Quantum Mechanics without the math

[Car-Guy]

I'm not so sure some of the Shakespeare I was forced to read was written in English.

Certainly was written in Texan slang either....

 

[O2Bfree]

It's interesting to see how QM is gradually making its way into the average person's life via modern media and also capitalism:

 

[braumeister]

It's interesting to see how QM is gradually making its way into the average person's life via modern media and also capitalism:

Alas, it's also merely another buzzword in some circles. That has long been a pet peeve of mine.

 

[O2Bfree]

Alas, it's also merely another buzzword in some circles. That has long been a pet peeve of mine.

Right, physicists admit they don't fully understand it, but those guys do!

 

[Out-to-Lunch]

Alas, it's also merely another buzzword in some circles. That has long been a pet peeve of mine.

^^^^ This. A thousand times this.

 

[audreyh1]

You can't study piezo electric crystals and some semiconductors without learning some Quantum Mechanics.

 

[SnowballCamper]

Physics without math is like English without vowels, just sayin...

EDIT: I see now that I'm late to this party... so here are a few more

Physics without math is like Calculus without algebra

Physics without math is like early retirement without knowing your spending

Physics without math is like sociology without psychology

So yeah, you can talk about physics without math, but you're not going to do physics without math.

 

[ERD50]

You can't study piezo electric crystals and some semiconductors without learning some Quantum Mechanics.

I guess it depends what you mean by "study". I've built circuits with piezoelectric crystals and many semi-conductors. I studied up on their characteristics, enough to get them to do what I want.

Do I understand the deeper level of how they do what they do? No. But that's not a roadblock to understanding how to work with them, and to having a very good understanding of their characteristics in a circuit.

-ERD50

 

[audreyh1]

I guess it depends what you mean by "study". I've built circuits with piezoelectric crystals and many semi-conductors. I studied up on their characteristics, enough to get them to do what I want.

Do I understand the deeper level of how they do what they do? No. But that's not a roadblock to understanding how to work with them, and to having a very good understanding of their characteristics in a circuit.

-ERD50

Yes, in my semiconductor materials classes we studied how they work.

 

[Out-to-Lunch]

Physics without math is like English without vowels, just sayin...

EDIT: I see now that I'm late to this party... so here are a few more

Physics without math is like Calculus without algebra

Physics without math is like early retirement without knowing your spending

Physics without math is like sociology without psychology

So yeah, you can talk about physics without math, but you're not going to do physics without math.

You may want to explain your line of thinking to Michael Faraday.

 

[JoeWras]

Yes, in my semiconductor materials classes we studied how they work.

Bingo. Even though I was pretty sure programming would be my thing, the Computer Engineering track required one course in physical electronics. This is the basic course for those who want to design the actual chips to go into the fab plant -- not the circuits laid down on them.

I hated every minute of it. If I could create a truckload of "holes" out of nowhere, I would have dumped it on that class to make it disappear.

On the opposite side of EE classes was "Field theory." Antenna design. Analog. Extremely math intensive, including some math unique to the discipline.

There's a reason EE's call it "FM." It doesn't stand for Frequency Modulation. It stands for F'ing Magic, because that's what it is.

But guess what? When I got my first job and we were designing computers, both vaguely applied. Board and chip layout of the circuits had to take into account analog effects and deal with where the stuff ends up on our custom chip. I was writing a memory test and could talk the same language with our chip designer when it came to issues like metal-migration, etc.

 

[ERD50]

You may want to explain your line of thinking to Michael Faraday.

I don't think I was aware of all that. Here's an excerpt:

Faraday was an excellent experimentalist who conveyed his ideas in clear and simple language; his mathematical abilities, however, did not extend as far as trigonometry and were limited to the simplest algebra. James Clerk Maxwell took the work of Faraday and others and summarized it in a set of equations which is accepted as the basis of all modern theories of electromagnetic phenomena. On Faraday's uses of lines of force, Maxwell wrote that they show Faraday "to have been in reality a mathematician of a very high order – one from whom the mathematicians of the future may derive valuable and fertile methods."[5] The SI unit of capacitance is named in his honour: the farad.

-ERD50

 

[DaveLeeNC]

Back in the 70's and 80's I was designing (at the transitor level) logic gates implemented on Large (at the time) Scale Integrated circuits. I was an electrical engineer in college. It was important that I understood how (for example) PN junctions work. But for what I was doing the math of this operation was unimportant as I worked from abstract models of things like that. And my job was (in part) to generate models that the logic designers and layout guys could use where they would not even have to understand those abstract models that I worked from.

