Science a GoGo's Home Page Forums General Discussion Physics Forum Light From Distant Galaxies.

So, let's talk about potential energy. The first thing to remember about potential energy is that it is relative. The potential energy that anything contains is relative to the lowest energy level it can move to. So if you pick up the rock from the ground its potential energy is relative to ground level. But if you move it over a well its potential energy is relative to the bottom of the well. The difference is strictly due to the fact that over the well it can fall longer and achieve a greater speed before it hits bottom. The potential energy an object contains is the amount of kinetic energy that it can gain by falling to the ground or other surface below it. The kinetic energy it can gain by falling a few feet to the ground is much less than the kinetic energy it can gain by falling many feet to the bottom of a well.

Now let's talk about how the attraction of gravity falls off with distance.

F = G*M1*m2/r^2

That one should be familiar to you. Newton's law of gravitation. Notice that the force between 2 bodies is inversely proportional to the distance between them. This is known as the inverse square law. That distance is actually the distance between their centers. Let's look at why that is.

I'm not going to find a diagram and insert it here, I will let you make your own. First draw a circle. Now draw a bunch of straight lines through the center of the circle at 15 degree increments. There is nothing magic about the increment size, I just chose 15 degrees because it means the circle will be evenly divided by the lines. Let the ends of the lines all stick out a long way beyond the circle. Now let's pretend that the lines represent the gravitational field from a body. This is a standard representation of field lines around any kind of source. Now draw another circle around the first one, but twice as far out. Notice that the field lines are much more widely separated where they pass through the second circle. If you imagine the circles to be spheres and the field lines drawn at 15 degrees intervals in all 3 dimensions you will see that the area between field lines varies with the square of the radius. Well, gravity works just the same way. Close to the center of a body the gravitational attraction of a body is much greater than it is farther away from the body. That is why gravitational attraction doesn't act like a spring. It works the same way as electromagnetic radiation (light). If you look at a light source up close it is very bright, but as you move away it begins to be dimmer and dimmer. It is also obeying the inverse square law.

Now you may say, but I don't see any difference in gravity between different heights. I better mention that. Let's assume that there is a enormously large planet, say a million km in radius. Never mind that such a planet couldn't exist, this is just a thought experiment. Now if you start drawing your lines through the center of the planet you will find that 15 degree separation means that you can't even see one line when you are standing by another one. So you keep on drawing more lines until you finally get a whole bunch of them in your field of view. Well, the angle between those lines is going to be extremely small. In fact it would take some very fine measurements to find out that there was an angle between them. And the force produced by those almost parallel lines would chage very slowly with altitude. Guess what! The Earth is large enough that the angle between force line is almost undetectable. However, it can be measured, particularly from a space craft. So at great altitudes the force of gravity from the Earth is smaller.

Of course the Moons gravity works the same way, so its gravitational attraction is greater than the Earths gravitational attraction when a spacecraft get closer to it than it is to the Earth. There is a point between the Earth and the Moon (on a line between their centers) where the gravitational attraction is equal from both of them. So before that point a spacecraft would tend to fall to Earth and beyound it would tend to fall to Moon. Of course it doesn't actually "fall". The thing is that spacecraft don't travel in straight lines. They always travel in orbits. The orbits may not be closed orbits, but they are orbits, so that they have enough sideways speed to keep from falling directly to the ground.

Bill Gill

Thanks for the response, Bill.

Let's stick with the potential energy for a moment.


If, instead of picking up the stone, I dig a deep hole beside it, then push it in, can I be said to increase its potential energy when I dig the hole, or when I push it over the edge? On the other hand, perhaps it would be more accurate to say that the stone already had the potential energy to take it to the centre of the Earth, but there was rather a lot of matter in its way. This is really the point I was working towards; that every particle of matter in the Universe has enough potential energy to bring it back into contact with every other particle. All we do when we pick up rocks, or send craft into space, is make a slight local alteration to potential energy that is already there.

It doesn't matter much what you do about potential energy. The fact is that potential energy is just book keeping. It isn't anything special. It is merely a way of looking at something to determine how much energy you can get out of it, in the system that you are looking at. Heck I remember one dumb science fiction story I read one time where the protagonist needed more energy than he had available, so he just redefined the reference point for his system as being on another planet. From that point of view he had an enormous amount of potential energy. Of course the fact is that there is no way to get the energy out of a difference between 2 planets. And no, every particle of matter doesn't have enough energy to bring it back into contact with every other particle. Keep in mind that the universe is expanding, and apparently the expansion rate is increasing. If your hypothesis were true then the universe would be slowing down and/or collapsing.

Bill Gill

My original point was:
"...there is sufficient potential energy within the Universe to bring every particle back to an infinitesimally small speck, unless some external force intervenes."

It seems that the something intervening is dark energy. I believe there is a suggestion that this could be gravity acting as a repulsive force on a grand scale. That could really mess things up.

Well, my point is that potential energy isn't really all that important. What is important is energy period. As far as I am aware potential energy is mostly used to figure out how much energy we can get out of a system. For example in a hydroelectric power station the potential energy of the water at the top of the inlet with respect to the generator is very important. But if we are talking about space flight we are more interested in momentum.

As far as "some external force", dark energy isn't external, it is a part of the universe. What it is is, so far as I know, completely unknown. Any ideas as to what it is are basically just that, ideas. There is a lot of evidence that indicates it is there, but there is no good theoretical way to incorporate it into our view of the universe.

Bill Gill

The potential energy bucket to balance up that you are trying to understand is given in the friedmann equations (http://en.wikipedia.org/wiki/Friedmann_equations)

It is a way of calculating the pressure on spacetime to bring energy into being.

