Gravity effect on observed speed of light

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  • #1
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Main Question or Discussion Point

An observer (in zero gravity) witnesses two parallel but widely separated beams of light that are transmited at the same time. One of the beams experiences zero gravity. The other beam travels between two massive objects with a very strong gravitational field, but arranged so that the beam direction is not changed.

Do the beams arrive at some destination point at the same time?

Perhaps a simpler situation would be the observation of the apparent speed of light from a beam of light headed directly towards a black hole. (The observer would again be in zero gravity).
 

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  • #2
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This is called Shapiro delay:
http://en.wikipedia.org/wiki/Shapiro_delay

The speed of light is always locally c, but over large distances speed becomes nonsensical in curved spacetime. It is probably better to think that because of the curvature the distance is longer for the one path than the other.
 
  • #3
cos
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An observer (in zero gravity) witnesses two parallel but widely separated beams of light that are transmited at the same time. One of the beams experiences zero gravity. The other beam travels between two massive objects with a very strong gravitational field, but arranged so that the beam direction is not changed. Do the beams arrive at some destination point at the same time?
I believe that the latter beam will accelerate as it approaches those objects then slow down as it travels away from same thereby arriving at the destination simultaneously with the uninterrupted beam.
 
  • #4
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I believe that the latter beam will accelerate as it approaches those objects then slow down as it travels away from same thereby arriving at the destination simultaneously with the uninterrupted beam.
Not so - the link given in #2 is correct. You are probably thinking of a matter particle re acceleration/deceleration, but even there, it would arrive later than it's 'zero g' twin.
(EDIT: Actually, if ultrarelativistic, a material particle will behave trajectory wise essentially as light (below). Otherwise, acceleration on entry and deceleration on exit apply, and such a gravitational slingshot will have that particle arriving earlier, not later, at least for assumed weak gravity case. There will be one intermediate case where these effects exactly cancel.)
As seen by a distant observer, light always slows when approaching a massive object and conversely speeds up when moving away. This can be seen by examining the Schwarzschild metric or it's isotropic version http://en.wikipedia.org/wiki/Schwarzschild_metric. The two give equivalent overall predictions for signal delay, but attribute different contributions from time dilation and length contraction.
Can't trust everything on the web, for instance this site gets it wrong: http://curious.astro.cornell.edu/question.php?number=266 [Broken] - only the locally observed value of c is a constant.
 
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  • #5
cos
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Not so - the link given in #2 is correct.
That link refers to a single gravitational source past which a beam of light moves in a curved trajectory whereas the OP referred to two masses between which the beam moves in a straight line.
You are probably thinking of a matter particle re acceleration/deceleration
No.
As seen by a distant observer, light always slows when approaching a massive object and conversely speeds up when moving away.
I stand by my comment.
 
  • #6
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That link refers to a single gravitational source past which a beam of light moves in a curved trajectory whereas the OP referred to two masses between which the beam moves in a straight line.
Right, but I'd say two masses were specified to simplify things - the light paths stay parallel. If you're implying Shapiro time delay is wholly or mainly owing to the extra length from light bending, no, it is second order in effect and can be neglected. Can't offhand give you a link to support that, but it is specifically stated in sect. 5.2 'Radar Ranging in the Solar System' (Gravitation and Relativity; M.G.Bowler) where it says "The change in path length due to deflection in the Sun's gravitational field is second order in the small quantity GM/(rc2)...".
I stand by my comment.
Why exactly? Time always runs slower and, depending on which coordinate system used, at least the radial component of length is always shortened near a gravitating mass, as per the first link in #4. So how can you have the two beams arriving together?
 
  • #7
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I believe that the latter beam will accelerate as it approaches those objects then slow down as it travels away from same thereby arriving at the destination simultaneously with the uninterrupted beam.
Even if the first part of this statement was true (which it is not), the conclusion does not follow from the premise. If this premise was true, the beam that passes through the gravity well would arrive before the uninterrupted beam.

However, your premise is exactly backwards. The speed of light inside a gravity well as computed by an observer well outside of the gravity well is always less than c. The beam that passes through the gravity well will arrive later than the uninterrupted beam.

