Quantum Mechanics - for those looking to take the next step - Printable Version

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Quantum Mechanics - for those looking to take the next step - Gamma - 10-05-2015

Like most of you I am fascinated by science. Particularly quantum mechanics and relativity theory.

I have read tons of books "explaining" the strange and wonderful world of quantum mechanics. And for a long time it felt like I was going round in circles.



My Dad is a retired physics teacher and about a year ago he started studying quantum mechanics again. In a chat with him he repeatedly explained that quantum mechanics is a giant mathematical system. And unless you grapple with the maths you are wasting your time.

I remember rolling my eyes at this. I trolled him a little by telling him I did philosophy at university. And so I am interested in the big "ideas" and unconcerned with the petty mathematics.

But you know what? He was damn right.



And once you start to head down this path you realise that most popular science books addressing quantum mechanics do more harm than good.

One of the most important ideas in quantum mechanics is Heisenberg's Uncertainty Principle. Sometimes you hear people say that it comes about due to the imprecise nature of measurement. In order to measure a system you have to disrupt it in some way - and that disruption introduces an uncertainty that can never be completely eliminated.

It is a bit like measuring the temperature of a glass of water with a thermometer. Once you place the thermometer in the glass of water - the thermometer itself will slightly lower the temperature of the glass of water. So no matter how accurate your thermometer is - it will always be unable to account for the slight temperature decrease that it causes each time you insert it into the water.

Anyway - none of this applies to quantum mechanics. The uncertainty in quantum mechanics is inherent to the nature of the subject and is not caused by the imperfections of bought about by the instruments in measurement.

Now in the case of Heisenberg's Uncertainty Principle - the only way to truly understand it is by grappling with the maths.

Now - I hate maths as much as the next guy. Seriously. But it is the only way of truly understanding some of the basics of quantum mechanics.

The following videos (in my next post) are from a channel called DrPhysicsA. He is a brilliant teacher. My Dad recommended him to me and I agree with him that he is the best physics teacher I have ever seen.

Anyway - if you spend a few hours watching his first four videos - you will finally be in a position to fully understand Heisenberg's Uncertainty Principle.

This is important since it is the most fundamental idea underpinning quantum mechanics.

But these videos have another important point as well. For those of us who are not studying physics at university - it is a chance to dip your toes inside the "real work" of physics. And move on from those confusing popularizations which (in hindsight) probably do more harm than good.

Sometimes the hard way is the easy way. And that is certainly true of quantum mechanics.

The analogy I have is that it is like teaching somebody to tie their shoelaces. You could make it "fun" and "easy to understand" by dressing it up in cute analogies. The yin and yang of the left and right shoelaces are only in harmony when they are interlocked and pulling on each other.

Or you could grab their hands and just show them where the laces go.

The thing about quantum mechanics is you end up with shit like "...and this is not possible because you cannot find the square root of a negative number". [I am ignoring imaginary numbers here...]

Now you could take that mathematical fact and say - well what the maths is trying to tell us here is that the cat is both dead and alive.

Or you could just treat the information on its own terms - and accept it as a purely mathematical fact. And realise that once you start translating those numbers into ideas - you are adding a lot of your own interpretation to the concept.

And ultimately that complicates things more than simply accepting the mathematical answer on its own terms.

And this is the conclusion I have come to after spending a few months looking at the mathematics of quantum mechanics.

I fucking hate mathematics. And I am rubbish at it. But it is not too hard if you stick at it. And - more importantly - it is the only way to truly understand this subject. I often take a break and then come back to it. This is something you need to spend years dipping in and out of.

It is better to make slow (slightly) painful progress. Than take the easy option of going round in circles and not make any progress at all.

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Book and video recommendations to follow...

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Quantum Mechanics - for those looking to take the next step - Gamma - 10-05-2015

First of all here are those DrPhysicsA videos I mentioned before.

If you watch the first four videos in this series. You will understand the basic mathematical structure of quantum mechanics. And you will see how Heisenberg's Uncertainty Principle is derived.

At that point you will have a clearer understanding of QM than somebody who has read a hundred popular science books on the subject. I know this because I am one of those dudes who has read a ton of "accessible" books on this subject.

https://www.youtube.com/watch?v=pBh7Xqbh...jYWW1wYkIM

[WATCH VIDEOS 1-4]

Like I mentioned before - the teacher in these videos is brilliant.

If you want to step up the pace some more - you should check out the lectures that (world famous physicist) Leonard Susskind has put up on Youtube.

http://theoreticalminimum.com/courses/qu...012/winter

Leonard Susskind saw a gap in the market for those non-physicists who want a deeper understanding of QM other than what is given in the usual popular science approaches. So as well as these lectures - he also released a book which takes the general reader through the mathematics of this field.



http://www.amazon.com/Quantum-Mechanics-...024100344X

The original book that tried to clearly explain the mathematics of QM to a general audience was the following book which came out in the 60's.



http://www.amazon.com/Quantum-Mechanics-...atrix+form

I have this book but haven't really made much progress with it yet. So cannot give a fair review of it so far.

