What is Gravitational redshift: Definition and 47 Discussions

In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is that phenomenon in which electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, known as a redshift. The opposite effect, whereby photons (seem to) gain energy when travelling into a gravitational well, is known as a gravitational blueshift. The effect was first described by Einstein in 1907, eight years before his publication of the full theory of relativity.
Gravitational redshift can be interpreted as a consequence of the equivalence principle (that gravity and acceleration are equivalent and the redshift is caused by the Doppler effect) or as a consequence of the mass-energy equivalence ('falling' photons gain energy), though there are numerous subtleties that complicate a rigorous derivation. A gravitational redshift can also equivalently be interpreted as gravitational time dilation at the source of the radiation: if two oscillators (producing electromagnetic radiation) are operating at different gravitational potentials, the oscillator at the higher gravitational potential (farther from the attracting body) will seem to ‘tick’ faster; that is, when observed from the same location, it will have a higher measured frequency than the oscillator at the lower gravitational potential (closer to the attracting body).
To first approximation, gravitational redshift is proportional to the difference in gravitational potential divided by the speed of light squared, thus resulting in a very small effect. Light escaping from the surface of the sun was predicted by Einstein in 1911 to be redshifted by roughly 2 ppm or 2 × 10−6. Navigational signals from GPS satellites orbiting at 20,000 km altitude are perceived blueshifted by approximately 0.5 ppb or 5 × 10−10, corresponding to an increase of less than 1 Hz in the frequency of a 1.5 GHz signal. Accounting for the accompanying gravitational time dilation affecting the atomic clock in the satellite is however crucially important for accurate navigation.
In astronomy, the magnitude of a gravitational redshift is often expressed as the velocity that would create an equivalent shift through the relativistic Doppler effect. In such units, the 2 ppm sunlight redshift corresponds to a 633 m/s receding velocity, roughly of the same magnitude as convective motions in the sun, thus complicating the measurement. The GPS satellite gravitational blueshift velocity equivalent is less than 0,2 m/s, which is negligible compared to the actual Doppler shift resulting from its orbital velocity. In astronomical objects with strong gravitational fields the redshift can be much greater; for example, light from the surface of a white dwarf is gravitationally redshifted on average by around 50 km/s/c.Observing the gravitational redshift in the solar system is one of the classical tests of general relativity. Measuring the gravitational redshift to high precision with atomic clocks can serve as a test of Lorentz symmetry and guide searches for dark matter.

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  1. cianfa72

    I Time dilation vs Differential aging vs Redshift

    Hi, I would like to ask for a clarification about the terms time dilation vs differential aging vs gravitational redshit. As far as I can tell, time dilation is nothing but the rate of change of an object's proper time ##\tau## w.r.t. the coordinate time ##t## of a given coordinate chart (aka...
  2. I

    B Could you use LIGO-technology to measure gravitational redshift?

    Don't know if this is the right forum, but I'll give it a try: If you build a bridge over a gorge that's a couple km deep the middle of the bridge would be as far away from the mountains on both sides as possible (and therefore as far away from the mountains' gravitational field as possible)...
  3. E

    I Calculation of gravitational redshift in an accelerating elevator

    When we derive the formula of the redshift by the equivalence principle we imagine a light ray which goes from the bottom to the top of the elevator and which would take a duration t = h/c to make the journey, with h = height of the elevator. I don't understand why t = h/c, because while the ray...
  4. SH2372 General Relativity - Lecture 11

    SH2372 General Relativity - Lecture 11

    0:00 Perihelion precession of Mercury 17:15 Bending of light 24:48 Shapiro delay 33:32 Pound-Rebka experiment 41:40 Spectral lines of stars 44:58 Gravitational waves 49:22 Other important effects
  5. SH2372 General Relativity - Lecture 7

    SH2372 General Relativity - Lecture 7

    0:00 Gravitational time dilation 12:06 Gravitational redshift 14:43 Dynamics of spacetime 34:17 Matter in spacetime 51:07 The stress-energy tensor 1:03:00 Ideal fluids
  6. GeniVasc

