# Looking for Layman's Physical Explanation for Gravitational Time Dilation

1. Dec 3, 2008

### stuper

I'm looking for a simple physical explanation of gravitational time dilation, so I can provide a brief explanation to interested laypeople (not to mention just to help myself understand better). Does anybody want to take a crack at it? Or am I asking for the impossible?

2. Dec 3, 2008

3. Dec 3, 2008

### George Jones

Staff Emeritus
4. Dec 3, 2008

### Jonathan Scott

I don't know exactly what you're looking for, but the basic principle is simply that where in Newtonian gravity you have potential energy, in relativistic gravity you have time dilation.

For example, if you move something of mass m from distance r1 to distance r2 from a mass M, the change in potential energy is

-m(GM/r2 - GM/r1)

= -GMm(1/r2 - 1/r1)

Dividing by the rest energy mc2, that means the fraction by which the time rate changes is as follows:

-(GM/c2) (1/r2 - 1/r1)

This is only an approximation, but a very accurate one for weak gravitational fields such as those within the solar system.

5. Dec 3, 2008

### stuper

Thanks for the responses so far. George, I need to spend a bit more time on your's -- it looks promising, although at first glance it seems to be backwards from what I understood from the book I'm currently reading (Schutz's "Gravity from the ground up").

Here's what I'm looking for more precisely. Let's say I'm having a casual conversation with a relatively (NPI) non-scientific friend, and I mention that time runs slower near a large mass than it does in outer space. He/she is immediately going to ask for an explanation. How am I going to explain this idea in non-technical language without getting into the equivalence principle and the frequency of light waves, etc.? Is there any short, simple way of giving a layperson at least a little inkling of the physical basis behind this phenomenon?

At this point, the simplest explanation I've heard is that both time and space become more curved and thus more dense near a large mass. However, when I think about this it seems to me that time should move faster near a large mass. If you imagine time/space laid out in a grid sort of like latitude/longitude lines, more curved and dense means that the lines are closer together, which means it should be easier to cross more lines (i.e., time moves faster, which I know is not the right conclusion). I'm know I'm thinking about this backwards somehow, but I can't quite see how closer together grid lines translate to slower time.

Then again, maybe somebody else has an even better way of explaining it without the grid lines idea.

6. Dec 4, 2008

### Jonathan Scott

The idea that space-time is "denser" near masses is a possible approach. One way to think about it is to assume that the coordinate speed of light c gets slower closer to masses, by a fraction 2Gm/rc2. In an isotropic coordinate system (one where the variation of c is the same in all directions) rulers shrink approximately by Gm/rc2 and clocks run slower by the same factor. This means that locally observers can't detect this change in the speed of light.

7. Dec 4, 2008

### A.T.

Not sure what you mean with "physical explanation". Here is a simple explanation how gravitational time dilation follows from the geometrical model of GR.
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

8. Dec 4, 2008

### DrGreg

Consider an apple dropped from the top of a tall building. According to Newtonian theory, the building is stationary and the apple accelerates downwards. According to general relativity, the apple is stationary (or, more accurately, "inertial") and the building accelerates upwards.

The acceleration due to gravity varies with height: it's higher at low altitudes. So the bottom of the building accelerates more than the top of the building. Yet the height of the building is constant. The only way to make sense of this is that the two accelerations are being measured by different clocks ticking at different rates.

That's a gross over-simplification, but in essence that's what gravitational time dilation is. (It's an oversimplification because distance as well as time is affected and the argument above isn't good enough to distinguish both effects.)

9. Dec 4, 2008

### A.T.

Sounds very misleading to me. In a homogeneous G-field the acceleration doesn't vary with height, but clocks rates still do.

10. Dec 4, 2008

### DrGreg

If, by a "homogeneous G-field" you mean a "uniform" field, i.e. as described by the Rindler metric, you are wrong, the acceleration does vary with height. If you mean something else then maybe it doesn't, but I suspect in that case there might be no dilation either.

11. Dec 4, 2008

### A.T.

What if not acceleration is uniform in a uniform gravitational field?

12. Dec 5, 2008

### DrGreg

Sorry, I don't understand your question. Can you rephrase it?

13. Dec 5, 2008

### A.T.

I'm just trying to understand, what quantity is "uniform" in a "uniform gravitational field", since you claim that acceleration is different at different places in such a field.

