Gravity effect on observed speed of light

[rcgldr]

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).

 

[Dale]

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.

 

[cos]

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.

 

[Q-reeus]

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 - only the locally observed value of c is a constant.

 

[cos]

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.

 

[Q-reeus]

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?

 

[D H]

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.

 

[Dale]

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.

 

[cos]

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!

 

[cos]

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.

 

[D H]

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.

 

[Q-reeus]

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 canceled 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.

 

[harrylin]

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."

 

[harrylin]

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.

 

[harrylin]

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

 

[cos]

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.

 

[D H]

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."​

 

[cos]

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 canceled 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.

 

[D H]

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.

 

[cos]

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.

 

[harrylin]

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. ​

 

[Q-reeus]

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.

 

[harrylin]

[..] 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

It's a big document but worth waiting for it to download if you have a slow connection.
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.

 

[D H]

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.

 

[Naty1]

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!

 

[harrylin]

What exactly do you mean by this? It appears that you are once again putting words in my mouth (or on my fingers).

Mea culpa if this time I put words in your mouth!

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.
[..]
That other interpretations inevitably yield the same prediction for any experiment is somehow irrelevant.

Dear D H, obviously neither the arguments of Einstein or Okun could convince you. Perhaps it was due to lack of attention from your part - or perhaps it was due to an escape route that you know, but unknown to myself, Okun and Einstein. Let's see!

Actually, your arguments didn't even touch on their arguments which I briefly presented. I'll try to make their arguments more specific with an exaggerated example that combines both Einstein and Okun!

A radio signal of 100 MHz is emitted from the top of a 300 m high radio tower straight down to a receiver on the ground. For simplicity, let independent clocks on the ground suffer from extreme gravitational time dilation with a factor of 1+1E-6, so that 1 ground second corresponds to 1.000001 tower second.

1. (argument based on Okun:) What frequency will the ground receiver measure, considering the time dilation of the ground receiver and the blue shift of the light? Is that in agreement with measurements?

2. (argument based on Einstein:) After sending for 10 tower seconds, how many cycles or wave fronts:
a. are approximately "in flight"
b. have been emitted from the tower
c. have been received 300 m lower (same precision as under a)

I will answer these questions myself next time, but as last time I already indicated my answers as well as the reason why, I would appreciate to see this time your answers first!

 

[D H]

Mea culpa if this time I put words in your mouth!

Dear D H, obviously neither the arguments of Einstein or Okun could convince you. Perhaps it was due to lack of attention from your part - or perhaps it was due to an escape route that you know, but unknown to myself, Okun and Einstein. Let's see!

Oh, please. Lack of attention! Escape route! How much more excrement can you throw at the fan in the hopes that it hits me?

The problem is that you are insisting that your technique is the one and only true technique. I admit that your technique yields the same ultimate answers as does the "physical constants are constant / local observability trumps all" approach that I favor. I favor that approach because I tend to like physical constants to be constant and because apparently I have an archaic experimentalist mindset. That approach just happens to suit me; I am not so arrogant as to say that it is the only valid interpretation.

We are not in disagreement over any observable phenomena. We are in disagreement over which is the only valid way to interpret these observed phenomena. I do tend to favor one approach, but my true viewpoint is that any interpretation that explains all observable phenomena is valid. You apparently think otherwise. That isn't physics. It's religion.

Your questions encourage looking at things from your favored perspective. There's nothing wrong with that per se. Since some questions are more easily using one interpretation, others with another, being able to flip amongst interpretations is the best way to solve a problem.

But, right back atcha, the operator at the top of the hill calculates that in the operator's rest frame, the effective radiated power of the antenna is 100,000 watts per steradian.
1. In the operator's rest frame, what is the the energy of each of these 100 MhZ photons?
2. In the operator's rest frame, how many photons are being transmitted per second per steradian?
3. In the receiver's rest frame, what is the frequency of the received signal?
4. In the receiver's rest frame, what is the energy of each received photon?
5. In the receiver's rest frame, how many photons are being received per second per steradian?
6. In the receiver's rest frame, what is the effective radiated power of the antenna in watts/steradian?

 

[PAllen]

Mea culpa if this time I put words in your mouth!

