I can prove there's something smaller than a photon

[nonsqtr]

Berkenstein's hypothesis

Bekenstein-Hawking entropy - Scholarpedia

This what resulted in Hawkings Information paradox.

See, I can't respond to that, don't know enough. As near as I can tell the Bekenstein logic is based on Planck-sized patches, and... see... the very first thing that happens is they start talking about "entropy", which as we all now know, has to do with number of states and not occupancy.

It's kinda like they're using circular reasoning. Casini's proof is kinda self-referential. This whole business of defining information in terms of the expectation value is ... imprecise. I don't know, I shouldn't open my yap yet.

I think Casini's contribution in the area of "bounds" is pretty exciting though. You physicists are used to thinking like that, I'm not. I'm kind of an old control systems guy. (Phase plane, ha ha).

[nonsqtr]

Well in physics, measurements are important,and to measure anything at the Planck scale, you’d need a particle with sufficiently high energy to probe it. ..to get down to Planck lengths, you need a particle at the Planck energy: ~10¹⁹ GeV, or so. At such ultra-high energies,the momentum of the particle would be so large that the energy-momentum uncertainty would render that particle indistinguishable from a black hole. This is truly the scale at which our laws of physics break down.

At present, there is no way to predict what’s going to happen on distance scales that are smaller than about 10^-35 meters, nor on timescales that are smaller than about 10^-43 seconds. These values are set by the fundamental constants that govern our Universe. In the context of General Relativity and quantum physics, we can go no farther than these limits without getting nonsense out of our equations in return for our troubles.

If we decide to go down to below about 10^-35 meters ⁠— the Planck distance scale ⁠— our conventional laws of physics would need many quantum corrections,or else would give nonsensical answers.. there are quantum corrections of order ~ħ that arise. There are corrections of all orders: ~ħ, ~ħ2, ~ħ3, and so on,and at Planck scale we cannot ignore the higher order corrections,as we do at larger length scales.

At the Planck distance scale, this implies the appearance of black holes and quantum-scale wormholes, which we cannot investigate.

But at these ultra-intense energy, the curvature of space is unknown. We cannot calculate anything meaningful.

If you put a particle in a box that’s the Planck length or smaller, the uncertainty in its position becomes greater than the size of the box.

The background curvature of space that we use to perform quantum calculations is unreliable, and the uncertainty relation ensures that our uncertainty is larger in magnitude than any prediction we can make. The physics that we know can no longer be applied,a la Ethan Siegel blog post.

That is why we limit space at Planck scale,to avoid a breakdown of known laws. Physicists put a fundamental minimum scale . Of course, a finite, minimum length scale would create its own set of problems. That would imply questioning the fundamentality of Lorentz invariance,and Einstein relativity.

May be we need some fundamental paradigm shifts to transcend Planck epoch.According to Brian Greene, there's a minimum possible length beyond which getting smaller is mathematically equivalent to getting larger. Anyhoo, I thought you were a fan of Loop Quantum Gravity, which make space itself discrete on the scale of the planck length.

Seems to me we're 20 orders of magnitude away from anything Planck. I'd be happy if we got... y'know .. halfway there...

I like the discrete models mainly because they're simpler. Usually if I start simple and discrete, I can "conceptualize" in the limit. Not always, but my math needs are pretty simple, it's rare that I have to grapple with corner cases.

So... conceptually... "the" Hamiltonian (or LaGrangian) defines the boundaries of the system. In other words, if we apply an operator to "dv" we get a different answer than if we apply it to delta-v, like v2 - v1, and we get yet a different answer if we apply it to (v2-v1)(A) + (v2-v1)(B) + ... and etc. The Ising structure is instructive because it's a non-local optimization, the Hamiltonian contains "influence terms" between neighboring dipoles.

Scale is important, and bounds are important. I agree that there is such a thing as a "bit", an indivisible unit of information. I just think that word "information" doesn't mean quite what we think it means.

If you redefine it in terms of occupancy instead of states, first of all physics suddenly starts matching your intuition again, and secondly the relationship between entropy (states) and actual information becomes treatable mathematically, and thirdly it then allows you to formulate a conservation law in terms of a symmetry, which is pretty much the keys to this particular kingdom.

So, instead of defining "symmetry breaking" as the average result of zillions of outcomes, we want to reduce scale and look at the symmetry "within" an outcome. In the same way that you conceptualize the Higgs field forming an energy "shape" that breaks symmetry, we want to consider that same symmetry breaking process occurring "within" the generator, actualizing what is mathematically equivalent to the random selection of a member from the set of available states (each state being identified with a "possible outcome").

I'm sorry, I can't speak English yet. Working on it, senor.

[nonsqtr]

I guess what I was trying to say is, we're not changing anything. Entropy is still entropy. We're just being "more precise" about the steps between the initiation of the selection and the definition of the outcome. The physicists call that definition a "measurement", they say it's an operator being applied to a state. What does that really tell us? Nothing! You perturb the state and it changes... like, duh.

They're totally completely glossing over the issue of the choice of operator. They say "you have an operator", and you ask them "where did you get it", and then their eyes glaze over for a second and you know what they say? "Pick one, the choice of operator is irrelevant". Well no, it ain't. lol

What we really want to know is, can we influence the generator. In physics you have mostly either a Gaussian "distribution", or a Poisson "distribution" (both of which happen to be smooth functions, but that's beside the point... or is it?)