One way of looking at this is that light decelerates as it falls into a gravity well and accelerates as it climbs out. I don't like this POV myself; light always moves (locally) at c. Period. I look at space and time themselves as being distorted by the gravity field rather than the speed of light.
 
  • #8
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One way of looking at this is that light decelerates as it falls into a gravity well and accelerates as it climbs out. I don't like this POV myself; light always moves (locally) at c. Period. I look at space and time themselves as being distorted by the gravity field rather than the speed of light.
I agree.
 
  • #9
cos
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Right, but I'd say two masses were specified to simplify things - the light paths stay parallel.
Thus ensuring that there is no relative delay created by that beam being diverted.
If you're implying Shapiro time delay is wholly or mainly owing to the extra length from light bending, no, it is second order in effect and can be neglected.
The extract you provided contained "The change in path length due to deflection in the Sun's gravitational field is second order..."

The OP referred to masses that could be neutron stars or black 'holes' independently resulting in a vastly greater degree of deflection than that generated by our comparatively small star.
Why exactly? Time always runs slower and, depending on which coordinate system used, at least the radial component of length is always shortened near a gravitating mass, as per the first link in #4.
Whilst time always runs slower near a gravitating mass this has absolutely no effect whatsoever on the rate of operation of the far distant observer's clock and it is his clock that he is using to measure the speed of that beam!

It should be possible (and I believe is preferable - in an attempt to eliminate obfuscation) to stick with the coordinate system introduced in the OP.

Although the first link in #4 may show that "...the radial component of length is always shortened near a gravitating mass..." I understand that if an object is falling into a massive gravitational field it becomes stretched in that direction (spaghettification) not shortened.
So how can you have the two beams arriving together?
I have already explained why I have the two beams arriving together!
 
  • #10
cos
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One way of looking at this is that light ..... accelerates as it climbs out [of a gravity well].
Why, then, did Pound determine redshift for the outward bound gamma rays?

If they were accelerating they would have blueshifted.
 
  • #11
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Why, then, did Pound determine redshift for the outward bound gamma rays?

If they were accelerating they would have blueshifted.
Wrong.

As I said earlier, you can look at things as if light was decelerates while falling into a gravity well and accelerates while climbing out. This viewpoint leads to some apparently paradoxical results. It is much easier is to look at space and time themselves being distorted by the gravity field. It takes longer for light to climb out of a gravity well because of time dilation and length contraction. Redshifting is a different but related phenomenon. As light climbs out of a gravity well it loses energy. Since light can only travel at c the only way it can lose energy is by a reduction in the frequency.
 
  • #12
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Thus ensuring that there is no relative delay created by that beam being diverted.
You're not following the message myself and DH in #6 have been trying to get across - one spacetime path is longer despite the paths remaining parallel in this scenario.
The extract you provided contained "The change in path length due to deflection in the Sun's gravitational field is second order..."

The OP referred to masses that could be neutron stars or black 'holes' independently resulting in a vastly greater degree of deflection than that generated by our comparatively small star.
I will concede things can drastically alter in really strong gravity, so much so the light beam could theoretically endlessly circle around a nominal BH - or simply get swallowed up. But except for quite recently, all Shapiro type tests have involved weak gravity where that quote was perfectly apt. Anyway in the OP's setup bending is completely cancelled so that is here a non-issue.
Whilst time always runs slower near a gravitating mass this has absolutely no effect whatsoever on the rate of operation of the far distant observer's clock and it is his clock that he is using to measure the speed of that beam!
Confusion on your part. Of course the distant observer's clock (and meter stick) is unaffected - that's not the point. There is a race between two light beams, and it very much matters how fast the clocks are ticking and the meter sticks are measuring in the local paths of the two light beams - as determined by that distant observer. You can think of it as two trains running on parallel tracks, but where one train enters a mysterious region where the train shrinks in length and the engine's wheels are turning slower. Will the two trains arrive together? No.
It should be possible (and I believe is preferable - in an attempt to eliminate obfuscation) to stick with the coordinate system introduced in the OP.
We have - calculations of relative time delay are all referenced to that coordinate system.
Although the first link in #4 may show that "...the radial component of length is always shortened near a gravitating mass..." I understand that if an object is falling into a massive gravitational field it becomes stretched in that direction (spaghettification) not shortened.
A different effect - gravitational tidal force that is irrelevant to this situation - light beam won't spaghettify like a material object.
 
