Is the Redshift of Light at a Black Hole's Surface Infinite?

[Macro]

The gravitational redshift to light at emission is known
as the Einstein shift.

There is a problem with it in General Relativity.
It becomes infinite at the surface of a black hole.
Light emitted there will be infinitely redshifted.
GR predicts this energyless light. In this way
as Hawking has said: GR predicts its own downfall.

Energyless Light?
Light of infinite wavelength emitted?

Sorry but Einstein himself didn't believe in
black holes and this prediction is reason
not to believe in them.

The redshift must remain finite in the strongest
of gravity. That will be one of the results of
modifying GR.

Mitch Raemsch

 

[quasar987]

Thus spoke Mitch Raemsch the magnificient.

 

[Tide]

Light of infinite wavelength emitted?

Yes, along with zero frequency! Can you guess its observed energy will be? :)

 

[lightgrav]

Yes, Reamsch, we only pay attention to theories
that make predictions which *might* be wrong.
But the prediction you've selected (grav.red-shift)
is on pretty SOLID experimental CONFIRMATION,
(at least to first power in dh)

 

[pmb_phy]

All this is a very terrible interpretation of the facts. If the photon is emitted *at* the event horrizon then it can't escape from the horizon and therefore nobody will measure the photon's energy at all since you'd have to have an instrument sitting at rest at the event horizon and that is impossible. But the energy of a photon will not change as it moves through a gravitational field, neither will its frequency. That too is a misconception. The only thing that will change is when the light energy is measured locally at different places. Okun et al wrote an article on this as did I (my website is not being nice now since I was unable to locate my web page on this.)

See
On the Interpretation of the Redshift in a Static Gravitational Field, L.B. Okun, K.G. Selivanov, V.L. Telegdi, Am.J.Phys. 68 (2000) 115

This is online at - http://xxx.lanl.gov/abs/physics/9907017

Pete

 

[Garth]

See
On the Interpretation of the Redshift in a Static Gravitational Field, L.B. Okun, K.G. Selivanov, V.L. Telegdi, Am.J.Phys. 68 (2000) 115

This is online at - http://xxx.lanl.gov/abs/physics/9907017

Pete

Thank you Pete, this is a brilliant paper on grs in GR - I think it's "brilliant" because it says what I've being trying to get across for ages!

Sometimes this description is loosely phrased as a degradation of the photon’s energy as it climbs out of gravitational potential well. (Some other classical textbooks also use this loose phrasing [15].) However, the non-experts should be warned that the mathematics underlying this description is radically different from the heuristic (and wrong) arguments presented in many elementary texts, e.g. [16]. These authors claim to deduce the “work against gravity” viewpoint by pretending that the photon is like a normal, low-velocity, massive particle and thus has a “photon mass” and “photon potential energy”

It goes on later

In the static gravitational potential the picture simplifies because there is a distinguished time – the one on which metric is independent. This time can be chosen as a universal (world) one. Under this choice the energy difference between two atomic levels increases with the distance of the atom from the Earth while the energy of the propagating photon does not change. (In what follows we speak of the earth, but it could be any other massive body.) Thus what is called the redshift of the photon is actually a blueshift of the atom. As for the proper times at different points, they are related to the universal time via a multiplier which depends on gravitational potential and hence has different values at different points.

(Emphasis mine)
The question is, "How is red shift measured?, What is being compared with what?"
That paper goes on:

By contrast, the majority of the reviews of gravitational experiments [10] quote the Harvard
result as a test of the behaviour of clocks. In fact the result must be interpreted as a relative shift of the photon frequency with respect to the nuclear one since the experiment does not measure these frequencies independently.

If one now imposes the GR requirement that rest mass is constant you obtain the standard GR interpretation that the photon has lost energy and "proper times have different values at different points". However it is possible to interpret the result as in Vankov's Proposal of Experimental Test of General Relativity Theory, which I have just found as it is co-cited with the above.

