What constitutes negative and positive energy

[DiracPool]

I'm a little confused over what constitutes negative and positive energy. I've heard it said that we have a zero energy universe because the mass of the galaxies, etc. counts as positive energy which is exactly balanced out by gravity, or the gravitational potential, which counts as negative energy. Ok, that's understandable.

But what about negative energy as in "antimatter." The negative energy solutions to say, the Dirac equation, talk about negative energy electrons with negative mass. This type of negative energy seems qualitatively different from a negative energy which seems equivalent to "potential energy." What's going on here?

 

[Simon Bridge]

Antimatter has positive energy.
The negative energy solutions to the Dirac equation are artifacts of the way Dirac did his maths ... in math you can encode anything as positive or negative or complex or whatever you like. In Dirac's case he managed, unintentionally, because of the way he set up the equations, to use the negative sign to encode a symmetry between matter and antimatter. Much like you may use positive and negative signs to help talk about "left" and "right".

In cosmology, what matters is the Einstein field equations. Energy that comes out negative there is what is usually meant when talking about "negative energy".

 

[DiracPool]

Antimatter has positive energy.

Ok, let's talk about the "Dirac sea" then, the negative energy electrons and other negative energy particles that remain below the negative energy line and don't creates "holes" that manifest as positive energy anti-matter. How do these negative-energy masses relate to the negative energy gravitational potential? Or do they? And if they don't, why are we using the same same term, "negative energy," to refer to two different things?

 

[PeterDonis]

let's talk about the "Dirac sea"

This is not a good model to use. It happened to work ok for Dirac's original purpose, but it doesn't work well generally, and it is not part of modern relativistic quantum field theory. It certainly is not a good model to use when trying to understand gravitational effects.

 

[DiracPool]

This is not a good model to use. It happened to work ok for Dirac's original purpose, but it doesn't work well generally, and it is not part of modern relativistic quantum field theory. It certainly is not a good model to use when trying to understand gravitational effects.

Ok, so does this mean that, when we are talking about the zero-energy universe, we are talking only about the negative potential energy contribution from gravity and are eschewing any contribution from what may be considered negative mass-energy particles?

 

[Simon Bridge]

The "Dirac Sea" has nothing to do with cosmology. It is an old, outdated, and discarded model.
It contributes nothing to the cosmological energy balance for the same reason we don't count luminiferous aether, phlogestron, or the mass of the celestial spheres.

Note: negative mass-energy particles, if we could find any, would need to be included in large scale cosmology. The dirac sea does not describe negative mass-energy particles in Nature. It is an imaginary model that works OK for a very narrow application.

The question being posed is more along the line of "are there two meaning to the term negative energy"?
Perhaps physicists are being accused of being inconsistent in their terms?

The answer is that "negative energy" strictly refers to energy that has a negative value in the model we are interested in.
In that sense physicists are being quite consistent.

What you should understand when someone talks about negative energy depends on the context.
i.e. in a finite square well of depth V, it is common to represent solutions with energies E>0 to represent free states and energies -V<E<0 to represent bound states. So it is OK to say that bound states are negative energy states. That is because it is the schrodinger equation that counts here. In cosmology, other equations count.

 

[haushofer]

Ok, so does this mean that, when we are talking about the zero-energy universe, we are talking only about the negative potential energy contribution from gravity and are eschewing any contribution from what may be considered negative mass-energy particles?

Yes.

 

[bcrowell]

GR does not provide any way of defining global conservation of energy in a cosmological spacetime. Therefore when people talk about this idea of a universe with zero total energy, it's not meaningful.

 

[Simon Bridge]

... well, it means they have to specify what they mean.
But iirc the "zero energy universe" is not formally taken seriously in cosmology.
It tends to come up in response to lay questions like "how can you get something from nothing?".

 

[bcrowell]

... well, it means they have to specify what they mean.

