Mutiple Zero Point Fields and the Cosmological Constant

Question

Duality of elementary particles like electrons or photons is well known if not fully understood. There is ample research suggesting elementary particles are simply high energy states of universal fields. What appears to be an electron particle could in fact be the high energy excitations of a universal electron field, much like an iceberg is only a fraction of its larger submerged mass. This is the basis of Quantum Field Theory.

Particle properties are manifested when fluctuations within universal fields produce energy spikes that 'push' particles into existence. Below this threshold value, only waveforms would exist in a universal energy field. "In cosmology, zero-point energy is related to the cosmological constant." Zero Point Fluctuations….

"Vacuum Energy is the zero-point energy of ALL the fields in space, which in the Standard Model includes the electromagnetic field, other gauge fields, fermionic fields, and the Higgs field. It is the energy of the vacuum, which in quantum field theory is defined not as empty space but as the ground state of the fields." https://www.scribd.com/document/175053727/Zero-Point-Energy-Wikipedia-The-Free-Encyclopedia….

And research finds the energy difference between vacuum energy and the CC is a 30 order of magnitude difference." If the recent observations pointing toward a cosmological constant of astrophysically relevant magnitude are confirmed, we will be faced with the challenge of explaining not only why the vacuum energy is smaller than expected, but also why it has the specific nonzero value it does." https://core.ac.uk/download/pdf/11920173.pdf https://ned.ipac.caltech.edu/level5/Carroll2/Carroll4.html.

So current known fields contribute to the CC but there are still missing energies, meaning more fields may exist. http://www.dailygalaxy.com/my_weblog/2011/09/the-beast-does-an-undiscovered-quantum-field-collapse-neutron-stars-into-black-holes.html.

My question is: Are there separate universal fields for each elementary particle? And if so, would each field be boundless or infinite in size? I'd love to know if fields actually enter then EXIT black holes. This seems to contradict current theory as even EMR is unable to to escape the Event Horizon but if fields can't exit then they are interrupted or even broken within a black hole.. http://www.iiserpune.ac.in/qft/qft2011/pdf/QFT23/Spenta_Wadia.pdf

Answer 1

Wave-particle duality here is not really related, and anyway I think this notion can be disregarded when approaching quantum mechanics whether it be Quantum Field Theory (QFT) or non-relativistic formulations. Also, I have never heard of the expression "zero-point field". It is therefore unclear what you're asking. However, I'll try to give a few elements about the relationship between zero point energy and the cosmological constant :

Why we can't calculate the zero point energy

Zero-Point energy is indeed a thing in QFT. It corresponds to the lowest energy state of a field, namely the one with no particles at all. It is very analoguous to the energy levels of a quantum oscillator at frequency $2\pi \omega$, where $E_n$ would be the energy of the state with $n$ particles : \begin{equation} E_n(\omega) = \hbar \omega \left(n+\frac{1}{2}\right) \end{equation} So the zero point energy would be $E_0(\omega) = \hbar \omega/2$, the energy of the state with 0 particle. For this reason, we sometimes call it the "vacuum energy". But this is only the fraction of energy at pulsation $\omega$. One has to sum over all the possible configurations to get the total zero-point energy of a field, and this means summing over all momenta. For a massless particle, the momentum $\vec{p}$ is related to the pulsation by $\hbar\omega = |\vec{p}|c$. This means that the zero-point energy $E_0$ in a volume $V$ should be (in natural units, dropping the $\hbar$ and $c$ factors): \begin{equation} E_0 \sim V\int \dfrac{d^3 p}{(2\pi)^3} \frac{|\vec{p}|}{2} = \dfrac{V}{(2\pi)^2} \int_0^{+\infty} p^3 dp = +\infty \end{equation}

But as you can see, this quantity diverges ! So there has to be a problem somewhere. The easiest way to solve this embarrassing issue, is to consider the following argument : since our theory probably breaks down at some high energy scale (e.g. the planck scale, $E_{Pl} = 10^{19}$ GeV), we should not integrate momenta up to $+\infty$, but rather up to some cut-off scale $\Lambda_{cut-off}$ at best. In this case, we find for the energy density $E/V$ : \begin{equation} \rho_0 \sim \Lambda_{cut-off}^4 \end{equation}

Each field contributes to the vacuum energy, and all the contributions add up.

Why this is not so much of a problem

In general, not being able to compute the zero level energy is not a problem. What we really measure are energy differences between each state. As long as those remain finite, it seems alright to forget about the value of the ground state.

Why it is still a problem, and the cosmological constant

Our understanding of gravity and QFT seem to imply that vacuum energy should contribute to the stress-energy tensor and thus to curve space-time; In other words, vacuum energy should affect gravity. It was thought for a long time that the cosmological constant, which is equivalent to vacuum energy, was 0. Such a value would not have been too surprising for the vacuum energy. One could have argued that this had to be, for symmetry reasons. In particular, the above calculation should yield a positive contribution from bosons and a negative contribution from fermions, and one could imagine that they might cancel out this way. But it was not meant to be. Since 1998 several cosmological observations indicated that the vacuum energy was non-zero but positive. Its value, however, is very low - about 122 orders of magnitude less than the gross estimate of $\Lambda_{cut-off}^4$. Even if the cut-off scale is brought down to the electroweak scale (which has been well tested), the value is still many orders of magnitude to high. This is referred to as the cosmological constant problem.

As a conclusion : yes, simple considerations tend to the belief that the zero point energy should contribute to the cosmological constant. But we cannot calculate it, and crude estimates lead to ridiculously too large values. There can be many ways we are wrong, and this remains one of the most puzzling problems in physics nowadays.

Answer 2

This site works best if you ask one particular question; your question meanders a lot before alighting on three:

My question is: Are there separate universal fields for each elementary particle? And if so, would each field be boundless or infinite in size? I'd love to know if fields actually enter then EXIT black holes.

Taking these in order:

1. Yes, there are separate fields for electrons and muons, or for up-quarks and down-quarks, or for neutrinos and photons. There are not separate fields, however, for particles and their antiparticles: in some cases some neutral particles (like photons) are their own antiparticles, in the remaining cases we understand them to be negative-energy states, and the field is filled "turtles all the way down" from $-\infty$ to $0.$ However some of these particles arise from the normal rules of quantum mechanics combining together other fields into superpositions. For example we know that the electromagnetic field combines nicely with the weak nuclear force fields into a very aesthetically pleasing "electroweak" field which has also been the subject of a hugely successful prediction (evidence of the Higgs particle). This means that while we'd normally treat those bosons as belonging to different fields, those fields are actually orthogonal superpositions of the strongly-related "electroweak" fields. (There is a "spontaneous symmetry breaking" that goes on to take you from one to the other.)
2. It's not at all clear what you mean by "boundless or infinite in size"; the fields define a value for each point in space and presumably spacetime.
3. I mean, we don't have a well-accepted quantum theory of gravity so this last question about what quantum fields do near black holes is not presently answerable in general. However according to general relativity there is no problem with a massive particle falling into a black hole; it sees itself pass through the event horizon within a finite time. If a "quantum field" picture still worked it would be very, very strange if those fields did not extend into the interiors of black holes.