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  • #13
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Wrong.

As I said earlier, you can look at things as if light was decelerates while falling into a gravity well and accelerates while climbing out. This viewpoint leads to some apparently paradoxical results. It is much easier is to look at space and time themselves being distorted by the gravity field. It takes longer for light to climb out of a gravity well because of time dilation and length contraction. Redshifting is a different but related phenomenon. As light climbs out of a gravity well it loses energy. Since light can only travel at c the only way it can lose energy is by a reduction in the frequency.
Sorry but that is wrong: according to Einstein the number of cycles emitted in a certain time must also be received in the same time period in a stationary situation - that's a conservation law of wave theory and GRT maintains that law. No cycles can get lost in flight. See also Okun's article on redshift in the AJP of 2000:

"the phenomenon is explained through the behavior of clocks which run faster the higher they are located in the potential, whereas the energy and frequency of the propagating photon do not change with height. The light thus appears to be redshifted relative to the frequency of the clock. On the other hand, the phenomenon is alternatively discussed (even in some authoritative texts) in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body. [..] we assert that it is misleading."
 
  • #14
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Why, then, did Pound determine redshift for the outward bound gamma rays?

If they were accelerating they would have blueshifted.
No, that's a misunderstanding of wave theory. The frequency of a wave cannot be affected by a change of wave speed; instead the wave is simply stretched out so that its wavelength is increased. The redshift is due to the lower resonance frequency of objects at lower gravitational potential.
 
  • #15
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An observer (in zero gravity) witnesses two parallel but widely separated beams of light that are transmited at the same time. One of the beams experiences zero gravity. The other beam travels between two massive objects with a very strong gravitational field, but arranged so that the beam direction is not changed.

Do the beams arrive at some destination point at the same time?

Perhaps a simpler situation would be the observation of the apparent speed of light from a beam of light headed directly towards a black hole. (The observer would again be in zero gravity).
Although commonly called the Shapiro effect, it immediately follows from Einstein's light bending calculation. As observed with a reference system far away, the speed of light close to a star is slowed down. In your example the beam between two stars will not bend but spread out somewhat. And of course it will be delayed compared to an unaffected beam.

Harald
 
  • #16
cos
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Wrong.

As I said earlier, you can look at things as if light was decelerates while falling into a gravity well and accelerates while climbing out. This viewpoint leads to some apparently paradoxical results.
You may prefer to look at things from the point of view that light decelerates while falling into a gravity well and accelerates while climbing out however on the basis that this viewpoint leads to some apparently paradoxical results I prefer to look at things from the point of view that light accelerates while falling into a gravity well and decelerates whilst departing.
It is much easier is to look at space and time themselves being distorted by the gravity field. It takes longer for light to climb out of a gravity well because of time dilation and length contraction.
You wrote, above, that light accelerates as it departs a gravity well but, here, that it takes longer for light to climb out. 'Longer' relative to what?
Redshifting is a different but related phenomenon. As light climbs out of a gravity well it loses energy. Since light can only travel at c the only way it can lose energy is by a reduction in the frequency.
In special theory Einstein effectively wrote that light can only travel at c but in general theory he wrote that this law required a modification. In 'Relativity, the Special and General Theory' he effectively wrote that the special theory law of the constancy of the velocity of light does not apply when gravitational fields are involved. The masses to which the OP referred could have gravitational fields many times greater than the Earth's.
 
  • #17
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Sorry but that is wrong: according to Einstein the number of cycles emitted in a certain time must also be received in the same time period in a stationary situation - that's a conservation law of wave theory and GRT maintains that law.
That is a point of view dependent interpretation. It works, but I don't like it. Looking at the photons as loosing energy as they climb out of a gravity well also works, and also conserves energy. So arguing that one is wrong and the other right is a bit like arguing over which interpretation of quantum mechanics is right.

