Can someone explain Gravitational Time dilation?

[Radek01]

I were trying to figure out the "logic" why gravitation (acceleration) causes time dilation.

While at "velocity time dilation" its because (e.g) light in light clocks must travel longer distances.

As seen on those pics:
http://en.wikipedia.org/wiki/File:Time-dilation-001.svg
http://en.wikipedia.org/wiki/File:Time-dilation-002.svg

My problem is that material explaining "gravitation time dilation" is not much explaining. They rather say the effect is a fact, but doesn't bother to explain it same way as it's explained with velocity.

So I were thinking and I created my little "theory" why is that, so pls try to confirm or deny that:

1) look at the picture:
http://docs.google.com/File?id=dctmvpzh_61fk6ww7gr_b

2) Part A
There is a line which represents spacetime. Red dots show distance of 1 light year between the red dots. The yellow line inside a cube are my "light clocks". Meaning the yellow light will travel 1 light year to the red dot and 1 light year back to original middle red do.

3) Part B
As seen the "spacetime" is curved down, because there is an star which curve it.
So that the spacetime is curved down and distance between red dots is stretched - because of gravitation. (like human would get stretched near black hole)

And because this distance red-to-red is stratched, so it's not 1 light year anymore. Now it is let's say 1.5 light years. The same way the light years will be stretched and the yellow light will have to travel from middle red dot to the right red dot 1.5 light year, and same back. So the time will be 3 light years. So the time will be dilated.

So is this my way of understanding right? That mass objects stretch the spacetime, and therefor the light (which travels same speed in all frames) will have to travel longer distance.(like it travels during object moving.)

 

[Radek01]

I have better picture now:

http://docs.google.com/File?id=dctmvpzh_62cs97k54b_b

As visible on picture the full green line is a path of ship A - traveling thru spacetime with no gravitation influence.

While second green light shows path of ship B - which travel thru space and then travel around the high mass star. Because of gravitation it will have to travel longer distance (down to star and up from star) as shown in red color line. Which will cause time dilation.

Assume ship A has a light clock inside. And the light clock will measure 100 "cycles"
While in ship B the cycles will grow at same rate as in the ship A. Untill ship B fly to gravitation influence of star. And now because ship B (ship B's light clocks) is flying thru spacetime stretched by gravitation - so the beam in light clocks will have to travel longer distances - showing time dilation (similar to longer distances cause by movement of ship or light clocks)

a) Is this way of explanation correct?
b) How many "cycles" will ship B's light clock measure? Less then 100, more then 100, exactly 100??

 

[A.T.]

I have better picture now:
http://docs.google.com/File?id=dctmvpzh_62cs97k54b_b

[/URL]
That is not spacetime, just space. Without the time dimension in the diagram you cannot visualize gravitational time dilation.

Because of gravitation it will have to travel longer distance (down to star and up from star) as shown in red color line. Which will cause time dilation.

You idea is right, but you have to apply it to the time dimension:
http://www.physics.ucla.edu/demoweb...alence_and_general_relativity/curved_time.gif

 

[Radek01]

Thank you for reply.

Because of gravitation it will have to travel longer distance (down to star and up from star) as shown in red color line. Which will cause time dilation.

I realized this sounds bad. It sounds like I think the time is slower because it will fly more kilometres thru the "gravitation well". I ment it as it will take longer distance for the light beam inside "light clocks" to make one "cycle" inside the clocks. (while the speed is always same)

So this picture shows more accurately what I mean:
http://docs.google.com/File?id=dctmvpzh_63f22c6wdf_b

The yellow thing is sun. The tiny lines is space. Whole picture is seen from the "top". So the space bends to the sun = the space between the lines far from sun have 10 cm, and near sun the space between the lines is bigger then 10 cm.

The box with yellow V are those light clocks, where the yelow lines is light reflecting from bottom mirror to back to the top. So on the picture I assume that gravitation will cause stretch of space and the clocks itself, and the beam will take more time reflect from the mirror back to the top of clocks.

I tried to add that time curve factor, so is this correct what I wrote upwards?

 

[granpa]

imagine a rocket starting at rest beside a long line of synchronized clocks one light sec apart. as the rocket accelerates at 1G the clocks become more and more out of synch from the rockets point of view. that means that the clocks are running at different rates from the rockets point of view. if you do the math you will see that there is a point behind the rocket where time stops from the point of view of the rocket.

gravity = acceleration hence gravitational time dilation

 

[Radek01]

imagine a rocket starting at rest beside a long line of synchronized clocks one light sec apart. as the rocket accelerates at 1G the clocks become more and more out of synch from the rockets point of view. that means that the clocks are running at different rates from the rockets point of view. if you do the math you will see that there is a point behind the rocket where time stops from the point of view of the rocket.

gravity = acceleration hence gravitational time dilation

I know, I read this many times.
The problem I have is why acceleration and gravitation cause time dilation. (I know it dilate time, I don't know why it dilate time - the "logic" of this effect is what I don't know)


The logic at speed time dilation is simple - the light in "light clock" will have to travel longer path:
http://upload.wikimedia.org/wikipedia/en/thumb/a/a5/Time-dilation-002.svg/800px-Time-dilation-002.svg.png

But I don't know what's the "logic" of the grav. time dilation.

