On information, causality and their physical theories

Random thoughts on these things.

Quantum mechanics is a theory about information.

Information is something complex (the wave function)

Squaring a unit of information gives something causal. Actually squaring the wave function does not happen within quantum mechanics. It is an external process somehow.

Information (wave function) has infinite propagation speed.

Causality propagate with the speed of light.

Creating a black hole from non-linear optics

We know that

 and

Further, the Schwarzshild radius is

 

Assuming that the mass is uniformly spread out around the wavelength, or the size of one photon, we can look at the ratio between the wavelength and the Schwarzshild radius. Combining (1)-(3). When that quote becomes less than (approximately) 1, we have a higher mass density then what is required by a black hole:

Putting in the numbers, one arrives at

This looks like the upper frequency a photon can have (Isn't also a bit scary that the exponent is 42...?).

If it was possible to create two photons with

and one can make them interact via some non-linear process, one can make a black hole from two photons.

On Donald Hoffmans case against reality

To many, Donals Hoffmans ideas about reality are considered radical. To me they seem obvious and, not to sound arrogant but, rather mundane. However, there is one point where it gets very interesting, and which to me, he seem event to miss him self. And where actually I think I got some new enlightenment.
Sam and Donald talks about the relation between perceived reality (PR) and full reality (R) and Sam proposes that there must be some isomorphism between PR and R. Donald pointed out that the relation is surely complex; but what he did not say explicitly, but which make things interesting, is that there is no reason actually to expect this to be an isomorphism at all. It could rather be a projection. And if that is the case, it might well be that there is no way to recover R from that projection/PR. It seem there can be multiple things that can be the case here; it could possibly be that it is possible to recover R from PR due to that it happens that R only has one way to be, given the structure of PR space.
But it could also be that the projected structure (which is probably a better word than space) is compatible with an infinite number of different complete/full realities.
I guess it could also be something like an ill-conditioned problem, that the projected structure in principle is completely connect to the full reality, but some parts/links in that projection are so weak that it is essentially impossible to probe them.
I hate when people who don't know a squat about things like Quantum Mechanics talk about it and throw out uninformed thoughts. But I will still do it here, and perhaps I am at least not completely uninformed. The thought is that perhaps the wavefunction collapse is a consequence of this ill-condition and that is why it is so hard to probe past it.
Given the non-existing of very weak link between PR and R, perhaps the evolutionary pressure on us is only from PR and there might be other PRs with completely other evolutionary pressure.

The octonions are not the founation of physics

I recently read a very interesting piece on the octonions and some argument for that they should be used to form the foundation of physics.

My (current and not very informed) take on this is that they should not. The algebra of the octonions is non-associative. But our world is associative. This really says that our world is not based on he octonions. Instead one should focus on finding a generalized quantum theory based on the quaternions. They capture our world most closely by being non-commutative. As rotations in 4d space is.

Dark energy

Clearly dark energy is something that does not interact with anything but gravitation. Could it be that it is actually extremely high-frequency electromagnetic (EM) radiation?
The idea behind this suggestion is that at of high enough frequency, matter becomes transparent to EM radiation due to that the particle resonators (atoms in the case of crystals) no longer have any overlap with with the wave function of the EM radiation. This is a well known phenomenon for e.g. gamma radiation, or even UV, where the penetration depth increases with increasing frequency.
If we assume a T4-law of the radiation at Big Bang (BB), what temperature must it have been to generate 98% of the Universe energy at frequencies above interaction with the matter as we know it?

Taking this one step further, if the radiation frequency distribution at BB was some kind clock shape, there seem to be a division at different spectral lines which do not interact with each other since we are now in a situation where all radiation above this frequency is effectively non-interacting with the rest of the Universe. Except via gravitation.

Thus we need some gravitational process that is non-linear or lossy in its interaction with the high-frequency EM radiation to make a high-frequency photon decay into something with lower energy (frequency) to make it visible.

Why are there no physical theories depending on the continuum hypothesis?

The continuum hypothesis or its negation can be added to ZFC without changing its validity. Yet, to my knowledge, there are no known real-world consequences of either choice. How can that be? How do we decide which axioms in a fundamental mathematical theory matters?

Further, to me, if there are no observable effects of an axiom, it should be taken as false. This is of course a problematic position to take, since those observable effects might show up much later. Thus, it is probably sensible for mathematicians to investigate the consequences of choosing either that or that. In that way, a path to observability might be found.

But, my position might have a more fundamental issue. What axiom should be taken as false? Should I choose A or ¬A as false? This will probably come down to applicability. If A provides many weird theorems and applications (as e.g. the axiom of choice does) then probably A should be taken as false.

On local time, memory and hysteresis

I would like to propose a new view on time. Time evolution should be associated to each process that evolves. It should not be seen as an external parameter driving the equations. Instead it should be seen as a dependent variable. The dependence is from system evolution. This way, time can flow at any speed, depending on the evolution of the system.

Further, hysteresis and memory are the same thing and they are the stopping of local system time. Thus, objects (and beings) can interact over time in the sense that they are parts of a system where there is time evolution, but where them selves are in a time stopped state.

This is all a bit fuzzy, but I will try to extend the idea to be more coherent in future notes. In the mean time, here is an illustration of what I mean:

Why is God all mighty?

I just read an intriguing paper which discussed weather the Internet might become conscious. In connection to this it occurred to me that in the discussions about AI developing consciousness (C) and free will (FW) there are many people that point out that this emerging CFW might pose a danger to us humans. Embedded in the reasoning is usually an assumption that the CFW will be superior us, due to many different reasons.
Now. For this CFW, we are the creator. Maybe we could be considered Gods. On the other hand, our creation supersedes us. Can this be the case also with the humans - we supersede our creator. It is an interesting thought and actually compatible, I think, with standard physical models of the universe creation. However not quite compatible with the Christian God I guess.

On the limits of our knowledge, again.

By the way, I have to write another on. The talk I just discussed on limits of science. I have another interesting idea about the limits. There seems we are trapped within the big and the small. At large scales we are ultimately captured by the speed of light. On the small scale we are ultimately captured by quantum resolution. Now this to me looks like some tough limits on what we can know. Does it also indicate that someone trapped us...?

On " the unreasonable effectiveness of mathematics in the natural sciences"

There is allot of fuzz on this question out there. E.g. on fqxi. To me this is not so strange. If we assume nature has structure, and is not only chaos, then why would not any attempt to capture that structure succed?

The point is that any modeling structure that you can come up with will be sufficient to describe (that is, model) at least a part of reality (in  approximation). And from there it is just refinement. Science is an optimization process, or a search if you want. An optimization to minimize the error between model and measuremen.

Thus we (the humans) could have started from any mathematics and enevideble would have ended up with a physical model that will capture some part of reality.