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gib65

how does quantizing energy lead to QM anomolies?

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I tried not to make the title of this thread too long so it might not be clear what I'm asking. Let me elaborate. I've always wondered how the pivotal idea that started the field of quantum physics lead to all the strange discoveries that showed up as the field matured (like superposition, random collapsing, quantum entanglement, etc.). The pivotal idea I'm talking about is the idea that energy can be quantized into indivisable units akin to material particles (like the photon is to the electron). That makes sense out of the "quantum" part of quantum physics, but I don't see anything "quantum" about the odd anomolies that were discovered later (like superposition, random collapsing, quantum entanglement, etc.). How does the quantizing of energy lead to this? Does it follow logically somehow (i.e. a priori) or did they just so happen to be the discoveries made by the scientists who so happen to be persuing studies in quantum theory (that is, the pivotal idea starting quantum theory)?

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Black body radiation I believe. That and/ or the photo-electric effect.

 

Look up both those ideas, should be a good start.

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Most of the weirdness comes up due to the particle nature of radiation and matter. A wave isn't like a billiard ball, with a ball you can say "this ball sits at position x". A wave on the other hand cannot be defined so exactly, its indistinct, which leads to a number of odd, counterintuitive things due to its wave nature.

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I tried not to make the title of this thread too long so it might not be clear what I'm asking. Let me elaborate. I've always wondered how the pivotal idea that started the field of quantum physics lead to all the strange discoveries that showed up as the field matured (like superposition, random collapsing, quantum entanglement, etc.). The pivotal idea I'm talking about is the idea that energy can be quantized into indivisable units akin to material particles (like the photon is to the electron). That makes sense out of the "quantum" part of quantum physics, but I don't see anything "quantum" about the odd anomolies that were discovered later (like superposition, random collapsing, quantum entanglement, etc.). How does the quantizing of energy lead to this? Does it follow logically somehow (i.e. a priori) or did they just so happen to be the discoveries made by the scientists who so happen to be persuing studies in quantum theory (that is, the pivotal idea starting quantum theory)?

I must say I admire how your enquiries are leading you to dig for the roots of theories of physics, their logical foundations, and how the rules they imply lead to consequences that can then be observed(like the unintuitive consequences of Quantum Mechanics). I think if you combined that with a ready ability to be able to earn some maths in which to properly express and investigate this, you could become a pretty decent physicist:-) .

 

On the whole I agree with Tycho that once you start to combine the "wave" properties of matter with the "particle" properties, you begin to start seeing the consequences of what you are doing appearing(or as I said in your post on relativity "emerging"). A prudent way to lead into this is to consider experimental phenomena like blackbody radiation, the photoelectric effect, compton scattering that started to cast into doubt that light could outright be considered as a wave travelling in a medium(incidentally refuted by relativity).

 

At the same time however, if light, traditionally thought of as a wave could be considered a particle, could the reverse be true? This leads us to de Broglie's hypothesis, that the notion that applies to waves where:

[math]\lambda=h/\rho[/math] Could be extended to include "particles" such as electrons. Once wave properties of electrons were discovered this conjecture of symmetry was confirmed, and you could begin to apply differential equations similiar to the wave equation, taking into consideration the quantum properties already mentioned to things like atoms.

 

Once we start taking wave properties into consideration though, we have to consider that it is impossible to determine the location of a wave withina ny degree of uncertainty. This leads to the Heisenberg uncertainty principle, whereby the better we know the momentum of a quantum "particle" the less well define we have its position to be(hence greater uncertainty).

 

This may lead you to question, well what does it all mean if we have these wave and particle properties coalescing? We can rationalise them using a probablistic interpretation of Quantum Mechanics often referred to as the born interpretation whereby the square of the amlplitude of the "waves" coincides with the probability that we can detect the "particles" at a that location. I know that probably wasn't enough to clarify things, but I hope it gives you a picture with which you may be able to begin to resolve conceptual dificulties. But remember thats what makes this stuff fun;) ! It makes you think.

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I must say I admire how your enquiries are leading you to dig for the roots of theories of physics, their logical foundations, and how the rules they imply lead to consequences that can then be observed(like the unintuitive consequences of Quantum Mechanics). I think if you combined that with a ready ability to be able to earn some maths in which to properly express and investigate this, you could become a pretty decent physicist:-) .

