Why is a gravitational field negative energy ?

[andrewkirk]

Why is a gravitational field "negative energy"?

The idea about the universe having zero net energy, as explained for instance in http://en.wikipedia.org/wiki/Zero-energy_universe, seems to be that gravity has 'negative energy', which offsets the positive energy of all the matter and radiation. This may be the idea behind Lawrence Krauss's 'A Universe from Nothing', although I haven't read his book so I don't know.

Can anybody explain what it means to say that a gravitational field has negative energy, and why that is true? It seems very counterintuitive to me, but that may be just my being dense.

Thank you.

 

[Simon Bridge]

Most people start from the realization that gravitational potential energy at a particular position in space, defined as the work needed to remove a mass from that position, is always negative.

From there it does not seem so counter-intuitive.

As for Krauss:


Certainly if you want a Universe from nothing then for every positive something you need something to balance it out so that together you still have nothing. Otherwise you have some (even more) fancy footwork to do. I think Krauss is talking about vacuum fluctuations. [edit] sort of both - see the video at 33.00

 

[twofish-quant]

First of all, don't take what Krauss says too seriously. There is a kernel of speculation, but Krauss makes it sound like this is all confirmed stuff when its one step above a guess.

Now as far as energy goes...

Since you care about the difference in energy, you can set the zero point to be where ever you want it to be and it won't make any difference. For a gravitational object, a convenient "zero level" consists of the field at a very, very distant location. If you set that as "zero" then when you get close to the object, then the kinetic energy increases, the potential energy decreases, and so the energy relative to "zero" is negative.

Now you can ask, if we can set the zero point anywhere, then how can we say that the universe has "zero net energy" which is a good question and why a lot of people think the idea doesn't make any sense at all.

 

[Lino]

... when you get close to the object, then the kinetic energy increases, the potential energy decreases, and so the energy relative to "zero" is negative. ...

Twofish, I understand most of what is being said on this, but in relation to the above comment, are you saying that the (negative) change in potential energy is greater than the positive change in kinetic energy (and hence the overall negative change)?

Regards,

Noel.

 

[HallsofIvy]

I don't believe that is what he is saying. A gravitational field is "conservative" so the total energy remains constant- the decrease in potential energy should be equal to the increase in kinetic energy.

But the crucial point is that it is only the change that is important. The actual value of the potential energy is always relative to some arbitrarily chosen position where it is 0. The customary choice for potential energy in planetary (or cosmic) applications is "at infinity". And since the potential energy due to the gravitational field increases with distance from the planet, choosing "0" at infinity means the value at any finite distance (closer to the planet) is less than 0, negative.

Again, it is the change in potential energy that is important, not the value.

 

[Lino]

Thanks HallsofIvy. If I ignore the reference to "kinetic energy", I (kind-of) understand what you are saying. I can follow the second paragraph. For the purpose of this topic, is it safe to ignore kinetic energy?

Regards,

Noel.