Talk:Gravitational redshift

Round-trip gravity shifts?
"'Note from the formula above that the loss of energy of the photon is just equal to the difference in potential energy gh). You can't make a perpetuum mobile by having photons going up and down in a gravitational field, something that was, strictly speaking, possible within Newton's theory of gravity.'"

The "difference in potential energy" thing is a Newtonian calculation, see (Einstein 1911), or John Michell's 1784 paper on dark stars. I really don't think you can make a perpetuum mobile this way under Newtonian theory.

In fact, I think the Newtonian prediction is actually "lossy": if you first add and then subtract a fixed proportion of a photon's energy, the second operation is based on the photon's current energy, not the energy it had at the start of the experiment. You don't quite get back to where you started, e.g. 1*(1+0.5)*(1-0.5) is less than unity.

We can calculate the exact gravity-shift predictions of a theory by working out the velocity-change associated with a gravitational gradient, calculating the conventional motion shift associated with an object receding or approaching at that velocity, and then saying that a light-signal then has to undergo the same shift.

With special-relativity-based theory, we have the "relativistic Doppler" equaiton for motion shifts, so if the upper and lower observers can agree on the terminal velocity associated with a gradient, a photon passed downhill then uphill across the gradient returns with exactly the same energy it started with - this energy-conserved situaiton is possibly one of the reasons why Einstein may have felt that it was natural for the cosmology of GR to be pseudo-Euclidean, with lightbeams crossing large distances having their energies unchanged (on average) over large distances, and why he put in his gravitational constant to force that result.

But with Newtonian theory, a photon frequency-shifted by f'/f = (1+ v/c)(1- v/c) returns to its original height with a net energy-loss of (1- v^2/c^2), a Lorentz-squared redshift. So, Newtonian theory suggests that a photon travelling across the a reasonably uniform universe, encountering a switchback series of gravitational highs and lows, should actually be expected to show some sort of distance-dependent redshift, I think. ErkDemon 00:21, 30 July 2005 (UTC)

This isn't just a GR result ...
Just a few small points:
 * the prediction of gravitational shifts was made using Newtonian theory over a century before Einstein, as a consequence of light gaining or losing energy as it moves down or up across a gravitational potential gh (see, John Michell 1784, Laplace, dark stars).


 * The "novel" effect that Einstein introduced in the 1911 paper was not so much the shift effect, but the idea that gravitational shifts led inevitably to gravitational time dilation.


 * Last I heard, Pound-Snider (1965) was still the best experimental assessment of the gravitational velocity-shift law that we had. I've seen it written that these tests stopped after Pound-Snider, when people realised that the accuracy of tests using currently-available technology was still not good enough to distinguish between GR and Newtonian theory. Perhaps another factor might have been that techniques for focussing x-rays (useful for producing a parallel beam for use in longer-drop experiments) would still have been classified at the time because of their applications for hydrogen bomb design.


 * Spaceborne experiments do produce larger shift effects than Pound-Snider, but also introduce larger uncertainties over the "real" heights of the satellites involved. Using light to measure the distances by making certain assumptions about the effect of gravity on light, and then using these presumed distances to test the exact effect of gravity on light, can get a bit circular.


 * For "starlight" verifications of gravitational shifts, the page needs some references: I know that the "starlight" experiments cited by Einstein in his relativity book no longer appear in modern textbooks, apparently they've since been "dropped" as unreliable, and without a citation or a name, I can't tell whether the author had these discredited results in mind, or some newer ones.

So describing gravitational shifts as "the applied side of general relativity" is probably putting it a bit strongly. Proper textbooks and experimental writeups remember to put in a "caveat" that the gh/c^2 thingy is a Newtonian approximation that we use in these situations because it's very convenient and because in these situations we usually can't tell the difference between the diverging NM and SR-based predictions. I think that the sort of caveat used by these authors ought to also appear in the wiki page.

