General Relativity: Gravitational-Red Shift Confused with Doppler Effect?

  • #1

Main Question or Discussion Point

From the special relativity theory , for explaining the red-shifting of a photon, that has been red-shifted, is the following:

point O: origin point of emitted photo, in Galaxy GlxO
point R: receiving point of photon, in Galaxy GlxR

GlxO, O ---------->----------------R, GlxR

Suppose:

Observer O (ObserO) at GlxO: is moving away from point O at speed RS, relative to GlxO

Observer R (ObserR) at GlxR: is moving away from point O at speed RS, relative to GlxO

So, we have that ObserO and ObserR are in the same reference frame, relative to GlxO.

So, as ObserO is moving away from point O, ObserO sees the emitted photon red-shifted by amount FRS.

When photon arrives to ObserR, ObserR would also see the same amount of red-shift in the photon's frequency, FRS, because they are in the same frame of reference, relative to GlxO.

That makes perfect sense.

For General Relativity however, the standard convention, for explaining gravitational red-shifting, and the measuring of a photon's energy before and after its emission, seems to use the exact same principles as those used to explain red-shifting by the doppler effect in Special Relativity.

The exact same scenario as above, with different observers measuring different energies in different frames of reference, is used. The result is the same, that there is no energy lost by the photon, just different measurements due to different reference frames.

Great.

However, it seems that one thing is forgotten. That this photon is actually travelling through a gravitational field from point O to point R.

We know that photons are effected by gravitational fields, and that they bend around heavy objects in space.


Question:

Lets say GlxO is relatively more massive than GlxR. Then the gravity well of GlxO would be relatively deeper than the gravity well of GlxR.

If point O begins at a point, in a gravity well of GlxO, that is relatively deeper than the gravity well of point R, would the frequency of the photon be measured the same for the same observers, ObserO and ObserR?

It seems to me, that if you take into account the photon's path, through curved space due to gravitational fields, that the 2 observers would measure different frequencies, since both observers are travelling in 2 different gravitational fields, and would be measuring the photon's energy, having been gravitationally red-shifted by 2 different fields.


Thanks for the view. All replies welcome.
Mike F.
 

Answers and Replies

  • #2
Jonathan Scott
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In a static situation, gravitational red shift or blue shift is not something that "happens to" photons. It is purely due to relative differences in observer potential, which affects the time rate of the observer's clocks.

The photon itself has constant frequency relative to a static coordinate system, but an observer at a higher or lower potential will see it to have a different frequency compared with a photon created locally by means of a similar process, for example a particular transition between energy levels.
 
  • #3
Yes, I get the concept that measuring things is relative to the frame of reference and its time rate.

However, there must be something happening to the photon as it travels through curved space. The frame of reference must also take into account gravitational fields.

As the photon would be traveling through curved space, from point A to point B, its frequency would stretch or compress, which would mean that its energy would change between these 2 points.

This net change in the photon's frequency would be observed by any observer traveling in any frame of reference, since there is an actual direction to the gravitational force that is disturbing its space. Any observer would record a net change in the photons frequency.
 
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  • #4
PAllen
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Yes, I get the concept that measuring things is relative to the frame of reference and its time rate.

However, there must be something happening to the photon as it travels through curved space. The frame of reference must also take into account gravitational fields.

As the photon would be traveling through curved space, from point A to point B, its frequency would stretch or compress, which would mean that its energy would change between these 2 points.

This net change in the photon's frequency would be observed by any observer traveling in any frame of reference, since there is an actual direction to the gravitational force that is disturbing its space. Any observer would record a net change in the photons frequency.
Don't know if this will help, but gravity or no, at any point along the lights path, there are observers who will measure every possible frequency (different states of relative motion between observers). So trying to factor out change due to gravity versus relative motion means identifying which of these frames at different places and times are 'statically related', thus differences in frequency are then considered due to gravity. However, in general, there is no unique or preferred way to make such a global assignment; thus no unambiguous way to separate out gravity from relative motion. In effect, such an assignment amounts to a choice of coordinates. For any such choice, you can say "yes, there is mass/energy producing curvature", but different choices lead to different divisions of gravitational versus doppler shift.
 
