Gravitational Potential & Field: Doubts & Solutions

[BruceW]

Yeah, that is pretty interesting. I think maybe it is because of radio waves from one antennae getting absorbed by the other antennae, so they 'synchronise' in some way. (Again, I don't know much about antennae, but this seems plausible to me).

For certain, if there was only the radio waves in free space, then the radio waves must be coherent to be able to interfere with each other in a nice way. Perhaps this is what happens, since you were saying the frequencies need to be spot on. I think this is probably easier to do with radio waves than with most other forms of light simply because radio waves have a long wavelength, so you don't need to be as precise in the positioning of your detector to see where constructive and destructive interference occurs.

Edit: for clarity, I am not using the word 'coherent' in the QM context. I am using 'coherent' in the context of classical electromagnetism, i.e. same frequency and constant phase difference.

another Edit: I think we must also place restrictions on the polarisation, for coherence to occur. I would guess that for antennae, the geometry of the antennae sets the polarisation of the light given off in a particular direction from the antennae.

 

[sophiecentaur]

Yeah, that is pretty interesting. I think maybe it is because of radio waves from one antennae getting absorbed by the other antennae, so they 'synchronise' in some way. (Again, I don't know much about antennae, but this seems plausible to me).

For certain, if there was only the radio waves in free space, then the radio waves must be coherent to be able to interfere with each other in a nice way. Perhaps this is what happens, since you were saying the frequencies need to be spot on. I think this is probably easier to do with radio waves than with most other forms of light simply because radio waves have a long wavelength, so you don't need to be as precise in the positioning of your detector to see where constructive and destructive interference occurs.

Edit: for clarity, I am not using the word 'coherent' in the QM context. I am using 'coherent' in the context of classical electromagnetism, i.e. same frequency and constant phase difference.

another Edit: I think we must also place restrictions on the polarisation, for coherence to occur. I would guess that for antennae, the geometry of the antennae sets the polarisation of the light given off in a particular direction from the antennae.

Can't be that because the two antennae need not even point at one another. i.e. one could only be 'absorbing' a tiny fraction of the energy from the other.

There certainly is a vast difference in the lengths involved but I think it is more to do with the practical details in the way that laser (QM) radiation is produced. The radiation is essentially from individual atoms, stimulated to emit by a passing wave. There is an inherent frequency involved in the atomic transition. In a radio oscillator circuit, all the electrons are part of the same system of charges that are moving / changing energy level within the circuit and all subject to the same circuit elements / bits of resonant cavity / whatever. I guess I'm saying that an atomic emission can only be explained in QM terms whilst an emission at a much lower frequency can be explained in classical terms. I guess it would not be totally ridiculous to suggest that two lasers could be phase locked to a third oscillator and produce mutually coherent beams. That would again bring up the question of how to picture a 'photon' as a particle that would need to be taking a path through both lasers (/radio transmitters) just like the slightly more obvious case of photons 'going through' both of the two slits in the Young's case. I know that many much cleverer people than me insist that a photon is, essentially, a particle but a lot of those people may not have sat down and tried to reconcile that insistance with what goes on at 'non-QM' frequencies.
I'm easy with the notion of a Quantum of Energy being basic to what goes on but I really don't see why the particle needs to be a particle all the time. I haven't read anything that brings the two together satisfactorily.

Yes - polarisation needs to be considered for interference. When considering polaristion, the particle enthusiasts have to perform even more loops within loops to explain it.

 

[BruceW]

There may be a difference in the way light is made by a laser, and the way light is made by an antenna, but once the radiation is in free space, there is not necessarily any conceptual difference in the radiation. Only the fact the the wavelength of laser light is much shorter. And because the wavelength is shorter, it is much harder to cause the same kind of interference which you have mentioned is fairly easy to make using radiowaves.

About 'photons' and 'light', I agree in many 'classical' experiments it is not easy to see that the quantum description also gives the correct answer, but until an experiment is done which shows the quantum description to be false, I can't reject the quantum description.

 

[sophiecentaur]

Of course a photon is a photon. however generated but, if the model in our head involves any apparent paradoxes between the behaviours of high and low frequency photons then that could be revealing shortcomings in our model.

The idea that a photon interfering with itself yet also being capable of interfering with another photon is a very serious step. It really needs to be shown that photons have indisputably been shown to have interfered with other photons before the notion should be considered seriously.

