Gravitionel redshift – How is it working?

[Bjarne]

Experiential data shows that light on its way out of a gravitionel field is losing energy and become redshifted.

Q1.
But what about light that moves into a gravitionel field, - Is that gaining energy (getting more blue shifted) ?

Has we ever measured what happens with light that for example moves true a gravitionel field?

For example we could compare light from Jupiter.

“A” shows light that moves directly from Jupiter and to us (and hence only into the gravitational field of the Sun and the Earth)
“B” shows that now is Jupiter on the other site of the sun.

It is therefore possible to compare light from Jupiter, on the one hand when it moved directly to us, and therefore into the gravitational field of the Sun (exsample “A”) - and on the other hand “B” light that first moves into the Suns Gravitionel field and then out again until we revived it on Earth, on the opposite site of the Sun.

A.) Jupiter----------- ----------> Earth Sun
B.) Jupiter----------------------> Sun -------------> Earth

Q2.
Will light from Jupiter in these 2 cases be different redshiftet / blueshiftet ?

Q3
Has such measurement experiments ever been executed?

 

[Jonathan Scott]

Experiential data shows that light on its way out of a gravitionel field is losing energy and become redshifted.

Q1.
But what about light that moves into a gravitionel field, - Is that gaining energy (getting more blue shifted) ?

Has we ever measured what happens with light that for example moves true a gravitionel field?

For example we could compare light from Jupiter.

“A” shows light that moves directly from Jupiter and to us (and hence only into the gravitational field of the Sun and the Earth)
“B” shows that now is Jupiter on the other site of the sun.

It is therefore possible to compare light from Jupiter, on the one hand when it moved directly to us, and therefore into the gravitational field of the Sun (exsample “A”) - and on the other hand “B” light that first moves into the Suns Gravitionel field and then out again until we revived it on Earth, on the opposite site of the Sun.

A.) Jupiter----------- ----------> Earth Sun
B.) Jupiter----------------------> Sun -------------> Earth

Q2.
Will light from Jupiter in these 2 cases be different redshiftet / blueshiftet ?

Q3
Has such measurement experiments ever been executed?

Gravitational redshift (in a static gravitational field) is not something which happens to light. It is entirely due to differences of observer time rate due to gravitational time dilation. A free-falling photon has constant frequency relative to a static coordinate system. Local clocks and processes vary in frequency due to local gravitational time dilation, so when the frequency of an arriving photon is compared with one generated locally via a similar process, it will appear to be redshifted or blueshifted according to the difference in time rate.

Photons emitted from a lower or higher gravitational potential than the observer do not lose or gain energy in flight. They start off with a lower or higher frequency and keep that frequency. Relative to a series of local observers at different potentials they will appear to have higher or lower energy than a similar photon generated locally, but if any of those observers arranges to monitor the frequency at multiple locations, the observations at each location will all show the same frequency.

 

[Naty1]

Except for Jonathon's first sentence, which might be subject to misinterpretation, I'd readily agree with his description.

Wikipeida's opening is this:

...gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that is in gravitational field is reduced in frequency, or redshifted, when OBSERVED in a region of a weaker gravitational field. This is as a direct result of Gravitational time dilation, frequency of the electromagnetic radiation is reduced in an area of a lower gravitational potential...

Notice that Jonathon says

Gravitational redshift ... is not something which happens to light.

while Wikipedia says redshift is an observed [local measurement] phenomena...so both views are I think technically correct, but the complementary description helps to clarify what is meant. Some will argue all that matters is what is OBSERVED...that's what is 'real'.

A quickie answer might be: different observers have different clock rates, different rates of ticks, so they will observe [measure] different frequencies...

Simple answer:
[a] yes,
no.
[c] I'm sure they have, but I don't know about your exact example. Same situation happens when CMBR passes through galaxies...but other effects like gravitational lensing may also observed...light curves...