On the basis of the relativistic mass-energy concept we found that a proper mass of a test particle in a gravitational field depends on a potential energy, hence, a freely falling particle has a varying proper mass.

If proper mass is thus defined:
$$m(x^{\mu})=m_0\exp{\Phi(x^{\mu})}$$ where $$\Phi(x^{\mu})$$ is the dimensionless Newtonian potential at $$x^{\mu}$$ then the proper time is the same at all points and grs is clearly the result not of the photon mysteriously losing energy but the apparatus it interacts with gaining it. That is why I have been interested in Pete's use of "relativistic mass" in many heated exchanges on these Forums!

Of course you have to consistently develop such a definition of 'rest' or 'proper' mass, as it violates the equivalence principle. This I have attempted in http://www.kluweronline.com/oasis.htm/5092775. We shall see how successful it has been when Gravity Probe B delivers the goods!

Garth

 

[pmb_phy]

You're most welcome Garth. Here is my own page on this topic.

http://www.geocities.com/physics_world/gr/red_shift.htm

The bottom is messed up so ignore it for now.

Pete

 

[Garth]

Thank you. To draw the time dilation properly you have to do it on a 'bent' piece of paper, a 'funnel'!

My analysis of grs can be found in gr-qc/0302088]The derivation of the coupling constant in the new Self Creation Cosmology[/URL] pages 20 - 24.
Assuming the local conservation of energy I show that not only does the time dilation red shift, when seen by an observer 'at infinity', given by:
$$\nu(r) = \nu_0[-g_{00}(r)]^\frac{1}{2}$$ apply to photons, but also it applies to proper masses of particles as well as a component of the full expression.
$$m_c\left( r\right) =m_0\exp \left[ \Phi _N\left( r\right) \right] \left[ -g_{00}\left( r\right) \right] ^{\frac 12}$$.
The act of making the red shift observation is a comparison of the energy of the photon and the total energy (rest or proper mass) of the stationary apparatus.
The two equations above are compared to yield:
$$\frac{m_p\left( r\right) }{\nu \left( r\right) }=\frac{m_0}{\nu _0}\exp \left[ \Phi _N\left( r\right) \right]$$ and the time dilation, $$[-g_{00}(r)]^\frac{1}{2}$$, cancels out.
Now imposing the principle of equivalence and the constant rest mass of atomic particles we are left with the normal loss of energy by the photon:
$$\nu \left( \widetilde{r}\right) =\nu _0\left( 1-\widetilde{\Phi }_N\left( \widetilde{r}\right) +...\right)$$ - the Einstein conformal frame of SCC.
However, if we define (rest) mass as
$$m_c\left( r\right) =m_0\exp \left[ \Phi _N\left( r\right) \right] \left$$ then the frequency of the photon becomes:
$$\nu \left( r\right) =\nu _0$$, which is the Jordan conformal frame of SCC.
It becomes clear that "what is called the redshift of the photon is actually a blueshift of the atom" (From Okun et al. Pete's link above).

Garth

 

[pmb_phy]

Thank you. To draw the time dilation properly you have to do it on a 'bent' piece of paper, a 'funnel'!

That is incorrect. You're confusing the time dimension with spatial curvature. There is no assumtion about spatial curvature in that web page. Gravitational redshift does not imply either space curvature or spacetime curvature.

Pete

 

[pervect]

All this is a very terrible interpretation of the facts. If the photon is emitted *at* the event horrizon then it can't escape from the horizon and therefore nobody will measure the photon's energy at all since you'd have to have an instrument sitting at rest at the event horizon and that is impossible.

Yep. You would think that when amateurs arrive at an apparent contradiction in a subject they havaen't studied much, that they would stop and think that perhaps it is their understanding at fault.

I think most people, in fact, do exercise such caution. I'm not quite sure what motivates people to attack science and relativity based on their own misunderstandings, but I've seen a lot of it.