I don't think there is any doubt about the quantisation of energy and the fact that the photon behaves 'as if' entities with energy, mass and momentum interact with it. When you talk of the photon "in free space" you are making an assumption that it is actually necessary for 'something' to be actually traveling there. Calling the photon 'a particle' brings a lot of semantic baggage with it and conclusions should only be reached after a massive amount of justification.
I seem to remember reading that experiments with low intensity beams have confirmed that photons only, in fact, produce interference on their own. Difficult to square this with the effects you can get with dual sources if you force yourself to regard photons as particles in the accepted sense. No problem if you don't try to force them to be 'like' anything else.

It is so dangerous to talk in terms of what 'really is'. The search for 'truth' can so easily turn into the search for something familiar.

 

[K^2]

Can anyone give me a situation when the gravitational potential due is 0 but gravitational field is non-zero.

Anywhere you like. Zero in potential is arbitrary. You can take the sport where you sit and say that gravitational potential is precisely zero at that location. Feel gravity? Then your question is answered.

 

[sophiecentaur]

Zero Potential DIFFERENCE relative to another location is easy to find (somewhere just beside you, for instance) but zero (absolute) gravitational Potential is defined at an infinite distance away from any attractor.

 

[K^2]

There is no such thing as absolute zero potential. It's one of the classical gauge invariances. Choice of zero potential at infinity is just one gauge. Classical gravity works regardless of gauge choice. Whatever gauge you chose, I can add a constant to potential everywhere and arrive at a different gauge with equivalent description. For example, one where potential is zero at arbitrary point in space.

 

[MikeGomez]

I suppose we are all in agreement that the measurement of gravitational potential energy at the center Earth as zero, assuming a reference of zero potential at an infinite distance form the earth. It starts at zero at an infinite distance from the earth, reaches a maximum at about the surface of the Earth and reaches zero again at the center of the earth. Here we are ignoring variations due to continents, mountains, mass density, etc.

The gravitons at the center of the Earth supposedly cancel each other out.

I am having trouble coming to grips with the reason why they cancel. I am thinking that gravitons don’t annihilate each other out of existence at the center of the earth. I stubbornly hold on to the view that the gravitons exist at the center of the earth, and that their effect is balanced there.

The balanced effect is what I am talking about. Little grains of sand can move a ping pong ball. If the grains come from all directions and are balanced, then the ping pong ball will remain (basically) stationary. A ping pong ball at an infinite distance from the sand will remain stationary due to an equivalent zero force but for a different reason.

I know gravity is not like sand… this is only to demonstrate the balance effect.

So, do gravitons (whatever we call the mediators of the gravitational field) at the center actually cancel each other out of existence? Or is their effect just balanced?

 

[D H]

I suppose we are all in agreement that the measurement of gravitational potential energy at the center Earth as zero, assuming a reference of zero potential at an infinite distance form the earth.

Wrong.

Denoting gravitational potential energy at having a value of zero at an infinite distance makes the potential at any finite distance from a mass is negative. What about inside some mass? It's even more negative. Gravitational potential energy at the center of the Earth is very negative. At the center of Jupiter or the Sun, it's even more strongly negative.

 

[sophiecentaur]

Until Gravitons have actually been found, it might be as well not to use them in discussions about well established gravity matters.
As for potential being chosen as zero at the Earth's centre, that's new to me. How would it help with any practical calculations?

 

[K^2]

I am having trouble coming to grips with the reason why they cancel. I am thinking that gravitons don’t annihilate each other out of existence at the center of the earth. I stubbornly hold on to the view that the gravitons exist at the center of the earth, and that their effect is balanced there.

First of all, we are talking about classical gravity. In classical field theory there are no force carrier particles. There is just field. It's either zero or non-zero. At the center of a spherically symmetric body, the force is zero. Earth isn't perfectly spherically symmetric, but there is still a point inside the Earth where the force is exactly zero. That's not hard to prove. Potential energy inside the Earth is lower than outside and is finite. Therefore, there must be at least one local minimum. Therefore, there is at least one point where gravitational field is precisely zero.

Secondly, there is no self-consistent quantization of Gravity. That means, we have no reason to assume there is such a thing as a graviton. So any argument based on existence of gravitons is suspect at best.