 

[yuiop]

If we shine a light from an ordinary torch down towards a lead shield that is very close to a black hole and the light is blue shifted into the x-ray region, could that light from the torch pass through the lead shield, when ordinarily it would not in its unshifted state?

 

[Jonathan Scott]

If we shine a light from an ordinary torch down towards a lead shield that is very close to a black hole and the light is blue shifted into the x-ray region, could that light from the torch pass through the lead shield, when ordinarily it would not in its unshifted state?

Yes if it is sufficiently shifted to reach a frequency that penetrates lead.

 

[Austin0]

If we shine a light from an ordinary torch down towards a lead shield that is very close to a black hole and the light is blue shifted into the x-ray region, could that light from the torch pass through the lead shield, when ordinarily it would not in its unshifted state?

Great question but I thought x-rays frequencies could NOT penetrate lead whether they were emitted au natural or blue shifted to that range?

 

[yuiop]

Great question but I thought x-rays frequencies could NOT penetrate lead whether they were emitted au natural or blue shifted to that range?

I think x-rays of sufficiently high frequency will pass through a reasonably thin lead shield. If not, substitute steel sheet for lead shield.

 

[Austin0]

I think x-rays of sufficiently high frequency will pass through a reasonably thin lead shield. If not substitute steel sheet for lead shield.

Or just human bodies for that matter, it's the idea that's interesting and I wasn't quibbling just curious , mea culpa ;-(

 

[Naty1]

yuiop:

If we shine a light from an ordinary torch down towards a lead shield that is very close to a black hole and the light is blue shifted into the x-ray region,...

Good one!


Jonathan: How do you explain/reconcile your earlier post:

Gravitational redshift (in a static gravitational field) is not something which happens to light. It is entirely due to differences of observer time rate due to gravitational time dilation.

with your subsequent reply:

...Yes if it is sufficiently shifted to reach a frequency that penetrates lead.

they seem inconsistent...

I suspect his has to do with Schwarzschild coordinates being 'static' outside the event horizon but I have never been sure about the implications of that statement...Wikipedia is rather opaque [to me] on 'static spacetime'...

Is your target accelerating to maintain a fixed position outside the horizon, or is the target and observer you describe free falling??

 

[Jonathan Scott]

Jonathan: How do you explain/reconcile your earlier post:

Gravitational redshift (in a static gravitational field) is not something which happens to light. It is entirely due to differences of observer time rate due to gravitational time dilation.

with your subsequent reply:

...Yes if it is sufficiently shifted to reach a frequency that penetrates lead.

they seem inconsistent...

I suspect his has to do with Schwarzschild coordinates being 'static' outside the event horizon but I have never been sure about the implications of that statement...Wikipedia is rather opaque [to me] on 'static spacetime'...

Is your target accelerating to maintain a fixed position outside the horizon, or is the target and observer you describe free falling??

I'm assuming the target to be held in a fixed position. The target will be in a deeply time-dilated state, so the energy of the original beam relative to the target will effectively be enormously increased.

 

[Naty1]

Jonathan:

I'm assuming the target to be held in a fixed position. The target will be in a deeply time-dilated state, so the energy of the original beam relative to the target will effectively be enormously increased.

ok...so target and observer are in a fixed position outside the BH horizon in a static gravitational field ...[All I think I know about such a static field is that it doesn't hold inside the horizon.]

Light from the distant universe appears blue shifted [and time out there appears to be moving faster] because of the low local gravitational potential outside the BH horizon, but doesn't light also appears somewhat redshifted due to the local acceleration?

I say this because I think a free falling observer outside the horizon measures the local speed of light as the standard 'c'...so an accelerating observer would presumably not??

Don't these effects somewhat offset?? If so how do you know which is dominant??

 

[yuiop]

yuiop: Good one!

Thanks!

they seem inconsistent...

I suspect his has to do with Schwarzschild coordinates being 'static' outside the event horizon but I have never been sure about the implications of that statement...Wikipedia is rather opaque [to me] on 'static spacetime'...