FWIW, I'm not sure that Newtonian gravitational potential gives the correct gravity-shift relationships even for NM (I think that's more about the round-trip time dilation relationship than the one-way visible frequency change), but again, the divergences are so small in practice that we probably don't care if we are technically using the wrong set of math, it's still probably "close enough" to agree with the experiemntal data and to be counted as a usable first approximation. ErkDemon 02:38, 1 August 2005 (UTC)

Recent edits by 24.201.168.190
Please look over what you wrote and try to rewrite it to make more sense and to correspond better with mainstream. For example, "redshift of a photon" doesn't make much sense as written. Also, "it can be argued that star never collapses past horizon" is misleading in this context. Either explain what you mean by this or write it out, please. ---CH (talk) 00:57, 24 October 2005 (UTC)

Expert cleanup desperately needed
This article is currently in awful shape and needs to be thorougly rewritten. I agree with some points ErkDemon made (pleasant when this happens): it is important to stress that gravitational red shift is by no means a distinguishing feature of gtr among metric theories of gravitation, and applied side of gtr is a rather silly characterization which probably has no place here. See the todo list at top of this talk page. ---CH 05:50, 23 December 2005 (UTC)


 * I am no expert, but I believe I have redone most of the article and removed redundant unnecessary explanations. I also cut out the stuff about the Pound-Rebka experiment and replaced it with a sentence and link to the seperate article which already talks about that.  I also add a graphic with an appropriate caption.  I think this will provide a better framework for the article.  I sincerely hope you like this revision! Kmarinas86 02:20, 26 December 2005 (UTC)


 * It still won't satisfy all expert needs, however.Kmarinas86 02:21, 26 December 2005 (UTC)


 * There would have to be a section the gives the causal explanation of Gravitational Redshift according to rigourous gtr, someone else may do that, not me.Kmarinas86 02:26, 26 December 2005 (UTC)


 * Experiments concering gravitational redshift could be done on different articles and linked to by this one.Kmarinas86 02:28, 26 December 2005 (UTC)


 * I must say, this article look just fine. Some of you guys like to go around to all these articles to make yourselves look intelligent by claiming the article is lousy / sub-standard (doesn't that put you in the instructor's chair?  Does that feel nice, to have the wisdom and expertise to grade all these papers?).  Does this refer to you, Hillman CH?  Kmarinas, you've probably done a great job, why do you need the approval of Hillman?  This is the most annoying thing about Wikipedia.  What's more, every mundane point does not need a citation.  This can drive readers up a wall, and away from Wikipedia.  BETTER YET - if your so smart and knowledgeable enough to know that a citation is need -- FIND IT YOURSELF!  Of course, many times such a notation is fitting and appropriate, but the way it is presently being used is overboard, petty and obnoxious. Nick  —Preceding unsigned comment added by 65.27.203.75 (talk) 02:17, 15 May 2008 (UTC)

Illustration problems
I have no idea what the illustration is supposed to be showing. It needs a better caption here and on redshift. -- Beland 13:22, 25 March 2006 (UTC)

Todo list
As a courtesy, I have removed the "expert items" from the todo list. I am leaving WP and doubt anyone else will know how to implement the suggested improvements since this was mostly a note to myself.

This article concerns a topic dear to my heart, which unfortunately attracts many cranks. I hadn't the heart to closely monitor it during my year as a Wikipedia, but I did write the original todo list. As a courtesy, I have removed the "expert items" from the todo list. I am leaving WP and doubt anyone else will know how to implement the suggested improvements since this was mostly a note to myself.

Just wanted to provide notice that I emphatically do not vouch for anything you might see in more recent versions. Given past history, I have some reason to believe that at least some future versions are likely to present slanted information, misinformation, or disinformation.

Good luck to all students in your search for information, regardless!---CH 00:15, 1 July 2006 (UTC)

Define V in History
V is not defined.DLH (talk) 13:03, 8 November 2016 (UTC)

Doppler effect
I seem to miss a clear explanation on top of this page that Gravitational redshift is part of the Relativistic Doppler effect. When I type Gravitational shift I'm redirected to this page, but then I seem to miss a clear explanation of Gravitational shift itself as this is connected to light, time as well as space. A nice reference on this subject:Harvard study I might not be the expert needed, a generalist would be welcome here too for some general outline. What if the reader wants to know about gravitational blue shift ? Maybe some redirections should be changed ? Do I make a point ? --Homy 11:36, 5 August 2006 (UTC)

Nobody here, let's make some changes   --Homy 17:16, 7 August 2006 (UTC)