Anyway - that completes my overview for those who want to take the next step in their study of this area. I promise it is worth doing this. Since you will never truly understand quantum mechanics if you stick to those books that cut out all the maths and spend hundreds of pages going on about how a cat can be both dead and alive until it is observed.

In a weird way it is much more simple than that. And - due to the maths - much more difficult...

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Quantum Mechanics - for those looking to take the next step - RawGod - 10-05-2015

Good point about the maths. I came to the same conclusion after reading some of the popular books on the subject - you can't understand anything without delving into the equations. You are just dealing in analogies spoon-fed to you by the writer, and can't form any opinions.

When I realised that, I put it in the too-hard basket. But I might just take a look at some of the maths in the way you suggest. It could be a rewarding hobby in itself.

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Quantum Mechanics - for those looking to take the next step - Gamma - 10-05-2015

My Dad had the following analogy.

Imagine a person alive 150 years ago.

They are walking down a street and find a strange object on the ground.

The object is a simple pocket calculator. But 150 years ago - they didn't exist.

Anyway - the person in the past picks it up and starts playing with it. Eventually he realises that this object can answer any sum typed into it.

He then pulls it apart and tries to understand how it works. As he looks at all the digital components - he has absolutely no idea how it works.

All he knows is that when he types in a question - the correct answer pops out.

Well - this is true of Quantum Mechanics. A series of mathematical systems have been cobbled together over the years. And they are stunningly accurate.

Yet - when we think about why these systems give the right answer - we have no idea...

Which is why - with QM - the maths is the only thing that is real. Everything else is ultimately bullshit. It is just a giant algorithm that spits out the correct answers. And the only way to truly understand an algorithm is to understand it on its own terms. And that means learning some maths.

Any analogies trying to "explain" things or make them "clearer" are ultimately a waste of time.

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Quantum Mechanics - for those looking to take the next step - RexImperator - 10-05-2015

If you understand differential equations and linear algebra you can learn it. It just has its own notation which is weird to work with at first.

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Quantum Mechanics - for those looking to take the next step - Gamma - 10-05-2015

The appeal for me is jumping in and learning some of the basics.

I am never going to be smart enough to run that far with all this.

It is just refreshing to make real progress in this subject.

This thread is not so much about learning QM as pointing out that the popular science books on QM probably do more harm than good.

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Quantum Mechanics - for those looking to take the next step - Hannibal - 10-05-2015

You can learn all the math you'll need to know on Khan Academy for free. Calculus, linear algebra, and differential equations in that order. I would do all the physics courses, too. It's pretty basic, but at least you'll have some background on newtonian mechanics.

I studied physics in college, the other posters said this already but if you don't know the math it's not going to do you any good. When you do learn the math, those equations are really no different from any other, learn what the symbols mean and then it turns into a paint by numbers. Don't let the notation scare you.

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Quantum Mechanics - for those looking to take the next step - Hades - 10-05-2015

I don't really know why anybody would just jump into learning quantum mechanics if they have no foundation in even the basics like kinematics or statics or whatever.

I knew a lot of guys like this back in the day, they would love bantering at you with a hodge-podge of cherry-picked bullshit from the likes of Carl Sagan or that photogenic astrophysicist black guy with no credentials to speak of. They'd treat quantum mechanics like some new branch of philosophy when that's absolutely not the case. You'd show them a lorentz transformation or even intro calculus or some shit and they'd all scatter, maybe the ballsier among them would pretend to know what you're talking about. The one thing they have in common is they think they're smarter than they actually are and they're all hopeless at maths.

Well good luck OP.
If you want to take your hobby seriously then move to a college town, get a job that you can survive at, and just audit quantum physics classes and shit for fun. Figure out what book they're using and steal it off the internet. Look up some of those MIT lectures they post for free on the internets. You can do this on the cheap.

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Quantum Mechanics - for those looking to take the next step - Wutang - 10-05-2015

I actually started a thread a few days back asking how much one could learn about science from self-study:

thread-50782.html

I know you already kinda answered my question but could you go into more detail? How much do you think you learned from the self-study and do you think it's comparable to what someone learning physics at a uni would learn?

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Quantum Mechanics - for those looking to take the next step - Hades - 10-05-2015

Quote: (10-05-2015 09:15 PM)Wutang Wrote:  

I actually started a thread a few days back asking how much one could learn about science from self-study:

thread-50782.html

I know you already kinda answered my question but could you go into more detail? How much do you think you learned from the self-study and do you think it's comparable to what someone learning physics at a uni would learn?

