How can time dialation cause gravity?

[Paul77]

Hi,
I believe the general notion is that gravity is an effect caused by the warping of spacetime.
I've read that clocks are running faster in Satellites by about 50 micro seconds per day (or 2 micro seconds per hour) compared with on the Earth's surface.

As one moves from the Satellite towards the Earth and starts to experience the Earth's
gravitational field clocks start to slow so the difference in time with Earth reduces even further presumably.

Does'nt it seem odd that one million of a fraction of something can lead to a force of 9.8 m/s/s?

Are there any papers that have derived a value of g=9.8 m/s/s from such spacetime distortions?

Paul

 

[A.T.]

Does'nt it seem odd that one million of a fraction of something can lead to a force of 9.8 m/s/s?

Numerical values depend on the used units . And speaking of units: "9.8 m/s/s" is not a force.

 

[Paul77]

ok g, refers to the acceleration that the Earth imparts to objects on or near its surface
its not a force. The point I was making is that the laymen explanation for gravity normally involves a ball rolling round a curved spacetime surface but the scale looks all wrong if the surface is only curved by something like a factor of one millionth of a unit of spacetime - has anyone ever addressed this contradiction??

 

[A.T.]

The point I was making is that the laymen explanation for gravity normally involves a ball rolling round a curved spacetime surface

Try this, for better analogies:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

Or this:
http://www.relativitet.se/spacetime1.html

but the scale looks all wrong

Which scale? The usual scale is 1 second : 1 lightsecond.

 

[Jonathan Scott]

ok g, refers to the acceleration that the Earth imparts to objects on or near its surface
its not a force. The point I was making is that the laymen explanation for gravity normally involves a ball rolling round a curved spacetime surface but the scale looks all wrong if the surface is only curved by something like a factor of one millionth of a unit of spacetime - has anyone ever addressed this contradiction??

If you think of that tiny curvature of space-time as being something like 1/R for some huge value of R, then to convert it to an acceleration you multiply it by c², which is big.

 

[Dale]

Does'nt it seem odd that one million of a fraction of something can lead to a force of 9.8 m/s/s?

You have to remember that g = 9.8 m/s² is given in SI units, which are very anthropocentric, if you put g into natural units like Planck units you see that it is 1.7E-51 PlanckLengths/PlanckTimes². So g only appears large in human-sized units.

Another way to think of it is to realize that you have to scale time by c in order to get distance. So, if you drop a ball for 1 s it will fall 4.8 m in space and c 1s = 3E8 m in time. This leads to a ratio of about 1 in 60 million. So the small curvature in time is on the right order to be appropriate. (Note, this is all very much a "hand waving" argument, but it works out rigorously)

 

[Paul77]

If you think of that tiny curvature of space-time as being something like 1/R for some huge value of R, then to convert it to an acceleration you multiply it by c², which is big.

Presumably R is from the middle of the Earth's to say the satellite - since in space you are in zero gravity. So the spacetime curveture is very slight and I would'nt expect a ball to roll
down it. I don't see why the speed of light needs to be introduced - the Earth may be moving very fast in space but so is the object falling towards its surface.

 

[Paul77]

You have to remember that g = 9.8 m/s² is given in SI units, which are very anthropocentric, if you put g into natural units like Planck units you see that it is 1.7E-51 PlanckLengths/PlanckTimes². So g only appears large in human-sized units.

Another way to think of it is to realize that you have to scale time by c in order to get distance. So, if you drop a ball for 1 s it will fall 4.8 m in space and c 1s = 3E8 m in time. This leads to a ratio of about 1 in 60 million. So the small curvature in time is on the right order to be appropriate. (Note, this is all very much a "hand waving" argument, but it works out rigorously)

Re: Another way to think of it:
I'm sure your right but I don't see why you have to scale time by the speed of light.
"and c 1s = 3E8m in time" is that "and c x 1s = 3E8m in time"

 

[Jonathan Scott]

Re: Another way to think of it:
I'm sure your right but I don't see why you have to scale time by the speed of light.
"and c 1s = 3E8m in time" is that "and c x 1s = 3E8m in time"

The radius of curvature of space-time corresponding to a gravitational field is measured from the current point on the path in the direction of the field. Its value for acceleration g is g/c².