 * No, we shouldn't be trying to present this effect as somehow "belonging" to special relativity.
 * SR is a flat-spacetime, ~start-of-the-C20th theory, while gravity-shifts are usually reckoned to involve curved space(/time), and were suggested at the end of the C18th. The specific Doppler relationships referred to as "relativistic Doppler" are derived in modern relativity theory by assuming flat spacetime, and aren't neccessarily guaranteed to be correct when the geometry isn't flat. For instance, you don't often see the "relativistic Doppler" relationships mentioned in the context of cosmological redshifts, either ... if you ask about SR and Hubble shift, you'll likely be told that RD doesn;t neccessarily apply, because cosmological shifts are curvature-based, and are therefore a different class of problem. Similar objections could be applied to the "gravitational redshift" case, those are arguably curvature-based, too. ErkDemon 15:36, 16 September 2007 (UTC)

Deleting refs to Einstein shift, "Einstein effect"
I've removed a reference to "Einstein shift", since there are oodles of different effects that might reasonably be referred to as an Einstein shift. The term doesn't identify the effect, and is only intelligible is the reader already knows the exact context of the phrase. I'm sure that the phrase sometimes gets used in essays or lectures where the subject being discussed is already known, but it doesn't identify the subject. SR velocity redshift? SR transverse redshift? I don't think anyone will object to its loss. ErkDemon 00:36, 3 September 2007 (UTC)


 * I'm also deleting the sentence that says that this effect is sometimes referred to as the "Einstein effect" ... I'm sure it is, but there are probably 10-20 other effects that this loose phrase might refer to, covering anything from special relativity to general relativity to quantum mechanics, to the way that tealeaves move towards the centre of your teacup when you stir (seriously, Einstein wrote an excellent paper on that effect). Since the phrase doesn't seem to mean much unless the reader already knows which topic is being discussed, I'm hitting delete. Again, I'm assuming that nobody will object. ErkDemon 00:48, 3 September 2007 (UTC)

In the article it says that there must be a difference in gravitational fields to see a gravitational redshift.

Can Dark Matter cause redshift?
My understanding is that gravity can bend space. If a great mass passes in front of light could one see a redshift since the distance now is farther than it was? the speed of light should be constant but I think that it relatively has to go father in the same time. Is this correct?

Also if the above is correct. What would be the effect of mass that was spread over great distances. Where I am going with this is :

Could dark matter spread out over billions of light years cause a red shift in a star that is not moving away from us in absolute terms? The thought is that the amount of dark matter that the light passed through could have quite a bit of gravity. Thus making far away objects appear that they are moving farther away from us quicker than they actually are.

--Tommac2 —Preceding unsigned comment added by 69.249.66.67 (talk) 04:15, 22 March 2008 (UTC)


 * The simplest form of the gravitational redshift depends only on the difference in gravitational potential. So if a large mass is between you and a distant galaxy,  the light would be blueshifted when it approaches the mass, and then redshifted by the same amount as it exits from the mass, and the total result would be that there would be no net redshift.
 * Dark matter does have gravity, so it causes gravitational redshift to exactly the same extent that ordinary matter does.  Geoffrey.landis (talk) 02:26, 25 March 2008 (UTC)

Clarification please
In the article it states:

r is the radius of the star you consider.

Does that mean the star that produced the light or the star that produced the gravitational redshift? --Tommac2


 * I tried to clear it up a little. In the example, the star emitting the light is the same as the one that's redshifting the light.  In the example, r is the distance from the center of the star from which the light is emitted, but it was a little to complicated to rewrite it, so I just stated that r is the radius of the star. Geoffrey.landis (talk) 02:38, 25 March 2008 (UTC)

Is Something Amiss?
I am confused, not so much by what is stated in this article as by what is not. Nowhere in the theory is the redshift value, z, represented as being dependent upon the emitted frequency, f0. Yet if z is not dependent upon frequency, then a very simple mathematical model demonstrates that the resulting equation for predicting z should be exponential in form.

Suppose we set up a coordinate system with the x axis perpendicular to the earth’s surface. We place an observer at each of the points x1 and x2. Let d1 be the distance between x0 and x1. Let d2 be the distance between x1 and x2. A photon of frequency f0 will be emitted at x0. When it reaches x1, its frequency shall be f1; when it reaches x2, f2. Since over short distances the variation in g from x0 to x2 is negligible, we can consider g as a constant; and if the gravitational redshift is independent of frequency, we consider z = (f0- f1)/f1 as a function, F(d1), of the vertical distance traversed:

(f0 - f1)/f1 = F(d1).