If you're married to the material and study from the book, and have the solutions manual to help you study (these are invaluable, it's not cheating, it's basically helping you cover something the text just implies, don't misuse them and they won't hinder your progress), you can make a lot of progress through self study.

I would say that it's comparable to what somebody learning physics at the university would learn since they're doing basically the exact same thing.

Even then you want to diversify your learning with software and lectures, these can be difficult to source (this is why scientists in general like khan academy, octave, sagemath, linux, etc - it's all free and/or open source).

If I had to put it through analogy, studying and learning some of the really dense physics is like watching a movie that's masterfully put together, you have to watch it like eight times to digest the whole thing. Some of this material you can study for years and not really be considered an expert at it, depressing as that might sound.

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Quantum Mechanics - for those looking to take the next step - poutsara - 10-05-2015

Quote: (10-05-2015 06:00 PM)Gamma Wrote:  

http://theoreticalminimum.com/courses/qu...012/winter

Leonard Susskind saw a gap in the market for those non-physicists who want a deeper understanding of QM other than what is given in the usual popular science approaches.

The Leonard Susskind lecture video there is excellent. Good find and thank you for sharing.

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Quantum Mechanics - for those looking to take the next step - britchard - 10-06-2015

The stuff that we DO know, or are pretty sure we think we know, is actually quite basic provided you have mathematical capability. If you do physics at school, you should be starting to learn this kind of stuff by 16, although it's clearly not for everyone.

However, thinking about and researching the stuff that we DON'T know is most often post graduate level work, i.e the kind of work done on the TV show, the Big Bang Theory.

I would also be hesitant to label quantum mechanics as purely being maths, physics or chemistry. It has a large application to chemistry and physics, and a theoretical mathematical side.

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Quantum Mechanics - for those looking to take the next step - Rutting Elephant - 10-06-2015

Quote: (10-05-2015 09:13 PM)Hades Wrote:  

that photogenic astrophysicist black guy with no credentials to speak of.

I'm looking at a list of Tyson's research papers, and judging from the titles plenty of math is involved.

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Quantum Mechanics - for those looking to take the next step - RexImperator - 10-06-2015

Quote:Quote:

If I had to put it through analogy, studying and learning some of the really dense physics is like watching a movie that's masterfully put together, you have to watch it like eight times to digest the whole thing. Some of this material you can study for years and not really be considered an expert at it, depressing as that might sound.

With a lot of these fundamental courses of science and engineering, when you are taking the class as a student, your instructor is often re-learning the material as they teach it. Teaching the class is a chance for them refresh their understanding of it as well.

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Quantum Mechanics - for those looking to take the next step - Blaster - 10-06-2015

The analytical and critical thinking skills you develop grappling with math and science will help a great deal understanding philosophy. It's not a substitute, you can point out plenty of scientists who clearly do not transfer those skill into other fields, but nevertheless the patient attention to detail and intellectual openness required to learn advanced science are generally useful cognitive skills. You'll find many new mental models you can use to interpret philosophical concepts.

In fact, you can probably observe the effects of science on modern philosophical language. Consider something like Moral Relativity. While the actual concepts go back to ancient times and much of the groundwork for the modern relativist philosophies were developed around the same that Einstein was working on relativity, nobody called it relativism until after Einstein's paper got famous. I doubt it's a coincidence that the guy who developed cultural relativism (which was later adapted to moral relativism) was originally trained in physics even if he didn't consciously rely on physics in his work.

Regardless, the exercise of understanding concepts like Observational Frame of Reference is likely to help you understand the value (and limitations) of relativistic analyses applied to culture and morality.

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Quantum Mechanics - for those looking to take the next step - Blaster - 10-06-2015

Probably one of the most significant difficulties studying science is motivating yourself in the absence of immediate problems to solve.

If you're working for a company who really wants to improve the bandwidth in its datacenters, you may have a lot of incentive to understand something like the Orbital Angular Momentum of Light. And even if you did have a problem to solve, most normal people aren't going to have the kind of equipment you need to actually experiment with this kind of thing.

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Quantum Mechanics - for those looking to take the next step - Hammerhead - 10-06-2015

The craziest Quantum Mechanics experiment I've seen recently is the Delayed Choice Quantum Eraser. It takes things a step further from the normal double split proving that the detection device isn't what's causing the waveform to collapse. If there is "information" available about which slit the photon passed through then we will see the recorded data show a particle. If that information is completely erased before reviewing the results then the recorded results will show the wave pattern. The existence or non-existence of the "which path" information is determining the results. If the "which path" information is later "erased" it will change the pre-recorded results to show a wave pattern. Somehow going back in time it seems.

https://www.youtube.com/watch?v=U7Z_TIw9InA

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Quantum Mechanics - for those looking to take the next step - Slim Shady - 10-06-2015

QED [Quantum Electro Dynamics] is at once the most precise [theories match experiments/observations to the closest degree of precision] science we have, while being inherently the only probabilistic and uncertain science. Once you somewhat begin to understand QM/QED you will have a great and humbling understanding of the Universe. Everything is random, and it can be peaceful or intensely frightening [usually both at the same time]. As a Physics person, I will probably contribute to this thread when I have more time to post. I am interested to see where this leads.

