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- Summary
- At very far distances the inverse square law does not hold. This is due to the universe expanding. Is it also due to quantum jitter of the stream of photons from a very distant star?

In "An Introduction to Modern Cosmology" by Andrew Liddle, page 130, paragraph A2.3 Luminosity distance, explains why the inverse square law does not hold at very far distances. One reason given is the expanding universe. (Another was the geometry of the Universe.)

Could there be also additional mechanisms which limit the range of the inverse square law? The very narrow stream of photons emitted by a very distant star probably jitters due to quantum effects, therefore the stream has a minimum cross section. (In "The Hidden Reality" Brian Green discusses quantum jitter.) When the image (in micro steradians or smaller) of an even more distant star falls below the minimum cross section of the stream of photons, then the inverse square law will vary as 1/r, not as 1/r^2. The number of photons emitted from this star will not decrease in this jittering stream anymore. The frequency of photon interactions between these two stars will decrease with distance, 1/r.

Consider the gravity between two very distant stars. These stars continuously interchange gravitons. The gravitons (and photons) follow geodesic lines. Again due to quantum jitter, this steam of gravitons will have an extremely small cross section, but it will not be a mathematical point. As more distant stars are considered, the images of very distant stars will eventually fall below the cross section of the stream of the gravitons. Now the frequency of graviton exchanges will not decrease by the inverse of the square, but by only by the inverse of the distance between these stars. This may explain the deep MOND regime.

After reading "An Introduction to Modern Cosmology", there is no doubt in my mind that cold dark matter must exist. Maybe both cold dark matter and a limit to the inverse square law are needed to explain galactic rotations and the formation of structure in the universe.

Could there be also additional mechanisms which limit the range of the inverse square law? The very narrow stream of photons emitted by a very distant star probably jitters due to quantum effects, therefore the stream has a minimum cross section. (In "The Hidden Reality" Brian Green discusses quantum jitter.) When the image (in micro steradians or smaller) of an even more distant star falls below the minimum cross section of the stream of photons, then the inverse square law will vary as 1/r, not as 1/r^2. The number of photons emitted from this star will not decrease in this jittering stream anymore. The frequency of photon interactions between these two stars will decrease with distance, 1/r.

Consider the gravity between two very distant stars. These stars continuously interchange gravitons. The gravitons (and photons) follow geodesic lines. Again due to quantum jitter, this steam of gravitons will have an extremely small cross section, but it will not be a mathematical point. As more distant stars are considered, the images of very distant stars will eventually fall below the cross section of the stream of the gravitons. Now the frequency of graviton exchanges will not decrease by the inverse of the square, but by only by the inverse of the distance between these stars. This may explain the deep MOND regime.

After reading "An Introduction to Modern Cosmology", there is no doubt in my mind that cold dark matter must exist. Maybe both cold dark matter and a limit to the inverse square law are needed to explain galactic rotations and the formation of structure in the universe.