But the guys generating the abstract models that I needed - a different story (and more likely than not they had physics degrees rather than engineering degrees).

dave

 

[Chuckanut]

Quantum Mechanics w/o the math: Part 2

The 2nd part of Quantum Mechanics is now on Ars Technica. As I read it I remembered that the author promised 'no math' not 'no effort'. I find reading it to be rather vigorous exercise for the brain.

https://arstechnica.com/science/202...ntum-mechanics-pt-2-the-particle-melting-pot/

In which lasers do things that make absolutely no sense but give us great clocks.

 

[Out-to-Lunch]

Physics without math is like English without vowels, just sayin...

EDIT: I see now that I'm late to this party... so here are a few more

Physics without math is like Calculus without algebra

Physics without math is like early retirement without knowing your spending

Physics without math is like sociology without psychology

So yeah, you can talk about physics without math, but you're not going to do physics without math.

You may want to explain your line of thinking to Michael Faraday.

I don't think I was aware of all that. Here's an excerpt:

I must admit that, despite my pushback about the unusual case of Faraday, I do agree with @SnowballCamper. You really must be able to understand math to make significant progress.

However, I do think that installment #1 shows that you can appreciate some of the characteristics of QM without knowing the math. I look forward to installment #2.

 

[stepford]

Math provides a (very) useful level of abstraction through which we can understand many physics problems. It's possible to do this without (most of) the math, but it's MUCH more work.

 

[Out-to-Lunch]

I look forward to installment #2.

Wow, I was blown away by a couple of aspects of this installment. And I am fairly inured to quantum weirdness!

 

[audreyh1]

The 2nd part of Quantum Mechanics is now on Ars Technica. As I read it I remembered that the author promised 'no math' not 'no effort'. I find reading it to be rather vigorous exercise for the brain.

https://arstechnica.com/science/202...ntum-mechanics-pt-2-the-particle-melting-pot/

In which lasers do things that make absolutely no sense but give us great clocks.

I took a lasers class too. Pretty complex math as I recall.

 

[MichaelB]

I took a lasers class too. Pretty complex math as I recall.

My definition of complex math is where you save money by spending it buying something on sale. DW understands it much better than I.

 

[stepford]

Since I played around with lasers semi-professionally for 30+ years I should point out that most laser phenomena and all the stuff in the 2nd chapter being discussed here can be thought about without much recourse to QM.

Everything can be described by classical wave mechanics except the behavior in the single photon limit. So while do need to refer to QM to explain how things work in this limiting case, most laser folks I knew rarely bothered with the quantum side of things.

 

[O2Bfree]

Heh, heh, just when we have a few folks who really understand quantum mechanics, along comes stuff like dark energy and dark matter. My gut tells me that if the humane race survives another 10,000 years, we'll have kids who can tell you all about quantum mechanics and even dark energy/matter but will not understand some new physical phenomenon or property that we discover. Physics as a science is good for a long time to come. Lots still to discover. Yay!

Yes, it just seems like the math can't possibly take into account all variables, ever.

There was a panel discussion at the 2017 World Science Festival hosted by Brian Greene that featured several physicists and a philosopher of physics. Among other things they discussed the Many Worlds theory. One of the panel members, Nobel laureate Gerard ‘t Hooft, explained that the theory arises from the limitations of math.

‘T HOOFT: When you asked me about this question about the wave function, you were nodding–I was supposed to nod “no,” and I nodded “yes.” And, I caught you off trap for a moment. And the point of this is that the quantum mechanics today is the best we have to do the calculation. But the best we have doesn’t mean that the calculation is extremely accurately correct. So, according to the equations, we get these many worlds. I agree with that statement. But I don’t agree with the statement that quantum mechanics is correct, so that we have to accept all these other universes for being real. No, the calculation is incomplete. There is much more going on that we didn’t take into account. And then again, you can mention the environment and other things that you forgot. So, we are so used to physics that unimportant secondary phenomena can be forgotten, it just leaves out everything taken for granted. But if you do that, you don’t get for certain what universe you’re in, you get a superposition of different universes. It doesn’t mean that the real outcome that was really happening is that the universe splits into a superposition of different universes. It means our calculation is inaccurate, and it could be done better. And that doesn’t mean that our theory is wrong, but that we made simplifications. We made lots of simplifications. Instead of describing the real world, we split up the real world in what I call templates. All the particles we talk about are not real particles, they are just mathematical abstractions of a real particle. We use that because it’s the best we can do, which is perfect. It’s by far the best we can do.