  • #5
PAllen
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Yes, I get the concept that measuring things is relative to the frame of reference and its time rate.

However, there must be something happening to the photon as it travels through curved space. The frame of reference must also take into account gravitational fields.

As the photon would be traveling through curved space, from point A to point B, its frequency would stretch or compress, which would mean that its energy would change between these 2 points.

This net change in the photon's frequency would be observed by any observer traveling in any frame of reference, since there is an actual direction to the gravitational force that is disturbing its space. Any observer would record a net change in the photons frequency.
Don't know if this will help, but gravity or no, at any point along the lights path, there are observers who will measure every possible frequency (different states of relative motion between observers). So trying to factor out change due to gravity versus relative motion means identifying which of these frames at different places and times are 'statically related', thus differences in frequency are then considered due to gravity. However, in general, there is no unique or preferred way to make such a global assignment; thus no unambiguous way to separate out gravity from relative motion. In effect, such an assignment amounts to a choice of coordinates. For any such choice, you can say "yes, there is mass/energy producing curvature", but different choices lead to different divisions of gravitational versus doppler shift.
Maybe a way to get at what you're thinking is to note asymmetry. Where there are no massive bodies, shift's are symmetric - A and B both see blue shift or both red shift, of the same amount. Where massive bodies of unequal mass are involved, all observers near the bodies will see asymmetry in shifts. If you arrange that B sees no red or blue shift from A, A will see a shift from B (blue if A is more massive, red if B is more massive). But this still doesn't mean anything has happened to the photon along the way - unless you want to say that photons going one way are unchanged, while they are changed the other way.
 
  • #6
Don't know if this will help, but gravity or no, at any point along the lights path, there are observers who will measure every possible frequency (different states of relative motion between observers). So trying to factor out change due to gravity versus relative motion means identifying which of these frames at different places and times are 'statically related', thus differences in frequency are then considered due to gravity. However, in general, there is no unique or preferred way to make such a global assignment; thus no unambiguous way to separate out gravity from relative motion. In effect, such an assignment amounts to a choice of coordinates. For any such choice, you can say "yes, there is mass/energy producing curvature", but different choices lead to different divisions of gravitational versus doppler shift.
Yes, unravelling the 2 effect would be difficult. Seems all photons out it space would be red-shifted by both gravitational red-shifting and red-shifting due to relative motions.

According to General Relativity, the 2 effects would be indistinguishable.
As, explained here: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html#c1
 
  • #7
Maybe a way to get at what you're thinking is to note asymmetry. Where there are no massive bodies, shift's are symmetric - A and B both see blue shift or both red shift, of the same amount. Where massive bodies of unequal mass are involved, all observers near the bodies will see asymmetry in shifts. If you arrange that B sees no red or blue shift from A, A will see a shift from B (blue if A is more massive, red if B is more massive). But this still doesn't mean anything has happened to the photon along the way - unless you want to say that photons going one way are unchanged, while they are changed the other way.
Thanks.

Considering General Relativity, there must be a net result change in a photon's frequency:

================
A photon's path between two points, A (emitted point:in galaxy GA), B (received point, in Galaxy GB):

A: point of photon's origin, in space

GFA: gravitational field force at point A, due to its position in galaxy's gravity well, from which photon originated

B: point of photon being received, in space

GFB: gravitational field force at point B, due to its position in galaxy's gravity well, from which photon was received
==================

galaxy GA------------------ galaxy GB
A ---------------->-------------B

photon travels from point A to point B

Next, consider the following:

- point A is deep in a gravity well, so the GFA (gravitational field force at point A) at that point of emission would be strong

- point B is in a shallower gravity well, so the GFB (grav. force at point B) at that receiving end would be weaker

So, GFA > than GFB , or the gravitational time well from which the photon originated is deeper than the gravitational time well where it was received. These different gravitational fields, are relatively larger or smaller to each other.

From point A, the photon would be travelling up the gravity well, due to the GFA. Or, another way to look at it, space would be stretched out, time rate slows, the speed of light stays the same, and the photons frequency would be stretched. However, here, the stretching would be due to gravitational red-shifting.

Along photon's path to point B, it would reach a point, somewhere in between the two galaxies, where the gravitational fields of galaxy GA and galaxy GB would cancel each other out, and space would be undisturbed. Lets call this point P1.