Dear D H, obviously neither the arguments of Einstein or Okun could convince you. Perhaps it was due to lack of attention from your part - or perhaps it was due to an escape route that you know, but unknown to myself, Okun and Einstein. Let's see!

Actually, your arguments didn't even touch on their arguments which I briefly presented. I'll try to make their arguments more specific with an exaggerated example that combines both Einstein and Okun!

A radio signal of 100 MHz is emitted from the top of a 300 m high radio tower straight down to a receiver on the ground. For simplicity, let independent clocks on the ground suffer from extreme gravitational time dilation with a factor of 1+1E-6, so that 1 ground second corresponds to 1.000001 tower second.

1. (argument based on Okun:) What frequency will the ground receiver measure, considering the time dilation of the ground receiver and the blue shift of the light? Is that in agreement with measurements?

2. (argument based on Einstein:) After sending for 10 tower seconds, how many cycles or wave fronts:
a. are approximately "in flight"
b. have been emitted from the tower
c. have been received 300 m lower (same precision as under a)

I will answer these questions myself next time, but as last time I already indicated my answers as well as the reason why, I would appreciate to see this time your answers first!

Mostly I don't want to enter this debate, but I do want to point out that 2)a) above is:

- not locally measurable
- coordinate dependent
- simultaneity convention dependent

In particular, there is nothing the forces the the emitter and receiver to agree on spacelike surfaces of simultaneity, so they need not agree on this purely theoretical, non-measurable, quantity.

 

[harrylin]

I wrote:
"Perhaps it was due to lack of attention from your part - or perhaps it was due to an escape route that you know, but unknown to myself, Okun and Einstein. Let's see!"

Oh, please. Lack of attention! Escape route! How much more excrement can you throw at the fan in the hopes that it hits me? [..]

excrement? throw it?!

Dear D H, I did not throw any dirt but started a serious scientific discussion with you. I was looking forward to see you demonstrate that your interpretation actually works for the cases in the literature that you chose to ignore. As I mentioned I saw two possibilities:

1. You never carefully examined their arguments, or
2. There is a way out that I overlooked, so that your interpretation is possible after all.

Actually, there is a third option that I can think of (but unlikely in view of your citation):
3. Our interpretations are identical, and we merely disagree with the way the other formulates it

As you refuse to discuss it in detail, I consider our discussion about this question closed.

Harald

 

[harrylin]

D H wrote: "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!

I would hope so... but I'm sorry, I still doubt it. Perhaps I'm too pessimistic?

Naty please remove my doubt! (and D H, please allow this test by refraining from commenting until after Naty replies).

Based on such explanations, what do you predict for what an observer on Earth will measure for the case of a sodium line coming from a star, with the following information:

1. gravitational time dilation is real: the light source at the star is 1% shifted to the red compared to the observer's sodium reference source.
2. the redshift is 1% to the red as the photon climbs out of the gravity well ("originating from the propagation of light", according to a recent paper).

Will he observe a 0%, 1% or 2% shift, and why?

Regards,
Harald

 

[cos]

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.

In fact we don't need any clocks or rods!

In compliance with the OP - the distant observer could see the beams emitted simultaneously (the sources are equidistant from him) and arrive at the finish line simultaneously.

As you point out - the position of the start and finish lines for both beams are seen, by the distant observer, to be the same ergo on the basis that the beams travel identical distances and, having been emitted simultaneously, arrive at the finish line simultaneously the observer is fully justified in concluding that, from HIS point of view, the beams took the same amount of time to make their trips.

So you agree time runs slower near a gravitating mass; but slower relative to what, if not to that distant gravity unaffected observer?

I freely admit that I am academically unqualified in the subject of physics but please stop treating me like a naive child.

As per above. Yes he is basing his findings on the gravity affected local values - all referenced to his own standards of measure!

As above. The situation as depicted is that there are NO gravity affected local values and he bases his conclusion on observation alone (simultaneous emission; the position of the start and finish lines for both beams are seen to be the same; simultaneous arrival at the finish line).

Alternately, as previously, he bases his determination of the identical distances using his meter stick held at arm's length and uses his clock in order to determine the time that it takes for the beams to make their trips. He cannot see the far distant clocks and rods.

