General Relativity: Gravitational time dilation of photons and Fabric of Space

Consider the following, from the prospective of General Relativity:

A photon's path between two points, point O (emitted point, from galaxy GO) to point R (received point, in Galaxy GR):

O: point of photon's origin, in space

GFO: gravitational field force at point O, due to its position in galaxy's gravity well, from which photon originated

R: point of photon being received, in space

GFR: gravitational field force at point R, due to its position in galaxy's gravity well, from which photon was received

galaxy GO galaxy GR
O ---------------->-------------R

photon travels from point O (in galaxy GO) to point R (in galaxy GR)

Next, consider the following:

- point O is deep in a gravity well, so the GFO at that point of emission would be strong

- point R is in a shallower gravity well, so the GFR at that receiving end would be weaker

So, GFO > than GFR , or the gravitational time well from which the photon originated is deeper than the gravitational time well where it was received.

Next, imagine space between those two points, for the photon, as seen through General Relativity.

The photon would travel along a path, through space, that would be shaped by gravity.

From the point of emission, the photon would be travelling up the gravity well at point O due to the GFO. Or, another way to look at it, space would be stretched out, time would appear to slow, the speed of light stays the same, and the photons frequency would be stretched, as in red-shifting. However, here, the stretching would be due to gravitational red-shifting, which would be due to gravitational time dilation.

Along photon's path to point O, it would reach a point, somewhere in between the two galaxies, where the gravitational fields of galaxy GO and galaxy GR would cancel each other out, and space would be undisturbed. This point shall be designated as P1.

Since the GFO is greater then GFR, Point P1, would be closer to the shallower gravity well.

So: the distance between O to P1 is greater than the distance between P1 and R.


galaxy GO galaxy GR
O --------------------P1----------R
Distance 1 Distance 2

At this point, P1, the photon would have reached its maximum red-shifting since having left its point of origin. After this point, it will undergo gravitational blue-shifting, as the photon begins to enter the gravity well of galaxy GR.

From point P1 to point R (photon's point of reception), the photon will undergo gravitational blue-shifting.

However, the frequency of the photon from when it was first emitted to when it was received, will have a net effect, of having been gravitationally red-shifted. This is so because the photon was red-shifted for a longer distance in space (or longer period of time) then it was blue-shifted, resulting in a net red-shifting of its frequency.

There is net lose of energy of the photon, due to its frequency having been gravitationally red-shifted, by the gravitational time dilation process. In gravitational red-shifting, the gravitational time dilation process would mean that the photon's frequency was stretched as it passed through stretched space, and results in the photon having less energy.

This may get into the quantum mechanics of General Relativity, but isn't it possible that the net red-shift in the photons frequency, could correspond to the amount of space left stretched in space, somewhere along it path from point O to R?
Since the photon arrived with a stretched wavelength, compared to its wavelength from point O, having lost some of its energy along the way. I believe this lost energy, lost in quantum amounts, was left out in space, along its travel, resulting in a net expansion of space.

Could this energy source be the source of Dark Energy?

What would the converse of the above situation be? (speculation, and just for fun, could it be dark matter?)

Any solid replies would be greatly appreciated.

====== added March 17, 2012

Following this photon along its path between these two gravity wells, and looking at it from the prospective of the Quantum Field Theory, as this photon is undergoing gravitational red-shifting, it would seem that as this photon is losing energy, and having its frequency red-shifted, it would be losing a quantum packet of energy as it is being gravitationally red-shifted. This photon would be losing quantum packets at a rate determined by its travel through curved space. The more space is stretched, the more quantum packets of energy are lost by the photon undergoing gravitational red-shifting due to gravitational time dilation. If a photon is received with less energy than when it arrived, those quantum packets are still out there, along its path.

For fun:
Seems there are quantum particles that connect photons (energy), to those tiny quantum particles that make up space, forming some sort of quantum field through which both photons and gravitons pass through, making both electromagnetic fields and gravitational fields.

Taking it further:

It seems that to form space, these tiny quantum particles are spaced apart, by varying amounts, which give shape to the curvature of space, by gravity. Also, these quantum particles have spins to them, which transmit electromagnetic radiation through space, and that create electromagnetic fields.

1 field transmitting both photons and gravitons. The electromagnetic force and the gravitational force together in one field.
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Wouldn't light travelling the other way gain an equal amount of energy giving a nett change of zero ?

(It's late so I can't attempt a serious answer).
Wouldn't light travelling the other way gain an equal amount of energy giving a nett change of zero ?

(It's late so I can't attempt a serious answer).
Thanks for the reply.

Yes, if photons are leaving from point O to point R at the same rate, as those from point R to point O.

The rate of photons being emitted, along the many paths connecting the two galaxies in space, by each galaxy seems to be a factor to consider.
As the photon loses quantum energy packets into space, seems space is being stretched more than it already was (where photon's lost energy ends up). Again looking at it with Quantum mechanics, during gravitational time dilation of photon (from gravitational red-shifting) along it's path.

If photon received has less energy then from when emitted, it lost energy is out there is stretched space. This would mean a net loss of quantum energy packets along photon's path.

A single Quantum energy packet seems to be lost as photon is gravitationally time dilated between two stretched (due to gravity) quantum points, as seen through quantum field theory and quantum mechanics, which result in a further stretching between these two points. Seems to explain, or at least help explain, the accelerated expansion of our universe.

Seems this is true. Any thoughts?
Hi prime axiom, welcome to PF. You may get more traction for your questions if you avoid the personal speculations and stick to mainstream science. Personal theories are against the rules to discuss here.
Thanks. Will do.

It's difficult to walk that line, when asking questions about subjects that are not understood very well.

I'm hoping to get solid answers to my questions, since they involve a deeper understanding of quantum mechanics and general relativity, in terms of the mathematics, than I have.

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