 # What Physicists Mean By "Creation From Nothing"

Does modern physics allows for creation from nothing? Here I will explain what physicists mean when we say that particles can come from “nothing” for a very simple case. The “Universe from Nothing” case is more complex, but the spirit is the same.

Caveat: this is an explanation for the lay audience; necessarily, many things are simplified and the very idea of rigor is treated more as a suggestion.

First, a couple of lessons from quantum field theory (the most successful physical theory of the 20th/21st century):

1. Fields are the stuff that fills the Universe, not matter or energy.
2. Particles are oscillations of fields

Those statements might mean nothing to you. Let’s explain things one by one.

What are Fields?
To understand fields, one need to first understand harmonic oscillators. Imagine the following apparatus laying flat on a table: Perhaps when you first buy it from the ball-on-a-spring store, it will look more like this: Where all of the spring is coiled together. If I pull the ball away from the spring and let go, I impart energy on the system. This causes the ball-on-a-spring to oscillate:

L here is the length of the spring when it is fully stretched. It depends on how far I pull the ball away from the spring, and on therefore on the amount of energy I impart on the system.

Now, imagine a whole bunch of these ball-on-a-spring systems:

Each of them has different energies, so each spring has different L’s.

Now suppose I have so many ball-on-a-spring that they blur together:

Each point in that blue line is a ball on a ball-on-a-spring system, I just have so many of them that it’s easier to draw them as a single line. I also forego drawing the springs, because it gets ridiculous.

This collection of many ball-on-a-spring systems is what a quantum field theorist would call a field.

Particles are oscillations of fields
In quantum field theory, particles are oscillations of fields. This means exactly what it sounds like:

1. The underlying objects are fields
2. If the field is oscillating, we (and our experiments) detect this oscillation as particles

To reiterate, there are no particles in this system:

This blue line is a bunch of mass-on-a-spring systems that are completely at rest. If I zoom in enough, each of them looks like In contrast, this system has particles in them:

Why are particles “oscillations of the field”? I can motivate it by appealing to the fact that you probably have heard of the “wave-particle” duality. Particles are just waves, i.e. oscillations.

Quantum mechanics and creation from "nothing"

In quantum mechanics, there is a relation called the time-energy uncertainty relation, which in math reads

\Delta t \Delta E \ge \frac{1}{2} \hbar

This is a cousin of the more famous Heisenberg Uncertainty Principle, i.e. the one saying that position and momentum of a particle cannot both be pinned down exactly. Similarly, what the time-energy uncertainty relation essentially says is that for every chunk of time \Delta t (which could be seconds, minutes, whatever), there is an intrinsic variance in the amount of energy of the system \Delta E. The energy could not be pinned down exactly unless the chunk of time we consider in our experiment is infinity.

Now, because the energy in a ball-on-a-spring system is related to how far the spring stretches, this is what the field looks like if the energy is always zero:

each of the individual ball-on-a-spring system does not stretch at all. This is just the no particles case.

But because of the time-energy uncertainty relation, the energy can not be pinned down exactly. There is always a variance in the energy, which causes a variance in “how far each spring stretches”, so this “energy is always zero”, i.e. the “no particles” case is impossible.

We can also see this from the standard Heisenberg Uncertainty Principle, that position and momentum of each particle cannot both be known simultaneously. In the “energy is always zero” case, the position of each ball is exactly at the center line, and their velocity is exactly zero. This is a case where we know both exactly and thus violates the Heisenberg Uncertainty Principle. So again, this case is impossible.

What physicists call quantum vacuum or ground state or lowest energy state, is the state of the system that has the lowest energy allowed by quantum mechanics. They are the closest to the no-particles case allowed by the Heisenberg Uncertainty Principle, but they are not the no-particles case. There are always wiggles in the blue line, and as we learn, these wiggles are what our experiments detect as particles.

This is what physicists mean when we say creation from nothing: in the closest thing to actual nothingness that is allowed by quantum mechanics, the field regularly oscillates, and thus particles regularly pop in and out of existence. Also, they do this without needing any energy input.

A philosophical point
Obviously, this is not actually creation from nothing. For one, we need to have fields, which is not nothing, and we need to have the laws of physics, which again is not nothing.

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My question is, why is it said that when there is no oscillation there is no particle? Could it be that when there is no oscillation that there’s just no possible way for humans to detect the particle even though it is there?

Unfortunately this is hard to explain, at least for me. You can think of it as a result of quantum field theory (QFT).