Is your target accelerating to maintain a fixed position outside the horizon, or is the target and observer you describe free falling??

I should of said that I intended the target to be at a fixed position relative to the gravitational field, so it would appear to be moving at high speed towards the source from the point of view of a free falling observer.

Using Schwarzschild coordinates, clocks lower down tick at slower coordinate rate that clocks higher up and the increase in frequency can be explained in terms of different clock rates at different heights. Ordinarily we attribute the penetrating power of x-rays to the high frequency but we could just as easily attribute it to the short wavelength because high frequency and short wavelength go hand in hand when the speed of light is constant. However, in Scharwzschild coordinates, the coordinate speed of light slows down lower down, and so even though the coordinate frequency is constant, the coordinate wavelength is shorter so maybe we can attribute the increased penetration to shorter wavelength in this case. The important point I am getting at here is that while coordinate observers and local observers disagree on the frequency of the light, they both agree that the wavelength is getting shorter and should both agree on whether the light penetrates the target or not.

From the point of view of the free falling observer, the light from the upper source is red shifted but he would see the target as moving at high velocity towards the source and should agree that the motion of the target towards the target causes a Doppler blue shift.

 

[PeterDonis]

Photons emitted from a lower or higher gravitational potential than the observer do not lose or gain energy in flight. They start off with a lower or higher frequency and keep that frequency. Relative to a series of local observers at different potentials they will appear to have higher or lower energy than a similar photon generated locally, but if any of those observers arranges to monitor the frequency at multiple locations, the observations at each location will all show the same frequency.

You have to be careful here how you define "frequency". Earlier you say "frequency relative to a static coordinate system", by which I think you mean the standard Schwarzschild coordinate system. Yes, the frequency of a given freely falling photon, relative to Schwarzschild coordinate time, does remain constant.

But "local observers at different potentials" can't directly measure the frequency of a passing light ray relative to Schwarzschild coordinate time; they can only directly measure the frequency relative to their proper time, which is "time dilated" relative to Schwarzschild coordinate time. The frequency of a given freely falling photon, measured relative to different local observers' proper time, *does* vary--it's what you refer to as the redshift/blueshift.

 

[Naty1]

PeterDonis:

Yes, the frequency of a given freely falling photon, relative to Schwarzschild coordinate time, does remain constant...But "local observers at different potentials" ... can only directly measure the frequency relative to their proper time, which is "time dilated" relative to Schwarzschild coordinate time.

Peter: Once again, very helpful...thanks!
Getting the right perspective between physical, observable relativity effects and keeping them distinct from coordinate system effects is not so 'obvious' as I would like...

 

[Naty1]

Can anyone explain how to reconcile these two descriptions...or is one [or both] incorrect??

yuiop posts:

The important point I am getting at here is that while coordinate observers and local observers disagree on the frequency of the light, they both agree that the wavelength is getting shorter and should both agree on whether the light penetrates the target or not.

[Does PeterDonis' post suggest the above is problamatic?]

...That the redshift factor is the same as the time dilation factor (well, so one's the reciprocal of the other, but that's just because the redshift factor is, conventionally, a ratio of wavelengths rather than a ratio of frequencies) is no coincidence. Photons are a good clocks. When a photon is redshifted, its frequency, the rate at which it ticks, slows down.

http://casa.colorado.edu/~ajsh/schwp.html

 

[Eimacman]

Greetings:

I would suggest that you consider that space as well as time is affected by a gravitational well. Time dilation etc would affect frequency, and spatial compression etc would affect wavelength. The relation of such an effect would naturally depend on the observer, its position in spacetime relative to the gravity well, and the instrumentation used.

As to the penetration of a target by blue shifted photons I am intrigued as to where the additional energy may come from.

 

[pervect]

Greetings:

I would suggest that you consider that space as well as time is affected by a gravitational well. Time dilation etc would affect frequency, and spatial compression etc would affect wavelength. The relation of such an effect would naturally depend on the observer, its position in spacetime relative to the gravity well, and the instrumentation used.