Finally, our best non-classical description of gravity is GR, which doesn't have such a thing as gravitational field. What we can find, however, is a point that is static with respect to Earth and is not accelerating. That is an equivalent of zero gravitational field in classic theory.

As for potential being chosen as zero at the Earth's centre, that's new to me. How would it help with any practical calculations?

Simpler-looking equations, so long as you are dealing only with potentials inside the Earth. I mean, if all you really care about is the difference anyways, would you rather work with U = GMr²/(2R³) or U = GMr²/(2R³) - 3GM/(2R). Later equation gives you -GM/R at the surface, which ensures 0 at infinity.

It's the same reason why we define U = mgh, rather than U = mgh - GM/R, which is the correct linearization with respect to the choice of U = 0 at infinity. The extra constant makes absolutely no difference in any computation, so we simply re-define the zero point and work with respect to that.

 

[Darwin123]

I suppose we are all in agreement that the measurement of gravitational potential energy at the center Earth as zero, assuming a reference of zero potential at an infinite distance form the earth. It starts at zero at an infinite distance from the earth, reaches a maximum at about the surface of the Earth and reaches zero again at the center of the earth.

None of us agrees with this statement. If the gravitational potential is zero at an infinite distance, then the gravitational potential near the center of the Earth has a value far below zero. In fact, the gravitational potential at the center of the Earth is at a local minimum.

The gravitational field strength starts at zero at an infinite distance, reaches a maximum at the center of the Earth and then reaches zero again at the center of the earth.

You keep on reversing the roles of gravitational field strength and gravitational potential. You keep on asserting that everyone knows that what you are saying is correct.

Your perception seems to be reversing the meaning of everybody else comments. If you are really interested in "understanding physics", then you should try to get to the bottom of why you are reversing the meaning.

1) Why do you keep saying that "everybody knows" these statements of yours?
2) Do you realize that "everybody" is saying these statements of yours are incorrect?
3) Who is this "everybody" or who are these "scientists" that you keep referring to that "know" all these falsehoods?

I have both tutored and taught physics. I "know" a perception problem when I see it. Perception problems can often be remedied by a person after the person learns to recognize it.

 

[K^2]

The gravitational field strength starts at zero at an infinite distance, reaches a maximum at the center of the Earth and then reaches zero again at the center of the earth.

Just to address a typo and some realities, the gravitational field is maximum at the surface, under assumption of uniform density. I'm sure that's what you were going for. Of course, Earth being much denser in the center, the actual maximum for gravitational field is far bellow the surface, near the boundary of the Earth's outer core. See this graph for details.

The rest still follows, of course.

 

[MikeGomez]

Wrong.

Denoting gravitational potential energy at having a value of zero at an infinite distance makes the potential at any finite distance from a mass is negative. What about inside some mass? It's even more negative. Gravitational potential energy at the center of the Earth is very negative. At the center of Jupiter or the Sun, it's even more strongly negative.

From ModusPwnd in post #3.
“I think of gravitational potential much like I think of other potentials - their values are arbitrary! That is, you can set your "zero" wherever you like.”

From sophiecentaur in post#36
“Zero Potential DIFFERENCE relative to another location is easy to find (somewhere just beside you, for instance) but zero (absolute) gravitational Potential is defined at an infinite distance away from any attractor.”

From K^2 in post#35
Anywhere you like. Zero in potential is arbitrary.

Then again from K^2 in post #37
There is no such thing as absolute zero potential. It's one of the classical gauge invariances. Choice of zero potential at infinity is just one gauge.

To summarize...
- you can set your “zero” of gravitational potential wherever you like
- Zero potential is arbitrary
- there is no such thing as absolute zero potential
- zero (absolute) gravitational Potential is defined at an infinite distance away from any attractor.

Wrong.

Sigh. Thanks DH. What I understand most at this point is that I am “wrong”. Of course I’m probably wrong about that too.

 

[Dale]

zero (absolute) gravitational Potential is defined at an infinite distance away from any attractor.

That is indeed the usual convention, but it is important to remember that it is simply a convention. You can add a constant to any potential to get another valid potential, thus effectively setting your 0 wherever you like.

 

[MikeGomez]

You keep on asserting that everyone knows that what you are saying is correct.

Sorry. I don’t mean to do this, and I will try not to anymore in the future.