 

[Cleonis]

I were trying to figure out the "logic" why gravitation (acceleration) causes time dilation.

For a interesting visualisation of gravitational time dilation, check out
http://arxiv.org/abs/gr-qc/0411060"

Max Tegmark uses the river model in his lectures.
http://mitupv.mit.edu/wp/attach/4581/barry.pdf"

As Andrew Hamilton emphasizes, the river model can't be taken literally, but it's a good heuristic. Anything that is visualized in terms of the river model will match the predictions in terms of spacetime curvature.

I think having several different models is better. It reminds me that none of the models can be taken literally; ultimately all models/visualizations are metaphors.

Cleonis

 

[granpa]

I know, I read this many times.
The problem I have is why acceleration and gravitation cause time dilation. (I know it dilate time, I don't know why it dilate time - the "logic" of this effect is what I don't know)The logic at speed time dilation is simple - the light in "light clock" will have to travel longer path:But I don't know what's the "logic" of the grav. time dilation.

actually it has more to do with relativity of simultaneity. (this is what confuses all beginners). when the rocket is stationary all the clocks are synchronized. they tick simultaneously.

look it up on wikipedia

 

[A.T.]

The logic at speed time dilation is simple - the light in "light clock" will have to travel longer path. But I don't know what's the "logic" of the grav. time dilation.

I had some thoughts on how you could conclude gravitational time dilation geometrically using a light clock. Here is what I came up with:

http://img38.imageshack.us/img38/2484/lightclocku.png

In an accelerated frame (left bottom) light doesn't move straight, so if the mirrors were parallel the beam would not hit the same point on the mirror (normal reflection). You could however manipulate the reflection so it does (adjusted reflection). Gravitational time dilation occurs in the accelerated frame (left bottom) because the length of the path varies with the position along the direction of acceleration.

I'm not sure if all that is correct and happy about comments.

 

[Radek01]

Thank you so much for the reply.
I think it's correct. It sounds logic.

But, this would mean the position of light clocks is also important ... while I have some sense that time dilation should be "general" - and not depending on position of clocks, let me explain:


http://docs.google.com/File?id=dctmvpzh_64d5zr3jdg_b

On the left the black light beam is attracted enough by the black hole so that the light will actually never reach the second mirror.

On the right side the light beam is just slowed down (or maybe only redshifted?) and in both cases will reach the second mirror.

Problem is that B]it is not universal[/B]. It depends on the position of clocks - if they are layed horizontal the beam will not reach the mirror, while vertical the beam would be slowed down (or redshifted - I don't know).

While motion time dilation is universal. No matter what position the clocks have - the beam always have to travel larger space - with unchanged speed, therefor time dilated.

On other hand what you say is logic to me, but it's not "universal" and I have some kind of "feeling" it shouldn't matter on what position the clocks have.(just like the motion time dilation)

a) as I wrote my "theory" or the way I try understand it - that gravitation stretches space and objects. Then no matter what position clocks are, the beam will travel longer path, with unchanged speed - therefor time dilated. - I have no idea whether it's correct or not.
b) I also heard, that time dilation in accelerated frames is caused because the "process" will take more energy to happen. But the energy itself will not be increased - therefor processes will be time dilated - but this seems to me as something not probable.

 

[granpa]

no. the photon on the right will never reach the second mirror if it is released from a point which from the point of view of the second mirror is an event horizon.

 

[Radek01]

no. the photon on the right will never reach the second mirror if it is released from a point which from the point of view of the second mirror is an event horizon.

No no, I mean it as the light is released above event horizon, the "light clocks" are not in even horizon, both mirrors are slightly above it. (slightly = simply I assume the gravitation will be able to bend the light as in example on the left side.)

 

[granpa]

no. the mirror thing isn't right. the only thing it could tell you is the rate at which a clock at that poist ticks. I gave a perfectly good explanation of gravitational time dilation below. it has to do with relativity of simultaneity from the point of view of an accelerating frame

imagine a rocket starting at rest beside a long line of synchronized clocks one light sec apart. as the rocket accelerates at 1G the clocks become more and more out of synch from the rockets point of view. that means that the clocks are running at different rates from the rockets point of view. if you do the math you will see that there is a point behind the rocket where time stops from the point of view of the rocket.

gravity = acceleration hence gravitational time dilation

 

[A.T.]

