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Author Topic: General Relativity Thought Experiment  (Read 1703 times)

Offline AndroidNeox

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General Relativity Thought Experiment
« on: 16/07/2015 03:12:13 »
A general relativity thought experiment considering time rates in different reference frames experiencing identical acceleration and no relative motion.

Suppose:
On  a planet-sized, non-spinning, homogeneous sphere, floating freely in space, there’s a tall tower. On the tower are a laser, a clock synchronized to the laser (counting wave cycles and dividing by the laser's fixed frequency, f0), & a light receiver that measures frequency of an incoming laser beam and runs a second clock (also counting f0 wave cycles per second). The laser and receiver are focused on an identical set of equipment located at the bottom of a vertical shaft, directly below the tower. And, the laser and detector at the bottom of the shaft are, likewise, focused on the detector and laser, respectively, on the tower.

The tower height and shaft depth are selected to have the same gravitational acceleration, g0, which is less than the surface gravity.

Because both locations experience identical gravity, and are stationary with respect to each other, relativity requires that clocks in each location will run at the same rate.

Observations:
Because the light path from shaft bottom to tower top is up-hill all the way, light arriving at the tower from the shaft will have diminished frequency (and its clock will run slower) while light originating on the tower will be blue shifted, to higher frequency, by the time it arrives at the bottom of the shaft. Both sets of clocks will show time running faster on the tower than down in the shaft. The two beams follow identical, though opposite, fixed-length paths, so the constantly accumulating difference in the wave cycle counts can only be explained by a difference in time rate.

My conclusions:
While the force vectors in 3-space can be canceled out, the total field and consequent time dilation must only accumulate. In this model, the center of mass of such a sphere would only be a local minima in spacetime. Just because there’s no net gravity in one location doesn’t mean it's not uphill and/or downhill from other frames of reference, also of zero gravity.

I am guessing the time dilation at the center of the sphere will be that one would expect from a field proportional to the sphere's mass density multiplied by its radius... mass divided by distance squared.

Changes in potential energy require changes in time rate.

I would appreciate your thoughts.


 

Offline chiralSPO

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Re: General Relativity Thought Experiment
« Reply #1 on: 16/07/2015 04:29:18 »
I'm certainly no expert in this field, but I suspect that if the acceleration at the base of the shaft and at the top of the tower are identical, then there will not be any redshift. And if any redshift were observed then the acceleration would have to be different.

Imagine for instance that you constructed the same type of setup, except instead of a tower and a shaft, the two laser/clock units are on the surface of the planet, on opposite sides, and the laser is shining through a tunnel that goes through the core of the planet. The acceleration values at the two positions are identical, and any shifting* of the light that occurs as it goes towards the center of the planet would be exactly cancelled out as it went away again, back to the surface on the other side. In the same way, in the setup you described, the light would shift as it went from the bottom of the shaft to regions of increasing acceleration, and then through decreasing acceleration up to the tower.

As far as I know, the observed frequency should depend only on the conditions of the observer and the emitter, and the original frequency of the light as emitted, and should have no dependence on the path taken by the light (unless it interacts directly with matter along the way...)

*What I mean is if an observer at any point along the path intercepted the light at these different positions, their observations would be different, unless they were in those special positions.
 

Offline David Cooper

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Re: General Relativity Thought Experiment
« Reply #2 on: 16/07/2015 22:22:55 »
It looks as if the experiment needed to settle this has not been done, and the reason for that may be that the density increases for some time as you go deeper underground and that this leads to gravity continuing to increase for a long time before it starts to fall. You'd need a hole going deep enough to get beyond the point where it finally starts to fall, and that might take you well down into the hot liquid stuff. So, it seems that we are left to guess what happens and are merely going by assumptions. The standard assumption appears to be that time will continue to run more slowly all the way down to the centre of the Earth where it will run 1.0000000003 times slower than it does at the surface. Quite how clocks know to slow down at depth is another matter, because if gravity is just the curving of space time (as in GR), it will need to have an additional physical aspect added to that structure to keep track of how deep in a gravity well it is so that the clock knows to run at the right rate (and light knows how much to slow down).
 