Let us assume that the OP involves a semblance of reality and there are two black holes between which a beam of light travels. There are NO clocks or sticks dangling in space so the distant observer can only determine his measurements in accordance with his own equipment however all of a sudden clocks and sticks apear along the path of the beam.

Does that affect (alter) the distant observer's measuring rod or clock in any way?

Of course it does NOT!

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?

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!

You wrote "...the booster is used up and he slows down to the same initial speed." My depiction is that he does not slow down to the same initial speed but that his speed is then slower than its initial speed thereby enabling the other beam to catch up.

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.

As I have previously pointed out - the Shapiro delay is relevant to a SINGLE gravitational field!

When somebody conducts a dual gravitational field experiment please let me know.

 

[cos]

Dear cos, contradictory claims are obviously not helpful!

Thanks for the response but there is nothing contradictory about the previous exchange.

A statement was made in relation to a beam of light traveling in a gravitational field and I simply asked in what direction it is traveling.

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

It's a big document but worth waiting for it to download if you have a slow connection.

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.

Whilst I appreciate your having gone to the trouble of providing that information my comments regarding the speed of light relative to a gravitational field are in relation to what physically takes place i.e. to reality.

As regards "...the effect on rods and clocks;" please see my message pointing out that the far distant observer is making his determinations on the basis of his own measuring devices not on the basis of rods and clocks located close to those gravitational fields.

He may not be able to see those extremely far-distant rods and clocks thus can only go by his own determinations.

If those rods and clocks suddenly appeared (or disappeared) along the beam's trajectory his own measuring devices would remain unaffected!

 

[atyy]

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.

So has the doppler shifted light in the twin paradox lost energy?

 

[harrylin]

Thanks for the response but there is nothing contradictory about the previous exchange.

A statement was made in relation to a beam of light traveling in a gravitational field and I simply asked in what direction it is traveling.

Whilst I appreciate your having gone to the trouble of providing that information my comments regarding the speed of light relative to a gravitational field are in relation to what physically takes place i.e. to reality.

As regards "...the effect on rods and clocks;" please see my message pointing out that the far distant observer is making his determinations on the basis of his own measuring devices not on the basis of rods and clocks located close to those gravitational fields.

He may not be able to see those extremely far-distant rods and clocks thus can only go by his own determinations.

If those rods and clocks suddenly appeared (or disappeared) along the beam's trajectory his own measuring devices would remain unaffected!

Einstein there explains how the new theory helps "to arrive at a closer approximation to reality"! (section 22), and he explains it roughly in the way you want it to be explained.

As a matter of fact, I recognise nothing at all of your issues in the text that you did not bother to read.

 

[PAllen]

So has the doppler shifted light in the twin paradox lost energy?

Isn't this obviously yes (?). KE and momentum are frame dependent, whether for light or bullets. In an accelerating frame, inertial objects appear to continuously change momentum and KE, and light appears to gain/lose energy. So, you can describe gravity well effects similarly.

 

[D H]

Let's get back to the original question.

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.

I'm going to rephrase it slightly in a way that I hope eliminates some of the ambiguity and simultaneity issues. I'll use our universe and a near carbon copy of our universe.

Suppose an observer simultaneously sees two bursts of light in different parts of the night sky. The path from each source to the observer is more or less flat (no significant gravity wells along the way). Now imagine an alternate universe that is exactly the same as ours except that now one of the signals travels between two massive objects with very strong gravitational fields arranged so that the beam direction is not changed. Does our alternate observer still see the bursts as arriving simultaneously?

 

[PAllen]

Let's get back to the original question.I'm going to rephrase it slightly in a way that I hope eliminates some of the ambiguity and simultaneity issues. I'll use our universe and a near carbon copy of our universe.

Suppose an observer simultaneously sees two bursts of light in different parts of the night sky. The path from each source to the observer is more or less flat (no significant gravity wells along the way). Now imagine an alternate universe that is exactly the same as ours except that now one of the signals travels between two massive objects with very strong gravitational fields arranged so that the beam direction is not changed. Does our alternate observer still see the bursts as arriving simultaneously?