    I Wavelength of Light Ray Affected by Gravity

    I was reading Einstein's 1911 paper named "On the Influence of Gravitation on the Propagation of Light" when stated the formula for frequencies measured by observers at different fixed positions (heights) on Earth surface. One observer is at the origin of some coordinate system and measures a...
  7. Z

    I Gravitational Redshift: Units, Velocity & Ratio Explained

    I noticed in physics papers that gravitational redshift is expressed in m/s or km/s. I assume that this must be the equivalent velocity to produce that same redshift. So for example, if the gravitational redshift was measured as 3x10 ↑ -4 then; z= v/c 3x10^-4= v/c v = 9x10^4 m/s v=90km/s...
  8. A

    A How deep in a gravitational well are we?

    As proven experimentally clocks tick slower deep in a gravitational well and the difference in energy levels between atomic/molecular quantum state also becomes smaller deep in a gravitational well. This is sometimes known as "gravitational time dilation" and "gravitational redshift" I think...
  9. Arman777

    B Gravitational Redshift and its effects on Photon

    Let us assume that we have a large gravitational field, then the gravitational redshift can be expressed as, $$\frac {v_{\infty}} {v_e} = (1-r_s/R_e)^{1/2}$$ In this equation ##v_{\infty}## represents the frequency of the light measured by an observer at infinity, ##v_e## is the frequency of...
  10. T

    B Gravitational Redshift: Will Two Lasers Operate Differently?

    If we run two identical lasers and put one at sea level and one on top of a high mountain, will they operate at different frequencies?
  11. redtree

    I Gravitational Redshift: Derivation from Static Metric

    I am trying to find a derivation of gravitational redshift from a static metric that does not depend on the equivalence principle and is not a heuristic Newtonian derivation. Any suggestions?
  12. FallenApple

    A Gravitational Redshift in Newtonian Equivalence Principle?

    So I was reading that the equivalence principle of Newton doesn't work because of a thought experiment. They said that an experimenter shoots bullets( 1 per second) from the bottom of the elevator to the top. This happens in outerspace where the elevator moves up with accleration g. And this...
  13. J

    Why doesn't the vertical light beam get out of a black hole?

    For this we need a thought experiment: imagine you're on a gedanken planet manning a gedanken laser cannon, and it's pointing straight up. The light doesn't curve round, or slow down as it ascends, or fall down. It goes straight up. Now let's keep you safe in a bubble of artistic licence, and...
  14. U

    Redshift in Frequency - Universe

    Homework Statement (a) Show the relation between frequency received and emitted (b) Find the proper area of sphere (c) Find ratio of fluxes Homework EquationsThe Attempt at a Solution Part (a) Metric is ##ds^2 = -c^2dt^2 + a(t)^2 \left( \frac{dr^2}{1-kr^2}+ r^2(d\theta^2 + \sin^2\theta)...
  15. Q

    Measuring Gravitational Redshift due to Galaxies without GR

    Hi guys. How do astrophysicists measure the redshift of electromagnetic waves from galaxies due to gravity without the use of General Relativity? If I can be more specific, how do astrophysicists know that the gravitational redshift of light emitted from some part of a galaxy or galaxy cluster...
  16. 2

    Deriving Gravitational Red Shift: Questions & Answers

    I am trying to derive the gravitational red shift effect but I think I am going about it all wrong. Specifically, I want to derive the change in frequency/ wavelength when a photon moves away from the surface of a star mass M and radius R. So I tried to use relativistic mass of the photon and I...
  17. B

    Gravitational red- or rather blue-shift when approaching Schwarzschild radius

    I found http://physicspages.com/2013/05/05/schwarzschild-metric-gravitational-redshift/: \frac{\lambda_R}{\lambda_E} = \sqrt{\frac{1-2GM/r_R}{1-2GM/r_E}} where the indexes R and E are for receiver and emitter respectively, and the speed of light is normalized to 1. Most other sources on the...
  18. aditya ver.2.0

    Gravitational Redshift: Exploring Frequency and Light Changes in G-Fields

    Is the change in frequency an actual change or is it like the Doppler effect? Does the speed of light also change in a g-field?
  19. E

    Gravitational redshift with time dilation?