 

Thank you. That's very kind.

 

So what can we say then? That quantum physics is the study of the smallest "quantum" of matter/energy? Does that link it all together?

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As has been said, most of the "strange behaviour" is due to the wave nature of particles.

 

Also on a technical point, the word "anomalies" has a very specific meaning in quantum theory.

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The historical perspective may be interesting, but set aside that I think that if you want to understand quantum mechanics better some key questions should be

 

1) What proper support do my presumed classical facts have? When does a extremely qualified expectation transform into a hard fact?

 

2) Try to mentally define things in terms of experiments, and some things become more clear. For example, momentum is defined in terms of changes in position. It means the definition of momentum means more than one position datapoint - you need change, imlplying you need several datapoints and make comparasions. This is one intuitive understanding of HUP. If x is exactly peaked, the momentum concepts makes no sens and the momentum is either undefined or "any momentum is as likely as any other".

 

Momentum is a measure of variation of position, or our information of position (see 1). Note that I mention variation in a neutral way, without specific reference to time. When you reference to time, you get the energy concept. Implicit in this is a connection between x and p, and E and t that's made explicit in QM and this contains the wave particle thing and implies the HUP.

 

Superposition is just the idea that all possibilities is accounted for in the expectation process. The expectations we have on a observable, is obviously a superposition of the possibilities, right? But upon observation only one of the possibilities is observed. It doesn't have to be more strange than that? One may be tempted to think in hidden variable ideas that perhaps the variable had that value all along and I just didn't know about it? Well, the point would be that what you don't know never impacts your action... this principle should apply to particles as well... a particle responds to information that is available... not to any hidden information. just like a poker player acts on to the information he has, not to the information he could have had (which is a completely ambigous way of reasoning in the first place).

 

How do You do? When you make a decision, your brain considers all the alternatives right? and you make some "averaging", trying to find the "best" action... but then eventually the response is only one of the options - the from your point of view, the estimated best. Suppose I were to model YOU.. I would of course assume that your dynamics is effectively a function of the information you get... you respond to the information you get, compare it with your memory and make a decistion.

 

This wasn't very well writte but maybe it gives some ideas.

 

/Fredrik

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Another intuitive brain comparasion is this:

 

A first your memory fills up.

You will see some kind of pattern - associate with p(x)

You may be tempted to think that you got it know.

 

But as more data is processed, you may see that the pattern is not stable.

 

So you may initiate some kind of online processing and keep track of wether there is perhaps (second best) a pattern in the changes in hte first pattern?

For example take the fourier transform and look for frequency patterns.

Associate here with momentum.

 

Now you have learned to see a pattern of a changes in a transformation of the original pattern. This imposes *an expected* constraint on changes in general.

 

Note that we're just guessing, based on experience. But humans are masters here. And this is undoubtedly proven to be successful.

 

Next you may find that there is still fluctuations the transformed pattern, you may repeat the strategy and decode more, until you can't resolve further patterns. Due to there is none, or that your sort of out of memory or whatever (ie imagine trying to storage information about the entire universe... there clearly has to be a limit, unless your a black hole eating the universe)

 

Anyway, know consider that you have two informations... x and a related variable p. The suggested construction now implies that there is a connection between these two that means it does not make sense to know x and p exactly at the same time. you can't specify a pattern, and it's variation ath same time. It makes no sense.

 

This is philosophical a bit fuzzy, but I've got the impression that Gib is a philosopher in the first place.

 

I'm working on formalisms for this, and I think it will reveal some of the logic used.

 

/Fredrik

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What I appeal to here is what I think is normal human intuition. Humans do not have intuitive first hand experience with electrons. But we do happen to live in the same universe, we are goverend by the same laws. And in the relational information approach I belive in, I can actually extract deep information about reality from a seemingly distinct system, by trying to make the appropriate abstractions. The nice part about studying yourself is that you have unlimited acccess to data.. every day is an experiment :)

 

So forget about the school days about newtonian world.. because it's obviously a severe simplification.. think deeper... how do You act... if information inference approach should work... all we need to find is the induction step... and why look where we can not see... when I've got prime access to one of the most amazing systems on earth at least...? That's my idea behind the old questions... can physics can from thought alone.... well it can't alone, but _some_ of the principles might... this is how I get most of my personal inspiration anyways. I do not have a lab. I've never seen an electron IRL, and I probably never will ;)

