Talk:Gravitational time dilation

Time dilation at the surface of the sun
How is the 66.4 seconds calculated? I got 66.9 seconds when I set r, the radial coordinate of the observer, to be ON the surface of the sun next to the proper time clock! But shouldn't the observer be very far away from the proper time clock? 2003:E5:1F0C:3685:D3C:A7B8:74AA:8477 (talk) 05:44, 4 July 2023 (UTC)

gravitational potential
Fisrt line in the article:

"Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential (closer to the center of a massive object), the more slowly clocks run."

This does not tally with the fact there is no gravitational potential the centre of a massive object. There seems to be a confusion about whether time dilation is caused by gravity i.e. curvature in space-time, or dilation in space-time, which is highest at the centre of a massive object. —Preceding unsigned comment added by 79.70.197.119 (talk) 07:47, 18 March 2010 (UTC)


 * If you choose the centre of the gravitational object as your reference, then clocks simply run faster as you ascend, which is equivalent to the statement quoted from the article.  However, this choice of reference does not seem to me to be a great idea, as the references for different mass gravitational objects will be inconsistent.   A standard way this problem is addressed is to assign zero to a theoretical location that has the highest possible gravitational potential and treat all gravitatiol potentials as negative values relative to this.  This is the basis for the expression "gravitational well"PhysicistQuery (talk) PhysicistQuery (talk) 14:03, 14 December 2022 (UTC)

There's a problem that all school children know that does not compute. A clock on a mountain moves slower than a clock at sea level because its farthur from the center of the Earth. Then Why does a clock slow as it crosses an event horizon, which has more gravitational forces acting on it? It should speed up not stop as observed from outside. Don't we slow down cocks in space so they stay current with ground based clocks? —Preceding unsigned comment added by 70.127.189.145 (talk) 03:53, 20 November 2010 (UTC)

The first comment above is suffering from severe confusion about force versus potential. There is zero gravitational FORCE at the center of a massive object, but it has a definite potential (relative to some other reference point). It's like the bottom of a valley: it may have zero slope, but it definitely has an altitude.

The second comment also starts from a false premise: a clock at higher altitude runs FASTER, not slower.

The current second sentence of the article is confusing because it also confuses strength of field with depth of potential well. The word "weaker" can only apply to the field strength. Potential cannot be weak or strong, just like altitude cannot be flat or steep.

Gravitational time dilation is a function of potential only; the field strength has nothing to do with it. (Just like air pressure is a function of altitude, and doesn't depend on how steep the ground under your feet is.) The force outside a galaxy-mass black hole is only around 1 G, but the time dilation is huge. Howard Landman (talk) 13:55, 4 February 2017 (UTC)

Magnitude of gravitational time dilation at the surface of the Earth
My own meager calculations led me to the conclusion that here on earth our gravitational time dilation is equal to 1.00000000009 days for every 1 day that passes to an observer outside the system. These were based on what is thought to be the current size of the black hole (299,460,000 km in diameter) at the center of the milkyway and our 26,000 light year distance from the black hole. Feel free to check my math, it's probably a off since i used the windows calculator. I felt obligated to put something here since no one else has yet.

(Note: unsigned commment 10:38, 6 December 2005 71.254.97.250.  In future, 71.254.97.250, please use ~ to sign your posts--- it helps alot in keeping track of who said what in talk pages, which can sometimes become very long and complicated!  And of course this is even more helpful if you have a static IP address or register an account (possibly under a pseudonym), but that's up to you.)


 * Interesting, but not possible to confirm. We can't yet observe from somewhere outside of our relative position in the Milky Way. Jeff Carr 11:52, 21 January 2006 (UTC)

Well, for starters, the very first sentence is wrong
Increasing the intensity of a gravitational field in a region reduces the effective rate of timeflow in the region? Not true. This doesn't even make sense. Time flows at the same rate everywhere, or in geometric terms, lapse of proper time corresponds to arc length along a timelike curve.

What the author should have said is that spacetime curvature can cause the divergence of null geodesics as they move outward from an isolated massive body. That means that a distant observer monitoring time signals from an second and much closer observer who uses his rocket engine to hover over the massive body will find the recieved signals to run slow relative to his own clock.---CH 21:09, 10 December 2005 (UTC)

Section The equation(s) for Gravitational Time Dilation is misleading
These formula only apply to: Suggest a careful and thorough rewrite.---CH 21:17, 10 December 2005 (UTC)
 * Schwarzschild exterior, i.e. static and spherically symmetric vacuum, so don't apply to field outside a nonrotating disk, outside a rotating black hole, outside a charged nonrotating spherically symmetric black hole, etc.
 * a pair of static observers, one at Schwarzschild radius r and the other "at spatial infinity", so don't apply as stated to say an Earth-orbiting satellite and someone standing on the surface of the Earth.

Organization
Oh boy, oh boy, I dunno how this article got in this state, but it needs a complete rewrite before it can be called a reasonable encyclopedia article. See the todo list for hints.---CH 21:25, 10 December 2005 (UTC)

Mischaracterization of meaning of the Schwarzschild radial coordinate
Ooops, just noticed another serious mistatement: Note that in General Relativity, the circumference of an orbit is less than $$2 \pi$$ the radius due to a mathematical consequence of the spherical spacetime geometry surrounding gravitating bodies. Of course, by definition, in any spherically symmetrical static spacetime, in the Schwarzschild coordinate chart, the radial coordinate accurately represents circumference and area of nested spheres (constant r). However, differences in r value do not correspond to radial distance (along radial spacelike geodesics with constant t). ---CH 22:37, 10 December 2005 (UTC)

--Kmarinas86 07:24, 11 December 2005 (UTC)I found a link that I think you might agree with: http://www.mathpages.com/rr/s6-04/6-04.htm

Perhaps the equation Gravitational Time Dilation=1/sqrt(1-2GM/rc²) itself is misleading, because I have been taking it at face value before I have start on Calculus III (I've already taken I and II).

BTW, this is the kind of attention from an expert that I needed, so your points of view are appreciated. You have clarified a few points that I was not sure of, in particlar, the point about the r coordinate corresponding to that circumference.

--Kmarinas86 08:05, 11 December 2005 (UTC)"However, differences in r value do not correspond to radial distance (along radial spacelike geodesics with constant t)." I'll see whether the escape velocity in General Relativity corresponds to the r value or the radial distance. Also, I think you implied that t affects the geodesic and thus the radial distance. I hope I understood that right.

More nonsense
Someone wrote:


 * There exists a place of no time flow, and where impact velocity for mass equals the speed of light, where mass is compressed to its Schwarzschild radius. Such matter has passed a region where Gravitational Time Dilation approaches infinity, is greater than 10^100 and passes a layer where gravitational time dilation is "undefined".


 * Therefore, one remains aloof about this strange paradox, until he or she is given an explanation.

This is sheer nonsense. KMarinas, the article by C. Nave you cite is an example of telling a white lie to students who don't have the background to follow gtr. Like many authors of semi-popular articles, he mixes up Newtonian gravitation with gtr, which of course leads to nonsense if you pursue this line of thought very far. For a better semipopular account, try
 * Leisurely pace, provides superb intuition for Schwarzschild geometry.


 * --Kmarinas86 07:35, 11 December 2005 (UTC)I understand how you are reacting to this, as it was sort of planned. It's a ironical statement, not that I actually believe there exists a place of "no time flow", I agree that it's nonsense.  I just have catalyzed a demand to improve this article, since I found it to be uncomprehensive, even before I edited it.  I have an Encyclopaedia Britannica from 1976 and I know what a real encyclopedia looks like, and the previous version of this article (before I edited it) was not an example of that.  The quantum mechanics page on Britannica is really technical, but simple enough for me to understand it.  Britannicas are way much better than World Book, or any other encyclopedia I have really looked into so far.  It's obvious that I can't make it as good as the Britannica.  Many of the articles on Wikipedia, but certainly not the majority, fit Britannica's standard.  I want this article to fit that standard.  I want it to be complete as well, not just a small inkling of what Gravitational Time Dilation is.  Because if :that's all Wikipedia can provide about Gravitational Time Dilation, then we are left wandering in other websites trying to :find out what it is exactly.

Actually, KMarinas86, you are supposed to add your signature at the end of your comments, not the beginning, but I that you know this. Also, the hypens represent an optional dash, they not part of the syntax. So you can type just ~ and you will get this. CH 23:12, 11 December 2005 (UTC)

Also, I advocate indenting comments for readability, by typing one more colons just before each paragraph to be indented. And when you say:




 * I understand how you are reacting to this, as it was sort of planned

please be careful to give the impression that you might be bragging about a successful troll. If your idea of improving the WP is to write deliberately misleading articles in hope of goading someone else into rewriting it (so that you can argue endlessly with them?), quite frankly I don't believe you are here to help the WP and in that case I would not regard your presence as welcome. And I certainly am not going to waste time talking to a troll.