Similarly, we obtain

(f1 - f2)/f2 = F(d2),

(f0 - f2)/f2 = F(d1 + d2).

Blending these equations so as to eliminate the fi, we get a functional equation F(d1 + d2) = F(d1) + F(d2) + F(d1) F(d2), whose only non-trival, continuous solution is

F(d) = (F(1) + 1)d - 1, or

f0/f1= kd.

This is the only solution that will predict gravitational redshift so that z is independent of frequency and the distance of separation between observers is additive. We can introduce b so that

f0/f1 = ebd.

To be linearly equivalent to current theory, as well as experimental results, b must have the value g/c2. Thus we end up with

f0 = f1 exp(gd/c2)

This result does not provide a reason for why the gravitational redshift occurs, but it does indicate the exact quantitative form for that redshift. If current principles do not yield such an equation, doesn’t that indicate something is amiss? Samdhatte (talk) 18:55, 24 June 2008 (UTC)


 * Your analysis is mathematically correct but it assumes that the gravitational field is constant, like at the surface of the earth. But in that case, it is misleading, because you are not taking into account the fact that the difference in frequency is small. When the frequency shift is small, an exponential dependence of the frequency on height is indistinguishable from a linear dependence.


 * When the frequency shift is large, like near the horizon of a black hole, the gravitational field is not constant in the way that is required for your argument to work. To simplify, your argument is noting that the shift in frequency is multiplicative, so that:


 * f(z) = R(z)f


 * Where R(z) is a function of height that obeys R(a+b)=R(a)R(b), meaning that the frequency shift after going up a+b is the product of the frequency shift going up a with the frequency shift going up b. That's saying that the frequency shift is multiplicative, which is true. Then you note that in the case where the frequency shift per unit length is constant, the dependence on height is going to be exponential, also true.


 * But when the shift is large enough so that an exponential dependence is distinguishable from a linear dependence, so that you can't use the approximation e^az = 1+az, then you are in a strong gravitational field region, and the naive notion of length and time are not appropriate. Then you need to use the full metric tensor to find the notion of length, and the notion of time in a static field, which determines the redshift, is the square root of the time-time component of the metric tensor.


 * The frequency shift in a static gravitational field when going from point a to point b is given by


 * $$ R(a,b) = {\sqrt{g_{00}(b)}\over \sqrt{g_{00}(a)} } $$


 * Which has the multiplicative property, as you required,


 * $$ R(a,b)R(b,c) = R(a,c) \,$$


 * But it depends on an arbitrary function $$g_{00}$$ of the position, so that the amount of shift per unit displacement is not constant as you move from point to point. The multiplicative property only tells you that the redshift factor from a to b, which a-priory could depend separately on both a and b, it could be an arbitrary function of two variables, is determined by $$g_{00}$$ which only depends on one variable. In the exceptional case that the gravitational field is constant in the sense that you define it, so that the redshift factor is the same per unit length, you would get an exponential dependence on height. But the solution with that property was only worked out relatively late, in the seventies or something. What people sometimes identify as a constant gravitational field is the uniformly accelerated metric, where the redshift factor per unit length is different from point to point, so that the field is not really uniform, appearing stronger to observers closer in to the location of the acceleration horizon.Likebox (talk) 20:54, 13 August 2008 (UTC)


 * Likebox’s gracious and thoughtful reply is greatly appreciated, and should be compelling. However, when  the mathematical model is changed so as to follow his suggestion, allowing g to vary along the photon’s path, the result still seems to be an exponential equation. Consider the following:   The origin of the x axis is positioned at the gravitational center of a plantary or stellar mass, and is molded to conform to the path of a photon fleeing perpendicular to the surface. The value of g = g(x) is now a function of position x, and (at least outside of the spherical mass) is given by k/x2, with k incorporating the gravitational constant as well as the relevant mass.
 * A photon of frequency f0 will leave position x0 and travel over the interval (x0, xn), with xn, temporarily fixed.  The interval between will be subdivided into numerous Δxi,   intervals, over each of which gi is nearly constant and the relationship below holds with a high degree of approximation..
 * fi-1 - fi = gi fi Δxi /c2.
 * Thus, summing up the equations for i = 1 to n, we have approximately
 * fn – f0 = - ∑ gi fi Δxi /c2.
 * which in the limit leads to the integral over the interval [x0, xn]
 * fn – f0 = - ∫ gfc-2 dx.
 * Replacing xn by the variable x and taking the derivative with respect to x of both sides produces the differential equation
 * f ’ = - g f / c2.
 * We can also write this as
 * f ’ = -kf/(c2x2).	     [1]