But, this would mean the position of light clocks is also important ... while I have some sense that time dilation should be "general" - and not depending on position of clocks

Gravitational time dilation does in fact depend on the position of the clock. Basically you are comparing two clocks at rest to each other, but at different positions.

But maybe by "position" you mean orientation? I think it will work as well if you rotate the clock by 90° it is just harder to visualize. The vertical clock above with infinitely extending mirrors is basically an infinite number of light clock placed along the direction of acceleration. But you need at least two clocks placed along the direction of acceleration to see gravitational time dilation. This is the spacetime diagram for two horizontal (beam parallel to acceleration direction) accelerating clocks.

http://img195.imageshack.us/img195/7529/lightclocks.png

 

[Radek01]

Yes, you're right, I ment orientation - vertical & horizontal.

The graph is amazing. It perfectly shows what I wanted to see. I worked with this when visualising the speed time dilation for me, and what you draw make sense to me.

I can now imagine acceleration time dilation vertical or horizontal in spaceship accelerating, also horizontal clocks near some gravitation source. But it still makes me the problem of vertical clocks above the gravitation source. (as I showed in my last picture - on right side)

I have already found out that light can't be slowed down by gravitation, it just undergo redshift, but its speed is constant. My problem now is to imagine that light will reach the vertical mirror slower, while its speed is constant.

 

[A.T.]

But it still makes me the problem of vertical clocks above the gravitation source. (as I showed in my last picture - on right side)

This exactly what is shown here:

http://img195.imageshack.us/img195/7529/lightclocks.png

Just rotate the whole picture. You have a clock at rest in a gravitational field. In relativity this clock is accelerated upwards. To see gravitational time dilation you need a second clock at rest to the first but a bit higher. To compare their rates easily the upper mirror of the lower clock is double sided and acts the lower mirror of the upper clock. Both signals are initially simultaneously emitted from the middle mirror, but they don't return at the same time, because the upper (right on the picture) clock is faster.

I have already found out that light can't be slowed down by gravitation, it just undergo redshift, but its speed is constant. My problem now is to imagine that light will reach the vertical mirror slower, while its speed is constant.

This is tricky, since the speed of light in accelerated frames is only locally c. But the light clock has some spatial extend, so the average speed of the beam is not c:
http://en.wikipedia.org/wiki/Propagation_of_light_in_non-inertial_reference_frames

 

[pervect]

You can think of GR as just drawing the space-time of SR on an appropriate geometric surface.

The actual surface you need is described in a paper by Marolf:
http://arxiv.org/PS_cache/gr-qc/pdf/9806/9806123v3.pdf

See figure 12 for the surface.

One of the difficulties here is that you have to be familiar with SR. The space-time diagrams you draw
on the curved surface of figure 12 transform via the Lorentz transforms, they do not transform via the
more familiar Galilean transforms. Another way of saying this - x^2 + (ct)^2 is not an invariant under a
change of reference, rather (x^2) - (ct)^2 is.

This doesn't explain WHY you have to do things way - there isn't really an explanation for "why" questions
in science. All we can say is that if you do it in this manner, it seems to agree very well with experiment.

 

[AubreyC]

Should we automatically assume that the light beam would hit the "clock" receptor in a relativistic c based frame of reference? The clock base is also moving forward at the speed of light and the photon could land behind it, especially if frame of reference "momentum" does not carry it forward. I know and understand all the mathematics that derives from this premise but I think it's flawed when applied to objects traveling near the speed of light, since lights top speed is independent of the frame of reference.

 

[A.T.]

Should we automatically assume that the light beam would hit the "clock" receptor in a relativistic c based frame of reference? The clock base is also moving forward at the speed of light

The clock cannot move at the the speed of light.

and the photon could land behind it,

Not if the clock moves inertially.

especially if frame of reference "momentum" does not carry it forward.

Frames of reference don't have momentum

I know and understand all the mathematics that derives from this premise

Which premise? Galilean relativity? Or that all observes must agree if the photon stays in the clock, or not?

but I think it's flawed when applied to objects traveling near the speed of light,

"Traveling near the speed of light" relative to what? Some observer? Why schould the clock care that it is moving relative to some observer? What about the observer at rest to the clock? If he sees the photon stay in the clock, the moving observer must do so as well.

since lights top speed is independent of the frame of reference.

This doesn't imply that the photon misses the mirror in one frame, and hits it in a different one. It just implies (together with Galilean relativity) that the clock ticks slower in a frame where it is moving.

 

[AubreyC]

But the "clocks" slowdown is based on a pythagorean principle that doesn't apply at relativistic speeds.

 

[A.T.]

But the "clocks" slowdown is based on a pythagorean principle

It is based on the principle that:
- All observers agree on the speed of the photon
- All observers agree that the photon stays in the clock

that doesn't apply at relativistic speeds.

