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

[prime axiom]

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 traveling 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 traveling 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.

 

[Jonathan Scott]

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.

 

[prime axiom]

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.

 

[PAllen]

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.

 

[PAllen]

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.

 

[prime axiom]

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

 

[prime axiom]

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 traveling 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. Let's 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.

 

[Jonathan Scott]

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.

 

[prime axiom]

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.

 

[pervect]

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?

 

[Austin0]

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

 

[prime axiom]

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.

 

[prime axiom]

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?

 

[Jonathan Scott]

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.

 

[Austin0]

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

 

[Naty1]

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).

 

[prime axiom]

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.
==================================================================

 

[prime axiom]

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?

 

[Jonathan Scott]

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 traveling 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.

 

[jartsa]

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.

 

[jartsa]

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?

 

[Austin0]

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.

 

[yuiop]

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.

 

[pervect]

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.

 

[Austin0]

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 :-)

 

[yuiop]

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?

I am pretty sure it is gamma^2, not 2x(gamma). It is very easily obtained from the Schwarzschild metric by setting ds=0 for a photon and solving for dr/dt.

PS Do you have some good idea how to actually measure the wavelength of photons with our contracted rulers :-)

I have always wondered how I would do that and hoped know one would ever put me on the spot and ask me that directly. Damn you! :P

Seriously, does anyone know if it is possible to measure wavelength directly, rather than infer it indirectly from frequency?

 

[prime axiom]

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. ...

Yes, the questions is exactly whether photons change dynamically with local conditions, by which I would mean local spacetime.

This is what I'm asking here, and looking for support helping prove that photons do in fact change dynamically with local conditions. From new research into the quantum mechanics of quantum spacetime, this seems to be the case.

I want these questions to be looked at in terms of General Relativity, and hopefully, down to the tiniest of scales, the realm of quantum mechanics. Photons change dynamically traveling along warped spacetime, and we have to look at quantum mechanics to tell us how this process happens.

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

I never said that. Those are 2 different phenomenon.

However I did say:

The 2 can be confused with one another, because they have the same effect. Source: http://hyperphysics.phy-astr.gsu.edu...gratim.html#c1

If we receive a photon from a galaxy, and note a red-shift in it, there could also be gravitational red & blue shifting in its overall wavelength change.

 

[prime axiom]

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 traveling 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.

Helpful. Thanks.

Yes, if the clock rate changes, the frequency would also change. That is a fact. Frequency change of photons is possible.

In terms of General Relativity, and imagining photons moving through spacetime, down at the quantum level, and imagining the quantum spacetime grid. Now imagine that quantum spacetime grid as it would be disturbed by a large mass. Photons traveling through this warped spacetime, would be traveling through spacetime that is either stretched or compressed, depending on relativity and gravitational field direction. These photons would be undergoing gravitational red or blue shifting, due to gravitational time dilation.

Since these photons are traveling through spacetime that is stretched or compressed, the clock rate for these photons would be changing. When the photons are traveling stretched space, for example, they are taking longer in doing so, and c stays c, clock rate slows, frequency stretches.

So we have it that photons change dynamically as they travel through warped spacetime. At least in terms of the Quantum mechanics of General Relativity.

Wouldn't you say so?

This is the key question. Do photons change dynamically as they travel through warped spacetime?

 

[prime axiom]

...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.

Gravitational red & blue shifting means there is a process effecting the wavelength. To look into the process would mean getting down to the quantum mechanics of General Relativity.

Photons change dynamically due to gravitational wavelength shifting, as they pass through curved spacetime. Only quantum mechanics can tell us how. This seems to be a hard to find, and recent area of study. Would love some insight into it.

 

[prime axiom]

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.

Yes, thanks.

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, great stuff.

In first post:

point O: origin point of emitted photo
point R: receiving point of photon

GlxO: Galaxy of origin
GlxR: Galaxy of reception

Lets say GlxO is relatively more massive than GlxR: gravity well of GlxO relatively deeper than the gravity well of GlxR

As the photon travels from Point O to R,

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

it would undergo gravitational wavelength shifting due to gravitational time dilation. Since GlxO is heavier, from any frame of reference, the photon would undergo a net red-shifting on its trip to R.

Would you folks not agree?
Would you yuiop?

 

[Austin0]

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.

Yes, the questions is exactly whether photons change dynamically with local conditions, by which I would mean local spacetime.

Sorry for the lack of clarity here. I meant; that was not the question because everybody already agrees there are dynamic changes. The area of disagreement and the actual question was: did those changes effect the end result [frequency shift] or not?

.

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

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

I never said that. Those are 2 different phenomenon

? ;-)
Another analogy would be:
Two sound sources in atmosphere. A low pressure front has created a pressure gradient between the two locations. The low pressure area being comparable to a low G potential.
Signals sent out from the low pressure locale starting off slower and then speeding up as they progressed towards the receiver. Of course the opposite in the other direction.

DO you think in this circumstance there would be any frequency shift between emission and reception??

 

[prime axiom]

...

