context.

    Almost everywhere in our universe there are gravitational fields such that to an extent (slight in slight fields) any photon soon changes its velocity relative to nearly all observers in the universe. (Always recognising that from the photon's point of view, everything (if anything) happens instantly!)

    If at time 0 the speed (NB!!!) of a photon in space is c in the direction (X0,Y0,Z0) and at time 1 (relevantly different from time 0) the speed still is c, but in the direction (X1,Y1,Z1) (not = (X0,Y0,Z0)), that is change in velocity. Change in velocity is acceleration whether the speed changes or not and whether the sign of the change is positive or not. The change of a photon's velocity could happen, not merely in our local space, but in intergalactic space far from the madding mirror, just coasting through gravitational gradients, but that duzzint make no neverminds -- any non-zero change in velocity still is acceleration.
    Otherwise what IS acceleration? If I swing a cat at constant speed, are you arguing that the thongs are not accelerating because a fly sitting on a thong notices no change in airspeed?
    If moving through an arc at constant speed is not acceleration, then acceleration aint what it used to be!
  5. Jan 25, 2016 #4


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    If you spin in a circle while your cat sits on the couch, is your cat accelerating? It is in that sense of the word acceleration that light accelerates as it moves near gravitating objects.
  6. Jan 25, 2016 #5


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    That is "coordinate acceleration" (dV/dt), which is frame dependent. But there is also the frame invariant "proper acceleration (what an accelerometer measures)" .
  7. Jan 25, 2016 #6
    Try working that out in GR, and the tensor values will explain why your static scourge on the couch (no one spoke of felines! That was why I spoke of a fly on the thong) experiences no stresses, whereas your ears do.
    Note that just as "centrifugal forces" will tell who is "spinning" with reference to "the fixed stars", similarly, the change of velocity (ahem! ) and therefore momentum, colour etc, will tell which photon passed through a gravitational field. All of that in any form demands acceleration whether there is a change of speed or not. Ask those fixed stars if you doubt me! :biggrin:
  8. Jan 25, 2016 #7
    Oh, and it emphatically is NOT in that sense of the word acceleration that light accelerates in gravitational fields. If you don't believe me, try measuring the red shift before and after the acceleration. The stationary cat experiences no change in red shift, while the swung cat does.
  9. Jan 25, 2016 #8


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    It most certainly is.
    Please keep up. You are the one arguing that the cat on the couch is accelerating.
  10. Jan 25, 2016 #9
    Nope! You are the one arguing that there is no change in the momentum or velocity of either scourge or your ears or in the red shift of the gravitationally refracted light!

    Nice try though!
  11. Jan 25, 2016 #10
    Both are actual physical acceleration either in GR or Sr or Newtonian physics.
    In particular both will affect for example the energy, momentum, or red shift that an unaccelerated observer will experience (measure) on encountering such an accelerated photon.
  12. Jan 25, 2016 #11


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    Please do not jump ahead.

    Before we can address the question of light, we must address the question of that cat on the couch. Is it accelerating or is it not? You have held that any change of velocity involves an acceleration. In coordinates in which you are stationary, the cat is moving around you in a circle with a constant speed and a changing velocity. May we take it that your position is that the cat is accelerating? Or may we take it that your position is that changes in velocity do not always involve accelerations?
  13. Jan 25, 2016 #12


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    This has gone very far beyond the scope and understanding of the OP (remember him/her?). At what point did people become oblivious to helping that person at a level that he/she can understand?

  14. Jan 25, 2016 #13
    Your point is not clear.
    The question was whether light can accelerate in a vacuum.
    Several persons have explained that it can because acceleration involves a change in velocity, not necessarily in speed, and gave examples of how and why.
    Some others have argued, patently fallaciously, that because light cannot change in speed it cannot accelerate.
    One of them apparently even argues that one cannot distinguish between accelerations of different entities (swung cats and all that).
    Surely it is no favour to the OP to let such assertions go unchallenged?
  15. Jan 25, 2016 #14


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    I split the threads, the original one is here. Please respect the level indicators - details of general relativity are certainly not [B].
  16. Jan 25, 2016 #15


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    Thank you, mfb for splitting the threads.
    Jon, no one is saying that one cannot distinguish between coordinate acceleration (a sitting cat) and proper acceleration (a swung cat).

    I am trying to get you to clarify which you are speaking of when you say that light experiences changes in velocity.
  17. Jan 25, 2016 #16


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    This is not correct; the photon has no "point of view" in this sense.
  18. Jan 25, 2016 #17
    It's just a fact, that the velocity of light in vacuum can't change without changing it's speed. At first view light deflection in a gravitational field seems to be an example for acceleration with constant speed. I also made the mistake to exclude the Shapiro delay in the attempt to keep it simple. But that's an oversimplification because there is no light deflection without Shapiro delay.
  19. Jan 25, 2016 #18


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    There is some ambiguity in what one might mean when one talks about "the speed of light". To simplify it as much as possible, consider a light beam right at the event horizon moving outwards. In one sense, which I'll call a coordinate sense, the "speed" of that light is zero, because the beam of light is staying right at the event horizon. In another sense, for instance if one measured the speed of light via an instrument falling through the black hole (see https://en.wikipedia.org/wiki/Fizeau–Foucault_apparatus for a detailed description of such an instrument) the instrument would not detect any change in the speed of light as the instrument was dropped into the black hole.

    So "the speed of light" is a constant in the later sense, the coordinate-independent sense of what an instrument would measure, while it is not necessarily a constant in terms of any given coordinate system (such as Schwarzschild coordinates - there's nothing necessarily fixed about the "speed" of light defined as a ratio of the distance coordinate divided by the time coordinate.).
  20. Jan 25, 2016 #19
    How does that affect the question, which was about whether light can be accelerated, not about whether its speed can be changed? It is not clear to me whether in terms of GR, Shapiro delay involves a conceptual change to the speed of light or not, and I for one did not address the question of constant speed at all.
    I still don't.
    All I was considering was "can light be accelerated", and clearly it can be and routinely is.
    Remember that gravitationally deflected light can be distinguished from undeflected light by where and when it arrives, by its red/blue shift and resultant energy etc, in ways that are closely analogous to the effects of the acceleration of massive matter.

    It quacks like a duck say I, and I quack back, saying: "Duck!"
  21. Jan 25, 2016 #20
    Depending on the coordinates the speed of light in vacuum is either constant or not and light is accelerated if and only if it's speed changes.
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