Since you are apparently a newbie, I'll give you a chance to think over what you said and to consider promising to adopt more straightforward and honest behavior at WP. In particular, I welcome requests in talk pages for "experts" to improve articles on technical subjects, but you won't win many friends at WP by attempting to manipulate users. Ask, don't trick; it's more honest and in the long run it works better for everyone.---CH 23:12, 11 December 2005 (UTC)

AffirmativeKmarinas86 01:22, 12 December 2005 (UTC)

Exact equation for Escape Velocity in GR
--Kmarinas86 07:55, 11 December 2005 (UTC)I know that the equations for Escape Velocity of Einstein's theory and of Newton's theory are not the same. I will see whether I can dig that up tonight.

--Kmarinas86 08:55, 11 December 2005 (UTC) Mass cannot travel at c, therefore escape velocity cannot be c ;)..... someone please give me an rational rebuttal to this... I know that the event horizon travels at c, but of course, the radius of the event horizon does not change unless mass is added under this event horizon. So the event horizon must be spinning, of course, this doesn't escape the understanding that matter travels inside this event horizon.

This leads me to another question, what is the equation for gravitational time dilation surrounding a rotating black hole? I haven't found an answer to that so far. Note that I'm speaking of gravitation time dilation, which I defined exculsive of the effects of special relativity. Perhaps that's the wrong approach (wrong definition)? I know that the books say that the movement of a object of a gravitational field moving through a gravitational field induces a greater gravitational field. That would imply more time dilation. But that depends on the actual velocity of the object at that point in space - both do vary by the way. If the black hole is not spinning it will not drag space time along with it (no frame dragging right?), though matter may be coming at an angle, then I not so sure what it would do. I know that some black holes are said to be non-rotating. Can they be non-rotating and have a disk as well? Um......

--Kmarinas86 09:19, 11 December 2005 (UTC)I know that velocity time dilation and velocity redshift are two seperate equations that should not be confused. The equation which I have been using are only for the non-rotating, uncharged black holes (schwarzschild solution), and the r coordinate is not the radial distance along curved line to the center of the black hole. The equations for time dilation in other solutions to the Einstien's field equation should be added. For a chart of four different types of solutions, see Rotating black hole.

My other question still isn't answered, does escape velocity in GR correspond to the r coordinate or the radial distance?


 * You don't need to worry about rotating black holes and escape velocities in an article on gravitational time dilation. Escape velocity is irrelevant, and the Kerr metric (which describes the spacetime surrounding a rotating massive object) is too complex to deal with here.
 * BTW - Given a Schwarzschild spacetime and for the radial coordinate r in Schwarzschild coordinates (which is what you are using in this article), the relativistic and Newtonian escape velocity equations are the same. As you note above, this escape velocity is >=c at the event horizon and within a black hole.  What this means is that you cannot escape from either.
 * Once more thing: The event horizon does not "travel".  It is simply a set of positions in spacetime that cannot be passsed through from below.  What travels are the objects falling through it. --EMS | Talk 18:57, 11 December 2005 (UTC)

Changed intro
The current editor of this page seems to be confusing gravitational time dilation with geodesic deviation. Gravitational time dilation can exist in the absense of a curved spacetime. All that is needed is to be in an accelerated frame of reference, and it appears. The source of the acceleration (such as the gravitational field of the Earth) is irrelevant. Similarly, the Albert Einstein quote does not belong here, since this is effect is a consequence of SR instead of being a refutation of it. (Of course, in the overall context of GR that quote does apply, but this article is not about GR itself.) --EMS | Talk 18:31, 11 December 2005 (UTC)

--Kmarinas86 18:43, 11 December 2005 (UTC)"All that is needed is to be in an accelerated frame of reference, and it appears." That object would have it's own gravitational field and thus it's own gravitational time dilation. But by having gravity, it curves space, so how can you have gravitational time dilation without gravity and gravity without curved space? Well it would would be linear motion, not spherical.


 * See the equivalence principle. An accelerating rocket ship in outer space will, for the people on the rocket ship, have a gravitational field.  That this gravitational field is generated by the mechanical acceration of the rocket ship instead of curved spacetime is irrelevant to its being a gravitational field.  Yes, this is a linear acceleration, but for the people on the rocket ship, gravitational time dilation is a reality all the same. --EMS | Talk 19:09, 11 December 2005 (UTC)

"The equation(s) for Gravitational Time Dilation"
To Kmarinas86 - This section is a joke, with its multiple renditions of the effect in a Schwarzschild spacetime. A proper treatment requires the situation to be examined in different situations. Examples:
 * In an accelerated box, the equation with respect to an arbitrary base observer is $$T_d = 1 - gh/c^2$$, where
 * $$T_d$$ is the time dilation at a distant position,
 * $$g$$ is the acceleration of the box as measured by the base observer, and
 * $$h$$ is the "vertical" distance between the observers.
 * On a rotating disk when the base observer is located at the center of the disk and co-rotating with it (which makes their view of spacetime non-inertial), the equation is $$T_d = \sqrt{1 - r^2 \omega^2/c^2}$$, where
 * $$r$$ is the distance from the center of the disk (which is the location of the base observer), and
 * $$\omega$$ is the angular velocity of the disk.
 * (It is no accident that in an inertial frame of reference this becomes the familiar velocity time dilation $$\sqrt{1 - v^2/c^2}$$).

Do note that these cases do not involve spacetime curvature, which makes them all the more valuable in my opinion. In the meantime, your second version of the Schwarzschild solution time dilation is the only one needed for that case.

I will not be as down on you as CH is, but I will warn you that it is obvious that you do not quite know what you are doing here. I see you as having done as almost much harm as good here, but your willingness to leave my edits alone speaks of someone who wants this to be a good article, and who is not the territorial type. Let's see if you can take what I am feeding you above and build something decent using it. If you can learn and adjust a bit, you may be able to bring things to a state where CH will gladly remove the accuracy tag. --EMS | Talk 03:50, 12 December 2005 (UTC)


 * I see that you used a reciprocal of the version of time dilation equation that I use. I presume that you are doing that because you are giving the value of time dilation of the external position against the value of the accelerated position where the value is less than 1.  For the equations I use, the value is greater than 1, but that's giving the value of the accelerated frame against distant frame (the reverse order).Kmarinas86 04:55, 14 December 2005 (UTC)


 * $$T_d = 1 - gh/c^2$$ is an approximation. http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html makes this "newtonian" error.  http://scienceworld.wolfram.com/physics/GravitationalRedshift.html says that $$T_d = 1 - gh/c^2$$ is approximate.Kmarinas86 15:49, 14 December 2005 (UTC)


 * Kindly indent your reponses. They are hard to notice otherwise.  I have taken the liberty of reformatting them this time.
 * Time dilation refers to time running slower. If the distant obsrver has a time rate of 1, the for one deep in a Schwarzcshild gravitional field the time time dilation will be $$\sqrt{1 - 2m/r}$$ where $$c=G=1$$.  At the least you are describing how the observer in the gravitational field perceives time for the distant observer, but that is not how it is usually done. --EMS | Talk 05:03, 17 December 2005 (UTC)

I noticed that you tried and then (thankfully) removed a section called "Analogues to gravitational time dilation" building on this. You are missing a very important point there: There are not analogs, but instead are bona-fide examples of gravitational time dilation. In each case, a gravitational field is present for the observer in that objects in inertial motion are being accelerated with respect to the observer. Gravitational time dilation is a feature and accelerated frames of reference, and it does not matter if the reason for the acceleration is spacetime curvature or the rocket firing its engines or ones choosing to spin around. --EMS | Talk 19:10, 13 December 2005 (UTC)

It appears that I should think about the equivalence principle more carefully before submitting my next revisions.Kmarinas86 04:55, 14 December 2005 (UTC)

From bad to worse
"Common mistakes" is a huge mistake!!! In an accelerated box, the acceleration perceived is a function of one's position in the box! Look at it this way: If the bottom accelerated at the same rate as the top as seen inertially, then the bottom would tend to move away from the top in thier own frame of reference because the inertial distance is actually subject to the Lorentz contraction. The only way to overcome this is with a' = a / (1 - aL/c^2). That makes the relationship consistent.