The path that a photon would take if it were emitted exactly at the event horion would be to "hang there" (at the event horizon) in Schwarzschild coordinates.

It would be possible for someone else who was falling through the black hole to encounter that photon - but it would not be possible for anyone outside the event horizon to encounter it.

The easiest experiment to imagine would be that someone was falling into a black hole on a longish space-ship. Right when the nose of the space-ship is calculated to enter the event horizon, the nose of the spaceship emits a pulse of light.

A receiver at the back of the space-ship would receive the light normally a short time later. The frequency of the light would be essentialy the same as the emitted light (tidal forces would cause a very small redshift).

This follows from the fact that nothing particularly special happens at the event horizon of a large black hole (other than normal tidal forces due to any large mass) from the viewpoint of someone unfortunate enough to be falling into it. The part that hurts is when they inevitably encounter the singularity at the center a short time later, and are torn apart by tidal forces.

But the energy of a photon will not change as it moves through a gravitational field, neither will its frequency. That too is a misconception. The only thing that will change is when the light energy is measured locally at different places. Okun et al wrote an article on this as did I (my website is not being nice now since I was unable to locate my web page on this.)

See
On the Interpretation of the Redshift in a Static Gravitational Field, L.B. Okun, K.G. Selivanov, V.L. Telegdi, Am.J.Phys. 68 (2000) 115

This is online at - http://xxx.lanl.gov/abs/physics/9907017

Pete

You are arguing philosophy again. These poor people are already confused enough, you don't need to confuse them more by providing alternative philosophical approaches to the explanation of gravitational redshift/blueshift.

Consider what they've gotten wrong already, and imagine the probability of them correctly understanding what you are saying.

If you _still_ must arge philosphy, please provide an actual experiment to argue about, arguing about vague things like whether a photon does or does not change energy doesn't make sense unless one specifies how the photon's energy is measured.

If we take the "Harvard tower" experiment as an example, where we have a Mossenbauer x-ray of a very well defined frequency emitted at the top of a tower, we can say that the Mossenbauer receiver (which is of necessity tuned to the exact same frequency as the transmitter, in the sense that the frequency cannot be adjusted) will NOT detect the photon emitted at the top of the tower.

While philosophically one can argue about wheter it is the photon that has changed (gravitational blueshift), or the reciever that has changed (gravitational time dilation), it is quite clear that one of them has changed.

Basically, it's a matter of personal preference to say which one has changed. It's important to be consistent about the issue in the approach one takes, but either approach works.

 

[pmb_phy]

You are arguing philosophy again. These poor people are already confused enough, you don't need to confuse them more by providing alternative philosophical approaches to the explanation of gravitational redshift/blueshift.

Whoooooaaaa Nelly! That is absolutely not true, i.e. what I stated is not an "alternative philosophy." Its standard GR physics. Look it up! The main point that you're missing is "time/energy" as measured by whom. If its time/energy as measured by one observer then what I said is exactly true as I've detailed in my web page ... I think??

In fact if you have Gravitation and Spacetime - Second Ed. by Ohanian and Rufini then turn to page 180 and read from the second paragraph on.

What you've been saying is something equivalent in Newtonian physics like this - Measure the potentential and kinetic energy of a rock at the top of a building. Call this a local experiment and define potential energy for a local experiment as zero, i.e. z = 0. So the total energy of the rock is zero. Now drop the rock and tell the person at the bottom to keep a heads up. He is performing locak experiments too. The bottom observer sees the rock fly by him and when it reaches z' = 0 in he measures the kinetic energy of the rock which is now no longer zero. He concludes that energy = kinetic + potential is has changed.

Recall that the energy of any particle moving through a conservative field (e.g. $g_{\mu\nu}$ do not depend on time) then the energy of the particle is conserved. For proof see
http://www.geocities.com/physics_world/gr/conserved_quantities.htm

I understand your philosophy so don't get me wrong. But please don't claim that I'm the lone gunman in this since I just posted an AJP article which agrees with me.

