# Questions about the inverse square law

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• KurtLudwig
In summary: What is the probability that the image of a distant star on a CCD pixel will jump to an adjacent pixel?In summary, the inverse square law does not hold at very far distances due to the expanding universe and the geometry of the universe. However, additional mechanisms such as quantum jitter and virtual particles may also limit the range of the inverse square law. This may explain the deep MOND regime and the need for both cold dark matter and a limit to the inverse square law to explain galactic rotations and the formation of structure in the universe. While General Relativity is a beautiful theory of gravity, it appears to break down in certain situations such as inside a black hole, leading physicists to search for a quantum theory of gravity that can make more accurate
KurtLudwig
Gold Member
TL;DR 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.

KurtLudwig said:
The very narrow stream of photons emitted by a very distant star probably jitters due to quantum effects

I'm not familiar with this 'jitter'. Can you elaborate?
KurtLudwig said:
Consider the gravity between two very distant stars. These stars continuously interchange gravitons. The gravitons (and photons) follow geodesic lines.

No this is incorrect. First, gravitation has yet to be quantized and cannot be accurately described using the particle-exchange idea. Second, even in forces that can be described that way, the force mediating particles do not travel anywhere. They are virtual particles, not real particles, and cannot be said to have a defined path through space, or even said to have traveled anywhere at all. There are no virtual particles moving from point A to point B.

weirdoguy
Quantum jitter - I thought that in quantum mechanics position is only known by probability and is not know precisely. For example: would the image of a distant star on a CCD pixel always stay on one particular pixel, or jump to adjacent pixels?

I appreciate your answer, but your answer is above my understanding of physics. I realize that I am a couple of orders of magnitude less educated and knowledgeable that you. I am interested in physics and am reading physics undergraduate textbooks, including the mathematics, to educate myself. From what I have read, General Relativity, a beautiful theory, is the theory of gravity. (Although I am struggling with the mathematics of General Relativity.) Yet physicists are looking for a theory of quantum gravity. Why?

Well then how do gravitons mediate the force of gravity between distant stars? Do gravitons travel between these stars as photons do?

Thanks for the link to virtual-particles-what-are-they. I have read it once, but will need to read it a couple of times. I have always wondered in Feynman diagrams what virtual particles are.

KurtLudwig said:
Quantum jitter - I thought that in quantum mechanics position is only known by probability and is not know precisely. For example: would the image of a distant star on a CCD pixel always stay on one particular pixel, or jump to adjacent pixels?

Incoming photons are spread across a region on the detector, with roughly 83.8% falling in the center of something called the Airy Disk. The rest fall further out, with decreasing probability with increasing distance from the center of the Airy Disk. This has nothing to do with quantum physics, it is purely a classical wave phenomenon. The location of the Airy Disk as a whole does not change. That is, it doesn't 'jitter'.

KurtLudwig said:
From what I have read, General Relativity, a beautiful theory, is the theory of gravity. (Although I am struggling with the mathematics of General Relativity.) Yet physicists are looking for a theory of quantum gravity. Why?

Basically, we know of times where General Relativity appears to break down, such as when describing the conditions inside a black hole at the singularity. It is thought that a quantum theory of gravity will be more accurate and make better predictions at the very high energy and density scales where classical GR breaks down. In addition, all other fundamental forces are described using quantum physics, so there is a strong push to try to unify gravitation with the other three fundamental forces, which are all described by quantum theories.

KurtLudwig said:
Well then how do gravitons mediate the force of gravity between distant stars? Do gravitons travel between these stars as photons do?

Virtual gravitons do not travel between stars. Think on an EM wave. It is emitted when charged particles are accelerated and it is composed of real photons, not virtual ones. Similarly, a gravitational wave (the things LIGO detects) would be composed of real gravitons. However, virtual gravitons do not travel between two masses, just like virtual photons do not travel between two charged particles.

The problem is that the term 'virtual particle' refers to the equations used in quantum field theory. My limited understanding is that the equations that describe how real particles interact with their real force mediators (photons, gluons, etc) also happen to be the same equations that describe how real particles interact with non-force-mediating particles. That is, the equations describing how an electron interacts with a photon can also be used to describe how an electron interacts with another electron. In this case the two electrons act 'as if' they had each interacted with a photon, even though this photon could not be a real photon for various reasons.

Some scientists view virtual particles simply as mathematical objects or 'artifacts' and not real things, but that's an entirely different discussion.

## 1. What is the inverse square law?

The inverse square law is a principle in physics that states that the intensity of a physical quantity, such as light or gravitational force, is inversely proportional to the square of the distance from the source.

## 2. What are some examples of the inverse square law?

Some examples of the inverse square law include the intensity of light from a point source, the strength of an electric field from an electric charge, and the force of gravity between two masses.

## 3. How is the inverse square law calculated?

The inverse square law is calculated by dividing the initial intensity of a physical quantity by the square of the distance from the source. The resulting value is the new intensity at the given distance.

## 4. What is the significance of the inverse square law?

The inverse square law is significant because it helps us understand how the intensity of a physical quantity changes with distance. It also allows us to make predictions and calculations in various fields of science, such as optics, electromagnetism, and astronomy.

## 5. Are there any exceptions to the inverse square law?

Yes, there are some exceptions to the inverse square law. For example, the force of gravity between two masses is only strictly inversely proportional to the square of the distance if the masses are point masses. In reality, most objects have a finite size and shape, which can affect the force of gravity between them.

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