I'll throw in an ammendment to elimintate the alternate universe complication. Two pulsars in different parts of the sky are magically synchronized. The path from both initially encounter no significant graviy well. However, two neutron stars are heading for a collision directly on the path from one of the pulsars, perpendicular to its line of sight from us. As they get close to collision on the path from one pulsar, do we see the synchronization break down, and in what direction?

[Edit: Further thought: the image of the affected pulsar may become some complex shape due to graviational lensing, around the same time the graviational effects on the light become significant. This may cause the pulse to appear smeared in space and time. However, assuming perfect symmetry, there should remain some central point of the smeared image that has not appeared to shift in the sky. Will this part of the pulse image remain synchronized? ]

 

[atyy]

Isn't this obviously yes (?). KE and momentum are frame dependent, whether for light or bullets. In an accelerating frame, inertial objects appear to continuously change momentum and KE, and light appears to gain/lose energy. So, you can describe gravity well effects similarly.

How about the point of view of the inertial twin?

 

[PAllen]

How about the point of view of the inertial twin?

Again, seems inevitable. Red light has different energy than blue, per photon. If turnaround twin is sending pulses of constant energy from his/her point of view, inertial twin will receive red pulses with less energy and blue pulses with more energy. How could it be otherwise?

To make this better defined, assume the emitted pulses are directed, not spherical. Then, the turnaround twin changes momentum and KE a tiny bit after each pulse. Further, note that the angle of receiver needed to capture a complete directed pulse will change from the red shift case to the blue shift case. Assume receiver is big enough to capture whole pulse in both cases (relativistic beaming effects eliminated). Then, clearly the receiver will, as I said above, receive red pulses of lower total energy compared to the blue pulses. Small momentum and KE changes to the emitting, turnaround twin, preserve conservation of energy and momentum.

 

[atyy]

Again, seems inevitable. Red light has different energy than blue, per photon. If turnaround twin is sending pulses of constant energy from his/her point of view, inertial twin will receive red pulses with less energy and blue pulses with more energy. How could it be otherwise?

So from the inertial twin's point of view, the light lost energy?

 

[PAllen]

So from the inertial twin's point of view, the light lost energy?

See edited explanation above.

 

[Q-reeus]

As you point out - the position of the start and finish lines for both beams are seen, by the distant observer, to be the same ergo on the basis that the beams travel identical distances and, having been emitted simultaneously, arrive at the finish line simultaneously the observer is fully justified in concluding that, from HIS point of view, the beams took the same amount of time to make their trips...
..As above. The situation as depicted is that there are NO gravity affected local values and he bases his conclusion on observation alone (simultaneous emission; the position of the start and finish lines for both beams are seen to be the same; simultaneous arrival at the finish line)...

Again, you are not accepting that gravity alters distance and time scales. Identical start and finish lines does not mean identical path traversal in between. Two open ended rubber bands bridge across an equal width gap. One is stretched straight, the other is depressed down - 'saggy'. Two insects crawl across at equal local crawl speed, one on each rubber band. Do both arrive together because the gap is the same (your logic), or will the one on the saggy band arrive last (GTR = gravity warps spacetime logic)? Think before answering.

Alternately, as previously, he bases his determination of the identical distances using his meter stick held at arm's length and uses his clock in order to determine the time that it takes for the beams to make their trips. He cannot see the far distant clocks and rods...
..Let us assume that the OP involves a semblance of reality and there are two black holes between which a beam of light travels. There are NO clocks or sticks dangling in space so the distant observer can only determine his measurements in accordance with his own equipment however all of a sudden clocks and sticks appear along the path of the beam...
Does that affect (alter) the distant observer's measuring rod or clock in any way? Of course it does NOT!

So you genuinely believe that literal clocks and rulers somehow need to be present locally in order to effect things?! No - it is a very useful 'figure of speech' to refer to clocks and rulers as indicative that time and distance measure are effected by gravity in this case. You accept that clocks are used to measure time, and rulers to measure length, right? Get used to these terms as simply representative of the 'actual' quantities.

You wrote "...the booster is used up and he slows down to the same initial speed." My depiction is that he does not slow down to the same initial speed but that his speed is then slower than its initial speed thereby enabling the other beam to catch up.