Going back to the original question: I think that gravitational time dilation would occur in a field with the same (non zero) acceleration at every point. By Analogy: In rocket with constant acceleration, the front clock runs faster than the back one, while both experience the same acceleration.

14. Dec 5, 2008

### DrGreg

Check out "Born rigid acceleration". The back of the rocket accelerates more than the front.

To maintain a constant length in its own frame, its length must contract in an inertial frame. To contract, the back must accelerate more that the front.

If both ends had the same acceleration, the rocket would get longer in its own rest frame. See "Bell's spaceship paradox".

Because of the "Born-rigid" effect, a "uniform gravitational field" is usually considered to be one in which free-falling objects that are initially stationary relative to each other will remain stationary relative to each other, and this implies a change in proper-acceleration over distance.

The Rindler metric applies equally to a Born-rigid accelerating rocket in empty space and a "stationary" observer in a "uniform gravitational field". Both spacetimes have zero curvature but exhibit "gravitational" time dilation.

I think I read somewhere (but I could be wrong) that a gravitational field with constant "acceleration" everywhere is impossible.

15. Dec 5, 2008

### A.T.

Thanks for the explanations DrGreg.
I didn't know this. But I assumed that in such a (potentially impossible field) there still would be a red/blue shift of light and therefore gravitational time dilation.

16. Dec 7, 2008

### feynmann

Alice and Bob are in a rocket accelerating upward in empty space. Alice, in the nose, emits signals at equal intervals on a clock there. The acceleration means that Bob, in the tail, measures a smaller interval between the received signals, why?
Einstein's equivalence principle says that acceleration and gravity are equivalent. So it should happen in a uniform gravitational field too.

17. Dec 7, 2008

### Staff: Mentor

Sometimes it helps to describe some experimental result first, and then describe the theory that explains it. So in this case I would start with a brief description of a gravitational redshift experiment, and then relate that to the speed of a clock, and then you have gravitational time dilation.

18. Dec 13, 2008

### feynmann

Kip Thorne's Black Holes and Time Warps. In it, he proposes a thought experiment (which he attributes to Einstein) which demonstrates gravitational time dilation.
--------------------------------------------------------------------

Take 2 identical clocks. Place one on the floor of a room next to a large hole, and attach the other to the room's ceiling by a short string.

The ceiling clock emits pulses of light at each tick and directs them downwards toward the floor clock. Immediately before the first pulse, cut the string so that the ceiling clock is now falling freely. If it is ticking fast enough, then the duration between the first few ticks will be governed by the 'ceiling' time, as it will not have fallen appreciably yet.

Immediately before the first pulse hits the floor clock, drop the floor clock into the hole. Similarly, this clock will feel 'floor' time for the first few ticks.

Now, because the ceiling clock was dropped before the floor clock, its downward speed is always greater than the floor clock. This implies that the floor clock will see the ceiling clock's pulses Doppler shifted (slightly faster). Since the time between pulses was regulated by the ceiling's time flow, this means that time must flow more slowly near the floor than near the ceiling; in other words, gravity must dilate the flow of time.

---------------------------------------------------------------------

19. Dec 14, 2008

### yuiop

First, an easy to visualise physical illustration of what is happening, before attempting an explanation. Imagine you have a cannon that is connected to clock and is designed to fire one baseball per minute. This device is lowered into a hole that goes deep into the massive body. (Imagine it is a bit more massive and dense than the Earth). Now, when the cannon is fired upwards the baseballs arrive at the surface at intervals of say 61 seconds, according to the clock of the observer at the surface. In this example it is not the frequency of individual baseballs that changing unlike the example given using photons and it easier to see in this case that the clock controlling the cannon really is running slower than the clock at the surface. Now the principle behind this is that whatever must happen to ensure a local observer will always measure the local speed of light as c will happen.

Another example was hinted at in another post and although it uses the equivalence principle, it is fairly intuitive if you accept that clocks moving at relativistic speeds relative to an observer, run slower (as predicted by Special Relativity). Consider a very long rocket that is so long it takes light one second to traverse the length of the rocket. Now imagine a signalling device in the nose of the rocket sends signals to the base of the rocket at one second intervals, as controlled by a clock in the nose of the rocket. Now if the rocket accelerates upwards at a rate of 10 m/s/s, the base of the rocket is always moving 10 m/s faster than the nose of rocket by the time a signal tranverses the length of the rocket. A clock at the base of the rocket will be running slower (due to SR time dilation) at the time it receives the signal, relative to the rate of the clock in the nose the time the signal was emitted. The observer in the base of the rocket perceives the signals to be arriving at interval of less than one second because his clock is effectively running slower at the time he receives the signals relative to the clock at the time the signals were sent. I am igoring length contraction of the rocket in this example, as that is probably getting too complicated for a laypersons explanation to a friend.