As to the penetration of a target by blue shifted photons I am intrigued as to where the additional energy may come from.

Do you have either a) a reference or b) a thought experiment which illustrates "spatial compression" due to gravity?

This topic comes up occasionally on the forum, but it seems hard to track the idea down to a source.

It mostly seems to come up from laypeople who think it should be obvious, but it always seems like the references or details are lacking

I should add that there is a reasonable amount written about "expanding space" in the context of cosmology, but the spatial expansion there isn't caused by gravity. In the end, in cosmology "expanding space" boils down to a coordinate choice.

 

[Austin0]

Do you have either a) a reference or b) a thought experiment which illustrates "spatial compression" due to gravity?

This topic comes up occasionally on the forum, but it seems hard to track the idea down to a source.

It mostly seems to come up from laypeople who think it should be obvious, but it always seems like the references or details are lacking

I should add that there is a reasonable amount written about "expanding space" in the context of cosmology, but the spatial expansion there isn't caused by gravity. In the end, in cosmology "expanding space" boils down to a coordinate choice.

Perhaps I'm not understanding you correctly but I thought that gravity was equivalent to acceleration and imposed a radial spatial contraction gradient??

Isn't contraction equivalent to compression in this context? Or is it the connotation of stress associated with compression that makes it inappropriate?

 

[Austin0]

Can anyone explain how to reconcile these two descriptions...or is one [or both] incorrect??

yuiop posts:

observers disagree on the frequency of the light, they both agree that the wavelength is getting shorter and should both agree on whether the light penetrates the target or not.

[Does PeterDonis' post suggest the above is problamatic?]

...That the redshift factor is the same as the time dilation factor (well, so one's the reciprocal of the other, but that's just because the redshift factor is, conventionally, a ratio of wavelengths rather than a ratio of frequencies) is no coincidence. Photons are a good clocks. When a photon is redshifted, its frequency, the rate at which it ticks, slows down.

http://casa.colorado.edu/~ajsh/schwp.html

According to Jonathon et al, the second would seem to be incorrect.

 

[Austin0]

Greetings:

I would suggest that you consider that space as well as time is affected by a gravitational well. Time dilation etc would affect frequency, and spatial compression etc would affect wavelength. The relation of such an effect would naturally depend on the observer, its position in spacetime relative to the gravity well, and the instrumentation used.

As to the penetration of a target by blue shifted photons I am intrigued as to where the additional energy may come from.

I just had occasion to look up e-rays and it appears that energy per se is not the prime criteria. The lower part of the x-ray range, although much more energetic that light, has little penetration capability.
Wiki

By contrast, soft X-rays hardly penetrate matter at all; the attenuation length of 600 eV (~2 nm) X-rays in water is less than 1 micrometer.[4]

Which seems to suggest that the probability of absorption is more dependent on resonant frequency correspondence than energy.
So it is not so much an increase in energy of the source [which frequency remains the same] as it is that the dilation of the target resonant frequencies drops them out of absorption range.
Hopefully there is some sense in here someplace.

 

[Naty1]

According to Jonathon et al, the second would seem to be incorrect.

I realize that; hence my post...

I have never seen such a description as Jonathan's previously. Right now I suspect U Colorado is the correct description and I think PeterDonis
description supports that view...

 

[Jonathan Scott]

Can anyone explain how to reconcile these two descriptions...or is one [or both] incorrect??

Any description of a photon "being redshifted" or "slowed down" is potentially misleading, so I'd say the second should not be taken literally.

If you describe separate photons being created with the same local energy at a series of locations with different gravitational potential, then they will appear to have different energies as viewed from a common location. However, this is not because of any change in flight, but because of the difference in time rate at the location where the photon was created.