 

/Fredrik

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Yet you have a lab photo in your posts ;) guess it aint yours then X

 

Can physics form thought alone? I guess you mean can our discovered knowledge (in only physics? or all knowledge) form or capture the mind fabric? no not yet... when we do , we will be flying *quickly* to the stars ;p

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Yet you have a lab photo in your posts ;) guess it aint yours then X

 

Hmm :) I do some experiments. But like I said, everyday is an "experiment" to me, wether I asked for it or not :)

 

Yes the pic is mine: It's a microscope shot of an iodine stain (for glycogen testing) of a culture of windsor brewers yeast, where the darker cells have higher glycogen pools. I made an experiment 3 years ago, which had two purposes, starting from more or less no bio background, I tried to understand and learn about yeast cells in a beer fermentation setting. During that process which was interesting in itself, I tried to study myself, how I tried to make progress. What struck me during this process is that it lead me to abstractions first all, and those abstractions showed similarities with the abstractiosn you typically end up with trying to solve about anything. Eventually I was looped back to physics by a connected series of reasoning. So atm I put the yeast stuff aside because I have no time for it. The idea I initiated was to make a computer simulation of the yeast, by a technique of metabolic network simulations, but I realized that since I could not model dna transcriptions etc in detail... I was going to find a measure that "optimizes the cell" this lead me to ask, what optimizes a cell? Growth rate? if so, the mean or the peak? survival rate? anyway... this ended up basically beeing a generic learning model... (as a note many success has been done with this ideas, metabolic network simulations where the gene expression is estimated by optimation routines (on a defined measure of a combination of growh rate and synthesis of precursors) has been reported to show remarkable agreement with gene expression analysis of real bacterial cultures... actually the real bacterial culture converged to the computer simulation suggestion only after a few generations...) anyway... this grew from a special case to the general case all on it's own... and then when I was trying to picture how the brain can learn howto decode the signals in nerves... from just a collection of electric signals to a perception of reality.... I got a deja vu feeling from 10 years ago... this was 3 months ago... and I resumed the physics project again.... my cellular friends have taught me alot but they will have to ignore then for a few years at least...

 

So I've done some silly experimenting, but to any significant extent and it's more of desktop experiment. Not anything near the billion dollar particle physics labs that is out there :)

 

/Fredrik

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So that is why that pic is in my profile. Those are my friends.

 

/Fredrik

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hehe Fredrik :) good stuff....By the way I ferment beer at home too, am a beer lover :X

 

Yes, you are mentioning neural networks...did computer science and one of my majors was neural networks... But i gave up on the whole comp sci.. and you sound to look for relations in somewhat a similar fashion like me (or I used to). I can also see the information networks interest from the previous posts. I also use to work a bit on how this abstractation layer of information is encoded so to speak (ha, that didn't make sense). I mean in terms of encoded information and how this can be exchanged in everything (so ye like the GUT, metaphysically speaking) is present in our universe, that which you say is a daily experimentation of observation. The direction I was heading into, I finally termed epistemological physics hehe...but I stopped philosophical work 3 years ago now. I wanted to combine through a metric , GR topology and substances of which the mind and emotions were made of. (Yes, this is not physics, but metaphysics, yes I assume mind and emotion to be nD objects greater than 3..yes all objects I assumed were of some dimensional magnitude (5)). Infinity and Eternity (the conceptual ideas) were actually set as dimensions, rather than time as 4th. But anyway, I didn't have the mathematical ability to try and do this in terms of tensors. After a while I had to give up simply due to time issues. MIght get back on it when I one day retire ;)

 

Disclaimer: I simply am mentioning some models and hypothesis I set up...it was far from any state of being any theory... the term epistemological physics was purely for myself and not any implication it deserved any such formal naming :)

 

 

sorry about off topic rambling, just can see a bit where you are coming from :)

 

oh , and in english : 'now' refers to the present in time, 'know' is to have knowledge of something :)

 

hej Sverige ^^

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I have often thought "Quantum Mechanics" is actually a rather bad name. Most of the time, when a quantity becomes "quantized" (in the sense that it comes in discrete chunks) it is because of boundary conditions imposed on the wave-nature of particles.