What if I could alter the probability density by mucking with the information structure? Your Mexican hat function would change into a French chapeau, and your ball would roll off the bill instead of into the well. Or for a more interesting example, what if I could change a 2-way symmetry into a 3-way symmetry, just by mucking with the generator? Like, the Mexican hat is symmetric "IF" the distribution of balls rolling off the top is symmetric, but what if I can arrange it so the cannon only fires to the left? In that case I haven't touched your geometry, but your outcomes are totally different

I'm interested in the relationship between the cosmological constant and the bit. I think there is one. The Renyi method allows us to approach it asymptotically, and you can go out to as many orders as your hardware will conveniently handle in your lifetime. If there's divergence to be found it'll usually happen pretty quickly

[nonsqtr]

See so, physicists see information in terms of spin. Why? Because it's the only thing that works for them. Because they deal with waves. Spin, waves... seems logical enough... until you begin to realize they're actually constraining themselves.

In the example of the ball rolling off the top of the Mexican sombrero, there are two competing but not necessarily mutually exclusive theories. The first one says the direction of motion is due to initial conditions, and the second one says it's due to quantum fluctuations. Seems to me, there's a third possibility.

[nonsqtr]

Here's another way of looking at it. The physicists look at states like information, but it's not. If I'm a poker player and I want to know what card you have in your hand, the fact that there are 52 cards in the deck tells me nothing. The "information" I want is defined by occupancy, not states. I care about the card that's "in your hand".

In physics we would like the path through the states, that tells us which ones are actually being occupied. Which is the idea behind the Feynman path integral, except well ... they get this far and then they give up.

Regarding the modes - every collection of separable modes also has separable energies. If you have a single photon showing multiple modes at once, it means part of the energy lives in one mode, and part of it lives in another. Therefore if you see multiple modes in a ground state it means you have subunits and you should decrease the scale of your "system".

Non-local interactions will support ground state modes too, once again suggesting the scale of the "system" is what matters.

For instance, in a Boltzmann gas each particle is guaranteed to collide with a wall. That's a shared boundary condition, so any model that doesn't include the wall is going to fail

[nonsqtr]

Berkenstein's hypothesis

Bekenstein-Hawking entropy - Scholarpedia

This what resulted in Hawkings Information paradox.

Okay, now I can respond to it.

"Bekenstein is full of it". lol

Why?

Quick and easy.

He defines quantum information in terms of "bits". Classical bits. No kidding. Shannon entropy. Read it and weep.

I don't know from ultraviolet divergences, but I know a lot about bits. That's what I meant by "circular reasoning". You can't prove something using the thing you're trying to prove.

[nonsqtr]

Look man, physicists just don't understand noise.

Their understanding of it is so restrictive, so... childish as to be practically useless.

And unfortunately, the world doesn't acknowledge the value of something until the physicists do.

For an example, you can look up the word "martingale", which describes almost nothing in real life, yet underlies almost the entirety of physics.

The biologists we're on to this LONG before the physicists we're, as a matter of fact the Lottka-Volterra model was around 1920, and they used "no geometry" to formulate their reaction-diffusion equation - instead what they did is collaborate with that fellow Kolmogorov I told you about, and what they came up with describes systems with memory.

The story is Volterra's son in law was wondering why the fish catch increased during WW2 when there was almost no fishing.

Volterra and Wiener series - Scholarpedia

Prigogine ended up getting the Nobel prize for something Volterra had already done 45 years earlier. Except no one knew it at the time. Now we know the two frameworks are equivalent, relative to outcomes.

[nonsqtr]

Here's a question for the physicists.

Can you get 1/f noise out of a photon?

Why or why not?

What happens if I have zero-mean noise energy?

Volterra says you can prove any physical system with noise. How come no one's used ensemble noise methods with weak measurement?

According to the Standard model we should be able to build a detector whose noise is opposite to that of a photon.

Noise, in this case equates with uncertainty. Not so much in terms of numbers of states, but more in terms of jitter.

[nonsqtr]

All right, here is some VERY strange behavior of photons.

The technology now, is good enough to where single photons can be emitted from a quantum dot, and guided into a cavity, where its phase can be altered pretty much at will (using lasers - and often a rubidium crystal).

And to verify results, there has to be a detector somewhere.

So here's the strange part.

Photons have a "shape". Which can be experimentally controlled. It's not exactly a shape in space like we ordinarily think of a shape (although that could happen too, don't know yet). What they call "photon shape" is a shape IN TIME, it's also called a temporal profile.

The strange part is, that a photon with a particular shape, will only register on a detector with the same shape.

Physics - How to Shape a Single Photon

Multidimensional quantum information based on single-photon temporal wavepackets

Okay? So, all this nonsense about Bekenstein bound is a bunch of hooey. There are degrees of freedom in photons, that we only discovered recently, and there are doubtlessly more we haven't discovered yet.

Kay, so, the beginning of nonsqtr's simple and self evident mathematics.

degrees of freedom = number of states = information "capacity"

occupancy = stochastic outcome = information

Remember that, you'll hear more about it.

Anyway - I interpret photon "shape" as evidence of varied internal construction. Supports the idea of subunits.

[nonsqtr]

Boom. Shape of a photon:



That looks like subunits to me.

Does that look like subunits to you?

Call them what you will (symmetries, or whatever) - in algebra they are "partitions".

You see the partitions in the image, yes? They're clear as day.