Does the inverse square law eventually fail?

[SLD]

It seems to me if gravity is mediated by a quantum particle, i.e. a graviton, then at some appreciable distance the inverse square law would ultimately fail as the gravitons from the source would be too diffuse. At some very long distance there’s just a single graviton moving through a region of space and it’s not diffusing at all.

Or am I missing something?

SLD

 

[repoman]

What about light?

 

[barbos]

It's not how it works. Analogy you use is incorrect.
As distance from the source increases virtual gravitons get progressively softer and softer but there are more and and more of them.
Basically, inverse square law does not apply here.

 

[steve_bank]

It is easier to see with light.

A theoretical isotropic radiator is an infintly small point radiating equaly in all directs. We treat distant stars as isotropic radiators.

Imagine a spjere around the radiator in cresing in diameter. Ognorring any losses the total energy crossing the spere at and radius is constant, conservation of energy. For an 1 meter square aera on the surface of the expanding sphere energy density goes down by inverse square. I have measured it with optical sensors.

As radius gets lathe a 1 square meter surface on the sphere appears flat. You can draw similar triangles and I believe derive 1/r^2 with a little trig. You can also look at the wiki page on solid angles.

Energy is the capacity to do work. Light is modeled as photon particles as energy carriers and as a wave. Gravity is measured as a force resulting from accelerating a mass.

It doesn't matter abut fields waves and particles. It is about energy density in joules however it is derived. If inverse square fails then energy has to show up somewhere.

 

[barbos]

If photons had mass there would have been no inverse square law, as is the case of electro-weak field.
There is also no inverse square law in strong force even though gluons have zero mass. (gluons have strong charge charge instead)
Analogy does not apply to fields.

It doesn't matter abut fields waves and particles. It is about energy density in joules however it is derived. If inverse square fails then energy has to show up somewhere.

If it were true and this simple analogy were applicable then object would be constantly losing said energy due to "radiation" of said particles.

 

[steve_bank]

Ut IMO has nothing to do with mass. It is about how wedefine and measure energy.



Imagine a small high density homogeneous mass.

Regardless of how big a sphere around the mass the total gravitational potential energy integrated over the sphere remains constant. If not conservation of energy says an increase must come from somewhere and a decrease must go somewhere.


A radio transmitter is radiating photons, the energy to radiate the photons comes from the power mains, the power station generates energy from coal, coal comes from.....ad infinitum.
A star is always loosing energy. And we now switch to a debate on cosmology...

 

[barbos]

You are confusing and conflating different things and simply wrong.

 

[steve_bank]

You are confusing and conflating different things and simply wrong.

Another conservation of energy denier? The Earh has a finite amount of gravitational potential energy. If not the off we go into infinity la la land.


Take a look at Potential Theory and Poisson's Equation. The equation shows up everywhere. It is not something I can jump into but all forms of static potential and dynamic forms of energy all take on the same mathematical form

https://en.wikipedia.org/wiki/Potential_theory


Looking at from Gauss's Divergence Theorem the total energy crossing the surface bounding a source is equal to the sum of the energy contained in sun of volumes as dxdydz goes to 0.

Energy reduces to curl, divergence, gradient, Laplace and Poisson.

We use all of it in engineering. Divergence theorem converts a surface integral of a closed surface to a summation of volumes within the surface.

https://en.wikipedia.org/wiki/Divergence_theorem

Any inverse-square law can instead be written in a Gauss's law-type form (with a differential and integral form, as described above). Two examples are Gauss's law (in electrostatics), which follows from the inverse-square Coulomb's law, and Gauss's law for gravity, which follows from the inverse-square Newton's law of universal gravitation. The derivation of the Gauss's law-type equation from the inverse-square formulation or vice versa is exactly the same in both cases; see either of those articles for details.[8]

https://physics.stackexchange.com/q...-gausss-law-for-gravity-in-general-relativity

I'd say your overall problem is not understanding that regardless of theory or form energy reduces to a measure in SI units. It is not theoretical abstractions. The effect of energy is a measured force. Even in GR when you make a measuring it will be a force. It is inescapable. Unless you argue in GR you can get more or less gravitational energy from a mass...

 

[barbos]

Dude, I have PhD in physics (particle physics)
You are talking nonsense.

 

[Sarpedon]

Yeah, I don't see why the Average amount of energy transmitted can't reduce ad infinitum. There's no limit to the amount an average can be divided to.

I'm not a physicist, but one take away I had from learning about it is that when discussing very small quantities, all one can talk about is averages and probabilities. That's kind of what Heisenberg's Uncertainty Principle is about. And when we are talking such small quantities, we have to be talking in Quantum Physics, not General Relativity. The fact that the two don't translate well to each other has been well known for more than a century.

