I believe that it is impossible to make a recommendation suitable for all cases. And in each case, to determine the boundary, it is necessary to compare the calculation results with the experiment. Best regards.

Hello Яков Аронович Рейзенкинд , Thank you, Akov. But that is not how physics or maths have been done, to throw our hands up in the air ... and give up. This approach is not productive, can one try better?

We know the answer, at least in the cases cited: network topology and photons. The first case is less than or equal six, the latter seems to be 10. This could indicate 10 as a reasonable starting point for electrons. One can also question 10 for photons, and try the least, two photons. We do not just give up.

We have evidence it is a small number, not billions of billions. The least number is two, of course. Could that, or close to the next order of magnitude, 10, be the case? Where is the evidence that supports the claim -- we do not work well with guesses.

Ed, I don't share your optimism. There are many collective effects, for which 10 objects are not enough. Is it possible to model a magnetron assuming that the cathode emitted only 10 electrons? Or simulate the formation of spiral galaxy arms with only 10 massive bodies?

Hello Яков Аронович Рейзенкинд : Thanks. In science, one could say that optimism comes from the probability that the evidence supports the claim. Some phenomena may depend on more objects in non-collective effects. It is also possible to use self-similarity and other principles, such as Pareto's power-law, to model collective behavior. In that case, just 10 massive bodies in a solar system like ours may help us understand spiral galaxies, like we do, without having left physically the solar system.

Cheers, Ed Gerck

Ed,

I had just read the same study you mentioned, that saw a collective forming with seven photons. Thanks for pointing out the other study that shows similar results.

I found this interesting because it adds a bit of confirmation for a new interpretation of quantum mechanics that I've been working on and was just published in a peer review journal. You can see more about it here:

Article The Lenses of Perception Interpretation of Quantum Mechanics

It is, of course, highly speculative and controversial, as all interpretations seem to be. However, it does offer some new insights into how fields first form at the quantum level. This has the potential to help with understanding better how the field of space might form, which can help with trying to solve the puzzle of quantum gravity.

What is interesting is that it applies to all fields, and it does give a theoretical minimum. It suggests that formation at the quantum level begins with three, but it will be virtually undetectable at this point, so four is probably the real limit for detection purposes.

However, the strength of the field effect will be incredibly weak at this point, since it grows with the number of particles by an exponential factor. It grows exponentially because all of the particles reinforce the field through their interactions with each of the other particles in the field collective.

This means that any background noise is going to easily overwhelm the effect when the number of particles is small. This suggests that if these two teams of scientists that you cited could reduce the background noise lower, they should see collective effects at perhaps four or five particles.

The two studies you cited provide some nice confirmation that these collective effects exist in small numbers.

Another wild possibility that has emerged from the interpretation of QM that I talked about above, but that I didn't discuss in my paper, is that it suggests the Higgs field may be made up of small numbers of particles. This explains why the Higgs boson is many orders of magnitude smaller than theory suggests it should be.

Theory suggests that the Higgs field effect should grow to equal the field of space. And it would, if my theory is right, if the Higgs field was allowed to grow. But it doesn't grow beyond small numbers of particles because as soon as the field starts to get larger it becomes consumed into the field of space and disappears as a separate field. In other words, the particles switch from being members of small Higgs fields to joining the universal field of space.

It is all high speculative, as I said, but it is nice to see some small bit of confirmation that this might be going down the right track.

Thanks,

Doug Marman.

Hello Doug Marman and all: Thanks. Our own number is that at least 2 photons are needed for collective effects -- the bare minimum. Not 3, or 10, or more. This is confirmed experimentally and theoretically in QM, but is a pre-publication result.

Ed,

I'll be interested to see your publication when it becomes available.

My paper shows that relationships between two definitely happen, but they are different from the "collectives" that we see with Bose-Einstein concentrates and the effect with photons that were being measured.

So, I will be curious to see if your findings agree.

Thanks.

Doug.

I am aware of at least one highly nontrivial collective effect with 3 entities: Efimov states. Much simplified, it's existence of trimer where there is no dimer.

On reflection, a highly nontrivial collective effect with 2 entities is hydrogen atom.

Hello L. I. Plimak , We can entertain Efimov states, but a hydrogen atom is a whole new enity -- not a collective effect of unchanged parts. In the collective effects of 2 photons that I mentioned, the 2 photons remain unchanged. Collective effects is not chemistry. The parts can be recognized, just a different effect is added or subtracted.