No cycles can get lost in flight.
That is a misinterpretation of what I said.

See also Okun's article on redshift in the AJP of 2000:
They assert that it is misleading. That's not surprising; it's a bit misleading (read: counterintuitive) no matter how you look at it. Special relativity is weird. General relativity is even weirder.

Here is a rather recent (February 2011!) article that uses the photons-lose-energy point of view:

Pasquini et al, "Gravitational redshifts in main-sequence and giant stars," Astronomy & Astrophysics 526, A127 (2011)
"One such effect is the gravitational redshift originating from the propagation of light between different gravitational potentials at the source and at the observer.

Any theory involving conservation of energy requires that radiation leaving a gravitational field loses energy, and with the early 20th century understanding of the photon and the relation between its energy and wavelength, predictions could be made of the wavelength displacement expected for radiation leaving various stars, and these effects have been sought observationally."​
 
  • #18
cos
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You're not following the message myself and DH in #6 have been trying to get across - one spacetime path is longer despite the paths remaining parallel in this scenario.
I'm not 'following the messages' because I do not accept same.

The event takes place as determined by the distant observer!

Using his meter stick (held at arm's length) he determines that the beams travel identical distances - from their source to the target. He does not measure 'a longer spacetime path' for one of those beams.
I will concede things can drastically alter in really strong gravity, so much so the light beam could theoretically endlessly circle around a nominal BH - or simply get swallowed up. But except for quite recently, all Shapiro type tests have involved weak gravity where that quote was perfectly apt. Anyway in the OP's setup bending is completely cancelled so that is here a non-issue.
The gravitational fields that would, under a different circumstance, create the bending are an issue in this instance!
Confusion on your part. Of course the distant observer's clock (and meter stick) is unaffected - that's not the point.
I wrote "Whilst time always runs slower near a gravitating mass this has absolutely no effect whatsoever on the rate of operation of the far distant observer's clock and it is his clock that he is using to measure the speed of that beam!" and you respond "Of course the distant observer's clock (and meter stick) is unaffected." yet insist that there is confusion on my part?
There is a race between two light beams, and it very much matters how fast the clocks are ticking and the meter sticks are measuring in the local paths of the two light beams - as determined by that distant observer.
It has already been pointed out to you that the distant observer is not basing his findings on clocks and meter sticks in the local paths of the light beams but is using his OWN gravity unaffected/undistorted clock and meter stick!

It seems that you are simply, perhaps deliberately, refusing to see this fact.
You can think of it as two trains running on parallel tracks, but where one train enters a mysterious region where the train shrinks in length and the engine's wheels are turning slower. Will the two trains arrive together? No.
In my interpretation the train accelerates as it travels toward the objects then slows down as it departs same thus presenting an overall time equivalence as determined by the distant observer's gravity unaffected clock and rod. Will the two trains arrive together? Yes.
A different effect - gravitational tidal force that is irrelevant to this situation - light beam won't spaghettify like a material object.
And why not pray tell?

Einstein pointed out that gravitational fields effectively invalidate the law of light speed constancy.

As the tip of a beam of light that is traveling radially toward a massive gravitational field enters progressively stronger gravitational tidal areas (areas of greater gravitational potential) that end of the beam will, in my opinion, be accelerating at a faster rate than the other end of that beam which is in a weaker gravitational tidal area.

According to your reasoning (that light decelerates as it approaches a mass) the tip of that beam of light will be traveling slower than the other end of the beam hence the beam will contract in length.
 
  • #19
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The event takes place as determined by the distant observer!

Using his meter stick (held at arm's length) he determines that the beams travel identical distances - from their source to the target. He does not measure 'a longer spacetime path' for one of those beams.
Citation needed.

No matter which point of view you take (the speed of light is lower in a gravity well / time is dilated in a gravity well), the beam that goes into and out of the gravity well is delayed compared to a beam that travels through flat space time.

I wrote "Whilst time always runs slower near a gravitating mass this has absolutely no effect whatsoever on the rate of operation of the far distant observer's clock and it is his clock that he is using to measure the speed of that beam!"
Once again, citation needed. You are talking about coordinate time and length, and in that sense light travels slower than c while passing through a gravity well.
 