Since the GFA is greater then GFB, Point P1, would be closer to the shallower gravity well.

So: the distance between A to P1 is greater than the distance between P1 and R.

So:

glxA--------------------------------------- glxB

A --------------------------P1--------------B

------Distance A to P1 -------Distance P1 to B

At this point, P1, the photon would have reached its maximum red-shifting potential since having left its point of origin. After this point, it will undergo gravitational blue-shifting, as the photon begins to enter the gravity well of galaxy GB.

From point P1 to point B (photon's point of reception), the photon will undergo gravitational blue-shifting.

From any frame of reference, the gravitational forces had the same relative directions to all observers (pulled back to A, then pulled towards B), and would would note an equal net change in the photons frequency.

The frequency of the photon from when it was first emitted to when it was received, will have a net effect, of having been gravitationally red-shifted. Since the photon was red-shifted for a longer distance in space (or longer period of time) then it was blue-shifted, all observers would note the same net amount of red-shift in its frequency.

Also, there really wouldn't be any balancing out, by having a photon go from B to A, since both these 2 sources emit photons at different rates.
 
  • #8
Jonathan Scott
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Considering General Relativity, there must be a net result change in a photon's frequency:
Talking about galaxies is a bit confusing here, as galaxies are typically moving relative towards one another, but to understand gravitational redshift we need a static picture.

When a photon moves in a gravitational field (assumed to be weak enough for linear approximations), then relative to a STATIC (locally approximately isotropic) coordinate system it does NOT change frequency (otherwise a continuous signal of a constant frequency would have different numbers of cycles at either end over a given period, which doesn't make sense).

The photon can change direction if there is a component of gravitational field perpendicular to the path, and our view of it is also affected by the coordinate speed of light, which varies twice as much as the gravitational potential. These two effects combine so that in a typical case the coordinate MOMENTUM of the photon, normally given by Ev/c^2 in the local frame, is continuously changing at exactly twice the Newtonian rate. However, the magnitude of its VELOCITY is always simply the coordinate speed of light.

To clarify this, consider a photon rising or falling radially near a large mass, and let c represent the coordinate speed of light rather than the standard value. In the expression Ev/c^2 within the coordinate system, the frequency is constant, and the magnitude of the velocity is c, so the radial momentum is E/c. Since this value of c decreases as the photon falls, the momentum increases, as in the Newtonian model of a falling object, but in GR the size of rulers changes as well as the rate of clocks, and c involves both, so the effect is double that from the Newtonian model.

Relative to a series of local static observers therefore, the apparent frequency of the photon varies only because the local clocks of those static observers differ. Relative to a specific observer, photons created on the sun are already red-shifted when created relative to photons created locally by the same effect, and continue to be red-shifted by that amount throughout their existence.

You can calculate the static redshift by working out how the field operates on the photon, but this is unnecessarily complicated because the result is simply the difference in the time rate between two locations.
 
  • #9
Thanks for all the input.

...
When a photon moves in a gravitational field (assumed to be weak enough for linear approximations), then relative to a STATIC (locally approximately isotropic) coordinate system it does NOT change frequency (otherwise a continuous signal of a constant frequency would have different numbers of cycles at either end over a given period, which doesn't make sense). ...
When a photon travels through a gravitational field (curved space), space will be stretched or compressed, because that space is affected by a mass, and that mass is there for any observer, in any frame of reference.

Since the photon is traveling through space that is stretched or compressed, and the speed of light is constant, and the time that the photon takes to travel through curved space is either slower or faster (red & blue shifting respectively) than through undisturbed space, then the photon's frequency changes, hence gravitational red or blue shifting.

When you get into the quantum mechanics of gravitational red-shifting and gravitational time dilation of photons, that's when things get really interesting.
 
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  • #10
pervect
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Thanks for all the input.



When a photon travels through a gravitational field (curved space), space will be stretched or compressed, because that space is affected by a mass, and that mass is there for any observer, in any frame of reference.
I'm not following this explanation at all. What do you mean by "space will be stretched or compressed"? Is this some idisoyncratic way of talking about the metric coefficients changing?

Did you come up with this idea from some popularization, or is it your own personal theory?
 
