question and where's the contradiction??!!

[GrannySmith]

Hallo all, my german exams are over, i think i made it, i will know in 8 (!) weeks for sure, but i think i will avoid capital letters for a while.

ANYWAY, i don't know where to put this, so i leave it here, hoping you can help me with it.

i've been inspired, i think, by a man talking like a tarot deck (on youtube but in greek), total random shit but somehow it got me thinking about some issues i have with well, (what science sees as) "reality", or actually better said, with quantum physics.

on the one hand, even though i'm a set theorist, i find it really hard to think of our four dimensions, as a continuous space. because continuous means infinitely dense. and that infinite can be really very huge (from a set theoretical point of view at least, and set theory is the base of our mathematics). somehow i got a strong hunch that there's a contradiction somewhere if we assume that our dimensions are a continuous space. there's even research on the quantum theory of gravity showing (haven't read the articles *yet*) that space should be "grainy".

on the other hand, our physics is based, and that's really based, in continuous mathematics. our equations assume continuity to work! so where's the contradiction?? 

and one more thing i'm wondering about, how come on the quantum level it's all about probabilities of existing in one place or in another, and we use aristotelian logic to understand it? we use aristotelian mathematics, even though there is a theory of quantum logic, which is a version of probabilistic logic (with truth values any real number between and including 0 and 1), and i do finally have time to learn about all this stuff (marburger's book had too many words, too few equations and concrete definitions, for my taste, i'm a logician and i like to start from the start ). but two questions about this logic:
how does it work side by side with aristotelian logic? is it embedded in it (in a mathematical sense)? does it "converge" there somehow? any ideas?
and how did that continuous "all truth values between 0 and 1" creep in there again?  where's my contradiction?!!?!

[Mesozoic Mister Nigel]

Over my head, but I just wanted to say good luck on your exams!

[GrannySmith]

Thanks Nigel it's already all oooveeeeeeeeerrrr  (and my self imposed english and greek ban is over  )
but they will send me the results in EIGHT WEEKS! 

[rong]

I think I've spent a lot of time pondering this (or something similar).  The conclusion (where I stopped thinking) that I came to was that reality is most likely discrete (see Planck length) and that continuous mathematical descriptions are approximations. 

Enjoy your quest.

[GrannySmith]

thanks Rong! that could very well be, i'd love to see how they are approximations, if you have any links or anything at all. that would be a bit unusual for me, i'm used to seeing discrete things approximate continuous ones, not the other way around, so i'm itching to understand how this works

[rong]

I'm not very well educated in the school of quantum mechanics, but what I was trying to say - I think - is illustrated by the following image:



the bars represent the REAL^tm data.  The red line represents the continuous function that best represents or approximates the REAL^tm data.

to put it another way - the continuous function y(x) = ax² + bx might describe the path of a cannon ball very well, but it does not necessarily mean that the cannon ball occupies a continuous string of positions for every x.  In fact, I do not believe that - in the REALLY REAL world - that the domain of this function is actually continuous.  In other words, the cannon ball probably actually jumps from one discrete position to the next.  What happens in between nobody knows - or maybe a better answer would be there is no in between

Since everything gets so dang tiny, I don't think we'll ever know for sure what's going on at the very bottom (or is it turtles all the way down?) but I think it is discrete

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Also, If you are not already familiar, I think you will enjoy Zeno's Paradoxes

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Where my thoughts changed direction on this subject involved an idea I had that kind of explains why the perceived dimensions of reality are discrete and how time possibly might work.  My idea was that time comes from the universe (or reality - or whatever you like to call the "all encompassing everything that exists") trying to resolve the law that matter can neither be created nor destroyed.

The big bang (or something similar) happened and reality was all like "whoops, matter was created - we can't have that! GTFO Matter!" so everything vanished, but then the universe was like, "ah, fuck - some matter just got destroyed" so all the matter re-appeared in the next iteration of everything.  And, repeat.

Throw in a little "information must be preserved" and you get kind of a foundation for progression of time with some kinda sorta explanation for how and why physical things change and there are discrete changes (not continuous ones) in states of things.

It's not a very well fleshed out idea, and the concepts are kind of right on the edge of what I know how to explain and talk about but I hope you get the idea.

[Mesozoic Mister Nigel]

My understanding is that quantum numbers basically represent probabilities. My only understanding of quantum numbers at this point is regarding electrons and their positions relative to atomic nuclei, though.

[LMNO]

GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.

Yes, I know that doesn't seem to make sense.  Quantum theory is non-intuitive.  And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.

That simply doesn't happen prior to decoherence.

[The Good Reverend Roger]

GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.

Yes, I know that doesn't seem to make sense.  Quantum theory is non-intuitive.  And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.

That simply doesn't happen prior to decoherence.

Quantum Mechanics:  If it doesn't piss you off, you didn't understand the work.

[rong]

I think maybe the problem he is having is that probability distributions are continuous functions...

[Mesozoic Mister Nigel]

GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.

Yes, I know that doesn't seem to make sense.  Quantum theory is non-intuitive.  And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.

That simply doesn't happen prior to decoherence.

Quantum Mechanics:  If it doesn't piss you off, you didn't understand the work.

You know, it didn't irritate me at all, and I didn't find it particularly difficult. Maybe I just don't get it? But I also wonder whether there's a cultural aspect, because I was raised with a flexible perspective about the state of "being"; I am not particularly attached to "is". Sometimes the answer to an either/or question is yes.

[The Good Reverend Roger]

GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.

Yes, I know that doesn't seem to make sense.  Quantum theory is non-intuitive.  And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.

That simply doesn't happen prior to decoherence.

Quantum Mechanics:  If it doesn't piss you off, you didn't understand the work.

You know, it didn't irritate me at all, and I didn't find it particularly difficult. Maybe I just don't get it? But I also wonder whether there's a cultural aspect, because I was raised with a flexible perspective about the state of "being"; I am not particularly attached to "is". Sometimes the answer to an either/or question is yes.

Look, the fucking cat IS or it ISN'T.  It's a particle or a wave. 

UNIVERSE WILL NOW MAKE UP ITS FUCKING MIND.  WE'RE ON A SCHEDULE.

[LMNO]

You'll need to provide the Universe with the proper paperwork.

[The Good Reverend Roger]

You'll need to provide the Universe with the proper paperwork.

Problem is, I know what paperwork is required, but not where it goes. 

[LMNO]