 * http://scienceworld.wolfram.com/physics/GravitationalRedshift.html Kmarinas86 21:22, 17 December 2005 (UTC)


 * http://en.wikipedia.org/w/index.php?title=Gravitational_time_dilation&oldid=31694780#Common_mistakes Kmarinas86 21:22, 17 December 2005 (UTC)


 * What is your point? Or are you just doing future readers the favor of seeing what we are talking about.  (If so, then that is good, and thanks.) --EMS | Talk 16:27, 18 December 2005 (UTC)

I am going to find the last "good" edit of this article and revert back to it. That may actually be my own previous edit, but if I can give you some slack I will. In the future, if you have an issue with what I ask of you, please inquire on this page. --EMS | Talk 04:20, 17 December 2005 (UTC)

P.S. To Kmarinas86 - I think that it is time for you to stop editing this page. I gave you a chance to do better, and instead got a bunch of original research. I have done my best to put this page into a reasonable shape now. What you had here before I stepped in was totally unacceptable. --EMS | Talk 05:05, 17 December 2005 (UTC)


 * I previously added the more exact equation for Gravitational Time Dilation and it came from your edits on the proper time page. How does that constitute original research?  I know myself some of what I did was original-looking, but I got some of those ideas from you.  I added what I thought were some of your ideas and put them on there.  Maybe this should be just a small article with not a lot in it?Kmarinas86 20:40, 17 December 2005 (UTC)


 * Your diatribe that the gravitational time dilation equation for the "Newtonian" case is self-contradictory was quite original, and that is what I am refereing to. You are not the first person to notice this, but since you cited no sources for it I am quite sure that you came up with it yourself.  (In fact that apparent contradiction drove me up a wall at one point until I figured out the answer.)
 * As for the use of my own material: I do admit that doing so was not original research.  However, you pasted it in without any formatting to make it "fit" into the article.  You even had my "exercise 3" heading in there!  So the intent was fine, but the implementation was not.  In the end I had to choose between a significant amount of editting or just taking it back out, and I chose to remove it.
 * I for one would love to see someone else work on this article, but the result needs to be article that is clear, concise, and correct. After a the point I reverted back to, I found myself with looking at less and less of all three of those.  I'm sorry if this is cruel, since I know that you are trying, but you seem to still be learning about relativity and to make matters even worse don't yet know how to sort the "wheat" from the "chaff". --EMS | Talk 04:10, 18 December 2005 (UTC)

From worse to good to better
The disputed material has been removed, so I'm taking down the dispute message.Kmarinas86 23:04, 25 December 2005 (UTC)

The layout I think is a little scatter brained. I'm going to see make the text clearer like how I attempted at gravitational redshift.Kmarinas86 23:08, 25 December 2005 (UTC)

I have taken the "Gravitational Redshift vs. Gravitational Time Dilation" section located in the history section of the Gravitational Time Dilation article and put it in the Gravitational Redshift article. Kmarinas86 16:52, 26 December 2005 (UTC)


 * I think that you are effectively "rearranging the chairs on the Titanic". You are obtaining a better grasp of the material, and for that I applaud you.  None-the-less, this is still far from being a good article on the subject.  The big offense right now are the terms "fast-acting" and "slow-acting":  These are neologisms, and their use is prohibited by the no original research policy. Also, there is no need to use new terms when describing a well-known phenomenon.  I therefore strongly call on you to get rid of those terms.  (Besides, what is "fast" or "slow" is not the observers but rather the rate of proper time passage at their location.) --EMS | Talk 18:25, 26 December 2005 (UTC)

New accuracy tag
Here are my complaints:


 * 1) Time dilation is the result of a gravitational field, not the presense of a massive object.  general relativity explains how massive objects generate gravitational fields, but that is not the only source of such fields.  In Einstein's definition, a gravitational fields exists in an accelerated box, and gravitational time dilation most certainly does also.  In addition, letting yourself spin like a top creates a world view with a gravitational field also, albeit one that is a function of your rate of spin.
 * 2) The Schwarzschild Solution is a good example of how gravitational time dilation is manifested, but it must be emphasized that this is for an idealized case (spherically symmetric non-rotating masses), and the equations for other cases (the accelerated box and the spinning observer) need to be dealt with also.

With my having gotten rid of a bunch of extraneous material, this article is now somewhat better than before. However, it still has a ways to go, and I will see if I can work on it sometime soon. --EMS | Talk 19:19, 28 December 2005 (UTC)

Experimental verification ???
Is there a source for the airplane atomic clock experiement? I've heard this claim before but have never been able to find sources. How did they tell that the clocks had drifted and how much did they drift? This lack of information on this experiment has bugged me for years. I'm starting to think it's just urban legend. Especially now that I know how hard it is to measure small amounts of time drift between clocks, I wonder how it was that someone measured the drift. Jeff Carr 12:31, 21 January 2006 (UTC)


 * Add also a request for a source that the GPS system uses this in it's calculation. I've also looked into that claim in the past and could never find verification. Jeff Carr 12:42, 21 January 2006 (UTC)


 * Further more, the white dwarf Sirius B and the Pound-Rebka experiment are both redshift experiments, not confirmation of time dilation. Jeff Carr 12:47, 21 January 2006 (UTC)


 * The experiment was done. However it is only of historical interest, imho; far more stringent tests have been passed since then. The amount of science confirming both SR and GR is massive, seriously doubting it isn't scientifically useful (in MOST contexts it is safe to take it as 'true'). OTOH, it is very unlikely to be the last word on the structure of spacetime, either. Abitslow (talk) 19:43, 4 January 2015 (UTC)

Is there such thing as experimental confirmation of a scientific prediction?(I must ask seeing this discussion.) No matter how much experimental tests does not confirm a theory, only it verifies that its predictions hold and cases of falsification have not been detected yet. Empirical evidence does not confirm a theory due to the problem of induction, only offers a provisional saving from disproving. I'll revert the recent reversion.--82.137.11.190 (talk) 18:13, 31 August 2016 (UTC)

Merge with Time Dilation
These two pages should be merged, but I'm too new to the Wikipedia to know the correct process of merging pages. Jeff Carr 05:07, 22 January 2006 (UTC)


 * See merge, but before you do that, kindly consider that these pages were originally together and another editor chose to split them. I myself an neutral on this.  I think that having the proper contents is more important than the organization.  However, do feel free to start a discussion.


 * BTW - New discussions are usually placed at the end of a talk page, and I will move this one down. --EMS | Talk 05:29, 22 January 2006 (UTC)


 * I "broke" convention by putting this at the top because both articles were tagged as needing expert attention. I'm still new to the wikipedia; it seemed appropriate to me. I was trying to save people's time. They both have almost identical content and both were in bad shape. These articles are the same: there is no difference between Gravitational time dilation or any other sort. The theory is premised on the assumption that gravity and acceleration are indestinguishable. Jeff Carr 21:40, 24 January 2006 (UTC)


 * I'm less bothered by your not knowing Wikipedia right now than I am at your not knowing relativity. (Velocity) time dilation and gravitational time dilation are not the same thing.  Time dilation as introduced in SR is an effect of velocity with respect to a fixed observer.  Gravitational time dilation is an effect that exists between fixed observers in a gravitational field.  So one involves velocity, and the other acceleration, and there is a difference between those. --EMS | Talk 05:34, 26 January 2006 (UTC)


 * Merging time dilation may be appropriate, but the two distinctly different and competing theories need to be clearly defined (time dilation due to constant speed as argued in the Time Dilation article versus time dilation due to acceleration including gravitational acceleration which is acceleration force generated by resisting the pull of gravity, as argued in the Gravitational Time Dilation article). Since recent experimental evidence proves the existence of gravitational time dilation (reference: http://www.sciencemag.org/cgi/content/abstract/329/5999/1630), and since speed based time dilation calculations are reported to not exactly match experimental results, this argument may heat up.  Jtankers (talk) 18:56, 17 October 2010 (UTC)
 * Since you are restarting the debate, I would say keep the articles separate, as this is a narrower term that can expand into more detail than the Time Dilation article. Graeme Bartlett (talk) 21:12, 17 October 2010 (UTC)

Edits by 87.217.89.114
, aka the Jazztel triple play services anon from Spain, wrote "Gravitational in GR means Fictitious force. Gravitational time dilation can be manifested at any kind of accelerated reference frame, and by virtue of the equivalence principle, it will apeear also by the presence of large mass...". The first sentence doesn't make much sense and is arguably seriously misleading; most would say that in gtr, gravitational effectes are identified with curvature effects in a Lorentzian spacetime. I reverted the change, although I agree that this article could use much improvement. ---CH 23:24, 13 June 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.