  • #11
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Thanks for all the input.



When a photon travels through a gravitational field (curved space), space will be stretched or compressed, because that space is affected by a mass, and that mass is there for any observer, in any frame of reference.

Since the photon is traveling through space that is stretched or compressed, and the speed of light is constant, and the time that the photon takes to travel through curved space is either slower or faster (red & blue shifting respectively) than through undisturbed space, then the photon's frequency changes, hence gravitational red or blue shifting.
I think this is the point of confusion. You are attributing the change to the photon itself due to the local conditions it passes through. Jonathon was explaining that the change is totally explained through time dilation, not as a change of the frequency of the photon itself in transit, but in the difference of the resonant frequencies of emitting and receiving electrons at different potentials .

Since gravitational time dilation is pretty well established and seems to completely cover [quantitatively] the phenomenon, I would think that additional contributing factors would be, not just superfluous , but simply wrong. IMHO
 
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  • #12
I'm not following this explanation at all. What do you mean by "space will be stretched or compressed"? Is this some idisoyncratic way of talking about the metric coefficients changing?

Did you come up with this idea from some popularization, or is it your own personal theory?
No, I didn't come up with this. The warping of spacetime, due to gravity, resulting in contraction or stretching is found in many different areas of study in general and special relativity. Most interesting of which involve quantum spacetime.


This might help you out:

============================================================
Source: http://www.thebigview.com/spacetime/timedilation.html

Time dilated by matter.

If acceleration is equivalent to gravitation, it follows that the predictions of Special Relativity must also be valid for very strong gravitational fields. The curvature of spacetime by matter therefore not only stretches or shrinks distances, depending on their direction with respect to the gravitational field, but also appears to slow down the flow of time. This effect is called gravitational time dilation. In most circumstances, such gravitational time dilation is minuscule and hardly observable, but it can become very significant when spacetime is curved by a massive object, such as a black hole.
===========================================================

There are also other sources for this concept, albeit, hard to find.
 
  • #13
I think this is the point of confusion. You are attributing the change to the photon itself due to the local conditions it passes through. Jonathon was explaining that the change is totally explained through time dilation, not as a change of the frequency of the photon itself in transit but in the difference of the frequency of the emitting and receiving electrons at different potentials.. A difference of measurement, not a physical change of the photon after emission. Since gravitational time dilation is pretty well established and seems to completely cover the phenomenon, I would think that additional contributing factors would be, not just superfluous , but simply wrong. IMHO
Thanks.

Time dilation, both gravitational and due to motion change a photons frequency. All photons get their frequencies shifted by both.

More into quantum mechanics, and sticking to the idea of quantum spacetime, a photon will take longer to travel between warped points of space. If this is so, the photon's frequency will change (time is greater, c stays c, frequency becomes red-shifted).

How can it be possible for a photon to stay the same, when it passes through different gravitational fields or different magnitudes of warped spacetime? Obviously it's frequency changes dynamically as it passes through different "textures" of spacetime.

I find it hard to believe that anyone would challenge that photons change dynamically as they pass through spacetime. Is that what is being challenged?
 
  • #14
Jonathan Scott
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How can it be possible for a photon to stay the same, when it passes through different gravitational fields or different magnitudes of warped spacetime? Obviously it's frequency changes dynamically as it passes through different "textures" of spacetime.

I find it hard to believe that anyone would challenge that photons change dynamically as they pass through spacetime. Is that what is being challenged?
The wavelength may change (and the way in which it changes depends on the coordinate system used ). The direction may change. The frequency does not change.

Think about a continuous signal being sent rather than a photon. The time delay along any part of the path is constant, so if the signal at the origin is oscillating in a particular way, the signal being received oscillates in exactly the same way a fixed time later.
 
  • #15
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Thanks.

Time dilation, both gravitational and due to motion change a photons frequency. All photons get their frequencies shifted by both.

More into quantum mechanics, and sticking to the idea of quantum spacetime, a photon will take longer to travel between warped points of space. If this is so, the photon's frequency will change (time is greater, c stays c, frequency becomes red-shifted).

How can it be possible for a photon to stay the same, when it passes through different gravitational fields or different magnitudes of warped spacetime? Obviously it's frequency changes dynamically as it passes through different "textures" of spacetime.

