Negative and positive energy and Hawking

Question

I don't have any physics background (except the material we did in high school-long time ago).
I was watching a documentary with Stephen Hawking about whether God created the Universe and I could not follow one of the arguments.
Note: This is not a theological question. I am not trying to determine if the conclusion about God is right or wrong, I am trying to understand the argument from the physics perspective.

One of the arguments (at least as much as I was able to understand it) was that:

For each positive energy in the universe (plannets etc) there is an equal negative energy. So the sum of both adds up to nothing. As a result there is no need for a God.

To make the argument more clear, the following analogy was presented:
A man on a flat area of sand or dirt wants to make a hill. So the man starts to dig and pile up the sand (or dirt) which is increasing and piling up as a hill.
In the end a hill has been created BUT at the same time a hole has also been created taking equal space as the hill in the oposite direction.
In this example it is clear that both do add up to nothing since if you reverse the process then you return to the original flat area.

What I can not understand are the following:

How can in the analogy and in reality things add up to nothing?I mean in the analogy with the pile of sand(dirt) the hill and the hole don't add up to nothing since you always have the original flat area with sand you started with. So how is this starting state ignored and it is stated that the 2 opposite forms add up to nothing? Why is the original flat area of sand which is a prerequisite for the existence of both the hole and the hill being ignored?

If someone could help me understand these, but explain it in layman's terms (as I have no physics background) it would be much appreciated.

Answer 1

No physical experiment can disprove the existance of God. Let's get that out of the way so we can concentrate on the interesting stuff.

If you consider some area of intergalactic space far from anything, then this is a pretty good definition of zero energy because there's nothing there. Quantum mechanics complicates this a bit, but for now lets ignore that and just take our vacuum as zero energy.

If we have some test mass, e.g. a baseball, and let it fall towards a planet then as it falls it picks up speed and therefore it has kinetic energy. But we believe in the conservation of energy, and we started with zero energy. If our baseball acquires (positive) kinetic energy as it falls into a gravity well then there must be an equal negative energy that balances it out, so the total energy stays at zero. This is why we say the energy of the gravity well is negative.

Now go back to our patch of vacuum. Suppose we want to create a baseball from nothing. This costs energy because even a stationary baseball has energy $E = mc^2$ (from Einstein's famous formula where $m$ is the mass of the baseball). But suppose at the same time we create the baseball we create a gravity well with a matching negative energy $-mc^2$. That means the total energy is still zero so we have created something from nothing, but without violating any physical laws.

Creating a baseball from nothing may seem an unreasonable thing to do, but quantum mechanics allows this sort of thing. Well, don't take my example too literally since you've probably noticed that baseballs don't pop into being every day. The point is that when you start thinking about the creation of the whole universe you can make the sums work. The positive energy of the mass in universe can be balanced out by the negative gravitational energy that all that mass creates.

But I think a health warning is in order here. All these ideas are speculative since we have no firm theory to describe how the universe started, just lots of interesting ideas.