Most of the effect of gravity is due to the curvature of space-time with respect to time. If you are moving slowly in space you are still moving through time at "full speed", which is c in equivalent units. In simple cases with central masses, the curvature with respect to space and time is approximately equal when expressed in equivalent units.

If you move with speed v through space on a path which is curved with radius R, your acceleration is v²/R. If you move through time with the same space-time curvature, your effective "speed" through time is c, so your acceleration is c²/R. For something moving through space at or near speed c, these effects (loosely speaking) add up and the acceleration is actually 2g, so for example light passing the sun is deflected twice as much as Newtonian gravity would predict.

 

[D H]

Presumably R is from the middle of the Earth's to say the satellite - since in space you are in zero gravity.

Whoa! In both Newtonian physics and general relativity, the Earth's gravitational influence does not stop just because something is outside the Earth's atmosphere. Think about it this way: The Moon is orbiting the Earth.


Now to the original post:

Does'nt it seem odd that one million of a fraction of something can lead to a force of 9.8 m/s/s?

You have cause and effect backwards. Time dilation does not cause gravity; it is gravitation that causes time dilation.

 

[Dale]

I'm sure your right but I don't see why you have to scale time by the speed of light.

In order to convert from seconds to meters. You have to have everything in the same units or the comparison doesn't make sense.

In your OP you compared the ratio of two times, which is a dimensionless number, and came away with the feeling that that dimensionless number is too small to make a difference for g. To see if that is correct you must compare it to another dimensionless number which is related to g. So the distance a ball falls is in units of length so we need to change the time it took to fall into a length also in order to get a dimensionless number. To turn a time into a length you multiply by c.

"and c 1s = 3E8m in time" is that "and c x 1s = 3E8m in time"

Yes.

 

[Paul77]

I'm still digesting all the other posts but wrt:

"You have cause and effect backwards. Time dilation does not cause gravity; it is gravitation that causes time dilation"

Have I really got this wrong as well! I thought that relativity is based on the idea that there is no absolute frame of reference to measure anything against and we have to rely on comparing
frames of frames - and that since electro-magnetic radiation has 'no mass' it represents the fastest frame you are going to get. And as there is a limit to speed, time and space are no longer fixed which leads to the concept of the curveture of spacetime and bodies such as the moon traversing the curveture created by the Earth, ie gravity derives from the curveture of space time which results from time and space dilation/contraction. Or is the speed of light being a limiting factor a red herring?

 

[Theheretic]

Wow I just had an epiphany moment thanks to you Paul77.

So EMR is massless and that's why it's considered the fastest speed possible in the universe because anything with any mass cannot possible go as fast as something massless without requiring infinite energy to get it to go that fast...is that the gist of it?

 

[Paul77]

Wow I just had an epiphany moment thanks to you Paul77.

So EMR is massless and that's why it's considered the fastest speed possible in the universe because anything with any mass cannot possible go as fast as something massless without requiring infinite energy to get it to go that fast...is that the gist of it?

Is'nt that the general idea? The proton beams in a collider can't reach the speed of light can they?

 

[D H]

I'm still digesting all the other posts but wrt:

You have cause and effect backwards. Time dilation does not cause gravity; it is gravitation that causes time dilation.

Have I really got this wrong as well!

Yes, you have that wrong as well. Time dilation, specifically gravitational time dilation, is a consequence of the Einstein field equations. Einstein's field equations are the best description of gravitation we have. You are writing as if it is the other way around, that time dilation causes gravitation. This is just bass-ackwards.

Where did you get the idea that time dilation causes gravity?


As a counter-argument, imagine two small spaceships in deep space moving toward one another at a speed close to that of light, but with the trajectories offset somewhat so that they don't collide at closest approach. Because these two spacecraft are moving very fast relative to one another, a large special relativist time dilation is involved. This does not cause gravitation.

I thought that relativity is based on the idea that there is no absolute frame of reference to measure anything against and we have to rely on comparing frames of frames - and that since electro-magnetic radiation has 'no mass' it represents the fastest frame you are going to get.

