What is Gravitational time dilation: Definition and 113 Discussions

Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational potential increases (the clock getting away from the source of gravitation). Albert Einstein originally predicted this effect in his theory of relativity and it has since been confirmed by tests of general relativity.This has been demonstrated by noting that atomic clocks at differing altitudes (and thus different gravitational potential) will eventually show different times. The effects detected in such Earth-bound experiments are extremely small, with differences being measured in nanoseconds. Relative to Earth's age in billions of years, Earth's core is effectively 2.5 years younger than its surface. Demonstrating larger effects would require greater distances from the Earth or a larger gravitational source.
Gravitational time dilation was first described by Albert Einstein in 1907 as a consequence of special relativity in accelerated frames of reference. In general relativity, it is considered to be a difference in the passage of proper time at different positions as described by a metric tensor of space-time. The existence of gravitational time dilation was first confirmed directly by the Pound–Rebka experiment in 1959, and later refined by Gravity Probe A and other experiments.

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  1. cianfa72

    I GPS system and general relativity

    Hi, we had a thread some time ago about GPS satellite system. One starts considering the ECI coordinate system in which the Earth's center is at rest with axes pointing towards fixed stars. One may assume it is an inertial frame in which the Earth's surface undergoes circular motion. Clocks on...
  2. Vick

    I What are the effects on a stationary observer for Kerr metric?

    A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm = \frac{r_S \pm \sqrt{r_S^2 -4a^2}}{2}$$ where ##a=\frac{J}{Mc}## and ##r_S## is the Schwarzschild radius. My question is, suppose I'm in a spacecraft, not in orbit, but stationary at a distance ##r##. I...

    B General Relativity & Grav. Time Dilation Qn

    hello I'm korean high school student and sorry for my poor English. I saw ## t_0=t_f\sqrt{1 -\frac{ 2GM}{rc^2}} ## in wikipedia. does ## \sqrt{1 -\frac{ 2GM}{rc^2}} ## of this equation have name like lorentz factor ## \frac{1}{\sqrt{1 -\frac{v^2}{c^2}}} ##of ## t=\frac{t_0}{\sqrt{1...
  4. 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
  5. I

    I Kinetic vs Gravitational Time Dilation: Perceived Speed

    As an object approaches a black hole’s event horizon, it experiences increasing gravitational time dilation, causing it to appear to an outside observer to slow down, until, at the event horizon, it appears to stop. An object traveling in space that increases its velocity from one...
  6. Buckethead

    B Clocks Vanishing into Thin Air - Gravitational Time Dilation

    With regard to relativity of simultaneity and the "block" universe and reflecting on the notion of skewed time slices associated with frames moving relative to each other, one observer sees one event a distance away (parallel to the direction of motion) occurring before another event a distance...
  7. Guillermo Navas

    I Thorne's error in explaining gravitational time dilation

    In Box 2.4 of the book "Black Holes & Time Warps" by Kip S. Thorne, he explains gravitational time dilation using the equivalence principle. For this he uses an experiment thought analogous to the one used by Einstein in 1911 to postulate the existence of a gravitational Doppler shift, but...
  8. J

    I Gravitational time dilation using an accelerating light-clock

    I've been trying to understand gravitational time dilation by considering a light-clock of length ##l## undergoing an equivalent acceleration ##a## from rest along the direction of the bouncing light pulse. I find that the time ##t## that the light pulse takes to travel to the forward receding...
  9. Chris Miller

    B Gravitational Time Dilation in L1 Point: Summed, Canceled or Else?