  • #20
cos
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Citation needed.
You require a citation in order to accept that if a person measures the distance between two points he has measured that distance?
No matter which point of view you take (the speed of light is lower in a gravity well / time is dilated in a gravity well), the beam that goes into and out of the gravity well is delayed compared to a beam that travels through flat space time.
It is relevant which point of view one takes; I am of the opinion that the statement "the speed of light is lower in a gravity well..." requires clarification; in which direction is the beam moving? Toward, away from or past the mass?

I previously wrote "Whilst time always runs slower near a gravitating mass this has absolutely no effect whatsoever on the rate of operation of the far distant observer's clock and it is his clock that he is using to measure the speed of that beam!" and you responded with -
Once again, citation needed.
You wrote, above, "...time is dilated in a gravity well..." The OP presented that the distant observer is (hypothetically) totally unaffected by the gravitational fields yet you now require a citation in order for you to accept that time is dilated in a gravity well?
You are talking about coordinate time and length
I am talking about the distant observer's determinations of length and time as distinct from determinations of lengths and times by instruments located adjacent to, i.e. extremely affected by, those masses.
and in that sense light travels slower than c while passing through a gravity well.
Are you referring to the OP depiction of light passing between two gravitational wells or to a beam that is moving toward, away from or past a single mass?

On the basis of your use of the singular 'well' I assume the latter whereas this discussion should be in relation to the former.
 
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  • #21
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harrylin wrote: "Sorry but that is wrong: according to Einstein the number of cycles emitted in a certain time must also be received in the same time period in a stationary situation - that's a conservation law of wave theory and GRT maintains that law."

That is a point of view dependent interpretation. It works, but I don't like it. Looking at the photons as loosing energy as they climb out of a gravity well also works, and also conserves energy. So arguing that one is wrong and the other right is a bit like arguing over which interpretation of quantum mechanics is right.
Your interpretation of GRT implies that gravitational time dilation is only an optical illusion, so that ideal clocks that run for a while at a different gravitational potential should indicate the same when brought together again. That is in conflict with GRT as well as with the facts.

harrylin wrote: " No cycles can get lost in flight."

That is a misinterpretation of what I said.
That is not an interpretation of what you said. That (together with the above) is Einstein's explanation of why frequency cannot change "in flight". He thus concluded that clock rate must be affected by gravitational potential. And GRT sticks with the resulting prediction as follows (emphasis mine):

"Thus the clock goes more slowly if set up in the neighbourhood of ponderable masses. From this it follows that the spectral lines of light reaching us from the surface of large stars must appear displaced towards the red end of the spectrum."
- Einstein 1916, The foundation of the general theory of relativity

harrylin wrote:
"See also Okun's article on redshift in the AJP of 2000: [..]"

They assert that it is misleading. That's not surprising; it's a bit misleading (read: counterintuitive) no matter how you look at it. Special relativity is weird. General relativity is even weirder.
No, that's not what they mean! They are merely polite in the abstract, you should read the paper. For example the conclusion (emphasis mine):

"it is very important that [General relativity] always be
taught in a simple but nevertheless correct way. That way
centers on the universal modification of the rate of a clock
exposed to a gravitational potential. An alternative explanation
in terms of a (presumed) gravitational mass of a light
pulse—and its (presumed) potential energy—is incorrect and
misleading. We exhibit its fallacy, and schematically discuss
redshift experiments in the framework of the correct approach.
We want to stress those experiments in which an
atomic clock was flown to, and kept at, high altitude and
subsequently compared with its twin that never left the
ground. The traveller clock was found to run ahead of its
earthbound twin. The blueshift of clocks with height has thus
been exhibited as an absolute phenomenon. One sees once
again that the explanation of the gravitational redshift in
terms of a naive ‘‘attraction of the photon by the earth’’ is
wrong."