Offline jeffreyH

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Re: General Relativity Thought Experiment
« Reply #3 on: 16/07/2015 23:23:20 »
This is like a situation with a cavity at the centre of gravity of a large mass. I did a lot of investigating on that one and came to some very erroneous conclusions. I have since corrected those. This sort of central cavity would be a good laboratory for investigations into the operation of gravity. As black holes collapse from the centre then the most extreme force must also reside here. Extreme is a relative term as for a mass of low density the forces would be weak. It is only when density increases significantly that the 'laboratory' becomes interesting. The forces focused at the centre of gravity may show some interesting effects. That is why I have asked questions as to whether the strength of gravity has been measured in deep mines in comparison with the surface strength.
 

Offline David Cooper

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Re: General Relativity Thought Experiment
« Reply #4 on: 17/07/2015 18:00:53 »
That is why I have asked questions as to whether the strength of gravity has been measured in deep mines in comparison with the surface strength.

Have you managed to find any answers? Are there any mines anywhere which you can go down and find your weight start to reduce as the mass above begins to cancel out the mass below? Even if there aren't any such mines, are there any where on any stretch your weight stays the same as you go deeper. That would be useful, because you could then do experiments with atomic clocks to find out if deeper is slower or if the clocks tick at the same rate where the G force is the same with one clock demonstrably higher in the gravity well than the other.
 

Offline AndroidNeox

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Re: General Relativity Thought Experiment
« Reply #5 on: 18/07/2015 00:01:29 »
If I'm correct, the force of gravity will decrease as one travels down into a mine, but time dilation would increase.
 

Offline CPT ArkAngel

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Re: General Relativity Thought Experiment
« Reply #6 on: 18/07/2015 09:58:09 »
There is no relative motion, therefore no acceleration. Only the gravitational potential is different here. The location down the shaft has a higher potential, thus a slower time rate. The gravitational potential of a point in space can be approximated by the sum of each particle's mass of the sphere divided by its distance to the point.
« Last Edit: 18/07/2015 15:34:20 by CPT ArkAngel »
 

Offline AndroidNeox

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Re: General Relativity Thought Experiment
« Reply #7 on: 18/07/2015 23:36:39 »
Acceleration due to change in motion is equivalent to gravitational acceleration, in General Relativity. It's called the equivalence principle.
 

Offline AndroidNeox

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Re: General Relativity Thought Experiment
« Reply #8 on: 27/10/2015 21:15:26 »
It turns out I was right that time runs slower for the observer inside the planet and faster for the one above the planet, though their subjective experience of acceleration is the same. The potential energy is the thing. General relativity is a bit more complex than I had realized (14 terms in the field equations, I guess). Thanks all for your inputs.
 

Offline GoC

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Re: General Relativity Thought Experiment
« Reply #9 on: 02/11/2015 14:50:47 »
A photon does not accelerate down a gravity well if it is constant. A postulate of relativity. Potential energy has a dilation value in a gravity well. When you include time it can be confusing. As you descend a gravity well dilation increases. If space is dilated than the electron travel distance might be increased by that space dilation. When the electron jumps to form a photon the cycle becomes longer (red shifted) by the surface detector. On the surface there is less dilation so the light is blue shifted when received by the detector lower in the gravity well. How we measure Time is also affected by the same dilation. In all dilated reference frames the light distance and the photon distances are affected equally to measure the same speed of light per electron frequency of dilated space. In the center of a circular body in space potential energy is non existent at planks length and most dilated position of that mass. Dilation increases with the inverse square of the distance to the center of mass.

Could dilation be the cause of gravity? Gravity (attraction) also follows the inverse square of the distance. Which is also related to potential energy. Which is also related to our measurement of time.
 

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Re: General Relativity Thought Experiment
« Reply #9 on: 02/11/2015 14:50:47 »

 

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