    In the Lagrangian (L1) point between two hypothetically massive (and close) objects , is gravitational time dilation effect summed or canceled, or something else?
  10. B

    I Issue With Derivation of Gravitational Time Dilation

    Why do we use the equation ##\frac {1}{2}mv^2 = \frac {GmM}{r}## to derive potential velocity, and then put that in the Lorentz factor in order to derive gravitational time dilation? Shouldn't we be using the relativistic definition of kinetic energy -> ##mc^2(\gamma - 1)## to derive the...
  11. 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...
  12. Z

    I Gravitational Time Dilation: Radius & Clock Rate Variation Explained

    (Apologies I posted this initially as a conversation. Not familiar with the format) I used the ‘gravitational time dilation’ equation to see how the clock rate varies with distance from the center of an object. I got the opposite result to what I was expecting.From Wikipedia; Gravitational...
  13. P

    B Does Gravitational Time Dilation Affect How We Measure Time on Earth?

    So I know gravity correlates with time dilation. If you have two individual equal size black holes close to each other, then at a point between them, gravity is equal to zero. Would the time dilation at that point be a sum of each individual black holes gravity or would the two time dilation...
  14. J

    B Can gravitational time dilation explain the photon's deflection near the Sun?

    For a photon passing close to the Sun, Newtonian physics predicts a deflection of 0.85o. GR gives the correct 1.7o. Can the true value alternatively be obtained via 1) a Newtonian model, and 2) gravitational time dilation: the photon's slower speed near the Sun leads to it spending more time in...
  15. K

    I Gravitational time dilation derivation

    If a beam of light is shot from a fast space ship, it travels a distance c*t1 according to their reference frame. The same beam of light seen from an outside observer goes at an angle and travels a distance c*t2. The distance the spaceship travels is equal to v*t2. Using the triangle made from...
  16. J

    B Gravitational Time Dilation: Math Formula for Clock-Slowing Factor

    What is the mathematical formula for the time dilation (clock-slowing factor) for a clock in a gravitational field g, equivalent to the Lorentz factor γ for a clock traveling at a relative speed v?
  17. P

    I Gravitational time dilation - acceleration vs potential

    What I know gravitational time dilation (based on GRT) is dependent on gravity potential and not on gravitational acceleration. That would mean, that for example in center of Earth is the gravitational acceleration zero, but the gravitational potential is bigger than on the surface of Earth...
  18. S

    I C Speed, Gravitational Time Dilation & 4-Velocity

    Hi 1-)If an object's total velocity through space-time(four-velocity)is c, for example even we stand still we move with velocity c (through time) and if mass slows down time, can we say mass also increase our velocity in space? 2-) Is Four-velocity magnitude constant in General Relativity...
  19. U

    I How does gravitational time dilation work?

    I understand time dilation due to speed, but am confused on why time dilates depending on the distance from a mass. Help?
  20. B

    I Clock hypothesis, gravity time dilation and Equivalence Principle

    1. The Clock Hypothesis states that the rate of a clock does not depend on its acceleration but only on its instantaneous velocity. This has been experimentally verified at very high accelerations. 2. A clock in a gravitational field experiences time dilation and runs slower that one not in a...
  21. H

    I Gravitational time dilation in Weinberg's "Cosmology"

    I have a question about the gravitational time dilation explained in Appendix B of the book "Cosmology" written by S. Weinberg. Why can the author say "In the negative gravitational potential at the surface of a star clocks therefore tick more slowly than in interstellar space, or in the much...
  22. haushofer

    I Gravitational time dilation, proper time and spacetime interval

    Dear all, I'm having confusion about the standard derivation of Schwarzschild's gravitational time dilation. For concreteness I'll follow the explanation of Schutz' "gravity from the ground up", but other texts argue the same. So let me rephrase Schutz's explanation (I surpress factors of c in...
  23. PeterDonis

    A Does gravitational time dilation imply spacetime curvature?

