The vacuum doesn’t weigh anything because there is nothing there.
Quantum field theory contradicts the relative weightlessness of the vacuum.
Nothing.
Void.
Emptiness.
All of these bring to mind the absence of anything. Yet, in our universe at least, counter-intuitively, no such thing exists. Nothingness is something that we do not experience. Even empty space, in the remotest regions of the universe, has energy.
The least thing that we can realize instead is vacuum, which is the absence of any kind of particle or field that we know about. Yet, the vacuum has energy.
Heisenberg’s uncertainty principle tells us that time and energy are duals of one another. The more certain your measurement of time the less certain you are of energy and vice versa. Therefore, a region of vacuum cannot have zero energy, since that would be a precise value.
Indeed, while the average electric and magnetic fields in a vacuum are zero, the sum of their squares, which is the energy, are not.
This energy is sometimes called zero-point energy, virtual particles, or quantum fluctuations. It theoretically has infinite density.
For most of quantum physics, the energy of the vacuum isn’t a problem because only changes in the energy matter. But gravity responds to all energy, including the infinite density of the vacuum.
If that is so, we should see the vacuum have vastly more gravity than anything else.
It turns out that this is not true. The vacuum appears to have almost no gravity. Dark energy appears to be a consequence of the energy it does have. That is, in a way, stranger than it having enormous gravity or zero gravity. While quantum field theory could readily be modified to accommodate either, modifying it to accommodate nearly nothing is a considerable feat.
Indeed, Dark Energy is the same order of magnitude as the amount of matter in the universe (dark matter + baryonic matter). This is quite a coincidence which is why it is called the Coincidence Problem. It is one of the greatest unsolved mysteries of the cosmos.
Of course, it is still possible that the vacuum does weigh nothing and Dark Energy is something else entirely. I find this unlikely.
Whatever DE is, because of the coincidence problem, it is almost certainly related to matter or the effects of matter or shares some cause with matter.
One compelling explanation is derived from the Holographic Principle, which says that the energy of the vacuum is related to the surface area of some connected region of the universe. For example, it could be related to the entanglement energy of the vacuum with itself which is a measure not of total energy but of energy deriving from correlations.
In any case, the more difficult problem is called the Fine Tuning problem, which deals with why the vacuum weighs almost nothing. The holographic principle purports to solve this easily with a clever argument which says that our universe should not have greater energy density than can be attributed to a black hole the same size. It turns out that a black hole the size of the universe would have an energy density around what is observed with Dark Energy given certain assumptions that I’ve written about elsewhere.
While this argument is certainly clever, it doesn’t really connect well with current physics of quantum field theory which still says the energy density of the vacuum is very, very large.
One way to avoid this problem might be to avoid vacuum fluctuations entirely.
Richard Feynman attempted to do this with his invention of Feynman diagrams, only to find that they failed to eliminate vacuum fluctuations. These, instead, show up as isolated loops with no inputs or outputs. These loops appear all over the place in quantum physics.
As I showed in my previous article on quantum fields, you can get away from vacuum loops by adding a 5th dimension to the universe. Quantum field theory can be built upon this 5D universe through a method developed in the 1960s-’80s called stochastic quantization. In that case, vacuum loops turn out to be consequences of statistical averaging over the 5th dimension. That is, they don’t exist. Instead they are a consequence of statistical uncertainty about the existence or non-existence of particles in the 5th dimension. In some places they exist and in others they don’t, but they have a measurable influence everywhere.
Pure vacuum loops are a consequence of particles that don’t interact with any certain or measured particles. They are completely isolated from known matter. In the 5D theory this means these particles are in a different part of the 5D universe from us.
If this is so, then the problem of dark energy may be much simpler than we thought. It is simply the result of particles that are statistically uncertain in one place versus another, i.e., dark energy is energy from real particle interactions but those interactions do not intersect our part of the 5th dimension and hence aren’t visible. Yet, they have a measurable gravitational effect.
Thus, the infinite density of quantum fields is the result of assuming a condition that is false, namely, that all possible configurations of fields exist. For most practical purposes, this is a justified assumption. Indeed, statistical physics makes it all the time even in ordinary statistical mechanics from which thermodynamics arises. Yet, on the scale of the universe, the assumption breaks down. For all practical purposes, time is finite. Space is finite.
In a 5D universe, likewise, the 5th dimension is finite.
We know that even if all these dimensions are actually infinite. Their influence on us is as if they were finite.
Time and the three spatial dimension have limits in terms of causality. In the case of time, back to the Big Bang. In the case of space, 46 billion lightyears away to the edge of the observable universe. (Because of the expansion of the universe, even after an infinite amount of time, the observable universe will remain finite size as far as causality goes.)
The 5th dimension should be no different but indeed related to the others in its causal extent. This puts a hard limit (both a high energy or ultraviolet and long wavelength or infrared) on quantum physical predictions. Indeed, likely the extent of the 5th dimension is on par with that of the other dimensions and thus we could explain the coincidence problem the same way as the fine tuning problem without even resorting to the holographic principle. Instead of going one dimension down to two spatial dimensions, we go one dimension up to four spatial dimensions.
The 5th dimension bounds the size of the vacuum energy density with a length scale similar to that used in holographic principle-based arguments. Yet it modifies quantum field theory, limiting the length scale of stochastic quantization, while the holographic principle persists in contradicting QFT.
Exactly what the nature of the 5th dimension and how it relates to current cosmology are open fields of study. For example, Liu and Wesson explored a compelling argument that the 5th dimension and time combine to create a kind of shockwave, which is the length scale of the universe expanding into the 5th dimension. If this is so, it would certainly put the size of the 5th dimension on par with other dimensions.
While there are other solutions to the 5D Einstein equations, with this one, you could make a strong case for stochastic quantization of fields over the entire universe resulting in the amount of dark energy we measure.
Why Feynman Diagrams Are So Important | Quanta Magazine
Richard Feynman looked tired when he wandered into my office. It was the end of a long, exhausting day in Santa…www.quantamagazine.org
Andersen, Timothy D. “Quantization of fields by averaging classical evolution equations.” Physical Review D 99.1 (2019): 016012.
Liu, Hongya, and Paul S. Wesson. “Cosmological solutions and their effective properties of matter in Kaluza-Klein theory.” International Journal of Modern Physics D 3.03 (1994): 627–637.
Liu, Hongya, and Paul S. Wesson. “Universe models with a variable cosmological “constant” and a “big bounce”.” The Astrophysical Journal 562.1 (2001): 1.