Quantum Mechanics without the math

[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]

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Originally Posted by 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]

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Originally Posted by Chuckanut 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/2021...e-melting-pot/ Quote: 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]

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Originally Posted by audreyh1 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]

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Originally Posted by Koolau 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.

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‘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]

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Originally Posted by Out-to-Lunch 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]

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Originally Posted by stepford 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]

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Originally Posted by ERD50 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!

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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.

[DaveLeeNC]

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Originally Posted by 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.

In the QM world it seems to me that the math is what is real (in the sense that we can, in principle, analyze quantum states as they propagate/interact 'unobserved' without error or unpredictability-probably decoherence is a better term here). The 'real world' (what we observe) seems kind of like an abstraction of the math. The math seems more real in some sense (to me).

dave

[Out-to-Lunch]

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Originally Posted by DaveLeeNC In the QM world it seems to me that the math is what is real (in the sense that we can, in principle, analyze quantum states as they propagate/interact 'unobserved' without error or unpredictability-probably decoherence is a better term here). The 'real world' (what we observe) seems kind of like an abstraction of the math. The math seems more real in some sense (to me). dave

Please tell me that you are not THIS David Lee: https://en.wikipedia.org/wiki/David_Lee_(physicist)

If you are, I will feel really, really silly.

[DaveLeeNC]

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Originally Posted by Out-to-Lunch Please tell me that you are not THIS David Lee: https://en.wikipedia.org/wiki/David_Lee_(physicist) If you are, I will feel really, really silly.

Not me - tempting to claim otherwise, but I doubt that I could have carried on such a charade for very long But I stand by my statement about math (since it is one of those things that is neither right or wrong).

dave

[ls99]

Hopefully when this series gets to the end we will be enlightened about the light, the speed of it, that is.

Seems there is a bit of problem with measuring the speed of the light in one direction.
https://phys.org/news/2021-01-there-...o-measure.html

"Special relativity is one of the most strongly validated theories humanity has ever devised. It is central to everything from space travel and GPS to our electrical power grid. Central to relativity is the fact that the speed of light in a vacuum is an absolute constant. The problem is, that fact has never been proven."

"But several physicists have pointed out that while relativity assumes the vacuum speed of light is a universal constant, it also shows the speed can never be measured. Specifically, relativity forbids you from measuring the time it takes light to travel from point A to point B. To measure the speed of light in one direction, you'd need a synchronized stopwatch at each end, but relative motion affects the rate of your clocks relative to the speed of light. You can't synchronize them without knowing the speed of light, which you can't know without measuring. What you can do is use a single stopwatch to measure the round trip time from A to B back to A, and this is what every measurement of the speed of light does."
I soppose this is true of any light created, including the coherent kind, like laser.


What if light is really anistropic?

[O2Bfree]

What I'd like to know is what are the quantum fields made of, i.e., what's the medium for the vibrations that are quantum particles?

I doubt if this series will answer that, I don't think anyone can yet, but it'll be fun to read anyways.

[audreyh1]

When working, I discovered that light was pretty slow - when traveling down a 2km fiber optic cable. I had to explain to my engineering bosses why the handshake took so long.....

[DaveLeeNC]

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Originally Posted by O2Bfree What I'd like to know is what are the quantum fields made of, i.e., what's the medium for the vibrations that are quantum particles? I doubt if this series will answer that, I don't think anyone can yet, but it'll be fun to read anyways.

I have not read/seen the referenced Ars Technical stuff (it has been added to my indoor cycling reading/viewing list). But there is an interesting theory out there that simply states that 'we are living in a simulator'. See https://www.scientificamerican.com/a...e-about-50-50/ (lots of others references out there). If you listed all the theories of just "what the heck is actually going on here??" from Coppenhagen to Many Worlds to De Broglie-Bohm to ... the simulation theory would be my choice. So in that case the math actually is what is real - and would make the (for example) question of the medium for quantum fields irrelevant.

But if they added one more choice to the above list - None of the Above" - I would pick that one.

dave

ps. The Simulation Theory is (at least potentially) falsifiable. If everything that we experience is just a bunch of calculations done on some machine, then it would have bandwidth limits and, in principle, we could create scenarios complicated enough to hit those limits and we would be able to detect such a thing. And the whole scenario leads to way more questions than answers.

[JoeWras]

Re: we are a simulation

A recent science fiction TV series gently hints at this. The series is still playing out, so I don't know what the conclusion will be, or whether the hint will evolve into actuality.

I won't name the series on fear of spoiling things. You'll have to explore the streaming services for yourself.

[corn18]

I had a whack out night of dreaming last night after watching a show on many worlds. What a trip!

[CaptTom]

One thing which I think helped me get closer to understanding is something someone (Maybe Neil Degrasse Tyson?) said.

He pointed out that, as one accelerates, time slows. As we approach the speed of light, time approaches a complete stop. So, the photon of light we see from a distant star comes into existence in the star, then from its point of view, is instantly absorbed by our eye (or telescope) even though to us, it seems to have traveled for billions of years.

I found this profound. And I really got to thinking. So, E=MC^2, where C is speed. Speed is just distance divided by time. Therefore:

E=(M(D/T))^2

Wait. Distance AND time in the same equation? Like, they can be equated somehow? This is starting to get creepy.