HELP ME, trapped in Aristotelian conception but must learn quantum physics

[sethman737]

So I went to St. Andrews University with the unbelievably stupid idea that I would be able to "handle" their physics. My university, reading only the course description, thought that fourth semester physics was equivalent to Baylor's second semester physics. I soon realized that they only considered the subject of the topics that were covered, not the mathematical principles that were necessitated by this course. As of now, I am informed that we are using concepts introduced in third semester calculus. I barely passed first semester calculus in my freshman year, which I necessarily endeavored to learn upon my realization of the level of math that was applied. I soon realized that mere cal I was in sufficient and endeavored to learn more mathematics principles to aid my understanding of the physics into which I have been thrust. Although I am making progress, I am coming to realize that this was a complete mistake as I, to this point, have been educated by Aristotelian structures of mathematics and logic; I realize that this makes me a helpless sheep in the presence of the vicious wolves of quantum physics and I want to change so that I am not bound to this outdated form of logic. While I can recite the basic principles of quantum physics that most second semester students of physics are asked to know, I completely lack the mathematical preface for quantum mechanics. Here in Scotland (don't be jealous, I haven't been able to enjoy it since I've been confined to my room on ALL of my free days trying to obtain the principles necessary to understand the calculations I am currently making) the Physics students study ONLY PHYSICS. Last week on a tour of a lab that was experimenting with microscopic macromolecular tweezers, the person leading the tour (a biologist) repeatedly referenced their excision of RNA from a single isolated cell, which I found fascinating, but my fascination was instantly changed to shear horror of my circumstances when one of the physics students on the tour asked "What is RNA." There is no such designation as BS and BA degrees. Rather, One is either a physics student, or a biologist. A chemist, or a Botanist. I would fall under the category of biologist/biochemist/organic chemist, relegated to the confines which Aristotelian thought has defined for me; BUT I HATE IT! I want to break my habitual resort to the Aristotelian description of things as either one thing or the other. I know that an object whose position is certain cannot have a definite momentum and that an objects whose momentum is certain cannot have a definite position but I don't understand why. My mind is dominated by the absolutism of Aristotelian thought, but under this ideology I can no more understand the mathematical principles behind Quantum Mechanics than a dog can understand the theological precepts of historical progression (which I don't even know). Please Help me, I know my request is probably as vague/Stupid as they come, but please; I'm lost, and there is no way out of this situation I've brought myself in to. Please don't be critical, I know I was foolish.

 

[Antiphon]

Forget about logic. It won't help. Start thinking about probabilities and statistics as if you were sampling a population. Then remember that in QM the functions that describe these probabilities also apply to indivisible entities (a quantum.). Get used the idea that there are no solid objects, things can act like waves. Nobody knows how a single entity can interfere in time and space with itself like ripples on a pond. You simply accept this as a given and use the math to compute the how. Don't ask why unless you are studying natural philosophy. (you can ask how but do it on your own time. The professor doesn't know and might get annoyed if he's trying to crank out a result.)

 

[jeblack3]

First, don't forget about logic. Your problem is not "Aristotelian thought." The problem isn't quantum mechanics, either. It's that you're taking quantum mechanics too literally. You say:

I know that an object whose position is certain cannot have a definite momentum and that an objects whose momentum is certain cannot have a definite position but I don't understand why.

No one knows that. We don't even know if objects have positions and momentums. These are properties of the model we use to describe objects, not necessarily of the objects themselves. The question "What properties does an object have?" may not even be answerable by scientific experiment. Several people have proposed answers, which you can learn more about by searching for "interpretations of quantum mechanics." But the trouble is that most of the proposals, even though they describe wildly different realities, predict the exact same experimental results. But for now, stop thinking about our theories of physics as accurate descriptions of the world. Think of them as calculational tools that predict experimental results, because that's all they are. And learn them. After you've learned how to do the calculations that have been found to correctly predict the results of experiments, then you can properly analyze whether a particular conception of reality is viable. You won't ever know if a conception is right, though.

 

[haael]

Quantum physics is perfectly Aristotelian and does not require any new logic. The only change one needs to do is to stop thinking that the world is what we see with our eyes. Real world is something completely abstract, our senses provide us with an illusion. Quite Platonic concept, I suppose, but id doesn't have anything to do with logic.

 

[Demystifier]

Sethman737, I believe you will be happy to know that even quantum physics can be understood in an "Aristotelian" way. Such a way is provided by the Bohmian interpretation of quantum physics. See e.g.
http://plato.stanford.edu/entries/qm-bohm/#li
http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory
http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html

It should be emphasized that nobody knows if this is how nature really works, but it is certainly a possibility consistent with all presently existing experiments. Not all physicists find this interpretation appealing, but those who want an Aristotelian view will certainly find it interesting.

 

[twofish-quant]

Although I am making progress, I am coming to realize that this was a complete mistake as I, to this point, have been educated by Aristotelian structures of mathematics and logic; I realize that this makes me a helpless sheep in the presence of the vicious wolves of quantum physics and I want to change so that I am not bound to this outdated form of logic.