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Quantum Mechanics - for those looking to take the next step - Menace - 10-06-2015

Understanding QM, unless your job/research is heavily dependent on it, is a big waste of time. I don't know why people are so fascinated by it; I think it's a status play to make it seem like they're more knowledgeable than someone else (not directed at you OP). Most of these people would panic and sweat if confronted by even an elementary differential equation.

I took graduate level QM (Q Chem really). It is 80% math (calculus, matrix algebra, etc.). The interesting part (for me), was you can see where atomic orbital shapes come from (they are just solutions to the two-body Schrodinger Equation). It is not easy to understand, and you won't know you understand until you actually solve problems than you have never seen. Just because you can integrate something doesn't mean you get it. Once we got to QM dipole moments, things got really hairy fast.

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Quantum Mechanics - for those looking to take the next step - Slim Shady - 10-06-2015

^ Yes a layman's "oh this shit is really cool" understanding of QM, or any kind of Cosmology/Particle Physics even, is a lot different that what actually goes on when doing this stuff, which is a lot of grunt work. Quantum Computing to me has to be one of the dreariest topics to work on that sounds extremely cool to everyone else.

At the same time if one does truly try to "get" it, and this takes a lot more work than reading a few wikipedia entries, one has a new appreciation of the world.

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Quantum Mechanics - for those looking to take the next step - Bad Hussar - 10-06-2015

Quote: (10-06-2015 12:25 PM)scallleywag Wrote:  

The craziest Quantum Mechanics experiment I've seen recently is the Delayed Choice Quantum Eraser. It takes things a step further from the normal double split proving that the detection device isn't what's causing the waveform to collapse. If there is "information" available about which slit the photon passed through then we will see the recorded data show a particle. If that information is completely erased before reviewing the results then the recorded results will show the wave pattern. The existence or non-existence of the "which path" information is determining the results. If the "which path" information is later "erased" it will change the pre-recorded results to show a wave pattern. Somehow going back in time it seems.

https://www.youtube.com/watch?v=U7Z_TIw9InA

Ja. The best explanation I've heard about how this could be, strictly from "popular science" accounts, is that a pilot wave is sent out at about the speed of light, reaches it's target, and then somehow returns faster than the speed of light to the source. Travelling faster than light results in it moving back in time, and the net effect is that the particle "knows" what it will encounter as it sets off.

I'm well aware that the above paragraph is exactly what the OP is rallying against. Think the idea is from a John Gribbin book. I have no real defense. It's just that waves travelling faster than light, and therefore backward in time seems like the most elegant, and least weird, explanation for what we observe in the double slit and similar experiments.

I actually quite like mathematics, though, and have seen the Suskind book at my local bookstore. So will probably grab it later this week.

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Quantum Mechanics - for those looking to take the next step - TonySandos - 10-06-2015

Mathematics > physics > engineering studies > biological studies > anthropological studies > history > philosophy > psychology > sociology

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Quantum Mechanics - for those looking to take the next step - Hades - 10-06-2015

Quote: (10-06-2015 05:33 AM)Rutting Elephant Wrote:  

Quote: (10-05-2015 09:13 PM)Hades Wrote:  

that photogenic astrophysicist black guy with no credentials to speak of.

I'm looking at a list of Tyson's research papers, and judging from the titles plenty of math is involved.

Yeah I kind of ran on with that sentence. The hipsters cherry-picking hodgepodges of bullshit had no credentials. Neil Degrasse Tyson does have credentials. He seems to contribute on a lot of research according to Wikipedia.

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Quantum Mechanics - for those looking to take the next step - Menace - 10-06-2015

Neil D. Tyson is a very average astrophysicist as far as I can tell. He went to some decent institutions and published some papers, none of which are particularly earth shattering. He is probably an effective communicator, and that is laudable. But he is beloved by the losers of reddit to a point well beyond reason. I hate to say this in this thread, but really it's a form of meta racism because he's so against type. Anyway, that's neither here nor there.

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Quantum Mechanics - for those looking to take the next step - Wutang - 10-06-2015

I hate the constant dick riding that surrounds NDT but at the same time I don't put the blame on him. That rests squarely on his fanboys. I don't know high level of a scientist he is but as long as he's competent I think that's enough for him to do what he does which is basically be a PR guy for science that talks to the general public. That's what he is famous and lauded for and it has to be admitted that he is effective at it.

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