 * Scalar multiples of the expression exp(gx/c2) are easily confirmed as solutions to [1], whereas no linear expression for f is a solution.  Thus, for the constant g case and now using k as a different constant, we have
 * f = k exp(gx/c2)          and
 * f0 = k exp(gx0/c2),
 * from which
 * f/f0 = exp((x-x0)g/c2) = exp(gh/c2   [2]
 * as previously. When g is not constant,
 * f/f0 = exp( (gx - g0x0)/c2).		 [3]
 * The difference between [2] and [3] for earth bound experiments remains undetectible.  It is also readily acknowledged that the difference between linear and exponential predictions is below the  threshold of earth-bound experimental verification, although the mathematical and hence theoretical difference does persist.  Frankly that makes me uneasy.  My ideal is that theory should be unified, exact, and singular, with only the experimental confirmations thereto remaining approximate. It does not seem healthy to have contrary theories even if they closely approximate each other.  When such do exist, shouldn’t the one more mathematically consistent be preferred?  Nor can I understand why the above derivation would not work even for regions having very high g values.  Something still seems amiss.  What now?  (Samdhatte (talk) 16:55, 27 September 2008 (UTC))


 * The exponential dependence you find when following a photon's path parametrizing it the way you do will be reproduced in general relativity. You didn't need to go into so much detail in the derivations--- you are right: if you parametrize the x-coordinate so that it follows a single photon's path, then the frequency shift is going to be the integral of the local value of "g" along the photon path (with an arbitrary constant which just determines the redshift at the startpoint which is where the frequency shift factor is going to be 1):


 * log(Redshift factor) = (integral) G/cx^2 = - G/(c^2x) = - (phi/c^2)


 * In the small redshift limit, this is Einstein's approximation: g_00 = 1 - 2phi/c^2, where phi is the gravitational potential. The redshift factor is the square root of g_00, which for phi small compared to c^2 is 1-phi/c^2, and you reproduce your result. But, as you noted, this is all at small fields, where you reproduce the usual results. People know that it is an approximation (but for the Earth and the Sun, it's so good that there's no point in going further).


 * If you want, you can change the definition of the x coordinate so that the redshift factor is constant, so that g(x) is constant the way you like to phrase it. But if you calculate the new x coordinate that you get in terms of the old one, you will see that it is very unnatural: for the G/x potential of a regular point mass the new x coordinate will run off to infinity at a finite value of x. Nobody wants to use these kinds of coordinates. This is why General Relativity is phrased in a way that is independent of the coordinates, and this also makes it complicated.


 * I want to point out also that your analysis of the redshift as you follow photons along is very special--- it requires that there is a well defined notion of "redshift" at any point in space, meaning that the redshift that a photon after bouncing from a bunch of mirrors to get from point A to point B only depends on the start-point and the end point, not on when and how you do it. This is only true in a static gravitational field, which means a field from a mass which isn't moving, a field which doesn't change in time. This is a special case in General Relativity--- the general theory applies to time-dependent things too, where your analysis is not valid because the redshift depends on the time, not just on position.


 * The way people usually phrase the type of analysis you do within GR is: along a null geodesic (path of a light ray) the frequency of a photon is given by starting another geodesic a little later in time, and seeing how the two separate as they move along. If you state everything in this language, it will be easier because your arguments will fall into a more standard language, and it might clear up your uneasiness.