    In a recent thread, the question came up of whether the presence of gravitational time dilation implies spacetime curvature. My answer in that thread was no: This was based on the obvious counterexample of observers at rest in Rindler coordinates in flat Minkowski spacetime; two observers at...
  24. D

    I Gravitational time dilation near Earth

    We know (measured) that a clock on a mountain "ticks" faster than a clock at sea level. At higher altitude, the clock runs even faster. Now, if we go much higher, towards the Sun, on the line between the center of the Earth and the center of the Sun, the clock should begin, at some point, to...
  25. A

    I Gravitational time dilation calculation near a Black Hole

    Hello to everyone! I am trying to understand in practice the Gravitational Time Dilation by calculating the time distortion near the supermassive black hole Sgr A* in our Galactic Center. According to Einstein's Theory of General Relativity, the time distortion near a black hole is calculated...
  26. G

    B Does gravitational time dilation cause gravity's attraction?

    Physics Videos by Eugene Khutoryansky (a widely respected channel) recently posted a video on YouTube suggesting this. I know that gravitational fields cause time dilation (with time passing more slowly the closer an object is to the centre of gravity, relative to more distant observers), but...
  27. T

    B Gravitational time dilation depth charge

    Hi. A student wishes to test gravitational time dilation near a black hole within her lifetime, so she travels to a location where a black hole is said to reside and parks her ship at distance where she is not affected by the hole's time dilation effects. She then fires a tethered capsule...
  28. M

    B Calculating Mass for Gravitational Time Dilation

    Hello all. I'm trying to determine the mass of an object required to make it so that a traveler on a massive planet experiences 1 day but on earth, or some infinitely distance away from the planet, 1000 years passes by. I'm using the following equation: t0 = tf*root(1-(2GM/rc^2)) Found here...
  29. E

    I How does gravity affect time on different planets?

    If a planet has gravity that is 3,000 m/s^2 instead of 9.8 m/s^2, would time passage be significantly different, or what would one second on Earth be compared to one second on that planet?
  30. G

    B Magnitude of gravitational time dilation

    Hello, I am wondering how is the magnitude of the time dilation in a gravity field related to the time dilation we know from special relativity. How does the dilation caused by just being in the field compare to the dilation you'd have from your velocity if you fell into the gravity field from...
  31. J

    Gravitational Time Dilation Problem

    Homework Statement A person lived 75 years in a city located 3.1km above sea level. How much longer could they have lived at sea level? (Times are measured by an observer at infinite distance). Homework Equations tr/t∞ = {1 - [ (2GM) / (r(c^2)) ]}^(1/2) Rc (Radius at city) = Rearth + 3.1km...
  32. Erland

    Gravitational time dilation, how much?

    OK, I could probably find the answer of this simple question somewhere, but... If an astronaut stays on space station, in a weightless state, for 30 years, how much older does he/she become compared to a person who stays on the Earth all the time? I think it is about one second. Am I...
  33. W

    Confusion about the gravitational time dilation formula

    Homework Statement I'm reading the book Relativity, Gravitation, Cosmology by Ta-Pei Cheng. I'm in the part where he derived the gravitational time dilation formula for static gravitational field, τ1=[1+(Φ1-Φ2)/c2]τ2. This implies that clocks at a higher gravitational potential will run...
  34. Warfen

    Gravitational Time Dilation & Orbits of Objects

    For example if there were two objects orbiting each other and one was much heavier than the other, for instance a dwarf star and a neutron star. Would the lighter object have a greater gravitational pull than it's mass would say it should because it's pull was operating longer on the heavier...
  35. H

    Gravitational Time Dilation: A Layman's Explanation

    I think I have a layman's understanding of time and length contraction. However, I don't really understand gravitational time delay or distance contraction. If we were to put two clocks at the front and end of a rocket, the one on the top would experience time more quickly than would the one on...
  36. W

    Time Dilation & Acceleration: Leaving Earth Effects

    Leaving Earth at constant acceleration will make time on board go slower. Acceleration will take the ship closer and closer to c Question is: How long will acceleration act on the ship? The time as measured on Earth or on the ship? The final v will be greatly different. Of course, given enough...
  37. P

    B Do Gravitational Time Dilation and Redshift Contradict Each Other?

    Timedilation seems clear when you study special relativity and read about the Hafele-Keating experiment. Gravitational redshift seems logical when you assume that light should lose energy when it is leaving a gravitational field. But the two seem to be contradictory to each other. Question 1...
  38. J

    Relationship between gravitational time dilation and energy?

