Electrons and Inertial Frames

[Ophiolite]

Thinking of an electron as orbiting a nucleus is not merely 'unhelpful' since it doesn't generate the correct energy levels, etc. It is not a good model, because it doesn't reflect the facts of quantum reality.

In my first or second year of secondary school I recall my science teacher observing that, based on what we knew of atoms, we could say they were "a hole, in a hole, round a hole, through a hole, on a hole". (I think that bad paraphrase was a quote of a quote.) I found that a useful encapsulation of the philosophical aspects of quantum mechanics and I recall it whenever reading any material on sub-atomic particles. I have a shorter version for myself - "It's not real!"

 

[J_B_]

It's not exactly variable. In the hydrogen atom, the angular momentum of the electron can only take on certain quantized values

A discrete variable is still a variable. Despite trying to make it sound mysterious by calling it "quantized", QM is not the only science that uses discrete variables.

[W]hat is charge? Again, it's a property assigned to the particle. We can say a capacitor plate is negatively charged because it has an excess of electrons on it. But we can hardly say an electron is charged because there is one more electron on it. Or I guess we do, since it's an inherent property of the electron. Just as spin is.

You asked a philosophical question? Tsk tsk. There is some merit to saying it's just a property and we don't know what it is - to knowing when to put philosophy aside. But there is also a downside. If science just becomes a matter of solving math problems and "tests" that generate numbers to confirm those equations, I think it's lost something.

I did some research before I picked Carroll's book on general relativity. I didn't want a pop science book, but something with real meat. So I checked physics curricula at various universities to see what text they were using. Carroll came up frequently.

But in the process I got this eerie sense that physics isn't physics anymore - that it's just a sister to the math department. Then, my real surprise was finding that UIUC has a philosophy class in its physics curriculum to discuss "what is time?", etc.

An orbital is a region where one is likely to find an electron. One cannot say very much about the movement of an electron in an orbital.

That's what I'm trying to understand. Is there even any sense that the electron is moving or is it just a statement that it might be here and then it might be there and no one knows how it might get from here to there.

It would be closer to the truth to say that it's jiggling around.

Actually, that comment was very helpful. Thanks.

It doesn't. It means behaviour which, mathematically, resembles angular momentum in large objects.

OK. If the terms are used in QM, relativity, etc. as generalizations of more classic concepts, I can get behind that. Carroll speaks of several things that way - a Lorentz Transform is a relativistic version of a Euclidean translation/rotation. Yeah, OK. I'm cool with that.

Yeah, pretty much. It would be more correct to say that an electron behaves, in its interaction with magnetic fields, kind of like a large charged object spinning on its axis. So we use the term "spin," although an electron isn't really "spinning on its axis."

OK. But what does the spin mean? What effect does it cause when interacting with a magnetic field? And where does the magnetic field come from? Just other particles or something else?

 

[J_B_]

I have a shorter version for myself - "It's not real!"

What's not real? We're describing physical phenomena aren't we? Or is this all just a math game in our heads?

 

[Radagast]

That's what I'm trying to understand. Is there even any sense that the electron is moving or is it just a statement that it might be here and then it might be there and no one knows how it might get from here to there.

Yeah, it can just "appear" over there: Quantum tunnelling - Wikipedia

And where does the magnetic field come from?

No, I meant, you can put matter inside large physical magnets. And you get effects like this: Zeeman effect - Wikipedia

 

[Radagast]

Or is this all just a math game in our heads?

No, that's what we call "string theory."

 

[Kaon]

You asked a philosophical question? Tsk tsk. There is some merit to saying it's just a property and we don't know what it is - to knowing when to put philosophy aside. But there is also a downside. If science just becomes a matter of solving math problems and "tests" that generate numbers to confirm those equations, I think it's lost something.

I agree with this.

I did some research before I picked Carroll's book on general relativity. I didn't want a pop science book, but something with real meat. So I checked physics curricula at various universities to see what text they were using. Carroll came up frequently.

But in the process I got this eerie sense that physics isn't physics anymore - that it's just a sister to the math department. Then, my real surprise was finding that UIUC has a philosophy class in its physics curriculum to discuss "what is time?", etc.