Note that special relativity is for me very intuitive and not weird at all. Until one reaches the point that a topic becomes intuitive, one cannot say that one understands it. The basics of general relativity as taught by Einstein (I only know the basics) are also quite intuitive for me.
Here is a rather recent (February 2011!) article that uses the photons-lose-energy point of view:
Pasquini et al, "Gravitational redshifts in main-sequence and giant stars," Astronomy & Astrophysics 526, A127 (2011)
"One such effect is the gravitational redshift originating from the propagation of light between different gravitational potentials at the source and at the observer."

They can formulate it like that, as long as they don't claim that their explanation is Einstein's GRT.
And wrong concepts are like a computer virus, they are easy to create but difficult to eradicate. :wink:
 
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  • #22
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Let's try and reduce this to three basic issues: Issue A, Issue B, and issue C:

Issue A: When talking about acceleration, speed, clock rate, distance measure, what is the consistent reference point here? You wrote:
...The event takes place as determined by the distant observer!
We all agree on that, but you have a different idea of what that implies.
Using his meter stick (held at arm's length) he determines that the beams travel identical distances - from their source to the target. He does not measure 'a longer spacetime path' for one of those beams.
Depends what you mean exactly. If you mean that the position of the start and finish lines for both beams are seen to be the same (assumed to be far away from the gravitational influence of the two masses), then yes. But it's what happens in between that counts, and in between the distance markers and clocks have altered for one of the two beams - as referenced to the distant observer's clock and ruler. And that counts.
...I wrote "Whilst time always runs slower near a gravitating mass this has absolutely no effect whatsoever on the rate of operation of the far distant observer's clock and it is his clock that he is using to measure the speed of that beam!..."
So you agree time runs slower near a gravitating mass; but slower relative to what, if not to that distant gravity unaffected observer? Do you imagine time is running slower relative to the gravity affected object's own reference frame? (EDIT: I should make it clear 'local' here means in the path of the beam but stationary wrt the masses. It is impossible to be in the frame of a photon moving at c) That is against everything Relativity is about. In the local reference frame everything is 'normal' - so it can only be relative to some other reference frame that 'slower', 'smaller' etc makes sense. Only in the worst of the worst B-grade Sci-Fi flicks could it be otherwise; "Why is everyone speaking slow? Why is everything getting smaller?"
It has already been pointed out to you that the distant observer is not basing his findings on clocks and meter sticks in the local paths of the light beams but is using his OWN gravity unaffected/undistorted clock and meter stick!
As per above. Yes he is basing his findings on the gravity affected local values - all referenced to his own standards of measure!

Issue B: Can it ever be true that any object having some initial velocity v can first accelerate (or decelerate), then decelerate (or accelerate), in the direction of motion, finishing back at the initial velocity v, and maintain the same average velocity v? You wrote:
In my interpretation the train accelerates as it travels toward the objects then slows down as it departs same thus presenting an overall time equivalence as determined by the distant observer's gravity unaffected clock and rod. Will the two trains arrive together? Yes...
It has been pointed out clearly in #7, #11 the reason that is not so. Let's use another example. Two cars are in a street drag race, only this race has a flying start where both cross the start line nose to nose and equal speed. Just like in 'Fast and Furious' one driver has a secret nitro booster that he activates and accelerates away, but not for too long - the booster is used up and he slows down to the same initial speed. From the vantage point of the other driver who had no such boost advantage, what will he have seen? Clearly the other car has gained ground during the boost phase, and despite both finishing at the same final speed = initial speed, the nitro driver wins. Conversely, if the other vehicle developed temporary engine trouble and slowed, then picked up to the original speed, he has lost ground and will finish behind. Do you not agree? Don't confuse equality of initial and final speed with equality of average speed!