Your philosophy states that the only energy to be spoken of in the Grail of gravitational redshift is the locally measured energy. That's the E = hf energy. This can be interpreted as kinetic energy. In this sense it is dt that does not change but $d\tau$ (proper time as measured by a clock which is receiving the light) that changes with position.

What part of Okun et al's article do you object with (since he and I agree, for very goo reasons too).

Pete

ps - I refuse to dumb down since I consider it an insult to the person trying to learn.

 

[lightgrav]

The OP did not claim that GR had an apparent contradiction;
the claim was that Nature would surely not allow such a result.
This can't be decided by theory, it depends on observation.

The results of LABORATORY experiments that I'm familiar with
don't nail down the functional form of the grav.red-shift
well enough to extrapolate all the way to the event horizon.
So I think it's very premature to obsess about "exactly at"
the event horizon, as some recent posts:

macro: "...It becomes infinite at the surface of a black hole ..."
pmb_phy:"...is emitted *at* the event horrizon ..."
pervect: "...if it were emitted exactly at the event horion ..."

We'll never get data about event horizon light-emission,
except IN THE LIMIT as the source approaches the horizon.

 

[pervect]

I understand your philosophy so don't get me wrong. But please don't claim that I'm the lone gunman in this since I just posted an AJP article which agrees with me.

I'm not claiming that your philosophy doesn't exist, just that it is very likely to confuse the Original Poster at best (and to be used as part of an anti-science agenda at the worst).

As I recall, Garth has similar views. I would not, however, agree that the concept of gravitational red-shift is wrong. I *would* instead say that sometimes the presentation of gravitational red-shift is over-simplfied, and that Einstein's original motivation of the conservation of energy is presented as justifying the pheonomenon in detail, while it turns out that the gory details of how energy is actually conserved in GR are considerably more complex.

I don't have the particular articles that you refer to, and it's getting a bit late - I'll re-read some of your more detailed comments tommorrow or later today when I have more time.

 

[pmb_phy]

I'm not claiming that your philosophy doesn't exist, just that it is very likely to confuse the Original Poster at best (and to be used as part of an anti-science agenda at the worst).

As I mentioned, I'd never hold to something that I didn't hold was true for the purpose of not confusing the OP. In this case the OP doesn't even seem to know GR. However many people read these posts besides the OP.

I *would* instead say that sometimes the presentation of gravitational red-shift is over-simplfied, and that Einstein's original motivation of the conservation of energy is presented as justifying the pheonomenon in detail, while it turns out that the gory details of how energy is actually conserved in GR are considerably more complex.

We each have our own way of responding. When you don't like someone's response then simply post to them what you hold to be easier to understand. But it was Garth that I was respondimg to.

I don't have the particular articles that you refer to, and it's getting a bit late - I'll re-read some of your more detailed comments tommorrow or later today when I have more time.

I recall that Einstein's 1911 paper uses energy conservation of light moving through a field too.

Also there is little confusion about what "energy" means regarding a photon. There are two terms commonly used regarding the energy of a photon - Energy and Locally measured energy.

Regarding once more this

If we take the "Harvard tower" experiment as an example, where we have a Mossenbauer x-ray of a very well defined frequency emitted at the top of a tower, we can say that the Mossenbauer receiver (which is of necessity tuned to the exact same frequency as the transmitter, in the sense that the frequency cannot be adjusted) will NOT detect the photon emitted at the top of the tower.

This is an experiment designed to measure locally measured energy as I recall. The exeperiment (whose publication is around here somewhere) was to verify Einstein's derivation of a particular result. But guess what pervect?! Einstein's equations in which he derived what Robert Pound was testing at Harvard, show that, when the equivalence principle is employed, the energy of the photon is conserved! As I said before - This is not my "philosophy" this is simply fact. Unless you call the principle of energy conservation a "philosophy." Einsteins 1911 paper On the influence of the gravitation on the propagation of light is online somewhere but as I recall I provided that derivation in the above link.