The structure of GR is such that any specification they give will not be something we should care about. For example, they could define something coordinate-dependent, but that means we shouldn't care about it because it's coordinate-dependent. General relativity doesn't permit a conserved scalar mass-energy that can be defined in all spacetimes. There's a good discussion of this in MTW, p. 457.

 

[Simon Bridge]

... OK. But do you have something that answers the original question?

 

[bcrowell]

... OK. But do you have something that answers the original question?

Yes. The original question is based on a misconception. Explaining the misconception answers the question.

 

[Simon Bridge]

OK ... so when people talk about a "zero energy Universe", they are not making sense? Gotcha.

 

[DiracPool]

Yes. The original question is based on a misconception. Explaining the misconception answers the question.

Can we really toss aside the zero-energy universe concept so cavalierly? This isn't just a pop-sci proposition, as far as I can tell. Although it has it's pop-sci adherents such as Krause, Kaku, Greene, Filippenko, etc., it is also invoked by more "serious" popular cosmologists such as Alan Guth, Andrei Linde, Sean Carroll, and others. Put more specifically, it seems to play no small part in how the inflation model relates to models of eternal inflation and the "multiverse:"

http://www.livescience.com/33129-total-energy-universe-zero.html:

"Cosmologists have constructed a theory called inflation that accounts for the way in which a small volume of space occupied by a virtual particle pair could have ballooned to become the vast universe we see today. Alan Guth, one of the main brains behind inflationary cosmology, thus described the universe as "the ultimate free lunch."

In a lecture, Caltech cosmologist Sean Carroll put it this way: "You can create a compact, self-contained universe without needing any energy at all."

https://www.astrosociety.org/publications/a-universe-from-nothing/

"More recently, Guth has expressed his belief that our Fred Hoyle’s discredited steady-state theory). He believes that the entire cosmos was created by quantum fluctuations from nothingness (which he argues is perfectly consistent with the Law of Conservation of Energy because its total energy value remains zero), and is quoted as saying that “the universe is the ultimate free lunch”.

 

[PeterDonis]

Can we really toss aside the zero-energy universe concept so cavalierly? This isn't just a pop-sci proposition, as far as I can tell.

The two articles you linked to are pop sci articles. Can you find any actual published, peer-reviewed papers?

 

[DiracPool]

The two articles you linked to are pop sci articles. Can you find any actual published, peer-reviewed papers?

My point in my post #14 was not to rigorously defend the zero-energy universe concept per se, I'm not qualified to attempt this; my point was that that a good number of qualified cosmologists do not seem to write off the zero-energy universe concept as "meaningless," as bcrowell suggested this concept was in his post #8. We don't need a peer-reviewed paper to verify quotations and sources, we just need to verify the quotations and sources. So, rather than risk equivocation on relying on the integrity of pop-sci websites to accurately quote their sources, we can just hear it directly from the "horses mouth," so to speak:

Alan Guth: FF to 33:00



Sean Carroll: FF to 54:00



Lawrence Krause:



Michio Kaku:

 

[PeterDonis]

my point was that that a good number of qualified cosmologists do not seem to write off the zero-energy universe concept as "meaningless," as bcrowell suggested this concept was in his post #8

The answer is still the same: you don't show this by pop science sources. You show it by peer-reviewed papers or textbooks or some other technical source. Scientists will say lots of things in pop science books, articles, and videos that they know they can't get away with in actual peer-reviewed papers, because it's their personal opinion rather than actual science. Pop science is not science; bcrowell was talking about the science, and if you want to show that he's wrong, you need to show it with science, not pop science.

 

[DiracPool]

Pop science is not science; bcrowell was talking about the science, and if you want to show that he's wrong, you need to show it with science, not pop science.