If you are really interested in "understanding physics", then you should try to get to the bottom of why you are reversing the meaning.

Yes, I really am trying to understand physics. Please don’t give up on me.

who are these "scientists" that you keep referring to

I don’t recall mentioning any scientists in this thread, but if you say so the I must have. Was it this thread or another? From now on, if and when I do mention any scientists I will give their name and I will provide full references of the material.

You keep on reversing the roles of gravitational field strength and gravitational potential.

Great! Something to work on there for sure. I will research and get back to you. Thank you.

all these falsehoods

I don’t mean to be spewing a bunch of falsehoods. How about I just start from what I “think” I understood, one step at a time. No stupid analogies, no falsehoods, no references to scientists. Then as soon as one step is incorrect stop me right there in might tracks, and ignore all other steps until I understand and correct my mistake.

I think I understand…
From the Standard model, there are four known forces of nature.

I think I understand…
Those four forces are gravity, electromagnetism, strong force, weak force.

I think I understand…
Perhaps there are three forces if we accept the unification of electromagnetism and the weak force into one electro-weak force.

I think I understand…
A force is that which has the ability to change momentum.

I think I understand…
A field, either in mathematics or in physics is that which is continuous.

I think I understand…
A field in physics is a representation of some physical value at every point in space.

I think I understand…
A field in physics can be scalar, vector, or tensor, depending on what it represents.

I think I understand…
A force field is a vector field.

I think I understand…
The electromagnetic force is mediated by photons.

I think I understand…
The weak force is mediated by W+, W-, and Z bosons.

I think I understand…
The strong force is felt by quarks, and is mediated by gluons which have color charge.

I’ll stop here for now. I probably got it wrong on the first or second step anyway.

 

[K^2]

To summarize...
- you can set your “zero” of gravitational potential wherever you like
- Zero potential is arbitrary
- there is no such thing as absolute zero potential
- zero (absolute) gravitational Potential is defined at an infinite distance away from any attractor.

You can chose zero potential ONCE. You can say, "THIS point is zero potential." Once you set it, potential at every other point is defined with respect to it.

You cannot set zero potential BOTH at the center of Earth AND at infinity. You can chose one or the other depending on which is more convenient.

 

[sophiecentaur]

That is indeed the usual convention, but it is important to remember that it is simply a convention. You can add a constant to any potential to get another valid potential, thus effectively setting your 0 wherever you like.

Imagine you are contemplating a space voyage, calling at various planets. Firstly, you would need an idea of the 'escape velocity' from each planet. True, you may not actually want to escape - just get to the next planet in the chain but wouldn't the relevant amount of energy correspond to my Infinity based Potential. As you move from planet to planet, landing sometimes and doing a slingshot on other occasions. Would it be better to use the surface of the starter planet or Infinity? The energy for a slingshot is all to do with the energy transferred from the helper planet and the distance down the potential well you find yourself. (Depth below zero) I tried to think of a practical example of applying GPE where it could actually help to use anything other than Infinity - except for the obvious ones where we are starting off from Earth and falling back again.
Where do you start to decide if a dying start could form a black hole, for instance?

I think the statement that GPE can be referred to 'anywhere' is only relevant for proving a (valid) point. But, there again, I'm an Engineer, basically and that could explain my attitude. That could be why I come out in spots at the mention of gravitons - except when the person who introduces them is a BRAIN.

 

[K^2]

So as an engineer, you never approximated gravitational potential energy as mgh? You've always subtracted mMG/R from it? What is and isn't convenient may be case-dependent. An engineer should appreciate it more than anyone else. Choice of zero potential you want for interplanetary mission is not going to be the same that you want to use if you are designing a rollercoaster.

 

[sophiecentaur]

Did you read all of my last post? Of course, the mgh situation is obvious and I mentioned it. As we never get deeper than a few km, a reference below ground would hardly be worth our attention. Do you, in fact, have a suggestion for an alternative reference that isn't on a planet's surface - which I'd certainly use when appropriate. But then it would normally call for the mgh approximation.

 

[Dale]

I tried to think of a practical example of applying GPE where it could actually help to use anything other than Infinity - except for the obvious ones where we are starting off from Earth and falling back again.