Sadly, I am now abandoning this article to its fate. I emphatically do not vouch for anything you might see in more recent versions. Given past history, I have reason to believe that at least some future versions of this article are likely to contain slanted information, misinformation, or disinformation. Beware also of external links to other websites, which may be cranky.

Good luck to all students in your search for information, regardless!---CH 00:19, 1 July 2006 (UTC)


 * You're right, this is a pretty horrible article, fraught with bad wording and just plain old mistakes. It's lacking a lot. 93.172.41.139 (talk) 06:51, 16 May 2009 (UTC)

Error in section "Inside a non-rotating sphere"
The last sentence of the following extract is in error:

If one is inside the sphere, the sphere can be split in two parts: a hollow sphere above and a solid sphere below. One is weightless anywhere in the interior of a uniform hollow sphere. With respect to one's gravitational potential, it is as if the hollow sphere is not there.

It is true that with respect to the gravitational field (the gradient of the potential), it is as if the hollow sphere is not there. However, the potential inside the sphere is everywhere the same as that reached when moving inwards to the inner surface of the sphere. This is a standard textbook result.

The following paragraph is also incorrect:

The implication is that the gravitational time dilation reaches its maximum at the surface of the non-rotating massive spherically-symmetric object, and that the gravitational time dilation reaches its minimum at the center of the sphere.

The gravitational time dilation actually continues increasing to a maximum at the center of the sphere, so this is misinformation. I have seen a couple of cases in physics forums and newsgroups where people have been misled by this specific sentence in this article. This section therefore needs rewriting to correct this error.

Jonathan A Scott (talk) 11:28, 20 February 2008 (UTC)

The equation presented in that section is also horribly wrong. It appears to be original research that Rijkbenik (talk) did in September 2007, based on the assumption that the gravitational potential inside a hollow sphere is as if the hollow sphere was not there. That assumption is incorrect, as Jonathan A Scott points out above.

I don’t have a reliable source giving a correct equation for the case of inside of a sphere, and the whole section just consists of that equation and an explanation of how Rijkbenik derived it, so I will simply delete the entire section. Red Act (talk) 16:51, 29 July 2009 (UTC)

Why not just present basic equations and their combination:
Why not just explain in that:

$$F1 = F2 = (M1 x M2)/r^2$$ $$F = MA^2$$ $$Td = Td/Square Root of v^2c^2$$

Response: Because your layperson, your average Wikipedia article reader will not understand them. They should be presented. But they need to be explained rather than just expecting the person to understand what each variable means.75.133.90.126 (talk) 19:32, 27 December 2012 (UTC)

Capitalization
Why isn't the "time dilation" in "Gravitational time dilation" capitalized in the title? 65.24.171.166 (talk) 21:47, 16 December 2008 (UTC)

Citations, and encyclopedic character
I just added reference sources including an online text (English translation) for the Einstein 1907 paper referred to in the lead paragraph.

Comments elsewhere on this talk page have shown the tensions that there can be in this subject-matter area over the addition of material that represents physical/mathematical mistakes, or original research, or possible fringe or crank theories.

I offer the following suggestion about possible improvements to the encyclopedic character of the article.

It seems to me that among the existing strengths of the article (whatever its discussed defects), is the part of the (curiously-named) definition section that mentions, and to some extent describes, how the equivalence principle can be applied to specific classes of case -- such as linear acceleration and the rotating disk, giving expressions associated with each. It's a strength because it shows the interrelationships, and to some extent enables them to be followed up (which it would do better if there were also some inline references).

One of the arguable weaknesses, on the other hand, is that the description of the (Schwarzschild) case of the massive sphere gives no hint at all about the existence let alone the detail of a major peculiarity, the anisotropic character of the Schwarzschild coordinates. While 'periti mathematici' may consider that this matter goes without saying, and/or can be found elsewhere (which seems so far hardly the case for WP), it's arguably the kind of point on which an encyclopedic text differs from a professional text, and it would be helpful not only to point it out but also to give alternative forms, in isotropic coordinates, which might better point out the way in which approximations have been derived and used.

One of the partial safeguards against mistakes, original research and crank theories would be the provision of plenty of inline references pointing to strongly reputable sources. Again, 'periti mathematici' often write as if they are apt to think it's enough that the text should provide its own cogency. Maybe for some such reason, there's a general scarcity of references in WP mathematical articles to which experts have given their welcome attention. But many encyclopedic readers can not judge that, and are much helped when they are able to see the provenance as well as the content.

With good wishes, Terry0051 (talk) 14:18, 13 August 2009 (UTC)

Redshift?
I am wondering, could the gravitational time dilation cause a redshift? Mevistoveles (talk) 19:37, 2 February 2010 (UTC)
 * That's basically what gravitational redshift is (though I notice that article is tagged as needing expert attention so I don't know how helpful you'll find it). Also, article talk pages are designed for discussing improvements to their associated articles; if you have more questions about the subject matter you might want to try the science section of the reference desk. Olaf Davis (talk) 20:03, 2 February 2010 (UTC)

…dragster or space shuttle
Please, rectify these links. I am not an English speaker and can’t easily realize what effect this text is about. Incnis Mrsi (talk) 08:49, 28 February 2010 (UTC)

Time vs. clocks
Jsolebello and 76.106.186.17 have been changing the first sentence to read "Gravitational time dilation is the effect of [atomic] clocks working at different speeds in regions of different gravitational potential" instead of "Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential". I disagree with this because I think it's misleading to the reader. Although relativists often talk about sets of 'clocks' inhabiting regions of spacetime, they're really talking about measurements of the rate at which time passes at different points - the clocks are essentially a metaphor. Someone unfamiliar with this terminology reading the article could easily think it meant "my clock will tick once every two seconds in one place and once a second in another" instead of "half a second passes in one place while one second passes in another", which is actually correct. Changing it to atomic clocks is I think even more confusing, since an atomic clock is definitely not a metaphor but a physical object. Although we've observed time dilation using atomic clocks, saying "gravitational time dilation is the effect of atomic clocks..." is wrong in the same way as "gravitational attraction is the effect of the Moon orbiting the Earth".

Also, I think that 'rate' is a better word to describe how quickly time/a clock runs than 'speed', but this is less important than the first point.

Any thoughts? Olaf Davis (talk) 08:54, 5 August 2010 (UTC)
 * I fully agree; mentioning atomic clocks makes it more confusing for people not familiar with this specific terminology Isaac Euler (talk) 16:34, 5 August 2010 (UTC)

Folks, it is a very simple distinction. Saying that "time passes at a different rate" is misleading and almost blasphemous. Please do not change it again. —Preceding unsigned comment added by Jsolebello (talk • contribs) 17:46, 5 August 2010 (UTC)
 * This effect is demonstrated by various sources of electromagnetic waves, see gravitational redshift, not only by "atomic clock". Change from the time in general to a some particular type of clock is an unacceptable over-specification of the topic. And please, Jsolebello, look better what do you revert. Further attempts to revert indiscriminately, breaking non-controversial improvements like Pound–Rebka experiment back to Pound-Rebka experiment, may be considered as a bad faith and rolled back. Incnis Mrsi (talk) 18:56, 5 August 2010 (UTC)


 * Jsolebello, it might help convince the several editors who apparently disagree with you if you explain why you think your version is more accurate. Also I note that you reverted changes beyond what's discussed above - do you disagree with those too? Olaf Davis (talk) 20:15, 5 August 2010 (UTC)

It is already clear that it is very difficult to explain to you. I already explained it. You "apparently" do not understand English very well. It is marked in Ignis' page that he only has an intermediate level on English. —Preceding unsigned comment added by Jsolebello (talk • contribs) 21:15, 5 August 2010 (UTC)
 * If you want to clarify it to say not only atomic clocks, then you should do that. It should never say that time slows down or changes speeds.  Jsolebello (talk) 21:31, 5 August 2010 (UTC)Joe E Solebello
 * But many others think that it should. Must the introduction of an article obey to a personal point of view of Jsolebello? Incnis Mrsi (talk) 21:58, 5 August 2010 (UTC)

You are lost to ask such a stupid question. It is funny that you posted on my personal page that I am engaged in an edit war. Did you post one on your own page?