It is perfectly reasonable to refer to the amount by which the photon frequency has been redshifted or blueshifted, and to note that this varies depending on the location at which the photon was created. However, it is not correct to infer from this that redshifting is a dynamic process which occurs in flight. It is merely due to the photon being created at a different potential.

 

[Jonathan Scott]

...
So it is not so much an increase in energy of the source [which frequency remains the same] as it is that the dilation of the target resonant frequencies drops them out of absorption range.
Hopefully there is some sense in here someplace.

I agree with that description.

 

[Jonathan Scott]

Do you have either a) a reference or b) a thought experiment which illustrates "spatial compression" due to gravity?

This topic comes up occasionally on the forum, but it seems hard to track the idea down to a source.

In an isotropic coordinate system for a central mass, local rulers shrink more (isotropically) in a lower gravitational potential relative to the coordinate system. This can be extended at post-Newtonian accuracy to a system containing an arbitrary collection of sources, as in Carroll "Spacetime and Geometry" equation 7.59.

The details of this "shrinkage" obviously depend on the choice of coordinate system, and in Schwarzschild coordinates rulers still shrink tangentially but not radially relative to the coordinate system. However, the assumption that clocks slow and rulers shrink by the Newtonian potential in an isotropic coordinate system provides a model sufficiently accurate to reproduce all observed solar system effects of GR.

 

[Q-reeus]

The details of this "shrinkage" obviously depend on the choice of coordinate system, and in Schwarzschild coordinates rulers still shrink tangentially but not radially relative to the coordinate system.

Other way around - for standard Schwarzschild coordinates, relative to coordinate observer ruler 'shrinkage' is in radial direction whereas transverse components are unaffected. And as per my recent thread, this imo leads to inconsistencies that mostly go unnoticed.

 

[yuiop]

... As to the penetration of a target by blue shifted photons I am intrigued as to where the additional energy may come from.

It seems most people here have avoided your question on where the energy comes from. I guess a simple answer is the photons gain frequency energy as they lose gravitational potential energy similar to how conventional falling objects convert potential energy to kinetic energy. In Schwarzschild coordinate terms, the frequency remains constant, so there is no need to invoke the concept of photons losing potential energy.

 

[yuiop]

I should add that there is a reasonable amount written about "expanding space" in the context of cosmology, but the spatial expansion there isn't caused by gravity. In the end, in cosmology "expanding space" boils down to a coordinate choice.

I used to think the same. The observed red shifting of receding galaxies appears to just as easily explained by high recession velocities in flat static space. I presume cosmologists have other reasons for assuming space itself is expanding such as the observed apparent brightness of distant objects. I think the greatest argument for assuming space itself is expanding is the CMBR because rapidly receding distant objects are by and large at rest with local CMBR. Also, the observed low frequency of the CMBR is consistent with the background radiation wavelength being stretched over billions of years as space expands and this is difficult to explain in any model that does not involve expanding space.

 

[PeterDonis]

If you describe separate photons being created with the same local energy at a series of locations with different gravitational potential, then they will appear to have different energies as viewed from a common location.

To avoid confusion, I would operationalize "created with the same local energy" to something directly measurable, like "measured locally to have a particular frequency, for example by spectroscopy". This makes it clear how you are ensuring that the photons all have the same "local energy" where they are being created.

It is perfectly reasonable to refer to the amount by which the photon frequency has been redshifted or blueshifted, and to note that this varies depending on the location at which the photon was created. However, it is not correct to infer from this that redshifting is a dynamic process which occurs in flight. It is merely due to the photon being created at a different potential.

This is one way of looking at it, which works fine in static situations where a "potential" can be defined. But I'm not sure this picture generalizes well to non-static spacetimes. How, for example, would you use this conceptual scheme to explain the redshift of light coming from distant quasars?

 

[PeterDonis]

[Does PeterDonis' post suggest the above is problamatic?]

I don't think so. Jonathan Scott is correct that whether or not the x-ray penetrates the shield depends on the *relative* energy of the two, and that is affected by the "potential" or "time dilation" factor at the shield's location, relative to the location where the x-ray was emitted.