    The rate that a stationary clock slows down near a massive object, relative to one far away, can be read off from the Schwartzschild metric: $$c^2d\tau^2=\left(1-\frac{r_s}{r}\right)c^2dt^2-\left(1-\frac{r_s}{r}\right)^{-1}dr^2-r^2\left(d\theta^2+\sin^2\theta d\phi^2\right)$$ by setting...
  39. M

    Gravitational Time Dilation at Event Horizon

    According to Wikipedia, the gravitational time dilation formula is given by t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}} = t_f \sqrt{1 - \frac{r_0}{r}} where t0 is the proper time between events A and B for a slow-ticking observer within the gravitational field, tf is the coordinate time between...
  40. R

    Question About Gravitational Time Dilation

    According To Einstein's Relativity. Supposing a Man Went To Another Planet That Has a Gravity More Than Earth Hundreds Of Time Which Means That Time Is Too Slower There Than Earth. If We Say That 1 Hour In That Planet Is 10 Years On Earth And He Stayed 2 Hours There Will He Comeback To Earth...
  41. SpiderET

    Some easier equotation for gravitational time dilation?

    Im looking for some easy equotation which would help me to make graph of time dilation depending on gravity expressed not in relation to Schwarzschild radius but simply and directly to gravitational acceleration. I would like to get some easy graph similar to this...
  42. S

    Do gravitational time dilation effects cancel out or add up?

    If we use one gravitational field in GR and try to desribe it, we will see that from the perspective of the observer on the centre of mass of the object the clock on the hovering observer (farther away from the gravitational field) runs faster, while from the hovering observer's perspective the...
  43. Einstein Devotee

    Time dilation why or how, Special Relativity causes

    I understand the theory of special relativity and the mathematics which support it. I even understand that the time dilation has been proven. Therefore I am going to ask a question which on first blush may appear that I disagree with it but that is not the case. The question I can not seem to...
  44. W

    Exploring Gravitational Time Dilation & Event Horizons

    I want to ask a question about science/physics. To me and my level of education, this has not been answered, though I am sure there is someone out there that can provide the answer. It regards something I have been pondering due to gravitational time dilation (and space dilation I suppose, if...
  45. O

    Gravitational Time Dilation: Observing Planet Life

    Hello , my question is : If we could observe a planet life so far away from the Earth with so much gravity that it makes time pass more slowly on that planet , what would we see? Like what can we say about motions of lifeforms living on that planet? Would they be moving in slow-motion in the...
  46. M

    Does gravity have a similar effect on energy as it does with time?

    I've been doing some recreational physics and wanted to see if I could come up with a formula for energy/time equivalence. I decided to start with the formula for gravitational time dilation. $$ y=Z\sqrt{1-(2GM/rc^2)} $$ This formula shows what time would look like to an outside observer...
  47. 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...
  48. S

    Gravitational Time Dilation and Age of Astronaut

    Hello Everyone, I am new to this forum. I understood from sources that space-time is like a fabric. The massive bodies bend the space around it, hence the gravity. If time is 4rth dimension, so, the space is bent in time due to mass. that pretty much explains stopping of time in black holes as...
  49. J

    How Does Gravitational Time Dilation Affect Human Physiology and GPS Technology?

    Hi people, please could someone enlighten me on gravitational time dilation. I have read online that some places, such as neutrons stars, warp time so much that time can pass 100 times slower than it does on Earth. I was just thinking about a human heart beating. If a healthy heart rate on Earth...
  50. GeorgeDishman

    Gravitational time dilation for a spherical body of finite radius

    I am considering the gravitational time dilation at the centre of a spherical, non-rotating body (such as the Earth). The usual formula for gravitational time dilation is √(1-r_s/r) where r_s is the Schwarzschild Radius and r is the radius of the clock compared to one at infinity, however, this...