In conclusion, you recognize that there is a Proper Time, but then say that "time passes at different rates".Jsolebello (talk) 01:38, 6 August 2010 (UTC)Joe E Solebello
 * So, you suggest to use some euphemism which could cover such phenomena as atomic clocks, optical spectra, microwave generators, but avoid mentioning that all these can measure the "time". What for? Incnis Mrsi (talk) 07:17, 6 August 2010 (UTC)


 * Actually, English is my native language. I did understand your statement that my version is "misleading and almost blasphemous", but since you didn't explain why it's misleading I can't really understand your position. In general you are more likely to persuade people on Wikipedia if you give detailed reasons for your position.
 * "you recognize that there is a Proper Time, but then say that time passes at different rates" - yes, this is correct. In relativity 'proper time' has a very specific meaning: it's the time between two events as measured in the reference frame in which those events have the same spatial position. It doesn't imply that time is immutable and unaffected by gravity. Olaf Davis (talk) 10:23, 6 August 2010 (UTC)

Time is not affected by gravity. Only machines that measure time are.. —Preceding unsigned comment added by Jsolebello (talk • contribs) 03:38, 7 August 2010 (UTC)


 * To Jsolebello: What do you mean by "time"? Please give us your definition. JRSpriggs (talk) 13:56, 7 August 2010 (UTC)

The whole argument I've read so far by Jsolebello seems incoherent at best.Chhe (talk) 04:22, 8 August 2010 (UTC)

"Time is not affected by gravity. Only machines that measure time are." Clocks measure crystal vibrations to express Time. The more constrained the crystal, the faster it vibrates. Think about a ball bouncing between 2 walls an inch apart (underground) vs walls 3 inches apart (surface) vs one foot apart (space), thus clocks run at different rates depending on the gravity of the space they occupy.

the lower the gravitational potential (closer to the center of a massive object), the less proper time will be elapsed there in the same temporal interval…
I look for objections about this piece of text persistently removed by and once today – by. What is so wrong in it that you remove it compeletly? Also note that Pound-Rebka experiment is a redirect and incorrect typography. My change to direct link and correct typography was reverted three times by these users without explanations. Incnis Mrsi (talk) 15:53, 7 August 2010 (UTC)


 * I simply reverted to the July 3rd version, before started their edits. I thought this version was clearer than your version. However, I see that restoring the phrase "clocks run" may appear to give support to Jsolebello's nonsense, so I have now replaced it with "time passes". I have also restored your Pound–Rebka experiment correction. Gandalf61 (talk) 16:47, 7 August 2010 (UTC)

Folks, for this crowd, I give the analogy of the wet meterstick. Should you attempt to measure a meter in the water, the stick will get wet, and possibly break. You would then be unable to measure a meter properly.

Good luck,

Should you need me to review and clarify any other topic, please send me a message and it will be considered.76.106.186.17 (talk) 06:12, 9 August 2010 (UTC)Joe E Solebello

"Imporrtant things to stress"
Does anyone else think that the section headed Important things to stress is mostly either incomprehensible or nonsense ? Phrases such as "radiation and matter may be equally affected, since they are made of the same essence"; "as long as an observer is forced to observe only the photons which intercept the observing faculties" and "When the other, distant light intercepts the distant observer, it will come at c from the distant observer's perspective" make little or no sense to me. Gandalf61 (talk) 16:17, 13 January 2011 (UTC)

Gravitational Potencial vs Distance From Body
There is a big error in the start of the definition: "Clocks which are far from massive bodies (or at higher gravitational potentials[dubious – discuss]) run faster, and clocks close to massive bodies (or at lower gravitational potentials[dubious – discuss]) run slower (slow is low)."

A clock which is farther from a massive body is at lower gravitational potential than a clock which is closer, not higher. Considering the base relationship between distance from massive bodys and gravitational potential is wrong, I wonder how correct all the affirmations that involve distance from earth can be.

In the beginning of the article: "the lower the gravitational potential, the more slowly time passes;" If this is correct, then the the definition must be wrong. If this is wrong, then the definition bust be right (despite the part about gravitation potential still being wrong). Aristidesfl (talk) 08:32, 28 July 2011 (UTC)


 * Hello, let me clarify. Here the Gravitational potential means the potential energy stored due to its vertical distance from the massive body. Remember the formula PE=mgh ? The same holds good here. By that we can say that if you are at mountain peak then you have greater Gravitational potential than you had when you were at the bottom of the mountain. So lower gravitational potential means nearer to massive body, higher gravitational potential means farther from massive body. About the time dilation, E=hf, f=1/T. As you are nearer to massive body the time runs slower and if you get away from it time runs faster. By this we can say that the above statement "the lower the gravitational potential, the more slowly time passes" is correct. Shriram (talk) 08:54, 28 July 2011 (UTC)


 * As Shriram says, the article is correct. To move an object away from a massive body such as a planet, you must do work on it, so you increase its gravitational potential energy (or, from an alternative point of view, you increase the potential energy stored in the gravitational field). Therefore the gravitational potential close to a massive body is lower than the gravitational potential further away. Think of it like stretching a spring - the potential energy of an unstretched spring is lower than that of a stretched spring. See gravitational potential for more details. Gandalf61 (talk) 08:57, 28 July 2011 (UTC)


 * I understand both you explanations. Perhaps it is a matter of correctness of the terms behing used, which I believe are behing confused. Despite that, in the gravitational potential article, there are multiple evidences that indicate the farther away you are from a massive body the lower gravitational potential is. Maybe the most immediate evidence, is the table at the end with some examples: Gravitational potential. Aristidesfl (talk) 23:03, 28 July 2011 (UTC)
 * Note that the sentence immediately above that table explains that the values shown in the table are absolute values of the gravitational potential. Gravitational potential is, by convention, negative everywhere (and notionally zero "at infinity"). So the actual values for gravitational potential with respect to the Earth are &minus;60 MJ/kg at the Earth's surface, &minus;57 MJ/kg at Low Earth Orbit etc. And &minus;60 is indeed lower than &minus;57. Where else, exactly, do you think the gravitational potential article supports your point of view ? Gandalf61 (talk) 10:05, 29 July 2011 (UTC)
 * Gandalf is correct. But Aristidesfl may have become confused because the absolute values do not have negative signs or may not have noticed the word absolute . So thought that they were positive. The first equation in the Gravitational potential itself suggests negative sign. But they are absolute values so negative sign is not considered. Shriram (talk) 11:58, 29 July 2011 (UTC)

Why Isn't e defined?
The variable e in the first equation the one about the accelerated box is undefined. Definition please!75.133.90.126 (talk) 20:35, 28 December 2012 (UTC)

Where does $e^{gh/c^{2}}|undefined$ comes from?
I think this is incorrect: "In an accelerated box, the equation with respect to an arbitrary base observer is $$T_d = e^{gh/c^2}$$"

There is a Rindler-horizon behind the accelerating obsever according to this article. If the locally felt acceleration is $$\alpha$$, then the rinder horizont is at $$c^2/\alpha$$ behind the observer. So the $$1 + \alpha h / c^2$$ must be correct for linear acceleration. If you substitute $$-c^2/\alpha$$ into $$h$$ you get 0, as the time at the Rindler horizon stands still (like at the event horizon of a black hole).

This formula also justifies the paradoxical effects of Rindler coordinates. If an accelerating observer measures $$\alpha$$ at bottom of a spaceship. The hyperbola for the observer $$h$$ higher corresponds to the acceleration $$\frac{c^2}{c^2/\alpha + h}$$ which is a smaller acceleration. But as the observer accelerates the plane of simultaneity rotates, so the two ends always connect two points on the hyperbolas where the slopes of the two hyperbolas is the same, so the local speed is always the same along the object and the acceleration of the body remains uniform.

Now this is where the gravitational time dilation kicks in. The rate of the two accelerations is exactly $$1 + \alpha h / c^2$$. Although the acceleration is uniform, observer $$h$$ higher will indeed measure smaller acceleration because his clock is faster.

So to sum up I would edit that formula.

I would also split the article into two parts. One that discusses the accelerating bodies (in flat spacetime) and the another one that discusses the effects of spacetime curvature.