So, in practice, that is just fine. But you just have to be careful in interpreting your result. The result does not mean that the universe splits into many other universes. The result means, yes, this answer is the best answer you can get. Now, look at the amplitude of the universes that you get out. The one with the biggest amplitude, is most likely the rightest answer. But, all the other answers could be correct or could be wrong if we add more details, which we are unable to do. Today, and perhaps also tomorrow. We will also, we will be unable to do it exactly precisely correctly. So we will have to do with what we’ve got today. And what we got today is an incomplete theory. We should know better, but unfortunately we are not given the information that we need to do a more precise calculation. That precise calculation will show wave functions that do not peak at different points at the same time, like you had in Manhattan at this address or that address and we are at a superposition. No, in the real world, we are never in a superposition, because the real world takes every single phenomenon into account, and you cannot ignore what happens in the environment and so on. If you ignore that, then you get all this case superposition phenomena. If you were to do the calculation with infinite precision, which nobody can do, if you calculate everything that happens in this room and way beyond and take everything into account, you would find a wave function which doesn’t do that. You would find one which peaks only at the right answer and gives a zero at the wrong answer.

GREENE: Now, this view…

‘T HOOFT: But the theory is so unstable, that the most minute incorrectness in your calculation gives you these phony signals that say, maybe the universe did this, maybe the universe did that, maybe it did that. Only if you do it precisely correctly, then you only get one answer.

 

[ERD50]

I must admit that, despite my pushback about the unusual case of Faraday, I do agree with @SnowballCamper. You really must be able to understand math to make significant progress. ....

I'm not in disagreement with that at all, I was more expressing surprise that Faraday had such a low level of formal math training. That I did not know.

I sometimes peruse the forums at physics.org, and a few of the frequent contributors do what I would describe as "think in Math". Most of the time, the poster is trying to understand something, and "get their head around it", and want to be able to visualize it, or think in analogies. These "Math thinkers" will spit out a page of formulas and say something like "Why do you need an analogy? The math tells you exactly what is happening".

It's kind of like the difference between speaking and thinking in a foreign language, versus having to mentally translate in your head as you go.

I lean towards analogies and a "being able to get my head around it" style approach, but in an area where I have a good understanding of both the math and have developed an intuitive grasp of how it works, I guess I lean right into the math, and "think in Math" in those cases. But that can be hard for many of us when approaching something new.

I guess a very simple example would be the product over sum for parallel resistors, or some op-amp gain formulas. I no longer have to think those through, I just "think in Math" for those, and get right to the answer, and understand what the math is doing.

-ERD50

 

[martyp]

For those that do want a QM course with math I recommend the Leonard Susskind YouTube lectures. He is teaching those, like me, who got science degrees but want a less rigorous refresher or to learn something they missed in college. I listened to the General Relativity course and I think, after listening to a few of the QM lectures, it is similarly excellent.

 

[Out-to-Lunch]

Everything can be described by classical wave mechanics except the behavior in the single photon limit.

It was, indeed, the single-photon limit that bothered me. In particular, for the case of the two lasers joined by the prism.

At first, the two lasers joined by the half-silvered mirror bothered me (in the single-photon limit). But then I reasoned that the single photon from the first laser would be able to access the cavity of the second laser, providing the needed "paths" to exhibit interference.

Then I was bothered by the two lasers joined by the prism (again, in the single-photon limit). If my explanation of the above case is accurate, then it must be the Fresnel reflection at the prism surfaces? I.e., the electromagnetic field of the photon (following, as you say, classical E&M), must propulate the available modes of the whole system, including the cavity of the second laser.

Still pretty weird!

 

[Out-to-Lunch]

I'm not in disagreement with that at all, I was more expressing surprise that Faraday had such a low level of formal math training. That I did not know.

To be clear, I did not quote you to dispute what you said. I quoted you to provide context for me to dispute MYSELF!

I lean towards analogies and a "being able to get my head around it" style approach, but in an area where I have a good understanding of both the math and have developed an intuitive grasp of how it works, I guess I lean right into the math, and "think in Math" in those cases. But that can be hard for many of us when approaching something new.

I guess a very simple example would be the product over sum for parallel resistors, or some op-amp gain formulas. I no longer have to think those through, I just "think in Math" for those, and get right to the answer, and understand what the math is doing.

-ERD50

Sounds like a good analysis of the situation. (I believe I behave similarly to you.) Relatedly, I employ a lot of what I refer to as "cheesy analogies" in teaching QM. I use analogies as far-fetched and broad as: working by the hour vs. working by the piece; requirements to ride amusement park rides, namely, height vs. age; chucking rocks into a pond, bending of hacksaw blades, etc., etc.