 

[barbos]

Yeah, I don't see why the Average amount of energy transmitted can't reduce ad infinitum. There's no limit to the amount an average can be divided to.

I'm not a physicist, but one take away I had from learning about it is that when discussing very small quantities, all one can talk about is averages and probabilities. That's kind of what Heisenberg's Uncertainty Principle is about. And when we are talking such small quantities, we have to be talking in Quantum Physics, not General Relativity. The fact that the two don't translate well to each other has been well known for more than a century.

OP is not really limited to gravity. Quantum Electromagnetism has the same "problem". And I understand what and why OP is trying to say.

 

[SLD]

It's not how it works. Analogy you use is incorrect.
As distance from the source increases virtual gravitons get progressively softer and softer but there are more and and more of them.
Basically, inverse square law does not apply here.

I’m very confused by this response. Are gravitons reproducing? How does there become more of them the further away from the source? And what do you mean by softer?

How likely is it that our sun is exchanging gravitons with some red dwarf on the other side of the galaxy? Except maybe over a long period of time when a few reach us?

I don’t have a PhD but I took some Modern physics courses in undergrad. We never got to gravitons.

SLD

 

[barbos]

It's not how it works. Analogy you use is incorrect.
As distance from the source increases virtual gravitons get progressively softer and softer but there are more and and more of them.
Basically, inverse square law does not apply here.

I’m very confused by this response. Are gravitons reproducing? How does there become more of them the further away from the source? And what do you mean by softer?

How likely is it that our sun is exchanging gravitons with some red dwarf on the other side of the galaxy? Except maybe over a long period of time when a few reach us?

You clearly think of gravitational force as one body emitting gravitons which fly straight out and then eventually meet some other body and get absorbed. Hence 1/r^2.
That's not how it works. First of all these are virtual gravitons and second they don't really fly out, if they did you would clearly had a case of losing energy or something. Obviously your "theory" does not work.
Unlike real gravitons, virtual gravitons can not live forever. They get emitted and then they have to be absorbed by something. And most of the time they get absorbed by the source which emitted them. Amount of distance virtual graviton can travel basically depends on its momentum.
Large momentum can not travel too far. Small momentum can travel father. So massive body is surrounded by a cloud of virtual gravitons which get emitted and the absorbed back. but if you go father and father from the mass harder gravitons get less and less dense, they simply can't fly that far and have to effectivley turn back

So your problem does not really exist.

 

[steve_bank]

Dude, I have PhD in physics (particle physics)
You are talking nonsense.

Sorry, I have been around enough to not equate academic laurels with competency or comprehension. Authority by academic credentials gets you nowhere with me.You seem to be concussed with series and sequences. Anybody who wants to spend the time and money can get a PHD somewhere. It never interested me.

When I started I had academic knowledge. I could read books, do problems, and apply it. After some years and experience in different disciplines it sunk in on the fact that the math and basic models are all the same with different names in different areas. What I have seen with people with only a physics background is a belief that what they know is unique wen in fact in engineering the princi0les are common.

I went to work in an IR video company in the 80s. I go several books on optics. In electric circuits there is electrical frequency response. Frequency response determines rise time and time domain resolution.

Time and frequency are related by Laplace and Fourier Transforms.

To my surprise the Modulation Transfer Function in optics is the same. Trace a large number of rays and the transform of the points in the focal plane, the point spread function, is the spatial frequency response of the systems. Instead of volts/hertz the scale factor is line pairs per millimeter. It defines spatial resolution.

Electrical resonance, mechanical resonance, and quantum system resonate are al the same thing. Same principles. Cyclic [ENT][/ENT]transfer of energy between stoic and dynamic energy.

There is a complex mechanical impedance analogous to electrical impedance. An audio speaker mttches the amplifier impedance to the free air monarchical impedance.

What gravity 'is' is not knowable. The same conceptual principles apply to gravity as everything else, especially energy. When energy comes in so does conservation.

I went through this several times across different areas. Everything reduces to comservation, and when learning a new area one looks for how energy and mass is accounted for.

In an electric field it is conceptualy and mathematicaly mapped by moving a theretical point chage around and mapping the vector forces. For gravity a small test mass?



So, given a homogenous sphere, equal mass distribution, how much work can the total gravity do on another object?

And how is gravity measured? Newtonian gravity of GR how do you measure it?

 

[Sarpedon]

An infinite series can converge on a finite number...so why do you say that IF the Earth has finite potential energy, then these infinite series are some kind of 'la la' land?

And I always thought that gravity was measured by acceleration produced, e.g. 32 feet per second/per second. It's bonkers to talk about gravity in terms of energy, because that almost presupposes a non-existent universal reference system.