Calmarius (talk) 15:10, 21 June 2013 (UTC)
 * I agree with your criticism. One should specify how exactly the “box” accelerates, and, most importantly, is the space-time flat or curved. For Rindler observers, in the flat space-time, there would be no exponent, because magnitude of the acceleration depends inverse-proportionally on the $x$ coordinate, and after integration we’ll obtain exponent of a logarithm, i.e. a proportional dependence of proper time on $x$. Constant dependence of $g$ on what they call $h$ (≈ Rindler’s $x$) is impossible in a flat space-time, and is not a natural condition in a curved space-time. You may wreck the rogue exponent, but I think it would be better to replace it with exponent of the anti-derivative (integral) of the dependence of $g$ on $h$. Incnis Mrsi (talk) 16:38, 21 June 2013 (UTC)

If this is true, than millions of years in our planet life is not correct, time dilation in our center core and surrounding space (in time/time dilation), would made a deficit in moment, which would effect our planet and the rotation of planets, this theory its not very well thought trough!!! time dilatation has a time frame, which makes the dilatation bigger and bigger as time moves on. — Preceding unsigned comment added by 109.101.115.160 (talk) 09:14, 28 November 2013 (UTC)


 * Apparently older citations for the exponential equation exist from Weinberg and maybe Schwarzschild; but one place where it was derived can be found on the talk page for the wikipedia article Gravitational Red Shift, under the heading Is Something Amiss? Samdhatte (talk) 06:21, 10 February 2015 (UTC)

Concerning Merry-go-rounds
I questioned the statement made concerning time dilation in a merry-go-round. There you always stay at the same level in the gravitational well. It should be a quite straight-forward and simple experiment to perform. All you need is an atomic clock and a playground close to the university. My question is: has such an experiment ever been done, and if so, did it support such a statement? Has anyone, ever, placed an atomic clock in a merry-go-round and observed time dilation? If no such experiment has ever been successfully done, then I do not think that the claim that time dilation exists in a merry-go-round can be totally unquestionable. The reptile brain of wikipedia however immediately removed my 'reference needed'. Why not instead provide a reference to an experiment made, or a 'but this has not been proved experimentally yet' statement? And, of course, if I happened to insult someone's profound religious beliefs, then please accept my apologies. Hilmer B (talk) 20:35, 8 February 2014 (UTC)
 * The gravitational time dilation is a phenomenon. General Relativity with its equivalence principle is a physical theory. The theory reduces several phenomena to certain basic explanation (I mean non-inertial frames) – a good theory, but centripetal forces are certainly not gravitational forces. The example with Rindler’s acceleration can be considered: it is simple. The example with Ehrenfest’s disc is, mathematically, not so simple. I do not see any reason why should we dedicate sizeable fragments of this article to rotation-specific examples. I shall sleep now and can’t participate in the ongoing edit war with . can you cope with it? Incnis Mrsi (talk) 21:57, 8 February 2014 (UTC)
 * I agree that some articles have been written by authors that were maybe a bit too eager to cover it all and a bit more. Maybe that's the spirit of wikipedia. It will take time to get everything right, to which end we must all contribute, even if it's only a simple spelling error. So, I'm patient Hilmer B (talk) 11:12, 9 February 2014 (UTC)

I do not see where the http://www.cathodixx.com/pdfs/RELATIVITY.pdf source supports Coldcreation’s Spinning objects such as merry-go-rounds and ferris wheels are subjected to gravitational time dilation as a consequence of centripetal acceleration. formulation. Of course, due to equivalence principle centripetal and gravitational G-loads are equivalent, but who does assert they are identical? Possibly, Groen & Naess say something about it, but the book is long and a page number is needed. Incnis Mrsi (talk) 18:41, 9 February 2014 (UTC)


 * I would get some form of consensus before removing the material in question from this article. The very fact that the effect of time dilation in physical systems such as in an accelerated (gravitational) reference frame is indistinguishable from that in rotating coordinates (such as a merry-go-round, or rotating disc) makes the discussion relevant to this article. Coldcreation (talk) 18:49, 9 February 2014 (UTC)


 * Furthermore, the quote above (with merry-go-rounds etc) is not mine. I merely reverted an edit that had removed the phrase. Coldcreation (talk) 18:56, 9 February 2014 (UTC)
 * Certainly our discussion is relevant to the article. The question is whether the Ehrenfest’s disc, with its specific formulae for velocity and acceleration, is relevant to the article. Johan Prins quotes Einstein and considers the example himself, but I do not see where it is stated two things are the same. And what do Groen & Naess say? Incnis Mrsi (talk) 19:09, 9 February 2014 (UTC)

By performing more than three reverts on a single page within a 24-hour period, Incnis Mrsi (talk), you just violated The three-revert rule WP:3RR. Surely this topic merits a discussion here at Talk before you removed the material posted by other editors, something you've done, again, three times. Coldcreation (talk) 20:14, 9 February 2014 (UTC)
 * RoTFL. A person who can’t correctly count how many times certain Incnis_Mrsi edited the article in 2014 also removed certain Hilmer_B’s maintenance template because… okay, what namely merits a discussion in the article? Could you, Coldcreation, explain why my edition is minusminusungood? Which undisputedly relevant material did I remove? Incnis Mrsi (talk) 21:08, 9 February 2014 (UTC)

With differences being measured in nanoseconds?
In the second paragraph, the sentence "The effects detected in such experiments are extremely small, with differences being measured in nanoseconds." is meaningless. It tells us nothing.

The effect of time dilation is a systematic error in frequency as seen by a non-local observer. It is not a fixed offset between the two clocks, but an error that diverges over time, therefore the frequency error between two clocks is a unitless ratio. Let's say an error of 1ns accumulates every 1000s, then the error is 1ns/1000s = 1e-12 or 1 part per trillion.

I don't have at hand a realistic figure for observed time dilation, but it is obvious that "nanoseconds" is dimensionally invalid for measurements of the effect.

118.93.217.77 (talk) 13:23, 29 May 2014 (UTC)puddingpimp

Rubbish
This article is rubbish !! Apart from all the problems outlined below, the 4th paragraph of the opening "Definition" says: g(h)=c^2/(H+h) with constant H. ...without ever saying what "H" is !! Useless ! — Preceding unsigned comment added by 80.189.31.110 (talk) 18:18, 3 October 2014 (UTC)
 * I agree that that section is horrible. Not only is H left undefined, but g' is not defined nor mentioned in the text at all yet is used in the equation as the critical parameter.Abitslow (talk) 16:55, 9 January 2015 (UTC)
 * More than six years later, I agree also, which is why I looked at the talk pages.  In addition, H is not a constantPhysicistQuery (talk) 14:15, 14 December 2022 (UTC)

Clocks - a side-issue
The lede isn't very good. The difficulty in explaining what is meant by time dilation is poorly addressed. I would bet that most people reading the lede would conclude that the effect is ONLY on clocks. Its pretty simple: to an observer who is in a lesser gravitational field, the time observed to pass in a higher field is less. This means that clocks tick slower on the surface of the Earth than they would in outer space, but it also means that everything is 'slower': breathing, chemical reactions, atomic motion, everything. To an observer in the high gravitational field, seconds tick by one-by-one, s/he ages one second every second that passes, remembers one day, for every day that passes. Only when s/he compares events with someone in a (very) different field will differences be noted. In Special Relativity, velocity imparts time dilation but it is symmetrical: observer A sees observer B's clock ticking 'slower' and at the same time observer B sees A's clock ticking slower. This means they will NOT agree which is "really" running slower and which faster. In General Relativity gravity (acceleration) breaks the symmetry: the more gravity (acceleration) an observer experiences the slower the passage of time. If A is on Earth, and B in outer space or on Mars, then both A and B will see B's clock running faster than A's clock. They will agree that A's clock is slower than B's. The lede attempts to AVOID the use of proper time (which is probably good to start) but replacing the concept of the actual time someone is subject to with his/her clock time is confusing, imho. Here is my suggestion for the first two sentences:

1. Change "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." to "Gravitational time dilation is a form of time dilation, a comparative difference of the passage of time as measured by observers under different gravitatational acceleration. (For instance, compared at different heights from the surface of the Earth; or on the surface of Earth compared to on the surface of Mars. In any of these locations, an observer there will measure time passing normally, it is only upon comparison to observers under different gravity will differences be noted."