 

For example, in the hydrogen atom, the electrons obey the Schroedinger equation, whose solutions for the radial part are called Laguerre functions. There are infinitely many Laguerre functions, usually quantified by an index [math]\nu[/math]. All Laguerre functions were [math]\nu[/math] is non-integer diverge as we move infinitely far from the nucleus, so imposing boundary conditions that there is no electron field infinitly far away from the nucleus insists that the only acceptable solutions are those with integer [math]\nu[/math]. Since the energy of the state depends on [math]\nu[/math], the energy is quantised (only allowed to take certain values).

 

It is exactly the same for the harmonic oscillator, where one must restrict the Hermite functions to integer indices, thereby quantising the energy.

 

So quantisation of energy is really a consequence of 'quantum' mechanics representing particles as waves, rather than a postulate.

 

Indeed, the vocabulary has switched a bit to reflect this. When we say "first quantisation" we really mean that we change observables into operators. A much better term would have been 'operatorisation' (a bit of a mouthful) but I suppose the word 'quantisation' was already too deeply engrained.

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Interesting. But to understand your thinking here;

is indeed the continuum just that, continuous, and boundary conditions are more hmm mathematical or even precision based (planck lengths etc) or do the boundary values actually mirror the actual hmm structure of space at this sub-level?

 

I guess I can also ask, does it really matter? In computer programming, when working with integers, the real line does not exist, only quantas of whole numbers. Yet it's there. Will we later on realise that even between the quantum levels you mention, there is a positive vacuum energy densitym lets say?. Pardon me Severian I guess I am asking more rhetorically ..you made me ponder...I long ago realised that continuous things are impossible for us to imagine.. in fact, now when I think about it, it is this v being a non-integer which was part of what I said I played around with long ago, with seeing if setting infinity as D4 (dimension 4) would take me down a road of any interest.

 

sigh, it seems to me that sometimes

 

where reality is easily conceived, maths may be hard

where maths is easy, conceiving is hard

 

:/

 

it is easier to conceive the need for quantisation than conceiving continuity :P

 

right, this was probably an off topic reply,just sometimes one gets frustrated but science requires patience. PS. I am really looking forward to the LHC coming around, really hope the Higgs lad gets caught... would really help

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Also on a technical point, the word "anomalies" has a very specific meaning in quantum theory.

 

What exactly does it mean?

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What exactly does it mean?

 

A theory is said to be anomalous if a classical symmetry of the theory does not survive quantisation (or regularisation).

 

The anomaly itself is the failure of the expectation value of the conserved current to be (covariantly) conserved.

 

[math]D_{\mu}\langle j^{\mu} \rangle_{a} = \mathcal{A}_{a}[/math]

 

 

The calculation of anomalies is very interesting and involves geometry, topology, homological algebra and the such. I did my MSc project on the subject. You can find a copy of my thesis on my website if you are interested.

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A theory is said to be anomalous if a classical symmetry of the theory does not survive quantisation (or regularisation).

 

The anomaly itself is the failure of the expectation value of the conserved current to be (covariantly) conserved.

 

[math]D_{\mu}\langle j^{\mu} \rangle_{a} = \mathcal{A}_{a}[/math]

 

 

The calculation of anomalies is very interesting and involves geometry, topology, homological algebra and the such. I did my MSc project on the subject. You can find a copy of my thesis on my website if you are interested.

Intriguing, though I doubt I have the mathematical skill yet to properly understand; but is there a reason for the breaking of these symmetries? Or is it just a failure on the part of classical physics?

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Intriguing, though I doubt I have the mathematical skill yet to properly understand; but is there a reason for the breaking of these symmetries? Or is it just a failure on the part of classical physics?

 

It can be viewed in many different ways. The most easy way to see it is via Fujikawa's argument that the path integral measure is not (generally) invariant under all classical symmetries. Roughly, the anomaly appears as the Jacobian. More accurately, the regularisation scheme employed does not respect the symmetry. This method directly shows the relation between anomalies and the index theorem.

 

They also can be explained using BRST cohomology , K-theory or you can calculate the anomalous current directly using Feynman diagrams.

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