I think that the obvious example is a fine one. If you can do it in the obvious case, then you obviously can do it. Also, the obvious case you mention answers the OP's question since it would set the potential to 0 at the surface where the field is non-zero.

Also, you wouldn't necessarily use the mgh approximation, e.g. in launching a satellite or ICBM.

That could be why I come out in spots at the mention of gravitons - except when the person who introduces them is a BRAIN.

I agree. Gravitons are completely irrelevant to this discussion.

 

[sophiecentaur]

One other thing in favour of defining GPE relative to Infinity, of course, is the universality of it. We could have an excellent gravitational conversation with the scientists on the planet Zog, ten light years away and we'd all be talking the same language. We'd show them Hydrogen lines and a few other common phenomena to get our units agreeing and scaled up, then we would all know what we meant. The dimensions of the third rock from the Sun would probably not interest them very much, scientifically.
Not that it is a likely scenario for some while. Get a move on please, SETI..

 

[MikeGomez]

I suppose we are all in agreement that the measurement of gravitational potential energy at the center Earth as zero, assuming a reference of zero potential at an infinite distance form the earth.

OMG, what the heck was I thinking! Of course the logical location to assign zero potential gravity is at the surface of the Earth and a maximum at infinity.

I became extremely flustered when Darwin flipped the Bozo switch on me, but that is just an excuse. I promised to say I am wrong when I am wrong, and brother was I wrong. Profuse apologies to all.

 

[MikeGomez]

Until Gravitons have actually been found, it might be as well not to use them in discussions about well established gravity matters.

there is no self-consistent quantization of Gravity. That means, we have no reason to assume there is such a thing as a graviton.

Excellent, no gravitons.

our best non-classical description of gravity is GR, which doesn't have such a thing as gravitational field.

Wait a minute. Then what is meant by Einstein field equations of Einstein’s General Theory of Relativity?

From the Wikipedia article on the stress energy tensor.

"The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity."

 

[Nugatory]

Wait a minute. Then what is meant by Einstein field equations of Einstein’s General Theory of Relativity?

From the Wikipedia article on the stress energy tensor.

"The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity."

That's wikipedia being a bit sloppy. It's not really "just as"; and MTW's position (that there are multiple mathematical objects involved in the description of gravitational effects, no one of which is so uniquely important as to be called "the" gravitational field) is generally clearer.

 

[A.T.]

MTW's position (that there are multiple mathematical objects involved in the description of gravitational effects, no one of which is so uniquely important as to be called "the" gravitational field) is generally clearer.

Wouldn't the metric describing space-time geometry qualify as "the gravitational field of GR"?

 

[Dale]

Wouldn't the metric describing space-time geometry qualify as "the gravitational field of GR"?

Well, the metric doesn't really reduce to the Newtonian gravity field AFAIK.

I tend to think of the Christoffel symbols as being the most closely related to the Newtonian gravity field.

 

[K^2]

I tend to think of the Christoffel symbols as being the most closely related to the Newtonian gravity field.

But still, not really. Because I can take polar representation of Minkowski metric, which is flat and has no gravity, of course, modify it to be rotating at some angular velocity Ω, and now the Christoffel symbols represent centrifugal and Coriolis effects.

So Christoffel symbols are really whatever fictitious forces you happen to have. If you have curved space-time, then that includes gravity. But it still doesn't reduce to just gravity.

 

[Dale]

So Christoffel symbols are really whatever fictitious forces you happen to have. If you have curved space-time, then that includes gravity. But it still doesn't reduce to just gravity.

Yes, but I personally think that including other fictitious forces in gravity is more or less justified by the equivalence principle. However, since there isn't general agreement on the topic and since my justification is admittedly pretty sketchy I certainly don't push my viewpoint.

 

[MikeGomez]

That's wikipedia being a bit sloppy. It's not really "just as"; and MTW's position (that there are multiple mathematical objects involved in the description of gravitational effects, no one of which is so uniquely important as to be called "the" gravitational field) is generally clearer.

I agree with what you with what you are saying; that what has been called the gravitational field is not exactly the same sense as the electromagnetic, weak, and strong fields.

I have learned now, thanks to this forum, that there is no mediator of the "gravitational field", but still, doesn’t it seem useful to have a term for describing the intensity of gravitation? Would it be acceptable to speak of a “gravitational field” when referring to the values as given by the stress-energy tensor equations?