 * The intuition you have that exponential dependence of g is the most natural is correct and was shared by many people--- if you want to solve Einstein's equation for g in the static spherically symmetric case, then it is natural to parametrize the values of g like this (Weinberg does it this way, I think Schwarschild did too):


 * g_00 = e^\alpha
 * g_rr = e^\beta


 * and the reason things simplify when you write things exponentially is essentially the reason you give--- the exponential dependence of field is the most natural way to think of a constant gravitational field.Likebox (talk) 18:32, 27 September 2008 (UTC)


 * I appreciate the time you took for your kind and extensive reply. Thanks.  The reason I did not use the language you have suggested was because I did not know it.  Samdhatte (talk) 06:12, 10 February 2015 (UTC)

Lede image
This image has apparently been in the lede of the article since 2005, but I'm darned if I can see how it's supposed to represent gravitational redshift, even inexactly. It looks more like a new-age religious symbol than a scientific diagram to me. The image description page has no sources and no information about how it was calculated. Am I missing something? -- BenRG (talk) 14:19, 18 February 2009 (UTC)

Holey Moley
This is just the first paragraph of the article:

This article is in need of attention from an expert on the subject. WikiProject Physics or the Physics Portal may be able to help recruit one. (November 2008)

In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field. If applied to optical wave-lengths this manifests itself as a change in the colour of the light as the wavelength is shifted toward the red (making it less energetic, longer in wavelength, and lower in frequency) part of the spectrum. This effect is called gravitational redshift and other spectral lines found in the light will also be shifted towards the longer wavelength, or "red," end of the spectrum. This shift can be observed along the entire electromagnetic spectrum.

Light that has passed "downhill" into a region of stronger gravity shows a corresponding increase in energy, and is said to be gravitationally blueshifted.

Well, I'll be darned. It's in need of a lot less intensive reworking than that available from an 'expert' on the topic. Just look at the first paragraph:

'other forms of electromagnetic radiation'? What would those be? Sound waves? Winter boots?

'of a certain wavelength'? So at what wavelength is light no longer redshifted?

The grammar, clarity and thrust of this article obscure its very purpose. —Preceding unsigned comment added by 142.1.134.54 (talk) 22:53, 12 March 2009 (UTC)

Assessment comment
Substituted at 16:38, 29 April 2016 (UTC)

Rewrote first section
This article was quite nice in its original form as written by Chris Hillman in 2005 ( https://en.wikipedia.org/w/index.php?title=Gravitational_redshift&oldid=18056450 ), but seems to have suffered at the hands of less competent people in the years since CH left Wikipedia. I rewrote the first section, which in the recent version used cumbersome notation, belabored mathematical side issues, and didn't give even a sketch of the logical structure of the subject or where the formulas might have come from. This article is still in sorry shape and needs a lot more work. There is a lot of material that is disorganized and a lot that is written in an inappropriate style. I will bring back some of CH's nice descriptive material as well.--76.169.116.244 (talk) 18:27, 28 July 2018 (UTC)

Deleted two sections
I deleted the sections. The first, titled "Important points to stress," was unencyclopedic, disorganized and out of place, and it included some wrong physics (a claim that the Planck relation was relevant). The second, "Exact solutions," was largely irrelevant, disorganized, and contained incorrect physics (such as a claim that the black hole solutions are the only exact solutions to the Einstein field equations).--76.169.116.244 (talk) 18:36, 28 July 2018 (UTC)

Deleted two more sections
I deleted two more sections. One, titled "Application," consisted of a single value and uninformative sentence. The other, "Gravitational redshift versus gravitational time dilation," was logically muddled and uninformative section.--76.169.116.244 (talk) 18:39, 28 July 2018 (UTC)

Historical section
The historical section was a big block of dry historical and mathematical material that in my judgment would be of little interest to a modern reader who does not have a very strong interest in the grotty details of the early historical development of the theory. I've moved it down below the material on experimental tests. In my opinion this material should probably be deleted completely.--76.169.116.244 (talk) 18:43, 28 July 2018 (UTC)

Technical
I think a lot could be done to make this article more accessible to those of us who don't have higher math and physics degrees. I'll try to remember to come back to this article and not just tag and leave. 74.93.182.21 (talk) 15:04, 30 July 2018 (UTC)

Experimental Verification
Can we verify the referenc to 1971 in the below statement? The Hubble Space Telescope didn't exist until 1990.