I'm not trying to show anything, I'm trying to understand. It just seemed to me that there was something valid to the zero-energy universe concept because a large number of cosmologists seem to support it. I'm coming at this from a "B-prefix" perspective, so trying to split hairs over the details of the model using tech journal references is above my paygrade. I'm not really sure what you and bcrowell are saying here. Are you saying that the peer-reviewed science rules out the concept of the zero-energy universe, or are you simply saying that there isn't enough evidence to make a definite claim that the total energy of the universe amounts to zero? In other words, is the concept that matter-radiation amounts to positive energy and gravity amounts to negative energy a valid concept, only we don't know if the balance of the two adds up to zero, or is there a flaw in the premise of the concept in general? This distinction is what I'm not picking up here.

 

[PeterDonis]

I'm not really sure what you and bcrowell are saying here.

We're saying that the concept of "total energy of the universe" is not well-defined. See below.

is the concept that matter-radiation amounts to positive energy and gravity amounts to negative energy a valid concept, only we don't know if the balance of the two adds up to zero, or is there a flaw in the premise of the concept in general?

The latter. More precisely, there is a flaw in the claim that the concept has some invariant, coordinate-independent meaning. It doesn't. It is possible to pick particular coordinates and then show that, in those coordinates, a quantity can be defined that can be interpreted as "negative energy of gravity" that just balances the positive energy of matter and radiation. But it is also possible to pick other coordinates in which this "negative energy of gravity" disappears--there is no such quantity in those other coordinates. But no actual physics can depend on the choice of coordinates.

By contrast, it is impossible to pick any coordinates in which the positive energy of matter and radiation disappears; that positive energy is an invariant, independent of any choice of coordinates.

 

[DiracPool]

Ok, thanks for the clarification. So is this saying that the "zero-sum energy" of the universe is not "Lorentz co-variant?" If I'm using my terms right. That seems kind of odd that you'd get a zero-energy solution in one frame and a non-zero solution in another frame. Do we know what solution we get from the frame of the CMB?

 

[PeterDonis]

is this saying that the "zero-sum energy" of the universe is not "Lorentz co-variant?"

It's not covariant, period. No need for the "Lorentz" qualifier--since we're talking about curved spacetime, transformations between coordinate charts aren't Lorentz transformations anyway.

That seems kind of odd that you'd get a zero-energy solution in one frame and a non-zero solution in another frame.

That's not what I said. What I said was that "gravitational energy" can't even be defined except in particular coordinates. That means you can't even compare the "energy" in the different coordinate charts in this way, because you're comparing apples and oranges; you're counting "gravitational energy" in one coordinate chart but not in another. (Btw, "coordinate chart" is a better term than "frame".)

A proper comparison would only count the kinds of energy that are invariant--the same in all coordinate charts. The energy of matter and radiation meets that requirement; "gravitational energy" does not. So what you really have is a solution with nonzero energy, period.

Also, when we describe a spacetime using different coordinate charts, we are not describing two different "solutions"; we are describing the same solution--the same spacetime geometry--in two different coordinate charts. You might want to think about what that implies about coordinate-dependent quantities like "gravitational energy".

Do we know what solution we get from the frame of the CMB?

In standard cosmological coordinates (which is what you are referring to here), the "gravitational energy" can be defined; these are the usual coordinates that are implicitly being referred to by physicists who talk about a "zero energy universe". What they neglect to mention is the issue I described above. This "zero energy" does not refer to an invariant; it refers to a coordinate-dependent quantity.

 

[DiracPool]

We're saying that the concept of "total energy of the universe" is not well-defined. See below.

In standard cosmological coordinates (which is what you are referring to here), the "gravitational energy" can be defined; these are the usual coordinates that are implicitly being referred to by physicists who talk about a "zero energy universe". What they neglect to mention is the issue I described above. This "zero energy" does not refer to an invariant; it refers to a coordinate-dependent quantity.

Ok, good. That's the paragraph I was looking for to reconcile the posts in this thread. It's not so much that the pop sci characters I mentioned are wrong per se, it's just that they're espousing more of a special condition rather than a generality.