In QFT, there are these things called operators that you can use to mathematically “ask” a physical state various observable things. One of those operators is called the “number of particles” operator, which just gives you the number of particles in the state when applied to a particular state.

If you use the “number of particles” operator on a state like this:

it will output “no particles”.

If you use the same operator on a state that has oscillations, it will output some non-zero number of particles.

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Interesting. So it’s based on a mathematical output. What other indicators are there that would corroborate the claim that without oscillation the particle isn’t there?

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But that’s surely not to be taken literally, right? It’s not that there are literal ball-on-a-spring objects which collectively constitute a field whose oscillations are particles, even if the behavior of these “things” are similar to that of a ball-on-a-spring. What is a field really, then? It surely must be something physical and tangible, not mere Platonic mathematical objects, because particles (and atoms and molecules) are physical and tangible. I don’t think we think about this much in QFT - at some point we just write down an equation (analogous to the plots of oscillations that you drew) and proceed with calculations.

(For this discussion, let’s put aside the caveat that QFT is not a final theory, that it could really be strings, etc. - these only push back the discussion one step back.)

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I think it’s more accurate to put it this way: QFT is defined in such a way that mathematically, when there is no oscillation there is no particle. Of course, a definition by itself means little - QFT could be completely wrong. But, we have done many experimental tests of QFT and found that it corroborates extremely well to what we observe in nature. Thus, we have good reason to believe its claims - when there is no oscillation there is no particle.

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These are all interesting questions - as you know, physicists love to reduce things and be done with it. I suppose that whether fields are real or existing depends on what your definitions of real and existing are.

This is an interesting point:

Field to me is as tangible as particles. I have never seen a particle directly, I have only seen its affect on my experiments. That’s as far as I would go to ascribe some sort of tangibility to particles, but then I would say that the same is true for fields.

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So from what I can gather, the idea that there is no particle without oscillation is derived from interpreting a mathematical equation as such, and the only way it is corroborated is by confirming the equation works. Is that correct? And could the 0 in the equation be interpreted differently, e.g., as humanly undetectable?

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I’m curious, what is “ℏ” in the equation above?

This is correct.

This is sort of correct, but just to be clear: “the equation” here refers to QFT as a whole, not necessarily the statement about no particles in particular. I don’t know if anyone has directly experimentally verified specifically the statement that there are no particles when there is no oscillation. By itself, this statement doesn’t mean much to an experimental physicist. To actually test QFT, you need to convert theoretical, mathematical statements like these into statements about quantities that are accessible in the lab. This is we test QFT by say, measuring the magnetism (or g-factor) of the electron (see explanation here). Because QFT turns out to be extraordinarily correct in most of these tests, we think that it is a robust theory and we can believe its claims more generally without having to test every single equation directly (if that is even a coherent notion to talk about).

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The Planck’s constant divided by 2π. It’s just some number.

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So how do virtual particles fit into the narrative of creation from nothing. It seems they always enter this conversation at some point or another. Are they relevant to the discussion?

Virtual particles are particles, e.g. electrons, photons, etc, that do not have the right mass. They are most useful as a mathematical technique in integrating some quantities in quantum field theory. However, under certain circumstances they can produce observable effects. They result as a consequence from the energy-time uncertainty relation that I wrote in the main post:

\Delta E \Delta t \ge \frac{\hbar}{2}

Because the energy cannot be pinned down exactly, for a small enough length of time physics allows temporary violations of the conservation of energy that allows for these virtual particles to be generated.

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Does that mean it can’t be accurately measured?

No, there is an inherent variance in the energy. This is analogous to the uncertainty relation between momentum and position.

Oh, OK. So how is it determined what is happening with disturbances between energy fields in relation to virtual particles? Seems like it would create a bit of uncertainty as to what is actually going on if there is difficulty in “pinning down” both the energy and the particle, wouldn’t it?

I am not sure what are these “disturbances between energy fields” you are referring to.

Oh, I read that virtual particles are just a result of disturbances of an energy field caused by interference from a nearby energy field or fields. Is that not correct?

Virtual particles are the result of fluctuations of the quantum vacuum due to quantum uncertainty relations, such as the energy-time uncertainty relation I wrote in previous posts.

Note that despite its name, the “uncertainty” in “uncertainty principles” does not mean that we are “uncertain” of what physical process is going on. The “uncertainty” in “uncertainty principles” refers to the fact that things like energy or momentum are better described by a probability distribution. But we know exactly how these probability distributions behave through the well-corroborated equations of quantum mechanics.

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