Exploring Einstein's Theory of Gravity: Time Dilation and Tidal Forces

[klen]

I have some questions related to this video:

In the Einstein view of gravity, time is warped. Is this warped time same as the gravitational time dilation? In other words, is the curved time axis due to different clock speeds at different height in a gravitational field?
Further, can the tidal forces be explained in terms of gravitational time dilation?

 

[Nugatory]

In the Einstein view of gravity, time is warped.

It would be much more accurate to say that spacetime is curved. One of the effects of curvature is that initially parallel lines may converge of diverge. For example, if I pick two nearby points at the equator and draw lines due north the lines will be parallel at the equator yet will meet at the North pole.

Is this warped time same as the gravitational time dilation? In other words, is the curved time axis due to different clock speeds at different height in a gravitational field?
Further, can the tidal forces be explained in terms of gravitational time dilation?

No, for all three questions. Gravitational time dilation and the gravitational field are both caused by the curvature and not the other way around.

Tidal forces can easily be observed even when there is no gravitational time dilation. If I hold two clocks one meter apart and drop them in the Earth's gravitational field, there will be no time dilation - both clocks will read the same when they hit the floor, despite having taken different paths through spacetime - but there will be a tidal force that causes them to move closer to one another as they fall. To get time dilation, I have to send the clocks on paths of different length through spacetime, and that's quite unrelated to whether curvature causes these paths to converge or diverge.

 

[klen]

No, for all three questions. Gravitational time dilation and the gravitational field are both caused by the curvature and not the other way around.

Could you please explain the reason behind this. I see no flaw in saying that gravitational time dilation is time warping. I think the constant speed of light in the inertial frames is the cause of this time dilation which is manifested as a curved time (locally) in a gravitational field.

 

[Dale]

I see no flaw in saying that gravitational time dilation is time warping.

What is time warping?

 

[A.T.]

I have some questions related to this video:

In the Einstein view of gravity, time is warped. Is this warped time same as the gravitational time dilation? In other words, is the curved time axis due to different clock speeds at different height in a gravitational field?

Time alone cannot be "warped". You need at least one spatial dimension, with different clock rates along it. This can be interpreted geometrically as a metric of space-time.

Further, can the tidal forces be explained in terms of gravitational time dilation?

In simple terms: Gravitational acceleration is related to the first derivative of gravitational time dilation. Tidal effects are related to the second derivative of gravitational time dilation

 

[klen]

What is time warping?

The curvature of time axis is what I am calling time warping.

Time alone cannot be "warped". You need at least one spatial dimension, with different clock rates along it. This can be interpreted geometrically as a metric of space-time.

This is true, what I am saying is we can consider this time "warping" or the curvature of the time axis as can be seen in the video to be the gravitational time dilation. In other words, the difference in the clock rates at different heights is what is meant by this curved time line.

 

[Smattering]

The curvature of time axis is what I am calling time warping.

How do you define a curvature on only one dimension?

 

[klen]

How do you define a curvature on only one dimension?

Hi Smattering, as I said earlier, I am not trying to define curvature in one dimension. I am only talking about the curvilinear time coordinate which is used to explain the falling of the object "near" Earth's surface as is shown in the video, so I am neglecting the tidal effect. I understand the space-time in the given situation is flat but we are using a "curved" time coordinate since time flow now depends on height of the object. Thus I wanted to understand if the curvilinear time coordinate due to height dependent time.
I also found a link which gives a really good interpretation of GR:
http://spark.sciencemag.org/generalrelativity/
I think the explanation in the link is in line with what I was trying to say so I think I am right.

 

[Dale]

The curvature of time axis is what I am calling time warping.

As others have pointed out, a 1D line, like the time axis, has no intrinsic curvature. However, it can have extrinsic curvature. The extrinsic curvature of the time axis would represent the proper acceleration measured by an accelerometer at rest wrt the reference frame.

This is not what causes gravitational time dilation. Gravitational time dilation is due to a difference in the gravitational potential, not the gravitational acceleration. For example, a clock inside a hollow sphere will be time dilated despite having an "unwarped" time axis.

As a general suggestion, when learning a new field, it is better to try to learn the standard terminology rather than invent your own.

 

[klen]

As others have pointed out, a 1D line, like the time axis, has no intrinsic curvature. However, it can have extrinsic curvature. The extrinsic curvature of the time axis would represent the proper acceleration measured by an accelerometer at rest wrt the reference frame.

As I have already said I am not talking about curvature but curvilinear time coordinate:

Hi Smattering, as I said earlier, I am not trying to define curvature in one dimension. I am only talking about the curvilinear time coordinate which is used to explain the falling of the object "near" Earth's surface as is shown in the video, so I am neglecting the tidal effect. I understand the space-time in the given situation is flat but we are using a "curved" time coordinate since time flow now depends on height of the object.