 

[Jonathan Scott]

Other way around - for standard Schwarzschild coordinates, relative to coordinate observer ruler 'shrinkage' is in radial direction whereas transverse components are unaffected. And as per my recent thread, this imo leads to inconsistencies that mostly go unnoticed.

Uh, yes, well spotted.

I always think of isotropic coordinates as being the most "natural", and certainly the most practical.

 

[Naty1]

pervect:

Do you have either a) a reference or b) a thought experiment which illustrates "spatial compression" due to gravity?

The only thing I've seen that might relate is a description of Born rigid acceleration...via 'equivalence'...I don't have the source, but I just saw the tail end of a rigid rod described as having to accelerate faster than the front end due to 'Lorentz contraction'...that's in Rindler coordinates...which are apparently coordinate dependent, so what that all means is hardly crystal clear...

 

[Jonathan Scott]

This is one way of looking at it, which works fine in static situations where a "potential" can be defined. But I'm not sure this picture generalizes well to non-static spacetimes. How, for example, would you use this conceptual scheme to explain the redshift of light coming from distant quasars?

This thread is about gravitational redshift ... at least I assume that's what "Gravitionel" was intended to mean ... which can be isolated from other effects only in a static spacetime.

When it is combined with velocity effects, the overall redshift is the same as that obtained from multiplying the two factors together.

For cosmological cases, the overall shift of a given spectral line can typically be treated as a combination of a major velocity-like effect due to expansion combined with a tiny gravitational redshift due to the relative potential of the locations where spectral emission or absorption features were created.

 

[Naty1]

pervect:

In the end, in cosmology "expanding space" boils down to a coordinate choice.

Yuiop

I think the greatest argument for assuming space itself is expanding is the CMBR because rapidly receding distant objects are by and large at rest with local CMBR.

that's a logical conclusion at the least. And isn't the cosmological constant invarient? How can that phenomena be a coordinate choice?? Also from a recent discussion in these forums:

in brief: redshifts vary over time with the evolution of the universe...

http://arxiv.org/abs/0802.1532

Also, redshifts don't necessarily increase with time. Figure 1 from this paper plots redshift versus time. The three red curves are for objects in our universe. As we watch (over many years) a distant, high redshift object, A, we will see the object's redshift decrease, reach a minimum, and then increase. If we watch a much closer, lower redshift object, B, we see the object's redshift only increase.

Roughly, when light left A, the universe was in a decelerating matter-dominated phase, and when light left B, the universe was in the accelerating dark energy-dominated phase.

That seems difficult to interpret merely as coordinate choice...

Is there experimental evidence for such expansion variation??

 

[Naty1]

PeterDonis

...is affected by the "potential" or "time dilation" factor at the shield's location, relative to the location where the x-ray was emitted.[/QUOTE]

ah ha! Helpful again...

 

[PAllen]

pervect: Yuiopthat's a logical conclusion at the least. And isn't the cosmological constant invarient? How can that phenomena be a coordinate choice?? Also from a recent discussion in these forums:

in brief: redshifts vary over time with the evolution of the universe...
That seems difficult to interpret merely as coordinate choice...

Redshift measurements are not coordinate dependent. In a lambda-cdm model, lambda is invariant. However, 'expanding space' is an interpretation which comes from a coordinate choice. Note that the Milne coordinates in flat Minkowski space lead to 'expansion of space' without changing the manifold geometry (or, obviously, any observations). None of this is really surprising, because there is no global definition of distance in GR. Any definition of distance is coordinate dependent - thus also, any claimed expansion of distance. The particular aspect of coordinate choice that pins down distance is the choice of spacelike slices used (referred to as a foliation). Given these, distance along 3-geodesics of the chosen surfaces (using the induced 3-metric) give distances for the chosen foliation. Often, one wants a foliation such that 3-geodesics are also spacelike 4-geodesics, but this is not necessary.