    Hello, thanks for reading this. I need help trying to find a way to calculate the time dilation due to gravity, from a satellite 50,000km above the surface of the Earth, traveling 10,000km/h relative to a stationary observer on Earth. A signal is being sent from the satellite to the observer...
  20. P

    Gravitational Redshift and Hubble.

    Hey guys, I feel like an idiot for asking this. However, I wanted to make sure that my head was screwed on straight before I asked my old astronomy professor permission to use some of his old lecture notes. Is gravitational redshift one of the causes of Hubble's Law? Is the Redshift of the...
  21. S

    Derivation of gravitational redshift: Mass of a photon?

    This is not exactly a homework question. In a physics textbook, they derive an expression for gravitational redshift of a photon emitted by a star at a large distance from the source by taking photon as a mass traveling up, against a gravitational potential and hence expending its...
  22. 7

    Gravitational redshift inside a crystal - Pound-Rebeka experiment

    Homework Statement Some atoms emit X-rays at transition from excited to ground state. Energy of an excited state of the atom ##\scriptsize^{57}_{26}\textrm{Fe}## is ##\scriptsize14.4keV## larger than than the energy of it's ground state. The mass of the atom is...
  23. C

    General Relativity gravitational redshift

    Homework Statement The gravitational redshift tends to decrease the frequency of light as it travels upwards a distance h,\frac{\Delta{f}}{f_{0}}=\frac{-gh}{c^2} integrate both sides of this equation (from the surface of the gravitation body out to infinity) to derive the expression for the...
  24. C

    Question about gravitational redshift

    Here's my question first: If radio waves are transmitted from earth, are they actually redshifted, or is it that they appear redshifted when measured by an identical clock in space? Here's where I'm coming from. I'm trying to reconcile things I know. I think I know that (1) clocks further...
  25. MikeGomez

    Gravitational redshift question

    A photon emitted from a star with a large mass (strong gravitational field) will be redshifted more than a comparable photon emitted from a star with a weaker gravitational field (comparable meaning the two photons would otherwise be expected to have exactly the same values in both cases, i.e...
  26. T

    Gravitational Redshift really verification of GR?

    If we assume: E = mc^{2} and for photons: E = hv Then we can derive an effective mass: m = \frac{hv}{c^{2}} And using simple classical gravity obtain: hv - \frac{GMm}{r} = hv - \frac{GMhv}{c^{2}r} = Constant You can derive the constant by evaluating the equation above at...
  27. TrickyDicky

    Gravitational redshift, energy and the EP

    It is common knowledge that of the classical tests of GR, gravitational redshift is normally considered to be testing the Equivalence principle and conservation of energy rather than the full GR theory. So it is considered a more fundamental test of our basic principles of GR and physics in...
  28. C

    Question about the GR gravitational redshift experiment

    GR predict that a photon climbing in the Earth's gravitational field will lose energy and will consequently be redshifted. A test was done by Pound and Snider in 1965 using the Mossbauer effect They measured the redshift experienced by a 14.4 Kev rays from the decay of Fe in climbing up...
  29. B

    What is the formula for gravitational redshift and its time derivative?

    Gravitational redshift formula Hi, I am looking for the formula that describes the gravitational redshift as frequency2 = function(frequency1, radius1, radius2, gravitating_mass) What I find on the net is http://www.wolframalpha.com/input/?i=gravitational+redshift+from+r1+to+r2" the...
  30. TrickyDicky

    Gravitational redshift from doppler shift

    Hi, I'm interested in the derivation of the gravitational redshift formula from the Doppler shift in an accelerated frame formula (or viceversa), that are linked by the Equivalence principle, it should be pretty straightforward but I get stuck. Anyone can show me this or point me to a link with...
  31. stevenb

    Exploring Historical Context of GR Predicted Gravitational Redshift

    I was just reading the old document by H.A. Lorentz " The Einstein Theory of Relativity" which is freely available in ebook and text format. I find it interesting to read some of the comments from those times, and Lorentz provides a nice summary of the thoughts of the days soon after a second...
  32. Z

    Gravitational redshift equation

    Gravitational redshift is given by the following approximate equation; \frac{\lambda}{\lambda_o} = 1 - \frac{GM}{r c^2} From http://scienceworld.wolfram.com/physics/GravitationalRedshift.html Where \lambda is the shifted wavelength and \lambda_o is the rest wavelength. r is...
  33. M

    Is gravitational redshift taken into account in Hubble's Law?

