The idea that empty space simply has a uniform, non-zero energy level is a disappointing and kind of anti-climatic explanation for one of the greatest mysteries of physics and hints that our best models of the universe have huge gaps.
Put a pair of parallel conducting plates between a given bounded volume though, and interesting thing happens: while shorter, higher energy standing waves can still fit between them, the longer, lower energy ones cannot.
As a result, there is now no longer an unbounded number of virtual photons between the inside plates and the outside ones, and this manifests as a very slight force on the plates because you now have a higher energy on the outside then on the inside. But it's a lossy process: the plates can only exclude longer, lower energy wavelengths, so there's a very finite upper bound on how much energy any given arrangement of this system can produce since as you move the plates closer together the remaining energy inside grows much faster then the energy outside (shorter virtual wavelengths).
If you're wondering how this affects you: it's all around you. Vacuum energy - the Casimir force - is believed to account for most of the force known to be due to van der Waal's forces in chemistry - i.e. the basic force which sticks non-ionic, non-covalent things together. The difficulty of removing dust for example, is being driven by that.
EDIT: "Dark Energy" - which is what's being discussed here, is very different.
Wave functions can be seen as the sum of polynomial terms.
So a wave function of: x^3+3x^2+4x could be expressed as its coefficients [1,3,4].
Now if any of those coefficients are allowed to be zero, then you’d have, say, [0,3,4] for your polynomial which simplifies to an identical polynomial [3,4].
This just reduced the dimension of the problem by 1, but a wave function in n dimensions is fundamentally different than one with n-1 or n+1.
If you could reduce the dimension of a problem by zeroing a coefficient and still get accurate calculations then then “curse of dimensionality” would be moot because you could just keep reducing the dimension until the problem was tractable and then reverse the process to build back up to the original problem.
Unfortunately, the pigeon hole problem creeps up when the additional states of the higher dimension lack a direct analogue to its lower dimension.
Think of a binary tree. At each element draw two new elements branching from it on a line below. Allowing any leaf to be 0 effectively removes it and all of its parents and children from the model. So in order to retain the full tree all values at each leaf must be greater than 0.
Except reality has zero requirements to conform to mathematical models even if ours sometimes work to 10 decimal places there’s other cases they don’t work at all.
As soon as you step outside the area a model provides accurate answers you need to stop using it because some unaccounted for factor is now significant. It’s a depressingly common mistake. Read up on what people used to say about breaking the sound barrier despite known examples of bullies etc doing so. People literally knew the model was wrong in that region and yet they still used it to make predictions.
I bring it up now because natural language is just so difficult to employ in describing a concept that is itself a distillation of its description unambiguously. You can /say/ a mathematical operation is 'associative', but how do you /define/ associativity without just giving the mathematical expression?
All that to say, it's difficult to communicate these ideas, but I am unsure what your message here is?
I find what you wrote above to be an accurate account of the development of science, but I fail to see why it warrants the exacerbated tone or how it applies to what's being discussed.
What model is being applied here? What area does said method 'work' in, and how does the problem in question 'step outside the area [the] model provides'?
What model do you prefer for vacuum energy? How does it accurately model observation while affording a vacuum energy of 0?
> What model do you prefer for vacuum energy?
The standard model seems fine without vacuum energy > 0. ex: https://arxiv.org/pdf/hep-th/0503158.pdf
Are you aware of any experiment that suggests it, beyond the apparent acceleration of the expansion of the universe? Because IMO an explanation that only shows up after an observation and also only applies to a single observation isn’t a deeper explanation than the observation itself. (Edited for clarity.)
This a bit confusing due the vacuum energy being a part of standard model.
> Are you aware of any experiment that suggests it, beyond the apparent acceleration of the expansion of the universe?
Yes. Heisenberg uncertainty, the BCS theory of superconductivity, the Higgs field. Also, the paper you linked provides a few.
>> However, to my knowledge no one has shown that source theory or another S-matrix based approach can provide a complete description of QED to all orders.
Quantization of electrodynamics.
>> In QCD confinement would seem to present an insuperable challenge to an S-matrix based approach, since quarks and gluons do not appear in the physical S-matrix.
Quantum chromodynamics.
But ultimately, the paper you linked is uninterested in showing that the vacuum energy is 0, and rather is intended to show that from their formulation the Casimir effect is able to be explained away without a vacuum state > 0 under certain conditions. This important distinction is central to the paper.
>> Even if one could argue away quantum zero point contributions to the vacuum energy, the problem of spontaneous symmetry breaking remains: condensates that carry energy appear at many energy scales in the Standard Model.
That said I’m skeptical of their methods. Since you are clearly an advocate for this paper, can you explain the crux of the paper, namely:
>> Casimir forces can be calculated without reference to the vacuum and, like any other dynamical effect in QED, vanish as α → 0.
What is even meant by allowing the fine structure constant to go to 0?
Because the stability of the standard model requires it to be constant.
And how a model that allows such a thing is a better representation of what is “real“.
Because the conclusion gets a bit wishy washy as it moves from the rigor of its maths to philosophy. (“real” vs “unreal”)
>> Still, no known phenomenon, including the Casimir effect, demonstrates that zero point energies are “real”.
In that regard I think the author would agree with my gp that rather than worry about “real”ness, to look at vacuum state as a consequence of the model we use to describe what we collectively accept as “real”.
I disagree that it's really that simple an explanation, though. Our best theoretical prediction for dark energy is that it should be denser by dozens of orders of magnitude. It's not remotely clear why the actual value seems to be so small, especially since it's not exactly zero.
It is very clear actually: one or both of the models producing the conflicting result are wrong. Smart money's on both, because we have good other reasons to think each of them is wrong.
Exactly, and letting either of those two things to be 0 is effectively saying you’re measuring between one thing, which is a contradiction.
I'm not sure this follows. The set of positive integers is infinite. It means that there's always a larger integer, but it doesn't mean there's always a smaller one, or an infinite number of integers between 1 and 10.
Having four legs is accidental to being an animal, just as there being an infinite number of elements between any two elements in a set is accidental to its cardinality being infinite.
If it is as we suppose that the universe started all squeezed into a point at the beginning of time, and then explosively expanding out from there, then I don't see why we would expect a uniform distribution like that.
Wouldn't you run into the planck length at some point?
Nothing is infinite
It isn't infinite even if the universe is expanding forever - which is not commonly accepted as the big crunch exists as an idea.
Just bc we may never be able to see the whole picture doesn't mean there isn't one.
And it could change again. We’d all be dead before we knew what was happening.