That is because time is axiomatic, not necessarily a reality or dimension (and why it becomes a problem here and there). Our idea of a second is based on how "long" it takes to make about 9 billion hyperfine transitions in cesium-133. It is an arbitrary way to measure the ratio of action over the total energy available.

That's what I'm trying to understand. Is there even any sense that the electron is moving or is it just a statement that it might be here and then it might be there and no one knows how it might get from here to there.

The electron wave function measures the probability that the particle will exist in a given area. We can know the position of an electron but by the time it is observed its momentum has changed - which is why the product of uncertainty in position and momentum works out to 1/2 h-bar. But of a parameter "uncertainty" is simply the the standard deviation of a parameter - by having deviation it tells us we have limits on precision.

OK. But what does the spin mean? What effect does it cause when interacting with a magnetic field? And where does the magnetic field come from? Just other particles or something else?

Magnetic fields come from moving charges, so a moving electron inherently has a magnetic field about it - as long as it is moving. Spin acts as a magnetic moment for the particle so that it aligns to certain fields. If a particle has a spin, it can be affected by a magnetic field.

 

[Ophiolite]

What's not real? We're describing physical phenomena aren't we? Or is this all just a math game in our heads?

What's not real? Our perceptions are not real. They are real perceptions, but they are not reality. They are interpretations of highly selective input that give a flavour of one aspect of whatever "reality" is.

Our limited mumber of senses, their peculiar focus and their restricted ranges are totally unsuited and unprepared for appreciating the "reality" of the atomic and sub-atomic world. Highly intelligent, numerically inclined individuals, can characterise that world through mathematics. The rest of us have to rely upon simplistic models and arcane vocabulary that are equivalent to a three year old's painting of their mother compared with a Rembrandt. (And the Rembrandt does no more than give a biased, two-dimensional portrait of the subject at a point of time.)

 

[J_B_]

Magnetic fields come from moving charges, so a moving electron inherently has a magnetic field about it - as long as it is moving. Spin acts as a magnetic moment for the particle so that it aligns to certain fields. If a particle has a spin, it can be affected by a magnetic field.

Thanks. So the spin, in my preschool terminology, is what determines magnetic north.

 

[J_B_]

What's not real? Our perceptions are not real. They are real perceptions, but they are not reality. They are interpretations of highly selective input that give a flavour of one aspect of whatever "reality" is.

Our limited mumber of senses, their peculiar focus and their restricted ranges are totally unsuited and unprepared for appreciating the "reality" of the atomic and sub-atomic world. Highly intelligent, numerically inclined individuals, can characterise that world through mathematics. The rest of us have to rely upon simplistic models and arcane vocabulary that are equivalent to a three year old's painting of their mother compared with a Rembrandt. (And the Rembrandt does no more than give a biased, two-dimensional portrait of the subject at a point of time.)

I don't agree, but I'm not sure how much I (or you for that matter) want to get into it. I don't have any qualifications worth speaking about, so my speculations aren't worth spit in a hurricane. But I do have crazy ideas I like playing with, and educating myself on what and how the experts think is part of the game.

 

[Kaon]

Thanks. So the spin, in my preschool terminology, is what determines magnetic north.

Or south, yes. It is this spin that allows electrons to grab quanta of magnetic fields in Cooper Pairs, for example. Just like the earth, if the spin changes direction it is a big deal. Higgs has been shown to do this to electrons.

 

[Kaon]

I don't agree, but I'm not sure how much I (or you for that matter) want to get into it. I don't have any qualifications worth speaking about, so my speculations aren't worth spit in a hurricane. But I do have crazy ideas I like playing with, and educating myself on what and how the experts think is part of the game.

Your qualifications shouldn't matter in a philosophical exchange except if you need grant money for something. Otherwise, we would have to be fools to ignore what you say simply because you don't have a piece of paper vindicating your academic background.

We tend to limit ourselves based on our logic and reason of the generation - only to realize the insanity of the previous century is the canonical academia of today. One example of this is the juxtaposition of special relativity and quantum mechanics in field theory. Another is, of course, tachyonic matter and perceived tachyonic matter (i.e. leaving the object stationary while moving the space.

It would be interesting to hear an argument about the legitimacy of reality, perhaps another thread another time?

 

[Ophiolite]

I don't agree, but I'm not sure how much I (or you for that matter) want to get into it.