2. Change "The stronger the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes." to "The stronger the gravitational potential, the slower time is seen by an 'outside observer' to pass there." note that it isn't just about distance from the mass, it is also the size of the mass. (distance, density and mass; actually).Abitslow (talk) 20:43, 4 January 2015 (UTC)

Problem with the diagram in Experimental Confirmation section
The diagram shows two vertical lines; one representing the surface of the Earth and one labled "Shuttle Orbits" (which at this scale are essentially a single line). I wasn't able to quickly find the range and average of the 130+ Shuttle orbits, but the International Space Station, a common co-orbiting object, orbits at 380 km. On my monitor, the distance between 0 and 10,000 km is 44.4 mm. The lines are less than 0.5 mm apart (essentially, on top of each other) yet the distance between 6380 km and 6760 km would be about 2 mm. In other words, the two lines should be separated, slightly. I understand that shuttle orbits vary, but for illustrative purposes the way they are depicted is, imho, wrong/misleading. Oh, the 44.4 mm was on the diagram's 'home' page (expanded), but the image as depicted in this article has the same problem: the lines should be separated, slightly.Abitslow (talk) 17:17, 9 January 2015 (UTC)

Demonstrating greater effects would require greater distances from the Earth and/or a larger gravitational source.
Gravity is reciprocal to the squareroot of the distance. The gravitation on Earth compared to the gravitation 20200 km above the earth is about 17 times larger. So the difference of the gravitational component from earth the hight of a GPS satelite is reduced by a factor of 17. Any further reduction is small compared to this reduction. The effect of grafitational time dilation is far greater from the earth to the a GPS satellite than it is from a GPS satellite to the infinity and beyond. So the greater distances do not demonstrate a greater effect, the effect of greater distances is little compared to the effect from earth to a GPS satellite. Therefore my opinion is that reducing the above line to Demonstrating greater effects would require a larger gravitational source. Crazy Software Productions (talk) 12:05, 8 April 2016 (UTC)

Paradox of alignment
In the second paragraph it states "Relative to the earth's age in billion of years, the earth's core is effectively 2.5 years younger than the surface [2] leading to a paradox of alignment with the celestial sphere due to the rotation of the earth." What exactly is the paradox? Is it the Ehrenfest paradox or something else? I'm not disputing the statement it's just I don't understand? Can anyone clarify? Thanks — Preceding unsigned comment added by 207.34.27.84 (talk) 06:12, 2 December 2016 (UTC)

I removed this I'm sure it's spurious, unclear and uncited. 81.129.124.246 (talk) 23:59, 5 February 2018 (UTC)

Is it gravitational at all?
I know this effect is widely known as "gravitational time dilation" and defined as observers experiencing slower time the greater the gravitational field they're exposed to. Now, my issue is, is this really tied to gravity at all? If you are on a spaceship that's subject to constant acceleration, someone on said ship's nose would experience slower time than someone at said ship's tail. Therefore, time dilation is introduced by acceleration itself, and not gravitation (which is one of many ways to induce acceleration), and I'd say the rule is that you experience slower time the further ahead you are in the direction of the acceleration. The definition based on the gravitational field's intensity is just a coincidence due to the fact that gravitational fields increase in intensity as you get further ahead in the direction of acceleration. Am I missing something? --uKER (talk) 04:59, 15 August 2017 (UTC)


 * There are several problems with the way you deal with the subject. First of all, gravitational time dilation is proportional to the gravitational potential, not field, so that the clocks in the center of a star would do slower, than the same clock faraway, although neither experience noticeable acceleration relative to each other or the star. In general it is a slippery slope to try to pinpoint "who is exactly responsible" for a given phenomenon in general, but gravitation time dilation refers specifically to discrepancy to time pace for still clocks near a still gravitating body caused by the spacetime curvature, which in this particular case is present due to the body's gravity. So it is reasonable to call this gravity as a source, even if it works through general means of skewing the metric. L3erdnik (talk) 18:31, 16 August 2017 (UTC)
 * Just to avoid confusion, gravitational time dilation is not always defined by potential. For example, in the Friedman-Robertson-Walker metric, distant galaxies are said to have time dilation with respect to us, as evidenced by their redshift. But the redshift is due to the increasing scale factor a(t), which involves no potential. Of course, you specified "still", or static configurations, in which case what you said is qualitatively correct. But rigorously, time dilation is defined by the metric, and not by the potential, which is different. (Many metrics do contain terms proportional to potential of course.) 70.57.229.251 (talk) 20:07, 26 June 2018 (UTC) Karl Pomeroy


 * Sure, the proper time is affected by the whole range of possible peculiarities of the metric. However, particular model cases (that focus on a certain aspect in order to understand the majority of situations in terms of few simple model contribution) are pretty specific. Velocity time dilation focuses purely on the relative motion, Doppler effect focuses on how the change in distance affects the perceived time dilation purely by means of the signal having to travel, say, longer and longer distance (as an example being a part of the cosmological redshift, which you seem to talk about), and the gravitational time dilation focuses on the way a body affects the time flow purely by means of its gravity, while not trying to encompass all kinds of possible scenarios within GRT. L3erdnik (talk) 01:26, 27 June 2018 (UTC)

Time dilation inside a hollow shell
The article says, "According to the general theory of relativity, gravitational time dilation is copresent with the existence of aaccelerated reference frame. An exception is the center of a concentric distribution of matter, where there is no accelerated reference frame, yet clocks are still supposed to tick slowly." Supposed by which physicists to tick slowly? I derived an exact solution to Einstein's Field Equations for the static spherical nonvacuum, using a spherical Dirac delta mass distribution ρ=μδ(r) for μ the area density, and found that there is no time dilation inside a hollow massive shell. Clocks run at the same speed as they do at infinity. This is easily generalized to a non-hollow shell, with the same result. Another piece of evidence for lack of time dilation is the double Schwarzschild metric, an exact EFE solution for two black holes [presented in peer-reviewed article by Cunha et. al., Does the black hole shadow probe the event horizon geometry? Physical Review D 97, 084020 (2018)]. Between the black holes, there is no time dilation. These argument imply that the center of a concentric distribution of matter is not an exception as stated. There is a lot of confusion in physics forums about the truth of the quote above, and I have found no textbooks or peer-reviewed articles that clarify this. I would delete the whole sentence. If anyone knows the exact equation for the time dilation inside a massive sphere that comes from either rigorous textbooks or peer-reviewed journal articles, that would be a valuable contribution to the physics community. 70.57.229.251 (talk) 17:51, 26 June 2018 (UTC)Karl Pomeroy


 * I'd say as long as the resulting force is null, there is no dilation. Simple as that. If Earth was hollow and you were dead in its center, you'd be floating weightless, all gravity cancelling itself out, and therefore experiencing no gravity in practice. --uKER (talk) 18:25, 26 June 2018 (UTC)


 * Thanks UKER. I agree. No gravity = no time dilation. You'd be surprised how many people argue against this on physics forums. A lot of confusion out there. And still no peer-reviewed references. 70.57.229.251 (talk) 19:58, 26 June 2018 (UTC)Karl Pomeroy


 * If to take the first formula in the present article, it clearly describes time dilation in terms of g, so traveling to the center of a planet one accumulates strictly positive quantity, so here is time dilation. In the case of a thin shell there is no difference in time flow rates for different points inside the shell (as the spacetime is flat there) and - I presume - the same for the point on the surface as well, by extension. But outside of the shell it is just Schwarzschild metric with time passing quicker at higher altitudes. So when a planet is thought as a composite of thin shells, each of them slows time flow at the center relative to the surface of the planet (which is above most of the shells).
 * Regarding the paper you cited, I didn't find a specific mention of time dilation there, but the formula they write down for the metric directly implies slower time passage in between the black holes (the closer they are relatively - the slower). But that is irrelevant since their hypothetical - stationary BH's balanced by a singularity strut - is far from both resembling a case of a spherical body and being shown possible in our world.
 * All that said, I agree that the sentence you object to is somewhat weirdly phrased in general, and that a link to a derivation of the formula tying the dilation to the potential would be great. Will try to look for one. L3erdnik (talk) 02:28, 27 June 2018 (UTC)
 * Oh well, the second reference in the article ("The young centre of the Earth") is a peer-reviewed paper estimating the accumulated time difference in the center of the Earth due to gravitational time dilation. L3erdnik (talk) 02:41, 27 June 2018 (UTC)


 * A derivation using the equations in Synge: Relativity the General Theory shows that the interior of a hollow shell is isomorphic to flat Minkowski space as expected. As such inertial clocks inside the cavity tick at the same rate as clocks at infinity Theophilus71 (talk) 03:37, 25 July 2019 (UTC)Theophilus71
 * Does an observer inside a massive sphere see blue shift for the external universe? Certainly he does. Hence there is a time dilation inside, with respect to the external universe. If there is no gravity inside the sphere, then there are no differences in proper time for stationary observers situated inside the sphere – only that. Incnis Mrsi (talk) 14:57, 25 July 2019 (UTC)
 * Yes inside a hollow sphere there will be a blue shift of in-falling photons since they are gaining energy while traversing the gravitational field in the external region. That can be shown from the generalized frequency-shift formula (which requires a solution of the geodesic equations for the null geodesics). Once inside the shell there is no additional gravitational blue shift of the photon since it is flat space in the interior.  Time dilation and frequency shift are two different effects though they can jointly contribute to observed frequency changes.   However, this topic is on gravitational time dilation -- not the cause of frequency shifts in general and all of the other causes of such. Theophilus71 (talk) 21:30, 30 July 2019 (UTC)theophilus71
 * Time dilation and blue shift are essentially the same thing; a subtle difference in a manner of synchronization may be ignored for many cases. There are distinct articles IMHO mostly because methods of measurement differ drastically. Incnis Mrsi (talk) 08:04, 31 July 2019 (UTC)