So here in #31, you finally let it be known entry and exit speeds are in your universe unequal, without giving any hint in either #3:
"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. ", or #16:
"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.", or #18:
"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."

My strong suspicion is you meant equal in and out as suggested and inferred in the above three entries of yours, but when confronted with the inescapable logic that means necessarily unequal arrival times, you have shifted ground in order to preserve your assertion of equal arrival times. OK, you now want unequal in and out speed? Then realize this necessarily implies some kind of 'draggy' gravity theory at odds with both Newtonian theory and GTR. Recalling we are dealing with static, non-rotating masses as per OP, gravity is an entirely conservative effect - same in = same out, no if's, but's, or maybe's. You doubt that? Well argue it out with http://en.wikipedia.org/wiki/Conservative_force, and nothing changes qualitatively in GTR.

As I have previously pointed out - the Shapiro delay is relevant to a SINGLE gravitational field! When somebody conducts a dual gravitational field experiment please let me know.

No. The reference makes it plain curvature is insignificant, leaving only time delay. In the OP's setup (we have gone over this before), by symmetry of the twin masses curvature is canceled out, which only makes it worse from your pov - there is nothing but time delay as effect. Where do you go from there?

I freely admit that I am academically unqualified in the subject of physics but please stop treating me like a naive child.

Well so am I unqualified, but our difference is in the willingness to recognizing that 2+2 has to add up to 4, and if our pet idea disagrees, be man enough to acknowledge that, and move on a lit bit the wiser. That will make you a real adult. Cheers!

 

[PAllen]

I'll throw in an ammendment to elimintate the alternate universe complication. Two pulsars in different parts of the sky are magically synchronized. The path from both initially encounter no significant graviy well. However, two neutron stars are heading for a collision directly on the path from one of the pulsars, perpendicular to its line of sight from us. As they get close to collision on the path from one pulsar, do we see the synchronization break down, and in what direction?

[Edit: Further thought: the image of the affected pulsar may become some complex shape due to graviational lensing, around the same time the graviational effects on the light become significant. This may cause the pulse to appear smeared in space and time. However, assuming perfect symmetry, there should remain some central point of the smeared image that has not appeared to shift in the sky. Will this part of the pulse image remain synchronized? ]

Anyway, the upshot remains (based on the Shapiro effect analysis), that the pulsar whose signal path is affected by the converging neutron stars would fall out of synch, falling behind the other pulsar.

Is this the consensus of the experts (I'm not an expert)?

 

[Dale]

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.

Remember, we are talking about curved geometry here. In curved geometry it is possible for a figure to have 4 straight sides with 4 right angles and still have one side which is longer than the opposite side. Of course the observer may use a coordinate system such that the coordinate distance is the same, but all distances based on the metric (measuring rods or light pulses) will be longer for the path through the gravity well.

 

[cos]

I recognise nothing at all of your issues in the text that you did not bother to read.

In that case I'm glad I didn't waste my time reading it.

 

[cos]

Let's get back to the original question.

I'm going to rephrase it slightly in a way that I hope eliminates some of the ambiguity and simultaneity issues. I'll use our universe and a near carbon copy of our universe.

Suppose an observer simultaneously sees two bursts of light in different parts of the night sky. The path from each source to the observer is more or less flat (no significant gravity wells along the way). Now imagine an alternate universe that is exactly the same as ours except that now one of the signals travels between two massive objects with very strong gravitational fields arranged so that the beam direction is not changed. Does our alternate observer still see the bursts as arriving simultaneously?

Yes.

 

[cos]

I'll throw in an ammendment to elimintate the alternate universe complication. Two pulsars in different parts of the sky are magically synchronized. The path from both initially encounter no significant graviy well. However, two neutron stars are heading for a collision directly on the path from one of the pulsars, perpendicular to its line of sight from us. As they get close to collision on the path from one pulsar, do we see the synchronization break down, and in what direction?

The synchronization does not break down.

 

[harrylin]

In that case I'm glad I didn't waste my time reading it.

OK then, if you prefer to keep your issues, as you wish! I won't try anymore to help you get rid of them.