I find it hard to believe that anyone would challenge that photons change dynamically as they pass through spacetime. Is that what is being challenged?
The question is not whether photons change dynamically with local conditions.
Eg: Changing coordinate speed between the sun and earth with the varying potential magnitudes.

But those transitory changes along the way are not what is being measured.
What is being measured is the frequency of the light emitted from a known element on the sun,at a certain temp and and energy state, and comparing it to the frequency emitted by the same element etc on earth. Period.The beginning and the end of the trip.

The red shift that is detected is exactly the shift that is expected and calculated based on the time dilation factor due to the difference in potential.

If any of the transitory conditions had any relevant effect the result should then be dilation factor + or - some additional amount arising from the local "texture" passed through in transit. This does not seem to be the case.

PS I think you are incorrect about time dilation changing frequency in the case of motion Doppler . In that case it is purely a result of relative velocity. AFAIK
 
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  • #16
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PAllen had a nice succinct explanation I saved:

Redshift is a measured shift in received frequency versus emitted frequency. Doppler [shift] refers to one of two formulas (pre-relativistic; relativistic) for relating redshift to velocity. Doppler shift is a particular explanation of redshift, with a particular formula. It is not a measure of redshift.

Cosmological redshift is typically considered distinct from Doppler redshift because it is a relation between distance and redshift rather than speed and redshift, under the assumption that both source and target are motionless relative to center of mass of the local matter (here, local is quite large - galaxy or galaxy cluster).
 
  • #17
PAllen had a nice succinct explanation I saved:
Yes, the Cosmological redshift is considered distinct from the Doppler redshift, only if their is no acceleration of motion that is causing the Doppler redshift. If the motion causing the Doppler redshift is accelerating, then the two would be indistinct.

Explained here:
==============================================================
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html#c1

According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source could also be produced by the appropriate gravitational field. Thus the expected shift in radiation frequency in a gravitational field can be related to the relativistic doppler shift experienced from an accelerating light source.
==================================================================
 
  • #18
The wavelength may change (and the way in which it changes depends on the coordinate system used ). The direction may change. The frequency does not change.

Think about a continuous signal being sent rather than a photon. The time delay along any part of the path is constant, so if the signal at the origin is oscillating in a particular way, the signal being received oscillates in exactly the same way a fixed time later.
Okay, if I think about the signal, and not just the photon, seems like the same result.

The signal frequency will change. How could it not? If it passes through spacetime that is warped, it will be stretched or compressed, since it passed through warped spacetime and it took a longer or shorter time to do so.

Does anyone disagree that photon(s) are not effect and changed dynamically as they travel through different areas of warped spacetime?
 
  • #19
Jonathan Scott
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Okay, if I think about the signal, and not just the photon, seems like the same result.

The signal frequency will change. How could it not? If it passes through spacetime that is warped, it will be stretched or compressed, since it passed through warped spacetime and it took a longer or shorter time to do so.

Does anyone disagree that photon(s) are not effect and changed dynamically as they travel through different areas of warped spacetime?
The effect of gravity on space is indeed like stretching or compressing when mapped to a coordinate system, so waves travel faster and slower, in the same way for example as light is slowed when travelling through a transparent medium such as glass with a refractive index greater than one.

However, if you consider the amount of time it takes a particular event in the signal to travel along the whole path, and you are considering a STATIC situation (where the gravitational sources are not moving and the distance is fixed) then that amount of time is a constant, so the received signal is an identical copy of the transmitted one.

This is no different for example to watching someone wave a flag a long way away; if you are a fixed distance away, the frequency you see is exactly the same as the original frequency at which it happened. However, if your local clocks are running at a different rate because of a difference in gravitational potential, the received frequency according to your local clocks may appear to be different to the transmitted frequency according to a clock associated with the transmitting location.
 
  • #20
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Fast moving clock has a low ticking frequency, and a high Compton frequency. Time dilation does not apply to Compton frequency.

Free falling clock has a decreasing ticking frequency, and a constant Compton frequency.

A clock falling through atmosphere at terminal velocity has ticking frequency and Compton frequency decreasing the same way.
 