The last line in the article gives you the potential energy formula

Hope this translates properly I struggle with english at times.

Thanks, Orac. The maths in that link caused a major panic attack.
However, I shall return when I have a bit more time, and a lot more courage, to see if I can make any sense of it.

You have no need to worry about your English, some native users do a lot worse.

It's funny my first question I asked was about trying to explain the relevance of the 2nd law of thermodynamics to a group of physicists over the exact some problem.

I couldn't believe they didn't get that GR implies plasticity to spacetime it really makes it a fabric or foam.

They sort of view 2nd law as some sort of probability thing I had to explain no it implies plasticity via mathematics.

If I use the formula F = MA it is hard relationship,

if I say on average F = MA

what I am doing is imparting plasticity the average result is the same but to model it you have to answer a question how much noise about the average do you want. Its like I was pulling via a rubber band or pushing thru a rubber stopper.

If you look at the 2nd law there are two conditions within the law one is time the other is systemic you must have the whole system. If you look at GR for space thats the same parameters space and time .... they really are related.

To me as a modelling physicists GR is a description of the physical world, 2nd law is a description of the energy movements but they are in effect the same law.

When energy like light or radiation is produced on the spacetime fabric it builds up pressure on the spacetime fabric via the friedmann equations and the 2nd law guarantees the energy is resolved off the fabric to release the pressure.

It really is like a very very very large hydrolic system.

That's how we model it anyhow.

Orac, I hope you keep on bringing up good points. We need somebody to keep us going straight. I have been trying, but I don't pretend to know everything that is going on in physics. I will keep throwing out my half baked ideas but I won't object if somebody comes up with a correction to what I have to say.

So far I haven't had a problem with your English. Keep up the good work.

Bill Gill

Bill S. More reply to your long gravity post.


It seems to me that you are getting carried away with the analogy. Remember that the sheet with a weight on it is indeed just an analogy to give us a way to visualize something that we just cannot visualize. Then you try to extend the analogy by assuming the sheet in a no gravity situation. Well, that just doesn't work. No analogy can be extended too far and your idea certainly does that. In fact the energy required to warp spacetime is just the energy encapsulated in the mass that sits at the center of the warp. There is no other energy required to do the warp.

Bill Gill

Hmm my post's because they are moderated are very delayed think my other post will come up between these.

Okay we need to seperate gravity and energy pressure from the fabric of spacetime.

Imagine spacetime as a blowup camp bed putting mass on the blow up bed deforms spacetime (our bed) locally and does put a little pressure on spacetime. However think to make energy we put more pump more pressure in to the bed.

These are really bad analagies but they do show that as a foam or fabric, spacetime can build pressure in two ways.

It is probably somewhat useful because you can also sort of see what pressures would drive universe inflation.

Remember the only thing opposing our pressure we build up is gravity the only attactive force we know.

So in someways visualizing it as a blow up bed or ballon is a good way to view a very very large hyrdrolic like system.

This is the situation I keep coming back to, but each time I arrive there I ask myself: where else in nature can one find a situation in which energy does anything without an exchange that depletes the source?

Where else in nature? How about the Strong Force, mediated by gluons, that binds quarks together, Bill? That is a question rather than answer, I assure you.

Hopefully someone will come up with an answer, but I can confidently predict that I shall not be that one.

How do you distinguish between a force that causes something to happen indefinitely, without expenditure of energy, on the one hand, and perpetual motion, on the other?

I believe you get a mass deficit via good old Einsteins theory .. someone check :-) So I don't really believe this is an energy exchange without depletion even in this case which is what I think Bill is getting at.

I have expressed to you before Bill in some ways GR and the 2nd law of thermodynamics are different views of the same thing.

Given we expect GR to fail at small distances because of QM I would view the most likely places to look is around QM for violations like Red's suggestion ... and my answer is a thought not an answer too sorry :-)

Just checked and yes they are sort of saying what I would have guessed.

Sorry this is beyond my ability at english so I will use a quote



Hmm maybee QM does have another role ... time to ponder that.

Skipping merrily along I have now another comment on Bill S.'s book about gravity

Actually the "equal and opposite force" involved in a rock lifted above the surface of the Earth is the force that causes the Earth to move toward the rock. Let's skip the lifting part and look at the rock as it moves toward the ground, to simplify what we are talking about. The rock falls towards the Earth because gravity causes a force to act on the rock. But at the same time that the rock is falling toward the Earth, the Earth is falling toward the rock. The "equal and opposite force" is the force pulling the rock toward the Earth. The mass of the Earth is a lot larger than the mass of the rock, so the rock moves the farthest and fastest, but both of them are moving.

Bill Gill

Ok Orac Now I have a question about the following quote.



I am trying to get a feel for what you are saying here. My first thought is that F=MA is different if you are looking at it in Quantum way than if you are looking at it in a Classical way. I assume that "On average F=MA" takes into account the uncertainty principle. So that at small scales you do have to use Quantum principles to calculate how a system will act in response to an applied force. Of course at what we might call normal scales the uncertainty averages out so that a Classical system works according to F=MA in the hard sense.

I hope I have that somewhat right.

Bill Gill

I have a feeling your English might have been easier to cope with.

Thank for your latest comment, Bill. It seems to be an answer to the question"...where does it end?". I assume the intermediate stages such as my feet pressing harder on the ground, and the Earth pushing back, are still valid as intermediate stages.

BTW, Bill, I hope that one day you might do a similar dismantling job on "The Divided Universe".