 

[cos]

Again, you are not accepting that gravity alters distance and time scales. Identical start and finish lines does not mean identical path traversal in between. Two open ended rubber bands bridge across an equal width gap. One is stretched straight, the other is depressed down - 'saggy'. Two insects crawl across at equal local crawl speed, one on each rubber band. Do both arrive together because the gap is the same (your logic), or will the one on the saggy band arrive last (GTR = gravity warps spacetime logic)? Think before answering.

Your having resorted to personal insults will be dealt with later!

Where, and in which direction, is the 'downward' (?) 'depression' of the path followed by that specific beam of light? Does that route 'sag' or bend in any direction?

Alternately, as previously, he bases his determination of the identical distances using his meter stick held at arm's length and uses his clock in order to determine the time that it takes for the beams to make their trips. He cannot see the far distant clocks and rods...
..Let us assume that the OP involves a semblance of reality and there are two black holes between which a beam of light travels. There are NO clocks or sticks dangling in space so the distant observer can only determine his measurements in accordance with his own equipment however all of a sudden clocks and sticks appear along the path of the beam...
Does that affect (alter) the distant observer's measuring rod or clock in any way? Of course it does NOT!

So you genuinely believe that literal clocks and rulers somehow need to be present locally in order to effect things?!

Typical ill-thought out response aimed specifically at obfuscation and deception!

I point out that the presence or absence of local clocks and rules can have NO effect on the distant observer's measuring devices and you snidely insinuate that I believe the opposite!

(<snip>Similar ill-thought out response aimed specifically at obfuscation and deception.)

...be man enough to acknowledge that, and move on a lit bit the wiser. That will make you a real adult.

It is inevitable that when a person realizes that they are losing an argument they start posting obfuscatory and deceptive material as well as personal insults to which I have, above, responded in kind.

Our discussion is accordingly terminated.

 

[cos]

Remember, we are talking about curved geometry here. In curved geometry it is possible for a figure to have 4 straight sides with 4 right angles and still have one side which is longer than the opposite side. Of course the observer may use a coordinate system such that the coordinate distance is the same, but all distances based on the metric (measuring rods or light pulses) will be longer for the path through the gravity well.

Trepidatiously anticipating eventual ad hominem attacks as have inevitably previously taken place - I submit that a person is looking out into the night sky; he sees, off to his left-hand side, one object that will eventually represent the start line of the beam that will pass between two (yet-to-appear) massive objects and, off to his right-hand side, another object that will eventually become the finish line.

He sees, initially, a beam of light cross the start line when his clock reads zero seconds and arrive at the finish line when his clock reads 5 seconds.

What is his estimation of the distance between the start line and the finish line? Is it, as I suspect it to be, (close to) 1·5 million Ks?

Having thereby determined the distance between the start and finish lines our observer then 'sees' two neutron stars appear on either side of the original beam's route which, as per my assumption below regarding the OP, generate no gravitational 'pull' on the start/finish lines.

(I assume that, in the OP, it is accepted that the intervening masses have no effect on the distance between the start and finish lines; that the start /finish lines are hypothetically immovable objects.)

According to responses - it will then take longer for the beam to traverse that distance as measured by his clock.

Does he conclude that the finish line and the starting line have physically moved further apart?

Prior to the appearance of the masses - another observer, located next to the start line, attaches a very long tape measure to it then travels over to the finish line feeding out the tape as he goes. No surprise - he determines a distance of 1·5 million Ks.

The gravitational masses make their appearance (again without having any physical affect on the distance between the immovable start/finish lines) and he repeats his test.

As he enters progressively stronger gravitational tidal areas the tape measure, attached at the other end to an immovable object, proportionally stretches! It becomes spaghettified! The physical distances between the mm; cm; m; km divisions increase!

As he moves away from that midpoint the tape remains stretched albeit by progressively lesser amounts ergo, overall, he measures that the distance between the start/finish lines is shorter than it was before the masses appeared not longer as insisted upon in this thread.

I have no doubt whatsoever that it can be mathematically 'proven' that the physical results of his hands-on experiment are 'erroneous' - that the distance increases 'due to the Shapiro delay' however I know which version I would place my money on.