I don't quite understand this since there is nothing in quantum mechanics that contradicts Aristotelian structures of mathematics and logic. Quantum is perfectly Aristotelian.

Here in Scotland (don't be jealous, I haven't been able to enjoy it since I've been confined to my room on ALL of my free days trying to obtain the principles necessary to understand the calculations I am currently making) the Physics students study ONLY PHYSICS.

Something that works for me is to just do the calculations and don't think deeply about what they mean while I'm calculating. Once you can do the calculations, *then* you think deeply. The problem with thinking deeply about what quantum mechanics means is that this is something that you can end up doing for the rest of your life, whereas to be able to just do the calculations is something that you can reasonably expect to have done within a semester.

I know that an object whose position is certain cannot have a definite momentum and that an objects whose momentum is certain cannot have a definite position but I don't understand why.

There are different levels of understanding. Once you figure out that elementary particles have wave properties, then Heisenberg's uncertainty theorem falls out. Now, why elementary particles have wave properties... At some level you just have to say, well that's the way things are...

My mind is dominated by the absolutism of Aristotelian thought, but under this ideology I can no more understand the mathematical principles behind Quantum Mechanics.

First of all, you might want to read more Aristotle since I don't see the connection here. Aristotle was wrong about friction, so if you can deal with slipping on an icy lake, you can deal with Aristotle being wrong.

 

[twofish-quant]

I think I can safely say that nobody understands quantum mechanics - Richard Feynman

Forget about logic. It won't help. Start thinking about probabilities and statistics as if you were sampling a population.

That's a good way to start to get use to the math, but once you get in a bit deep, you'll find that this won't work.

Don't ask why unless you are studying natural philosophy.

I think it's good to ask why. You'll find that the answer is some variation of "I dunno."

 

[0xDEADBEEF]

Well, well, well. US universities have a slow start, because of all the humanities courses that get forced upon you in the first year.

Any part of physics can be taught with such depth that few people can follow. Usually you have a "quantum mechanics I" course to get you familiar with the idea to use wave functions. The "quantum mechanics II" course would go into more math, and maybe do second quantization. It seems you have mistaken the advanced course for the intro course, and now you are fighting with the concepts and the math at the same time. Plus you are missing one year of applied math, which physicists suck up along the way, which is actually more then what is taught in calculus.

It is hard to recommend something, but luckily the mind can still work in great confusion. Try to ignore the philosophical part of it, if you can. Many questions will answer themselves once you have seen enough examples, and this is not what the course teaches. For the math: nobody knows all the math in the beginning, try to get help from others. Things that you should probably stay away from: Feynman lectures (too little math, unorthodox approach), Bohmian Mechanics (has not shown to be relevant to anything), Field theory (too much math, plus relativity), and String theory (too advanced by any measure). These things give very deep insights only after you have the tools to read them well.

 

[DukeofDuke]

Things that you should probably stay away from: Feynman lectures (too little math, unorthodox approach), Bohmian Mechanics (has not shown to be relevant to anything), Field theory (too much math, plus relativity), and String theory (too advanced by any measure). These things give very deep insights only after you have the tools to read them well.

Heh, if by "too little math, unorthodox approach" you mean Feynman insists you should actually understand that F=ma is not a cute pairing of symbols but physics, and that one ought to think about things and be able to extend their knowledge through careful analysis of what they know (rather than shotgunning summation notation), then yes, I suppose there is too little math, and an unorthodox approach.

 

[Mr.Miyagi]

Nature really doesn't care about your beliefs or hopes regarding it. You're doing yourself a disservice to put classical notions on a pedestal. Try to have fun figuring out what the rules of quantum physics are actually implying, mathematically speaking.

On the other hand, I think it's never bad, at any level, to ask "why". The search for an answer can lead to creative thought and new ideas.

 

[presario]

Heh, if by "too little math, unorthodox approach" you mean Feynman insists you should actually understand that F=ma is not a cute pairing of symbols but physics, and that one ought to think about things and be able to extend their knowledge through careful analysis of what they know (rather than shotgunning summation notation), then yes, I suppose there is too little math, and an unorthodox approach.

The thing is, Mr Feynman understood his maths very well, that's why he was confident enough to extract all the physical information out of it.
There really is no right or wrong path in physics, its a matter of taste, people have different style, and each particular style would tackle different types of problem.