Sure, here on earth, you can calculate how much energy a falling object has, or how much work a rocket has to do to put a satellite in orbit. But how much work is the Milky Way Galaxy doing to hold the Lesser Magelleanic Cloud in position is kind of absurd. Gravity is about net force producing accelleration. An object far in space has many forces acting on it, so to talk in terms of that object's potential energy in regard to another object is pointless, if the two will never interact meaningfully. In theory, the potential energy between the earth and Alpha Centuari is enormous, but as the two things are never going to actually accellerate towards each other, it is pointless to calculate.

Just as you are not impressed by academic credentials, I'm not impressed by engineering credentials. I've worked with too many engineers to be awed by their cyclopean competence. Engineers are trained to be very good at one specialty, and far too many of them then think they can apply that one method they know to everything. It baffles me how so many people who are experts and expect people to defer to them in their own specialty then turn around and think they know better than specialists in other fields.

One thing that science has repeatedly proven (yes, PROVEN) is that systems of modelling that work perfectly well in one situation break down in others, especially at vastly different scales. For me, this is an easy thing to grasp, as I have been professionally trained to think of how things are experienced at different scales. Why assume that quantum interactions are bound by the same rules (which are not so much rules as they are short-cuts) that govern whatever electronic devices you happen to be working on? It is by observing that the real world does not always exactly follow existing models that scientists do their work. The engineer's job is to use existing models to achieve solutions to our problems.

I forget, steve, were you the one who was proposing a universal time or universal space reference, or was that someone else?

 

[lpetrich]

It seems to me if gravity is mediated by a quantum particle, i.e. a graviton, then at some appreciable distance the inverse square law would ultimately fail as the gravitons from the source would be too diffuse. At some very long distance there’s just a single graviton moving through a region of space and it’s not diffusing at all.

Or am I missing something?

That maximum range indeed happens for a massive force carrier. The force gets an exponential decline term, where the length scale is the reduced Compton wavelength of the particle. That is (hbar)/(mass*c). For a massless particle, that wavelength is infinite and the force's range is thus infinite.

Looking for evidence of such a length cutoff is how one finds upper limits of the mass of the photon. Jupiter's magnetosphere is the largest one in the Solar System, at around 3 million km, and it gives an upper limit of around 10^(-15) eV. Galactic magnetic fields do even better, though how well depends on the details of how the field is generated.

Using this approach, one can get an upper limit on the graviton's mass from the largest gravitationally-bound objects: galaxy superclusters. These extend over 100 megaparsecs or 10^21 km, giving a mass upper limit of 10^(-30) eV.

 

[steve_bank]

I should have learned my lesson on entering debars on infinity....they seem to never end. Pun intended. A series casn converge on a number but never get their.

1/x as x-> 0 approaches infinity but never gets there.

1/(2 + 1/x) as x -> infinity it goes to 1/3 but never gets there.

You can relate abstract math and math infinities to gravity unless you have an equation.

The question is given a homogenous mass far away from other sources of gravity what is the maxim work that can be done by the gravity? I do not have a ready answer. In demonstrated physical reality as a variable approaches zero in a system energy dermand goes to infinity but can not get there.

Interrupt the current in an inductor and a singularity starts to form but can not get there.

A finite mass can not n represent an infinite amount of gravitational potential energy.

 

[Wiploc]

It seems to me if gravity is mediated by a quantum particle, i.e. a graviton, then at some appreciable distance the inverse square law would ultimately fail as the gravitons from the source would be too diffuse. At some very long distance there’s just a single graviton moving through a region of space and it’s not diffusing at all.

Or am I missing something?

SLD

What happens when that last graviton strikes a target? Is there no gravity beyond that point? So I don't think it pays to think of a single last graviton. There's always more attraction going on.

People think in terms of particles when that's useful, when it makes predicting consequences easier. But particle theory is no more real or true than wave theory or warped-space theory.

 

[Sarpedon]

Again, averages.

The last graviton hits the target. Then the next one comes along. How long do you have to wait for it?

You don't have to divide a graviton in half to have an average of 1/2 of a graviton/sec/square meter.

There is no limit to the smallness, because you can change any of the terms.

You say you aren't looking for an average? Sorry, but in Quantum physics, that is all there is.

 

[Gun Nut]

Dude, I have PhD in physics (particle physics)
You are talking nonsense.

Sorry, I have been around enough to not equate academic laurels with competency or comprehension. Authority by academic credentials gets you nowhere with me... Anybody who wants to spend the time and money can get a PHD somewhere. It never interested me.

Exactly. This is how I know for certain that Global Warming is a hoax. My Certainty trumps the wishy washy nature of Science and all its "theories".