uncertainty of uncertainty

[AntonioLao]

The uncertainty principle of quantum mechanics stated explicitly that the uncertainty of uncertainty is always greater than or equal to Planck’s constant of action ℏ. It is never less than ℏ. Moreover, if one uncertainty by a simple miracle becomes absolute certainty, the other becomes absolute uncertainty. Numerically, absolute certainty is given by the absolute difference of space-time events. For one event: ∆�� = |��₂-��₁| or ∆�� = |��₁-��₂| and the absolute certainty of another event is given by the same absolute difference: ∆�� = |��₂-��₁| = |��₁-��₂|. Saying that either event is absolutely certain means simply that ∆�� = |��₂-��₁| = |��₁-��₂| = 0 or ∆�� = |��₂-��₁| = |��₁-��₂| = 0. Since uncertainty of uncertainty is given by ∆�� ≥ ℏ/∆�� or ∆�� ≥ ℏ/∆��, then if the denominator equals zero the expression is equal infinity. This implies that if one event does not change the other event changes infinitely. These inequalities do imply that changes greater than infinity is mathematically possible but unfortunately, these changes are physically meaningless.

Actually, the realistic quantum mechanical working principle asserts that ∆�� represents the changes of energy, while ∆�� represents the changes of time. At the least, both represent their respective uncertainties and their product is greater than or equal to Planck’s constant of action: ∆��∆�� ≥ ℏ. The square of both sides gives ∆��²∆��² ≥ ℏ². If the time uncertainty is fixed at 1 second then ∆��² is more certain than ∆�� and the infinite power of ∆�� is absolute certainty. On the other hand, the square root of ∆�� is more uncertain than ∆�� and the infinite root of ∆�� is exactly unity, which represents absolute uncertainty and complete decoupling of these space-time events between their temporal continuation and energy conservation. The final radicalization is the nonequivalence of inertial and gravitational mass and the total and complete separation of space and time as the manifestation of a completely unknowable and incomprehensible irrational reality.

[SteveA]

In a sense, there is no uncertainty except to the extent we believe it exists.

If we look at what the assumption of a continuous space time implies, there is an implicit assumption that distances and times could be determined on an infinitely accurate scale, meanwhile we're be surrounding all that with an infinite time line over which those infinitely precise events occurred.

Without specifying some rigid relationship between these two infinities, that's a degree of freedom too many for logic to work with. One needs to determine the other.

If we were at the beginning of the universe and made the first measurement, the unit could only be 1 (and there would be no need for any context beyond that - it would be the measurement. In a sense it would actually be the selection of a ruler and not even a measurement)

If we imagined that it might have been 1/2 or pi etc. on some other scale, then this adds uncertainty as it creates a structure that could not (yet) exist.

Similarly, we can have both infinitely small and infinitely large things exist, but they still need to be constructed from 1s and a measurement never has any more information than we assume it possesses (notice that the ability to construct an assumption is derived from a larger network than than a single thing).

So, for example, if you want infinitely small and infinitely large to both possess the same precision, then you need to center your "1" around scales of the square root of that single infinite that determines both.

If you want fractal layers of complexity on larger scales and something simpler on smaller scales, then you could, for example, center that 1 around a logarithmic growth on smaller and equivalent exponential growth on larger scales, though neither is as large as the single string of events that began both.

As a more detailed example, if we took a single string and threaded "between" according to a schedule of lim(log(n)) as n->infinity, the remainder of, lim(n-log(n)) as n->infinity, could be threaded "beyond" and we have "inward" perspectives of lim(log(n)/(n-log(n))) as n->infinity and inverse "outward" perspectives of lim((n-log(n))/log(n)) as n->infinity. If you wanted to add a bit more symmetrical feathering of the edges of these layers, we could instead use log(n+n^.5) as the "between" schedule, for example.

Of course, it's fundamentally discrete, so we're working with structures closer to those in integral calculus, but beyond that, they're specifically sequencial.

Now how could we deterministically add uncertainty? Well one possibility would be to construct a 6 way interleaving, using a pair of modulo 2 and modulo 3 interleavings and then make relative comparisons between them. A superposition would appear for which information in one space would not allow for the objects to be distinct and separable in the other as knowing a property in one base does not give information (at least over an infinite scale) regarding the other (though on finite scales, where the fundamental infinite form was not a multiple of 6 then an asymmetry would be present, otherwise we'd have "perfect randomness" ).

So what am I saying? ... I guess it's that there need be no uncertainty unless we want it.

P.S. My browser (Firefox) doesn't display the escape codes you used for your equations. Do you know if there's some plug-in I need to view them?

(Thank you too for the idea of uncertainty of uncertainty - in a sense, doubt is self defeating.)

[AntonioLao]

there is no uncertainty except to the extent we believe it exists

Is this the same as saying that uncertainty can only exist in the mind? Without a mind the whole universe would simply disappear. And it only needs an all knowing mind for the universe to exist.

My browser (Firefox) doesn't display the escape codes you used for your equations. Do you know if there's some plug-in I need to view them?

These equations use the special character symbols under the Cambria Math fonts provided by MS Office Word processor

[SteveA]

I was initially typing a longer reply but let me instead just point a couple ideas and let you consider them:

1) Can we see both matter and photons? If all information exists as photons and we're detecting photons, then how do we have additional information that those photons are simultaineously giving us information regarding matter they have interacted with.

It would seem we should either be seeing no photons and only matter directly or we should have some category of "photons" that are ironically not themselves photons that tell us when to interpret some other photon as instead being representative of information regarding some material object.