Yes, light speed is the universe's ultimate speed limit. However, it doesn't make sense to talk about a reference frame moving at c. For example, see http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html" at the physics FAQ and see [post=1088264]this post[/post] at this site (there are many others; this faulty concept keeps coming up).

 

[Paul77]

Where did you get the idea that time dilation causes gravity?

Because if time dilates in an event being observer then has’nt the time component of spacetime dilated?


To get a better understanding of time dilation have looked at the Kennedy-Thorndike experiment - one of the first experiments to demonstate time-dilation. My understanding of this is:

- a light beam is separated and when they are recombined a fringe pattern is produced.

- one light beam path, A, can be affected by changes in the velocity of the apparatus (due to the Earth’s spin/orbit being in the direction of that path) making the path of that beam shorter or longer (ie the distance it travels to the first mirror (M) it hits after being split). But the experimenter never observes a shift in the fringe pattern caused by the re-convergence of the two light beams.

- if for instance path A is lengthed then: the distance the light beam has traveled has increased but, the speed of the beam is still c, the fringe pattern has not altered therefore time has dilated (slowed).


-since the light beam (A) has to travel further, before hitting mirror (M), one would expect more wavelengths are produced to get there but that would mean the
recombined beams could be at a different phase. But since no change is observed in the resulting fringe pattern this implies that the same number of wavelengths are produced but that they are stretched out to cover a greater distance by being given more time.

Is this about right or wide of the mark?

 

[D H]

Because if time dilates in an event being observer then has’nt the time component of spacetime dilated?

No.

Moreover, this does not answer my question, which was what led you to the notion that time dilation causes gravity.

To get a better understanding of time dilation have looked at the Kennedy-Thorndike experiment - one of the first experiments to demonstate time-dilation.

The Kennedy-Thorndike experiment is a test of special relativity. It has nothing to do with gravitation.

 

[Paul77]

No.

Moreover, this does not answer my question, which was what led you to the notion that time dilation causes gravity.

I got the notion from the idea that if time dilates then spacetime dilates and so spacetime is warping, if you sum the warps you would get curved spacetime over a larger area and
objects will follow the curves in spacetime which gives the illusion of gravity.

The Kennedy-Thorndike experiment is a test of special relativity. It has nothing to do with gravitation.

Agreed its a test of special relativity. I was looking at it with a view to understanding more
about time dilation following your comments - but its originally where I got the above idea. Re: Kennedy-Thorndike - you have'nt commented on how I think the experiment works - what do you think of the idea that the number of wavelengths, on the path that has lengthened, remains the same even though the mirror has moved?

 

[D H]

This thread is verging on personal theories, which are a definite no-no at this site.

Your notion of spacetime dilating is mistaken. It implicitly assumes an absolute reference frame, and there is no such thing. Suppose you and I are in two spacecraft in deep space such that we are moving at a relativistic speed with respect to one another. Everything is normal as far as I am concerned. My watch reads just the same as it did before I saw your spacecraft ; the same goes for my meter stick. As far as I am concerned, it is your watch and your meter stick that are funky. Now let's look at things from your perspective. Everything is normal from your perspective, too. Your watch and your meter stick are just fine, thank you. It is my watch and my meter stick that are funky as far as you are concerned.

 

[Paul77]

Re: your example of two spacecraft - I'm aware of the idea of special relativity - but mainly I've been interested in how the theory originated. So I've read up on the Kennedy-Thorndike experiment, frames of reference, lorentz transformation, rapidities, how rapidity is a tanh and therefore how nothing can go faster than c which then causes time dilation.

Re: "your notion of dilating spacetime is mistaken" - what your saying here is that I'm mixing up the concepts in special relativity with those in general relativity - ie time dilation and spacetime and they are separate things.

 

[D H]

Exactly. Special relativity has nothing to do with gravitation. The word 'special' in this context means the theory pertains to inertial frames only. The concept of inertial frames in special relativity is identical to the concept of inertial frames in Newtonian physics.

In other words, no gravity.

If you truly are interested in the way special relativity originated you need to go back to Maxwell's equations.