This is like saying: "1 equals 2 at relativistic speeds". I have no idea what you mean. The Pythagorean theorem is a universal mathematical rule.

 

[coldarc]

time dilation is the change in the stretch of time like a rubber band with a finite length of space stretched in time reative to rubberband with less stretch in time.
its not light that moves at a constant of 186000 miles per second but time that
moves bend twist warp distort space trough light. think of space at a distance shortned down
in time. yo get more space compressed in a second in one frame of reference than another.
time is space compressed energy. space moves in waves like electromagnetic waves.
a frequencey is number of cycles per second. you can have wavelenghts from one million cycles per second to 1 cycle per million years. if the wavelenght of light remain constant
but the wavelenght of time change the wavelenght mesured is not the length of light.
in one spacetime reference where time moves faster the freqency of light will be below light
in a reference time moves slower the frequency will be above light. the frequencey of light
is 500 mhz differentiated in only one spacetime speed of time frame of reference relationship.
if you have a mass and travel toward the speed of light you will slow down in time but
the stars around you will move faster in time trough space. its like your at rest and the stars are the travlers. the stars will come to you. the problem is not to accelerete in space
but to slow down.
mabee i just wrote a bunch of ******** you deceide.

 

[starthaus]

Should we automatically assume that the light beam would hit the "clock" receptor in a relativistic c based frame of reference?

No, we shouldn't (and we don't). The fact that the light beam "hits the receptor" is provable, with strict mathematics.

The clock base is also moving forward at the speed of light and the photon could land behind it,

Sure, it "could" but we prove that it doesn't and experiment confirms our proof.

especially if frame of reference "momentum" does not carry it forward. I know and understand all the mathematics that derives from this premise but I think it's flawed when applied to objects traveling near the speed of light, since lights top speed is independent of the frame of reference.

The proof is done strictly within the confines of SR, so we do not violate the postulate of light speed independence of the speed of the source. So, you can stop worrying...

 

[Naty1]

Radek posts:

The problem I have is why acceleration and gravitation cause time dilation.

me too. Acceleration and gravity both curve spacetime, but in slightly different ways. (Doc Al has explained this very nicely...I'll try to my copy...)

Why would you accept special relativity time dilation?? likely because it's experimentally verified (I hope)...But it makes no "sense"...until you accept that space and time are NOT fixed but the speed of light IS...but why?? nobody knows.

http://en.wikipedia.org/wiki/Time_dilation...also see there the explanation of Gravitational Time Dilation...it's frame based akin to time dilation in special relativity...

You can draw all the diagrams in the world [and I just skimmed them briefly, neat diagrams all!) but pervect has the esssential answer, I think:

This doesn't explain WHY you have to do things way - there isn't really an explanation for "why" questions in science. All we can say is that if you do it in this manner, it seems to agree very well with experiment.

Radek, you started out with curved space...or spacetime in your diagram... WHY would you accept that?? That's the craziest explanation [curved spacetime] I have ever seen, but because experiment seems to verify it's predictions, I accept it...WHY space and time are viariable and not fixed, but the speed of light IS apparently fixed is one of many scientific unknowns.

Do you know how Einstein selected his final formulation of general relativity?? He finally chose one of several formulations that he thought would [intuitively] agree with experiment!. In fact at first Einstein did NOT have the correct formulation but realized his probable error before Eddington conducted his light curvature experiment which "confirmed" GR.

 

[coldarc]

its not about a curved space at all, it about a finite length tretched in another frame of reference. you differentiate length of space in time relative to another observer.

 

[yuiop]

Should we automatically assume that the light beam would hit the "clock" receptor in a relativistic c based frame of reference? The clock base is also moving forward at the speed of light and the photon could land behind it, especially if frame of reference "momentum" does not carry it forward. I know and understand all the mathematics that derives from this premise but I think it's flawed when applied to objects traveling near the speed of light, since lights top speed is independent of the frame of reference.

If our light clock is orientated in the y direction and the clock is moving in the x direction at constant velocity then if the light source is pointed directly at the mirror, it will always hit the mirror at exactly the same spot because the mirror and the source have the same velocity in the x direction. This is guaranteed for constant inertial non-accelerating motion. If the clock is accelerating in the x direction then the light will miss the mark on the mirror because the mirror is moving faster by the time the signal gets to it, compared to the velocity of the light source at the time the signal was emitted. This means the light source has to be pointed slightly forward to compensate and hit the target on the mirror. Now if we imagine an equivalent horizontal clock that is stationary in a gravitational field, we have to aim the source slightly above the mirror because the light signal "falls" and follows a curved path like a bullet. In this way, the light clock in the accelerating rocket is equivalent to the stationary light clock in a gravitational field, because in both cases, the light appears to follow a curved path due to the acceleration, from the point of view of the accelerated observer.