If we imagine that all the information of a photon can simultaineously be interpreted to be telling us everything about the photon as well as everything about the (assumed) emitters and detectors involved, then we're left with hopelessly too many degrees of freedom to precisely determine anything.

2) Where does all information in physics arise? Did we first know of atoms and subatomic particles or galaxies and super clusters of them or did we derive these concepts and their properties of interaction from just the typical "run of the mill" conscious experiences of seeing rocks and trees and flowers and people etc.?

The way I see it is that things have to go back to the first step and not assume anything beyond the immediate experience (which is inherently personal) and that the rest falls out of place from that. In a sense, it could be no other way and there never is truly any uncertainty unless we wonder if something else might have happened, in which all the realms of possibility are there to explore as well and yes, those can be described as possessing statistical properties, but fundamentally even those are still precise sets, which over the required period of time for their presentation is also something perfectly determinable.

For example, if I open a door and see what's behind it - this is in a sense perfectly predictable. It's the same unknown as opening any other identical door would have presented. If I then wonder what might have lay behind a different door, well another door will have to be opened and it will once again be the exact same source of the unknown as the first door contained and at the point of wondering, it was implied that that new unknown was not currently present, hence yes, you've created a new unknown to explore, but it was never really unknown or uncontrolled - you determined whether or not to decide there was something else that should be as well as the location in which it would arise and when it would be considered to have manifested - the jar was made, placed on the table and the "unknown" poured into it but you could have similarly asked if it really was a jar or was it really a table, or did you actually pour it and was it full etc. etc. etc.

In a sense, that unknown is the same thing that built everything else, including everything that is believed to not be unknown. The manner in which we position it relative to other things that (we believe) already exist determines the specific form it takes.

By assuming photons exist, we can now believe we're no longer seeing material objects, hence the conflict. It appears best to say that instead photons do not exist and that we're only seeing the properties of interconnected networks of matter (in which a good model would be that we're seeing things from the equivalent of the interior of a thread of DNA) or alternately that we're only seeing energy/photons (which I think is still basically the same thing).

I also have a strong feeling there's actually no relevant information that is left out and if we truly include every emotion, sense etc., the entire state is visible. Is it possible to actually capture and analyze all this at any moment?

(Looks like it's turning into a larger post ... old habits )

As an example of the direction to look, consider this - is experience ever not filled or unclear? I don't think so - even if you're in deep sleep, you don't remember not being conscious and if you were drunk or groggy, it's still in a sense perfectly clear that you are groggy etc.

So in a sense we could say that the conscious attention contains some fixed amount of information that never changes and that experiences "shift around" in this "window" of attention but are transformed into various experiences - do you see any analogies with a holographic properties in this? No matter where we believe we're "externally" looking, it's still on that same "window" and even the logic that we believe applies could be said to similarly be a projection on that, but I'll have to skip past the paradoxes implied by that as we could go on forever debating that subject.

So if we have some number of elements available for attention and we assume nothing is unknown beyond this, then the "unknown" itself is present as a discrete property within this that can also be moved into being present or not present.

If we have a conserved space of information, then we have a fixed volume of information and all pathways are cyclic (ignoring whatever process determines what current transformation is being applied - if we assume all (finitely pertinent) information is available then we should assume that the transformation is static.

(Dang, the post keeps growing and you're an intelligent individual who doesn't need lots of detailed thoughts but simply to be pointed in a promising direction. I'll skip "polluting" you with more of my ramblings and see if these spark any new insights for you)

I do recognize you're pursuing some very interesting and detailed avenues of exploration and I similarly enjoy pursuing those and those can be great tools to build new things upon, but the foundations might actually be quite simple and intuitive - that's what we began with and I don't think those went anywhere. The question could be whether or not we can understand how that is so. All we need is just a simple structure that possesses enough features to generate the rest of the complexity in number theory (consider that the motion of information within a conserved volume acts similar to a superfluid) and we're at least able to reach most everything currently present in the sciences.

(Again, also consider the paradox of seeing both matter and energy simultaineously - we've got a problem with that view in that there are too many degrees of freedom and we need to "consume information" from somewhere as to the context in which an observation occurs - what is a calibrated reference and is there anything beyond belief that something is precise or not that determines that it is? What is the evidence for a measurement that is mistaken - what precise piece of information is it that determines that another piece of information is precisely incorrect? We should be seeing either space and matter or energy and not both, without something else making the selection. Also, consider that physical models on scales not immediately observable were constructed from information that has always been immediately observable)

I think we can generalize upon things to denote the manner in which any and all possible transformations of a finite quantity of information can occur (basically we're just reordering elements within a single linear space and the "unobstructed" view should simple resemble permutations - already we have, over time the presence of different cycles within that segment and correlations with wavelengths and prime numbers as these pathways intersect and the manner in which they intersect naturally can determine the appearance of a motion through a space of independent dimensions with particles interacting within that space).

That's at least the general direction I've been looking - no guarantees on results but it's hard for me to imagine any other way it could be. It's really a very general purpose tool that is capable of describing most anything we could think of except growth - but that's a different story altogether and life doesn't appear to have the option of reading ahead a chapter, which for me at least, is perfectly fine. That's a property that I wouldn't want to leave out of the picture either

Hopefully there's something in there for you, Antonio. Thanks again for your ideas on the forum.

[AntonioLao]

1)Can we see both matter and photons?

Without the emission and absorption of photons we can see nothing. Seeing means there exists an energy gradient or analogously a temperature gradient. These can satisfy both of your question 1 and 2.