In any case I hold that I was overly clear on what I meant by all that I said here. I assumed you read my web page before you criticized what I was saying since I was exxtremely clear on what I was speaking about regarding energy. You did read that before "correcting" me right?

This is not an idea that I originated. It was by this gentleman named Albert Einstein.

Pete

ps - I plan on being at Harvard soon to discuss something me and one of their physics profs are working on. I can always get Robert Pound's opinion on what his experiment means if you'd like? He's a wonderful gentlemen. It was a pleasure to actuall chat with him. I was soon intimidated by how brilliant he was that's for sure. More on his paper and work later.

 

[pmb_phy]

Tom - Until such a time that I speak with Pound and get back you I can either e-mail his article which reported this experimental research work or I can place it on my website. This will require some work so let me know so I don't do it for nothing.

Until then the name of that article is Apparent weight of photons, Pound & Rebka, Physical Review, April 1 1960 (I was just more than an egg at that time )

The first sentance reads

As we proposed a few months ago, we have now measured the effect, originally hypothesized by Einstein, of gravitational potential of the frequency of electromagnetic radiation by using the sharply defined energy of recoil-free...

Its all about the potential energy of light that people are always leaving out. What a shame.

Then again even Pound screwed it up later by not speaking of he "locally measured energy" or "kinetic energy" of the photon. Its the kinetic energy of the photon that is changing and which is actually that which is being measured.

Pete

 

[Garth]

To draw the time dilation properly you have to do it on a 'bent' piece of paper, a 'funnel'!

That is incorrect. You're confusing the time dimension with spatial curvature. There is no assumtion about spatial curvature in that web page. Gravitational redshift does not imply either space curvature or spacetime curvature.

Pete

I was not confusing the curvature of space and the curvature of space-time, I was, however, a little imprecise about the word, "funnel", and I can see how that it could be confused with the space-like slice across a Schwarzschild space-time. I meant hyperbolic space-time, a anti-de Sitter (adS) 4D space, one in which 'parallel' or congruent null-geodesics diverge.

The question is: "If the energy of a photon or the proper mass of a particle varies how do you measure it?" In grs you compare the one with the other, either - or even possibly both, could vary but all you can measure is the difference between the two. You need a constant standard by which to measure the variation of the other.

One can adopt the convention of constant proper particle mass, which is consistent with the equivalence principle and is therefore the standard convention. Then you observe that the photon has lost energy - but may not be able to explain where it has gone and might resort to talk of "the photon losing PE as it climbs the gravitational potential well". In this convention grs may be interpreted as a time-dilation effect and is caused by the null-geodesics of “congruent”, or parallel, rays of light diverging in their paths across negative curvature space-time. If you treat light as a pulse of continuous radiation then with grs, although the intensity and therefore power of the pulse has diminished, the time taken for the pulse to be received has increased, thus the total energy received is conserved.

I would agree, however that other conventions are possible, such as the Jordan conformal frame of SCC, and may even be more consistent with SR and classical physics than GR, but I would be careful not to confuse anybody by being inconsistent in the use of possible conventions.

Garth

 

[mitchellmckain]

pmb_phy 's response to this topic seems adequate to me. However I would like to add some observations that should stir things up a bit.

Not only does the redshift approach infinity at the Schwartschild radius, so does the intensity of the Hawking radiation. In this case the two effects cancel each other out somewhat to prevent the black hole from instantly losing all of its energy.

This idea of infinite limits does not bother physicists with any familiarity with quantum field theory (including string theory), where the canceling of competing infinite limits is the bread and butter of everyday research.

I should also like to point out my observation that the Hawking radiation does not diverge (go to infinity) very quickly and that in fact the Hawking radiation is not a noticeable effect (even in close proximity) for any size of black hole that is known (cataogued as a black hole candidate).