    From what I understand: 1. The more massive the object, the stronger the gravitational field. This leads to the light being emitted from the surface to shift down in frequency. 2. The rate of expansion of the universe causes a redshift proportional its distance away. I'm new to this, but...
  34. A

    Expansion redshift VS gravitational redshift?

    While objects closer to us tend to shift both in direction red or blue, depending on their movement in relation to us, distant objects such as galaxies tend to only shift to the red. As I understand this is the base of the idea that the universe is expanding. But how are we sure that is the...
  35. N

    Gravitational redshift and time dilation

    It seems quite common to more or less equate gravitational redshift to gravitational time dilation. For example, the two might be explained as follows. We have two observers. A is standing on the surface of the earth, B on the top of a tower. A sends light up to B with some frequency, B...
  36. Z

    Gravitational redshift and time dilation

    Gravitational redshift seems to be measured as if gravitational time dilation has no effect upon it. What effect if any does gravitational time dilation have on the measurement of gravitational redshift?
  37. R

    Gravitational Redshift for Photon around Kerr Black Hole

    I have a hopefully straightforward question. It is well known that in the Schwarzschild metric the gravitational redshift is given by 1+z=(1-r_{s}/r)^{-1/2}. Clearly this is just the ratio of observed to emitted frequencies (or energies). I understand this so far. However, for the case of the...
  38. E

    What causes the gravitational redshift phenomenon?

    The item of gravitational redshift in the WIKIpedia says that this redshift is referred to the light of others forms of electromagnetic waves. This puzzles me. Other waves except electromagnetic waves have not this phenomenon, like sonic wave ? Is the gravitational redshift a result of...
  39. N

    Gravitational redshift and black holes

    Questions: Gravitational redshift and black holes I have some questions: 1. What does gravitational redshift do to light trying to escape a black hole? Is the light destroyed? 2. And what is the physical cause of this redshift? (I’m not interested in equations and math, only the physical...
  40. M

    Gravitational Redshift: Exploring Effects of Time & Space

    Based on the quote below and the link to Wikipedia, I believe the implication is that gravitational redshift will occur when a photon climbs out of the gravity well, while blueshift will occur when falling into the gravity well. However, I am trying to clarify whether both time dilation and...
  41. C

    Deriving gravitational redshift using the energy change approach

    An extremely elementary question but... Lets say we had a spaceship sitting on Earth under the influence of gravity. Light travels from the ship's floor to the ceiling. An observer 'A' stands near the ceiling. Hence the light loses gravitational potential energy, and therefore decreases...
  42. T

    Gravitational Redshift Contribution to Quasar Redshift: Explaining Hubbles Law

    Does anyone know how much percentage of the total redshift of a quasar is contributed by Gravitational redshift considering light from the Quasar is emitted by heavy active galactic nuclei ? If there is a significant contribution from gravitational redshift then how will the Hubbles law hold...
  43. N

    Correct formula for gravitational redshift

    Based on general relativity (see book Gravity; an introduction to Einstein's General relativity by James B. Hartle), the frequency of light (emitted at R) is modified by the factor SQRT (1 - 2 G M / c**2 R) (see page 191). On the other hand, based on the equivalence principle, one arrives at...
  44. M

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

    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...
  45. V

    Gravitational redshift +blackbody spectrum

    Hi, How can I prove that gravitational redshift preserves the characteristic shape of a blackbody spectrum?
  46. T

    If light experiences gravitational redshift as said by GR

    If light experiences gravitational redshift as said by GR, then, where did the difference between the initial and final energy, E = \frac {hc}{\lambda} go? From Hubble expansion, there is also redshift. Where did the energy difference go?
  47. O

    Gravitational Redshift: Exploring a Theory with Physics

    Having only just learned of the existence of this board I feel that I should make use of it as i spend most of my free time working on seemingly useless theories, might as well see what others think. I have read a little on gravitational redshift but have never really understood the theory...