Another analogy would be:
Two sound sources in atmosphere. A low pressure front has created a pressure gradient between the two locations. The low pressure area being comparable to a low G potential.
Signals sent out from the low pressure locale starting off slower and then speeding up as they progressed towards the receiver. Of course the opposite in the other direction.

DO you think in this circumstance there would be any frequency shift between emission and reception??

Great analogy. I haven't run into that one, but it seems to work quite well.

In the simpler model you set up, you basically have an emission point and reception point, with a gravity well in the middle.

In your case, there would be no frequency shift, because the frequency would have been compressed and stretched by the same amount, as it passed the low pressure area. Great analogy, once again.

In my case, however, there would be a NET frequency shift (observed by any reference frame), as modeled in my first post.

 

[Jonathan Scott]

Since these photons are traveling through spacetime that is stretched or compressed, the clock rate for these photons would be changing. When the photons are traveling stretched space, for example, they are taking longer in doing so, and c stays c, clock rate slows, frequency stretches.

This is still wrong.

Relative to some coordinate system that can be used to describe the whole path, c does not "stay c", as it is not possible to map a path containing gravitational fields to Minkowski space as used in Special Relativity. The apparent speed of light relative to the coordinate system varies, and may locally even be different in different directions. In most cases it varies approximately as the square of the time dilation factor.

Relative to that same coordinate system, if the situation is static, the photon frequency is constant. Local observers at each point may have clocks that run at different rates because of the time dilation effect of the gravitational potential, so they may record different frequencies relative to their local clocks, but that does not mean that the photon frequency speeds up or slows down.

This also applies to massive objects as well as photons. If they are freely falling through a static gravitational field, the total energy of the object as seen within the relevant coordinate system is constant. This matches the Newtonian concept that potential plus kinetic energy is constant.

 

[yuiop]

Great analogy. I haven't run into that one, but it seems to work quite well.

In the simpler model you set up, you basically have an emission point and reception point, with a gravity well in the middle.

In your case, there would be no frequency shift, because the frequency would have been compressed and stretched by the same amount, as it passed the low pressure area. Great analogy, once again.

In my case, however, there would be a NET frequency shift (observed by any reference frame), as modeled in my first post.

Here is an even better analogy, because you can actually do this at home and demonstrate to yourself what really happens. Get a piece of gutter or flexible curtain track or even a track for toy matchbox cars. Set up the track so that start is higher than the finish. Get some marbles and roll them down the track starting them off at one minute intervals. Notice that whatever the incline of the track they always arrive at the far end in one minute intervals. The conclusion you should reach is that the receiving frequency is always the same as the transmitting frequency. Now vary the track so that it slopes down at the beginning and then goes upwards on the last half. The marbles initially speed up on the first half of the track and then slow down on the last half of the track and yet they still arrive at the far end of the track at the same frequency. What does change is the speed and the distance between the marbles. You can think of individual marbles as peaks in a wave and the length of the gap between the peaks is the wavelength. Therefore a wave passing through various media at different speeds always maintains its frequency, but the speed and wavelength can change. If you have any doubts about the truth of that then actually do the experiment for real. It will only cost you some loose change. If that is still too much do a computer simulation with two sections of track with points traveling at one speed one first section of track and different speed on the second section of track and demonstrate that at any point along the track, the points always pass with the same frequency. If after all that you still not convinced yourself that frequency stays constant then I can only assume you lost your marbles.

The same is true for gravitational redshift. Using Schwarzschild coordinates, the wavelength and speed of a photon climbing out of a gravity well increases, but the frequency remains constant. It is only because the clocks of different observers at different heights run at different rates, that the frequency appears to slow down from the point of view of local observers.

In cosmology the redshift of light from distant galaxies is put down to stretching of space between galaxies as the universe expands which in turn stretches the wavelength of the light in transit and slows it down to a certain extent. (There are corrections for gravitational redshift due to the mass of the galaxies but this is a minor effect.) This is a difficult concept because it is difficult to imagine how a vacuum can stretch. How do we know the redshift is not simply due to the galaxies receding away from us in static space? The main clue is the cosmic microwave background (CMB) radiation. The frequency of the CMB is consistent with a extreme high frequencies during the big bang followed by billions of years of expanding space stretching the wavelength to the values we observe today.

 

[Austin0]

Great analogy. I haven't run into that one, but it seems to work quite well.

In the simpler model you set up, you basically have an emission point and reception point, with a gravity well in the middle.

In your case, there would be no frequency shift, because the frequency would have been compressed and stretched by the same amount, as it passed the low pressure area. Great analogy, once again.

In my case, however, there would be a NET frequency shift (observed by any reference frame), as modeled in my first post.

I think maybe you didn't understand my scenario. The low pressure area isn't in between
the two sources. One of the sources is in the middle of it and the other source is in high pressure. One signal goes from low pressure to high and the other goes from high to low.
Comparable to sending signals between a large mass and a higher altitude.
How is this essentially different from your problem other than the lack of time dilation?
The critical factor in both cases is the difference in potential/pressure at the locations.
As you just pointed out localized areas that are passed through in between aren't important.
Do you see there would be no frequency shift in this situation?