Question about a revert
Hi [Coldcreation], do you have a specific reason for reverting my edit over at Gravitational time dilation ? The r in question does refer to the 'slow-ticking' observer, and if you're someone who just wants to do a quick calculation, that section is clarified by making it explicit (it's explicit in all other occurence of 'observer' in the section). [| The diff page is here.] Ketarax (talk) 16:48, 15 February 2020 (UTC)
 * There is no such thing as a "slow-ticking observer". What was your former Username here at Wikipedia? Coldcreation (talk) 18:17, 15 February 2020 (UTC)


 * There's a "slow-ticking observer" in the clarification for t0 in that same section. There's a "fast-ticking observer" spelled out for tf.  This "fast-ticking observer" is at r=inf.  The r we're dealing with is for the "slow-ticking observer", ie. the one within the gravitational field; also, this r cannot < rs. If you want to talk about rigorous presentation of general relativity, fine, but given the purpose and present state of that page, my clarification is not making it any worse. I want you to explain to me why in your opinion it would be wrong to call the observer within the strong gravitational field "slow-ticking" in this case. Ketarax (talk) 09:38, 16 February 2020 (UTC)


 * I have never had any other accounts here at Wikipedia. I've only made a handful of minor edits (like the present one).  I started my userpage yesterday, because I wanted to make it absolutely sure you can contact me; figured out right after that it was not needed.  If you would, I'd like to also hear what about my transactions has you feeling I'm playing some username-games? Ketarax (talk) 09:20, 16 February 2020 (UTC)
 * There is no such thing as a "fast-ticking observer". More rigorous would be to write 'an observer whose clock is measured to run faster' and visa versa, instead of a "slow-ticking observer". Clocks tick, observers measure differences in time, or the relative speed at which observed clocks tick. Coldcreation (talk) 13:48, 16 February 2020 (UTC)
 * So, you are actually against the language used in the whole section. Why you didn't edit the other slow/fast-references, I don't know, but I can do that. The point I'm trying to get through here is that as it stands, the section is ambiguous about the parameter r, and that this ambiguity can be resolved by explicitly stating whose distance it refers to. I don't care if the end result speaks of slow/fast or Observer 1 and Observer 2, but this third "anonymous" observer that we currently have confuses the layman.  It might not confuse the expert -- but even an expert might overlook the ambiguity [| when pasting wikipedia in their book].  Please don't kickban (or w/e) me as a returning vandal if and when I edit it again.  I'm only interested in concise dissemination of the scientific topics I'm involved with. Ketarax (talk) 14:44, 16 February 2020 (UTC)
 * My proposed version is up now.Ketarax (talk) 15:35, 16 February 2020 (UTC)
 * Looks good. No need to use "fast-ticking" or "slow-ticking". I made a little tweak, removing the event names. - DVdm (talk) 16:06, 16 February 2020 (UTC)

Circular orbits: TD = potential TD * velocity TD
(continuation of parsing out potential and velocity TD)

You wrote "satellite speed as measured by a (hanging) shell observer is vs = sqrt(1/2 rs/r) and as measured by the far-away observer vf = sqrt( 1/2 rs/(r-rs) )" - I believe it should be the other way around. But we need the velocity as the "hanging still" clock see it, so the latter expression indeed is the v in sqrt(1-v^2) the /vel TD/. And then "/pot TD/ = sqrt( 1 - rs/r), doing this multiplication /pot TD/*/velocity TD/ would not produce sqrt( 1 - 3/2 rs/r )" - um, but ( 1 - rs/r )( 1 - ( 1/2 rs/(r-rs))) = 1 - 3/2 rs/r, exactly the (squared) full TD, no?

With regards to original research problem, I unfortunately don't have any GR books to find a reference specifically to the formula. However, wouldn't the sources you cited be enough to write something careful like "pot TD from above is /pot TD/, from /your source/ orbital velocity is such, so a satellite experiences further vel TD of sqrt(1-v^2) relative to the clocks hanging still. The total TD relative to distant observer is /TD/ which is equal to /pot TD/*/sqrt(1-v^2)/. The factorization of /TD/ in this way isn't universal." — Preceding unsigned comment added by L3erdnik (talk • contribs) 22:17, 25 September 2020 (UTC)


 * Please sign all your talk page messages with four tildes ( ~ ) — See Help:Using talk pages. Thanks.
 * Yes, sorry, it was the other way around—sloppy copy from my old T&W exercise notes . And then indeed it fits. Nice, but alas, unless we have a reliable source that makes this exact reasoning, we cannot include it in the article per wp:NOR and specifically wp:SYNTH. The reason for this is two-fold: (1) we might be making a mistake in our reasoning and the match could be a coincidence, and (2) without sources that cover this, there is no evidence of the noteworthyness of this result.
 * Furthermore, without a reliable source at hand we're not even allowed to discuss this here on the article talk page—see wp:TPG. Here we can discuss changes to the article based on RS only. That's one of the built-in safeguards of Wikipedia against never-ending arguments - DVdm (talk) 09:43, 26 September 2020 (UTC)


 * Ok, on the second thought I don't see much value in mentioning the connection itself, it can be misinterpreted easily, and I definitely don't want to fish for the reference. However, I feel it would be nice if the distinction was there, like "Shell hanging observer sees orbiter passing at the speed /v/ and time-dilated by /sqrt(1-v^2)/. Relative to faraway stationary observer, orbiter has TD of /Sqrt/." The first, you say, is in your source, and the second is already in the article. This way there should be less confusion, and there is no claim of connection, and it is (as you've personally seen:) not even suggested by the look of the expressions. That should be fine, right? L3erdnik (talk) 18:15, 27 September 2020 (UTC)
 * Alas, without a source we can't bring that time dilation factor in. There's some caveats here. For instance, that hanging shell observer is not an inertial observer, so the classic time dilation gamma doesn't necessarily apply. And dilation means "more" time, but a factor sqrt(1-v^2) gives "less" time. Dilation gamma is 1/sqrt(1-v^2). Sources, sources, sources... - DVdm (talk) 21:45, 27 September 2020 (UTC)

The closer to the source, the lower the gravitational potential??
The current text of the article reads: "The lower the gravitational potential (the closer the clock is to the source of gravitation)"... But wait... Actually, the closer the clock is to the source, the stronger is the gravitational attraction force, because the gravitational attraction force follows the inverse-square law (in this case it means that "the gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance"). So, the closer the clock is to the source of gravitation, the stronger will be the gravitational potential... Right? What did I miss here? --Siaraman (talk) 23:20, 11 December 2020 (UTC)


 * Usually the gravitational potential at a point in the vicinity of a mass is defined as the work needed to move a unit mass from infinity to that point. Thus GP is zero at infinity, and negative in the vicinity of a massive object — see Gravitational_potential:
 * $$V(\mathbf{x}) = -\frac{G M}{x},$$
 * The closer, the stronger, and thus the more negative aka lower. - DVdm (talk) 14:57, 12 December 2020 (UTC)

Where do gravitational and kinematic dilation cancel?
There is a graph near the end of this article indicating that the location of the circular orbit where there is no net time dilation is approximately at r=1.3 earth radii. When I did the calculation I found it to be closer to 6 earth radii, in the region of the geostationary orbits. I have found other sources which put it at the geostationary distance. Details can be seen at https://www.askthephysicist.com/ask_phys_q&a.html#gravdilation Ftbaker (talk) 12:15, 4 March 2024 (UTC)


 * I don't see that the article specifies this r = 1.3 earth radii. But see Time dilation, which is properly sourced, and which gives the place to be at r = 1.497. - DVdm (talk) 16:45, 4 March 2024 (UTC)
 * I withdraw my proposed correction. I was misled by an AI error, several incorrect internet posts, undue confidence in myself to be able to do the GR calculation! It is an excellent example of how incorrect an internet post can be and how AI probably learns from its memorizing everything on the web. I did more research because it seemed extremely odd that the geosynchronous orbit and the zero dilation orbit would be the same and the fact that my incorrect answer was about 10% smaller than the actual geosynchronous orbit. I believe that there is nothing significantly different from the other Wikipedia article on both relativistic and kinematic time dilation, en.wikipedia.org/wiki/Time_dilation
 * Ftbaker (talk) 16:55, 4 March 2024 (UTC)
 * Yes, when I went to that website and noticed that Artificial Idiocy entry, I closed it without even looking at the rest. Yikes. DVdm (talk) 17:15, 4 March 2024 (UTC)