Issue C: Will a light beam accelerate or decelerate on approach to a gravitating mass (or two masses)? You wrote:
..Einstein pointed out that gravitational fields effectively invalidate the law of light speed constancy...
Sure, as long as you understand (Issue A) it is relative to the distant observer. But which way does it change....
..As the tip of a beam of light that is traveling radially toward a massive gravitational field enters progressively stronger gravitational tidal areas (areas of greater gravitational potential) that end of the beam will, in my opinion, be accelerating at a faster rate than the other end of that beam which is in a weaker gravitational tidal area.
According to your reasoning (that light decelerates as it approaches a mass) the tip of that beam of light will be traveling slower than the other end of the beam hence the beam will contract in length.
Tidal forces are proportional to the distance rate-of-change of 'g-force', which in turn is proportional to the distance rate of change of potential. It follows a very different power law and 'directionality' to change in light speed c which is linked more directly to the potential itself. So what is the verdict on how light speed (remember Issue A here!) varies with gravitational potential? Well here's one reference that backs up my quote in #6: http://en.wikipedia.org/wiki/Tests_of_general_relativity#Light_travel_time_delay_testing. I think you will search in vain for a reference that will back what I hope is now just your former position on this.:grumpy:
 
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  • #23
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[..] I am of the opinion that the statement "the speed of light is lower in a gravity well..." requires clarification; in which direction is the beam moving? Toward, away from or past the mass? [..]
Dear cos, contradictory claims are obviously not helpful!
What almost certainly will be helpful is to read the last part of Einstein's paper as answer to your questions, which you can find here:

http://www.alberteinstein.info/gallery/gtext3.html [Broken]

It's a big document but worth waiting for it to download if you have a slow connection. :smile:
The answers to your question here above are in section 22, starting from on p.196 of the English version. Actually he describes clearer the effect on rods and clocks; but as you know that the ratio of distance/time must be c (normalised to 1 in that paper), you can easily figure it out (with added understanding!) from the predicted effect on rods and clocks. :cool:
 
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  • #24
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Your interpretation of GRT implies that gravitational time dilation is only an optical illusion
What exactly do you mean by this? It appears that you are once again putting words in my mouth (or on my fingers). I am not disputing that gravitational time dilation is real. That would be rather stupid given that GPS wouldn't function if the time dilation was a mere optical illusion (whatever that backhanded statement is supposed to mean). Nor am I disputing that redshift is not real. It most certainly is.

The issue is how to interpret the redshift and time dilation. I personally like explanations that are in concordance with observation. For example, of all of the explanations of the twin paradox, I personally like the doppler explanation best. I'm not so arrogant as to foist that explanation on others. If you like some other interpretation better, so be it. There are a bunch of ways to resolve the twin paradox, all of which yield the same ultimate answer.

Distant observers cannot see photons when they are deep inside a gravity well; they have to wait for the photons to reach them before they can see them. The only observers who can see photons deep inside a gravity well are observers who themselves are deep inside a gravity well. Suppose some observer well outside a gravity well conducts local experiments to ascertain physical constants such as the speed of light, Planck's constant, and the fine structure constant. They then take the necessary equipment deep inside a gravity well and re-perform the experiments. They will get the same values as they obtained outside the gravity well. The physical constants are, well, constant.

If you take the point of view that the physical constants such as c, h, and α truly are constants, then that a photon is redshifted as it climbs out of a gravity well means that its energy, computed locally as E=hc/λ, drops as a direct consequence of the redshift.

No, that's not what they mean! They are merely polite in the abstract, you should read the paper.
I did read the paper. I also saw that it has relatively few citations and that almost all of the citations are either by Okun himself or his cohorts. My interpretation of the paper: It is little different from papers that insist that a particular interpretation of quantum mechanics is the one and only valid interpretation. That other interpretations inevitably yield the same prediction for any experiment is somehow irrelevant.
 
  • #25
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Distant observers cannot see photons when they are deep inside a gravity well; they have to wait for the photons to reach them before they can see them. The only observers who can see photons deep inside a gravity well are observers who themselves are deep inside a gravity well. Suppose some observer well outside a gravity well conducts local experiments to ascertain physical constants such as the speed of light, Planck's constant, and the fine structure constant. They then take the necessary equipment deep inside a gravity well and re-perform the experiments. They will get the same values as they obtained outside the gravity well. The physical constants are, well, constant.

If you take the point of view that the physical constants such as c, h, and α truly are constants, then that a photon is redshifted as it climbs out of a gravity well means that its energy, computed locally as E=hc/λ, drops as a direct consequence of the redshift.
Excellent perspective and I think the clearest and least ambiguous explanation in this rather messy discussion!!!!!!
 

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