  • #21
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Frequency is conserved, in a closed system.

Let us consider a planet-photon system. The system has the same frequency whether the photon is close to the planet, or whether the photon has moved far away from the planet.

The simplest way that the frequency can be conserved is that the frequency of the planet stays the same, and the frequency of the photon stays the same.

Can we prove that the simplest way is the way that it happens?
 
  • #22
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According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source could also be produced by the appropriate gravitational field. Thus the expected shift in radiation frequency in a gravitational field can be related to the relativistic doppler shift experienced from an accelerating light source.
==================================================================
This is a good example. In an accelerating system there is both red shift and motion Doppler. The light radiating from the system in all directions is motion Doppler and is essentially relativistic Doppler, the same as an inertial system.

The equivalence to gravitational red shift is operative internally. With the dilation differential between back and front of the system being equivalent to the varying potential in a G field.

SO light emitted at the back [lower potential] is red shifted when received at the front [higher altitude/potential] and vice verse. And also similarly ,the coordinate speed of light can change with location and direction depending on the coordinate systems. But there is no suggestion that the change in light speed is an actual effect resulting from space time geometry, because in this case that is flat .

In this situation there is also a relativistic Doppler between the front and the back due to the relative velocity between the two but this is purely due to motion so doesn't seem to be equivalent to gravity at all.
 
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  • #23
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Yes, the Cosmological redshift is considered distinct from the Doppler redshift, only if their is no acceleration of motion that is causing the Doppler redshift. If the motion causing the Doppler redshift is accelerating, then the two would be indistinct.

Explained here:
==============================================================
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html#c1

According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source could also be produced by the appropriate gravitational field. Thus the expected shift in radiation frequency in a gravitational field can be related to the relativistic doppler shift experienced from an accelerating light source.
==================================================================

It does not have to be an accelerating source. A receding source with constant velocity will have a velocity doppler redshift indistinguishable from gravitational redshift. For single galaxies it is difficult to put the redshift down to the Doppler redshift due to the recession speed or gravitational time dilation or "the stretching of space itself" as the universe expands, without looking at the larger global picture.

I think this is the point of confusion. You are attributing the change to the photon itself due to the local conditions it passes through. Jonathon was explaining that the change is totally explained through time dilation, not as a change of the frequency of the photon itself in transit, but in the difference of the resonant frequencies of emitting and receiving electrons at different potentials .

Since gravitational time dilation is pretty well established and seems to completely cover [quantitatively] the phenomenon, I would think that additional contributing factors would be, not just superfluous , but simply wrong. IMHO
You are right that the frequency of a photon (in coordinate terms) does not change but that does not mean that nothing happens to the photon in transit. When we consder the equation c = w*f where w is wavelength and f is the frequency, we normally think of the speed of light as a constant, but in a gravitational field the coordinate speed of light is NOT constant and it is the frequency that is the constant. This means the wavelength is also NOT constant. As light falls, the coordinate wavelength contracts by a factor of gamma^2 as does the coordinate speed of light. Gravitational time dilation causes local observers to measure the frequency as speeding up by a factor of gamma and gravitational length contraction causes local observers to measure the wavelength as shorter by only a factor of gamma and the combined effects cause local observers to measure the speed of light as constant.
 
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  • #24
pervect
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No, I didn't come up with this. The warping of spacetime, due to gravity, resulting in contraction or stretching is found in many different areas of study in general and special relativity. Most interesting of which involve quantum spacetime.


This might help you out:

============================================================
Source: http://www.thebigview.com/spacetime/timedilation.html

Time dilated by matter.

If acceleration is equivalent to gravitation, it follows that the predictions of Special Relativity must also be valid for very strong gravitational fields. The curvature of spacetime by matter therefore not only stretches or shrinks distances, depending on their direction with respect to the gravitational field, but also appears to slow down the flow of time. This effect is called gravitational time dilation. In most circumstances, such gravitational time dilation is minuscule and hardly observable, but it can become very significant when spacetime is curved by a massive object, such as a black hole.
===========================================================

There are also other sources for this concept, albeit, hard to find.
Thanks for the reference. I'd put in in the category of a "popularization", because it has little mathematical content.