Also I do not understand what do you mean by time dilation inside a hollow sphere. Since it has no gravitational field, time would flow at same rate at any position inside hollow sphere. So when you are saying dilated, dilated with respect to what?

a clock inside a hollow sphere will be time dilated despite having an "unwarped" time axis

 

[Dale]

As I have already said I am not talking about curvature but curvilinear time coordinate:

Did you not read my comments on extrinsic curvature (the correct term for your "curvilinear or warped time) as well as the connection to proper acceleration and accelerometers at rest? I explained the physical meaning of your "curvilinear time coordinate"

It would very much help if you would adopt the standard terminology once it has been pointed out. I am trying to help you learn the language as well as the physics of the concepts you are grasping at.

Also I do not understand what do you mean by time dilation inside a hollow sphere. Since it has no gravitational field, time would flow at same rate at any position inside hollow sphere. So when you are saying dilated, dilated with respect to what

With respect to a clock outside the sphere

 

[klen]

With respect to a clock outside the sphere

If you are considering dilation w.r.t to clock outside the spherical shell, then I think you are wrong in saying that time does not have extrinsic curvature, now using the correct terminology according to you. This is because as we cross the boundary of the shell we would see the curved (extrinsic) time axis.Clearly, as you said, the dilation only makes sense once we cross the surface of the spherical shell because then only we can say that time inside the shell is dilated. So time is not "unwarped" as you said.

I am trying to help you learn the language as well as the physics of the concepts you are grasping at.

I understand that and I am also trying to learn from you but still not convinced with your arguments.

 

[Dale]

Clearly, as you said, the dilation only makes sense once we cross the surface of the spherical shell because then only we can say that time inside the shell is dilated.

The fact that you have to know the gravitational acceleration (extrinsic curvature of time axis) between the clocks is directly related to the fact that gravitational time dilation is a function of the gravitational potential.

See page 103 here http://arxiv.org/abs/gr-qc/9712019

I understand that and I am also trying to learn from you but still not convinced with your arguments.

I am not interested in arguing or convincing. If you are interested in learning then I am glad to help. Otherwise you can just read the textbook.

 

[klen]

The fact that you have to know the gravitational acceleration (extrinsic curvature of time axis) between the clocks is directly related to the fact that gravitational time dilation is a function of the gravitational potential.

I know all this and I in my original question I did not ask for reason as to why clocks in gravity run at different speeds. I was trying to ask about its implications.

a clock inside a hollow sphere will be time dilated despite having an "unwarped" time axis.

This is not true. The difference in gravitational potential between any two points inside hollow sphere is zero, so time is not dilated inside the hollow sphere if we are restricting ourselves inside the hollow sphere.
Hi DaleSpam,

With respect to a clock outside the sphere

If you are considering w.r.t. clock outside the sphere then there is gravitational potential between any point outside and inside the sphere so time is dilated and is not "unwarped" in this case. Again your original statement time can be dilated despite "unwarped" time axis is wrong.

Gravitational time dilation is due to a difference in the gravitational potential, not the gravitational acceleration

I never said this. In the original question I was asking about time dilation near the surface of the Earth and I know that acceleration due to gravity is same near the surface of the earth.

A note on terminology:
From mid-1911 to mid-1912, Einstein tried to explain tidal gravity
by assuming that time is warped, but space is flat
(Reference: Black Holes and Time Warps, Einstein's Outrageous Legacy - Kip Thorne, p. 107)

An example is the transition from an inertial reference frame (in which free particles coast along straight paths at constant speeds) to a rotating reference frame (in which extra terms corresponding to fictitious forces have to be introduced in order to explain particle motion): this is analogous to the transition from a Cartesiancoordinate system (in which the coordinate lines are straight lines) to a curved coordinate system (where coordinate lines need not be straight).
(Reference: Wikipedia, https://en.wikipedia.org/wiki/Introduction_to_general_relativity)

in general, rays of light are propagated curvilinearly in gravitational fields
(Reference: Relativity: The Special and General Theory - Albert Einstein, p.65)

These references are standard enough for me to use the terms from them in my question. These terms are not a product of my own neologism. Further, I know the difference between intrinsic and extrinsic curvature and it is totally irrelevant to what I intended to ask in my question.

If you are interested in learning then I am glad to help. Otherwise you can just read the textbook.

I am reading books on GR, thank-you for the advise. I would also advise you the same because looking at your answers I think you require to brush up your concepts.

 

[martinbn]

In my opinion, Klen, your phrasing is too imprecise and non-standard. That's what causes the miscommunication. Time is not a natural concept in relativity, except of course for proper time. Thus when you refer to time as if there is one unique such thing it is very unclear what you mean and it seems that you are using classical (non-relativistic) intuition. Forget the popular book, find one modern textbook on general relativity that uses the phrase " time is warped" and then we can see what you actually mean.

 

[Dale]

I know all this

Excellent. Since you already know all this then we can close this thread and help other people who do not have such advanced understanding as you.