How can the total amount of energy in the universe be zero?

Question

First of all, it is important to note that I'm not very savvy in neither general relativity nor any other area of expertise that answering this question may require. Therefore, I mean for the question to be answered in layman's terms.

Okay, now to the question itself: as far as I understand, for a given energy total in a system, its contents can theoretically be put into any other configuration of energies with the same total sum (if that makes sense). Therefore, if that sum is zero, the contents can be configured into, basically, 'nothing', which also has an energy total of zero.

However, with the universe, the only sources of negative energy are the fundamental forces. I think it may be reasonable to put all forces other than gravity aside, as only gravity is generated (sorry for funky wording) by something which itself is another source of energy (mass), and all the other forces eventually cancel out. If we also ignore the dark energy, we are left with a collection of masses that will eventually crunch together. Here is the problem I have with this: where will the mass go? Even if the potential energy of every point in the universe is zero (i.e. all the mass in the universe has now been smushed into a point), there is still mass to deal with, right?

I know I am probably wrong in many, many places in this question, but can you explain the general, underlying flaw behind my reasoning?

Answer 1

It really depends.. Settle for Feynman asserting the energy is conserved in the universe as a whole. Now you can call it $0$ if you wish. :)

According to Noether's Theorem time translation symmetry means conservation of, guess what.

Look at a free particle with momentum $p$ and energy $p^2/2m$.

So it has $0$ energy at rest? No. Einstein relation, and expand once in $p^2$

$$E=c \sqrt{m^2c^2+p^2} \approx mc^2+p^2/2m+...$$

What about the negative energies hiding there? What the hell does that mean anyway? It has an interesting meaning to it, but the important thing is the exclusion principle for electrons for example, and the apparent positive energy they all have, if there is any. They'd rather take a more relaxed lower energy. They cannot because there is a sort of sea of positrons occupying the negative band.

No one likes Smushed "points" of mass/energy. Some variants of the general theory are free of them.

If you do want to think of a crunch of a collection of masses to a small region which looks like a point, the rest of the universe is not "void". Wait a tiny moment and you have the particle but a tad later and not mathematically vanishing velocity. There can be space like interaction from the future point to the present point as felt by the present point, but upon reaching that future nothing is sent back. That's because the the now past particle knows it is coming and counters it with anti-interaction. :). And that's crazy, i.e virtual. that's why it is not infinite, and not 0.

You say you are probably wrong in many ways like it is a bad thing.

If you come to realize you are wrong at some point about something you gain a lot more than reading what you were thinking in an academic paper, for instance.

I'm no expert but I know enough to get numerous absurdities that would counter a $0$ energy pointy, something..?

On the other hand I can just tell you to look at 15 solutions to EFE. I can tell you to go read about the Dirac equation or better to see what it does to GR if taken as matter.

I can say that before and towards your crunch you still have a continuous symmetry and it is lost at the crunch and $Q$, the conserved Noether charge operator now proves a new massless boson crying lost energy due to a new vacuum state (Nambu-Goldstone boson for you). You take a symmetry you get energy, positive, energy. and you also get to avoid the rabbit hole of no more physics :).

Yesterday you turned off dark energy and imagined a "crunch" can occur as a result. Go back a bit because you have to consider dark energy after you switch it on or off... If you don't then you don't get to be wrong! And, you cannot deduce any conclusion about the conditions for the $0$ energy universe you postulate as a question.

Answer 2

The energy density of a gravitational field is negative, so it can serve as a "reservoir" of negative energy. If the total (negative) energy in gravitational fields throughout the universe is precisely equal in magnitude to the (positive) energy throughout the universe that resides in electromagnetic fields, kinetic energy of moving masses, "bare" particle rest masses, etc., then the total energy of the universe can be zero. However, it is not known whether the total energy of the universe is positive, zero, or negative.