 

[sethman737]

I'm beginning to grasp these concepts through a lot of studying, but I'm still left with these questions;
if the wave functions squared modulus is a probability density, then what does the wave function itself describe?
How are we expected to find an angular momentum and wave number when we are given neither and have been given no values for the velocity, momentum, or energy?
If finding the eigenvalue/vector of momentum requires multiplying the operator of momentum by the wave function, and the wave function has position x as a variable, how can we calculate a "definite value" for the momentum when the position must necessarily be undefined?(I know this is a confusing question, but I hope you understand what I'm implying...thing Heisenberg's uncertainty principle)
I "know" that you can calculate the angular momentum from the wave number, but how do you calculate the wave number if neither frequency nor momentum has been given? and how is this applicable even if we are given the momentum and this is only based in the probability of observing that momentum in a single state, but we are calculating the constants for that state based on a probability of observing one particular feature of the state?(i.e. how can we assume that the de broglie wavelength is characteristic of that state when it is calculated from the momentum which is merely the probability that that state will exhibit that momentum?)
Or do I show a fundamental misunderstanding of these matters which I have failed to account for?

 

[Klockan3]

if the wave functions squared modulus is a probability density, then what does the wave function itself describe?

What do the electric potential actually describe? In the end it is just a mathematical construct that have proven to be effective at describing the system. The only attributes of the system that we actually notice are the observables, the rest are just things to make the computation as fluid as possible.

How are we expected to find an angular momentum and wave number when we are given neither and have been given no values for the velocity, momentum, or energy?

can you explain what you are given, not what you are not given?

If finding the eigenvalue/vector of momentum requires multiplying the operator of momentum by the wave function, and the wave function has position x as a variable, how can we calculate a "definite value" for the momentum when the position must necessarily be undefined?(I know this is a confusing question, but I hope you understand what I'm implying...thing Heisenberg's uncertainty principle)

The wave function is the state described by the position basis, unless it is a dirac pulse you don't got definite position and if it is a dirac pulse you will see that your momentum is totally undefined.

I "know" that you can calculate the angular momentum from the wave number, but how do you calculate the wave number if neither frequency nor momentum has been given? and how is this applicable even if we are given the momentum and this is only based in the probability of observing that momentum in a single state, but we are calculating the constants for that state based on a probability of observing one particular feature of the state?(i.e. how can we assume that the de broglie wavelength is characteristic of that state when it is calculated from the momentum which is merely the probability that that state will exhibit that momentum?)

Again, what are you given? Don't ask "If this isn't given" ask "From this set of data...".

As for the other question, as long as the state isn't disturbed it acts roughly as if it had the weighted average of all of its observable quantities while as soon as it interacts it choses one of the possible eigenstates for the quantity it used in the interaction. It is all fairly strange so don't take my word for that.

 

[madness]

Just to clarify - in Scotland people don't just study physics. Usually 30% of the first two years are outside subjects, which can be anything although some people choose astronomy or acoustics etc. And there is a distinction between BA and Bsc in Scotland. I think it might be the case that university starts at a higher level in Scotland than in the US, but I have no direct experience in that area.

 

[Fredrik]

if the wave functions squared modulus is a probability density, then what does the wave function itself describe?

This is a very good question, and it's very important to understand that QM doesn't actually answer it! It's not at all clear that a wavefunction describes anything that exists in the real world at the given time. The only thing we can be sure of is that it's a mathematical representation of the statistical properties of an ensemble of identically prepared systems. (That ensemble can consist of the particles that participate in an experiment that you run a million times, perhaps by performing a million measurements at a million different times using the same lab equipment. And in that case, the ensemble isn't something that exists in the real world at any given time).

That's the only uncontroversial, interpretation-independent answer to your question. It would of course be interesting to know if the wavefunction is something more than that. These are the answers given by some of the popular "interpretations":

The ensemble interpretation: It's nothing more than the above. This means that QM doesn't actually describe reality at times between state preparation and measurement, and is just a set of rules that tells us how to calculate probabilities of possible results of experiments.

Many-worlds: It represents all the properties of the system. (Yes, this harmless-looking claim takes us deep into many-worlds territory. I'm not going to try to explain why, because it would take too long).

de Broglie-Bohm pilot wave theory: It's a kind of wave that guides the motion of the particle. (Demystifier can explain that better if you're interested. I know very little about this interpretation).

The Copenhagen intepretation: Depends on who you ask. I consider Copenhagen to be synonymous with the ensemble interpretation, but it seems that everyone has a different idea about what this interpretation is saying. A common claim is that Copenhagen would consider the wavefunction to be a representation of the properties of the system, just like the MWI, but a postulated mysterious physical process called "wavefunction collapse" is supposed to save us from the otherwise inevitable conclusion that there are many classical worlds.

My recommendation is that you stick with the ensemble interpretation and forget about the others, at least for the foreseeable future. Note that there is absolutely no reason to think that a theory of physics must describe reality at times between state preparation and measurement just because it's very good at telling us the probabilities of the possibilities at times of measurement. This isn't just "shut up and calculate". It's actually a fairly deep philosophical insight.

Also, one of the best reasons why you shouldn't spend too much time trying to understand the various interpretations is that most of the stuff that's been published about interpretations is pure ********. Don't say I didn't warn you.

I think you should consider buying Isham's book, "Lectures on quantum theory: Mathematical and structural foundations". And at some point, you might want to check out Ballentine's book too. It's a more difficult read, but it's a good book that strongly favors the ensemble interpretation.