"The redshift of Sirius B was finally measured by Greenstein et al. in 1971, obtaining the value for the gravitational redshift of 89±19 km/sec, with more accurate measurements by the Hubble Space Telescope, showing 80.4±4.8 km/sec." SquashEngineer (talk) 15:25, 29 July 2019 (UTC)

Disregard - I reread the sentence. SquashEngineer (talk) 12:56, 21 January 2021 (UTC)

doppler effect is caused by a speed (difference) not by acceleration
Thus I'm not following the reasoning in deriving the gravity effect on light by looking at an accelerated spaceship containing a light source vs. an free falling observer. Let's assume that the spaceship has a negative relative speed compared to the free falling ob server and accelerates toward him with a constant acceleration. When the spaceship has zero relative speed relative to the observer, there should be no doppler effect! I'm also not getting the argument, that light looses energy when leaving a gravity well (E=h*f), as a photon does not have mass. I could understand this, if the photon would have a mass -- like a bullet. A bullet certainly looses energy when shoot straight up in a gravity field. I understand, that once one accepts that a photon looses energy when climbing out of a gravity field, one can derive that space is curved, given that the scalar product of a 4 vector must be identical for different observers! Please help me with above question! — Preceding unsigned comment added by AchWasSoSo (talk • contribs) 23:31, 20 September 2019 (UTC)

OK -- I found the answer at https://physics.stackexchange.com/a/86956 Mass is equivalent to energy and thus one can derive a mass from the photons energy: E=m*c^2=h*f A mass looses energy when dropped in an gravitational field: E=m*g*deltaY. One can derive the 'equivalent' mass from the first equation, use it to derive the change of energy by lifting/dropping this mass in a gravitational field and then derive the new frequency of the light. m=h*f/c^2. deltaE = h*f/c^2*g*deltaY=h*deltaF. deltaF = f/c^2*g*deltaY. voila! — Preceding unsigned comment added by 2605:6000:101B:8650:5C6F:D38C:62E8:B695 (talk) 20:37, 21 September 2019 (UTC)

Importance of Schwarzschild metric
Suggestion: Since the Schwarzschild metric is the foundation of gravitational redshift computations for spherical bodies, it should be shown in full:

ds2=(1-2Gm/c2r)dt2 - (1-2Gm/c2r)-1dr2 - r2d&Omega;2

71.32.47.34 (talk) 21:40, 19 March 2020 (UTC)Kathleen Rosser

Schwarzschild first, equivalence principle second
The introductory paragraph is good. But the next section seems to be in the wrong order. It is confusing to read about the equivalence principle first and the Schwarzschild metric second. The standard method for calculating the gravitational redshift of spherical bodies utilizes the Schwarzschild metric. This should be shown first. The equivalence principle method is an approximation, and is of historic and heuristic interest only. It should be shown second. 71.32.47.34 (talk) 22:17, 19 March 2020 (UTC)Kathleen Rosser

Tenacious blueshift
A photon falling into a gravity well is blue shifted, no argument. Suppose the photon has zero energy mass, is it still blue shifted? Why not? The upshot is that gravity wells generate a constant supply of energy mass, the equivalent to that lost in inter massive space, to tenacious red shift. If this were not the case, energy mass would either overwhelm or underwhelm the Universe. This means stars can burn forever because we can abandon the fusion bonfire theory of stellar heat. Earth's interior, for instance, is heated by the same process. GuildCompounder (talk) 03:32, 6 July 2022 (UTC)


 * To clarify, a particle of energy mass can move from a compressed space to a decompressed space and redshift that way, or the space around the particle can decompress for the same effect (which I call tenacious since the particle need not move). Mass generates a compression field, which compresses space within the mass, and decompresses space radiating without the mass.  The Doppler effect is null. GuildCompounder (talk) 02:59, 12 July 2022 (UTC)

Illustration of redshift
The illustration of the gravitational redshift is very misleading. There is no observer who will judge a frequency of something travelling up in a gravitational potential to decrease due to GR. If a supply rocket leaves the ground once a week, a rocket will arrive once a week at the space station. But the astronauts on the space station will judge the frequency to be lower (e.g. take-offs and arrivals once per month in an extreme case) than the frequency judged by the ground staff (once a week). As a consequence, nobody will "see" an electromagnetic wave leaving the ground with a higher frequency than at some height. The entire wave looks red when viewed from the top and blue when viewed from the bottom. 147.147.166.106 (talk) 12:27, 9 August 2022 (UTC)