Now the equivalence principle says that if the rocket was standing on the surface of a gravitational body with a gravitational acceleration of 10m/s/s the measurements inside the rocket would be exactly the same and in order for that to be so, the lower clock has to run slower due to the presence of the gravitational field.

It would be easier for light to cross more lines in the grid where the grid lines are closer to each other and that would make light appear to be moving at greater than c according to a local observer, so everything has to slow down in the denser parts of the grid to make the speed of light constant where ever you are. It is a bit mysterious as to why nature insists that everyone should observe the speed of light to be locally constant, but that is the way it seems to work.

20. Dec 15, 2008

### A.T.

You are confused, because you mix up two different(but equivalent) ways to visualize curvature:

1)
A grid with different distances between grid lines, but same density everywhere. Here the distances between grid lines(of space and proper time) are greater near a mass, and every object advances with the same constant velocity(with respect to coordinate time). So objects near the mass need more coordinate time to reach the next grid line of their proper time.

For the laymen: Imagine you track a plane flying with a constant velocity to the west on a globe. You see it advancing with a constant speed, so if it is closer to the equator, its needs longer to pass meridians, due to greater spacing.

2)
A grid with equally spaced grid lines, but varying density between them. Here the density is greater near a mass, and objects advance slower trough that area. So again they need more coordinate time to reach the next grid line of their proper time in the denser area.

For the laymen: Imagine you track the same plane on a flat map of the world (http://en.wikipedia.org/wiki/Mercator_projection" [Broken]). The spacing of meridians is the same everywhere, but you see the plane advancing slower, near the equator, as if the area there was denser.

You can compare both ways here (left : way 2, right : way 1):

Last edited by a moderator: May 3, 2017
21. Dec 16, 2008

### feynmann

So we can explain gravitational time dilation using Newtonian gravity. We know gravitational time dilation and curvature of time are the same thing. Schutz explain that "All of Newtonian gravitation is simply the curvature of time." Isn't this reasoning circular?
So I think gravitational time dilation is more fundamental and it's better to explain it using Doppler effect in SR and equivalent principle. (Schutz book: Gravity from the Ground Up)
http://www.gravityfromthegroundup.org/pdf/timecurves.pdf

Last edited: Dec 16, 2008
22. Dec 16, 2008

### A.T.

Physics is about describing how nature works using math. It doesn't really explain anything.
Gravitational time dilation and Newtonian gravity are observed natural phenomena, which can be described using a mathematical model of curved spacetime. The observed phenomenon and the mathematical model are not the same thing.

23. Dec 16, 2008

### feynmann

What do you think a "theory" is? e.g. <Einstein's General Theory of Relativity>
Here is the Definition of theory from the Merriam-Webster Online Dictionary
Theory: a plausible or scientifically acceptable general principle or body of principles offered to EXPLAIN phenomena <the wave theory of light>

You mixed up two different things: gravity and Newtonian gravity.
Gravity is observed natural phenomena. Newtonian gravity is Newton's theory of gravity.
His theory can "explain" a lot of thing that agree with experiments!!

Last edited: Dec 16, 2008
24. Dec 17, 2008

### A.T.

If you accept what physical theories do as "explaining", thats fine with with me. For me an equitation doesn't really explain anything, it just describes.
Yes. And if you apply the same distinction, you don't get any "circular reasoning" you mentioned before:
Not "the same thing":
Gravitational time dilation - observed phenomenon
Curvature of time - mathematical model
No. Newtonian gravity describes only mass attraction. Curved time describes both: mass attraction and gravitational time dilation.

25. Dec 17, 2008

### michelcolman

This is a beautiful explanation, but... Wikipedia says gravitational time dilation is at its maximum at the surface of the sphere, and minimum at the center (and at infinity as well). Which makes sense, as the clock at the center does not experience any net gravity and is essentially in "free fall" while the clock at the surface is feeling an accelleration due to gravity.

So actually, the clock at the surface should be ticking more slowly, not the clock at the center. Right?

Disclaimer: I'm making my first baby steps in general relativity so I could be completely wrong.