I don't really think the idea that "The curvature of spacetime by matter ... stretches or shrinks distances" is a very good idea :-(. For instance, the Earth's surface is an example of a curved two-dimensional surface. But - would one say that the curvature of the Earth's surface "stretches or shrinks distances?" I wouldn't. And offhand I don't know of anyone who does.

In some general sense, it's partially true - 1 minute of arc of lattitude does represent a different distance at the equator than it does near the poles. But this has more to do with the relation between coordinates and distances, i.e. the metric, than it does with distances themselves "shrinking or expanding".

A rather better online reference, IMO, is Sean Carrol's lecture notes on General Relativity. http://arxiv.org/pdf/gr-qc/9712019v1.pdf. This is the draft version of his GR textbook. It's got the math to back up the generalizations, though it has those, too.

One of the quotes about redshift from Carroll's paper:

It therefore appears as if there is no natural way to uniquely move a vector from one
tangent space to another; we can always parallel transport it, but the result depends on the
path, and there is no natural choice of which path to take. Unlike some of the problems we
have encountered, there is no solution to this one — we simply must learn to live with the
fact that two vectors can only be compared in a natural way if they are elements of the same tangent space. For example, two particles passing by each other have a well-defined relative velocity (which cannot be greater than the speed of light). But two particles at different points on a curved manifold do not have any well-defined notion of relative velocity — the concept simply makes no sense. Of course, in certain special situations it is still useful to talk as if it did make sense, but it is necessary to understand that occasional usefulness is not a substitute for rigorous definition.

In cosmology, for example, the light from distant galaxies is redshifted with respect to the frequencies we would observe from a nearby stationary source. Since this phenomenon bears such a close resemblance to the conventional Doppler effect due to relative motion, it is very tempting to say that the galaxies are “receding away from us” at a speed defined by their redshift. At a rigorous level this is nonsense, what Wittgenstein would call a “grammatical mistake” — the galaxies are not receding, since the notion of their velocity with respect to us is not well-defined. What is actually happening is that the metric of spacetime between us and the galaxies has changed (the universe has expanded) along the path of the photon from here to there, leading to an increase in the wavelength of the light.
Baez also makes the same point about the tangent spaces, and the fact that the comparison of velocities at distant events is an ambiguous operation defined by convention rather than mathematics.

Note also that, while the idea that "space is expanding" is used in Carroll's description, said expansion of space is not directly due to gravity.

There's another section in Carrol's paper about gravitational redshift that might be of interest, but I'm not going to quote it here. I hope it suffices to say that light does experience some gravitational redshift when it leaves a large mass (the galaxy, say), and some blueshift when the reverse happens (it enters a target galaxy, for instance).

Cosmology makes the approximation that the universe is homogeneous and isotropic as a whole - lumps of matter like stars and galaxies are treated, at all, as a pertubation.

I also don't see the need to drag quantum mechanics into the picture at all. GR is a purely classical theory - dragging quantum mechanics into it doesn't serve any purpose unless your'e trying to do quantum gravity.
 
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I think this is the point of confusion. You are attributing the change to the photon itself due to the local conditions it passes throughh.
IMHO
You are right that the frequency of a photon (in coordinate terms) does not change but that does not mean that nothing happens to the photon in transit. When we consder the equation c = w*f where w is wavelength and f is the frequency, we normally think of the speed of light as a constant, but in a gravitational field the coordinate speed of light is NOT constant and it is the frequency that is the constant. This means the wavelength is also NOT constant. As light falls, the coordinate wavelength contracts by a factor of gamma^2 as does the coordinate speed of light. Gravitational time dilation causes local observers to measure the frequency as speeding up by a factor of gamma and gravitational length contraction causes local observers to measure the wavelength as shorter by only a factor of gamma and the combined effects cause local observers to measure the speed of light as constant.
Yes . The change referred to in my above quote was specifically change in frequency I.e. red/blue shift,,the subject of inquiry. Not a suggestion that other changes didn't occur but that they weren't relevant.
You have provided a nice description of why they aren't relevant to red shift ,
I understood that the change in coordinate speed c was 2x(gamma) not gamma^2.
Is this incorrect?
Thanks
PS Do you have some good idea how to actually measure the wavelength of photons with our contracted rulers :-)
 
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