Well, if you wish, you could specify which of these statements you disagree with and why:

• We have a limited number of senses
• Each of these senses has a restricted range
• The focus of phenomena the senses are attuned to is peculiar to the interests of human survival
• The senses are unsuitable for examination of the atomic world
• Consequently our description of that world can only proceed via metaphors, or mathematics

 

[J_B_]

Your qualifications shouldn't matter in a philosophical exchange except if you need grant money for something. Otherwise, we would have to be fools to ignore what you say simply because you don't have a piece of paper vindicating your academic background.

We tend to limit ourselves based on our logic and reason of the generation - only to realize the insanity of the previous century is the canonical academia of today. One example of this is the juxtaposition of special relativity and quantum mechanics in field theory. Another is, of course, tachyonic matter and perceived tachyonic matter (i.e. leaving the object stationary while moving the space.

It would be interesting to hear an argument about the legitimacy of reality, perhaps another thread another time?

Mmm ... maybe. I'm an old man staring down the barrel of retirement and irrelevance. I have a laminated card with fancy writing for my chosen field - just not physics. I have things I can point to in my career and say, "Yay, look at what I did!" but I never managed to enact the change that was most important to me. So, I'm gearing up to play chess in the park and talk about how bitter I am.

A bit of sarcasm to say the above is true but not true - sort of like that mysterious cat. I've had my disappointments, but in the end all it means is I'm ready to move on. And in doing so, I'm looking for some relaxing fun - at least in the short term - rather than a rancorous, pointless debate on an Internet forum. Had some of those too.

 

[J_B_]

Well, if you wish, you could specify which of these statements you disagree with and why:

1. We have a limited number of senses
2. Each of these senses has a restricted range
3.The focus of phenomena the senses are attuned to is peculiar to the interests of human survival
4. The senses are unsuitable for examination of the atomic world
5. Consequently our description of that world can only proceed via metaphors, or mathematics

I modified your statement to enumerate your list.

My answers wouldn't be yes's and no's. I would start off agreeing with #1, but by #5 I'd be making all kinds of qualifications.

 

[Ophiolite]

I modified your statement to enumerate your list.

My answers wouldn't be yes's and no's. I would start off agreeing with #1, but by #5 I'd be making all kinds of qualifications.

Well, for the moment, just process 1, 2 and 3. Or, since you seem hesitant to engage fully, just let me know you would rather stop.

 

[essentialsaltes]

it might be here and then it might be there and no one knows how it might get from here to there.

Pretty much. All of the mind-boggling stuff with the two-slit experiment seems relevant. It doesn't seem to make sense to say that an electron can go through both slits, but if you check to see which slit the electron goes through, you get a different result than if you just let the electron do whatever it does when it has access to both slits.

But what does the spin mean?

Particles with non-zero spin have an intrinsic angular momentum and an intrinsic magnetic moment. Because of the latter, they interact with magnetic fields.

 

[J_B_]

Or, since you seem hesitant to engage fully, just let me know you would rather stop.

Yeah, after giving it more thought, I don't want to go there.

One cannot say very much about the movement of an electron in an orbital.

Instead, I want to back up to this statement. The OP was whether an electron is in an inertial frame when in an orbital about a nucleus. Now that we've clarified a few things, I want to ask the question again in two different ways:

1) My simplified example made it obvious the particle was not in an inertial frame because the way I phrased it essentially begged the question. However, if we can't say anything about how the electron is moving, how do we know whether it is or isn't in an inertial frame? Isn't a body's motion important to determining the answer?

2) What is the probability of an electron's position in the absence of a nucleus, i.e. a free electron? Is it a straight line with constant velocity?

(FYI, I have a freighter's worth of questions to unpack that have been raised from reading through Carroll's book. This is only the first one, and there are so many I think I'm starting to forget them. I appreciate everyone's patience and hope I'm not wasting your time.)

 

[sjastro]

But in the process I got this eerie sense that physics isn't physics anymore - that it's just a sister to the math department. Then, my real surprise was finding that UIUC has a philosophy class in its physics curriculum to discuss "what is time?", etc.

Given that physics is a predictive science one would require mathematics to make quantitative predictions.
Mathematics gives us a deeper understanding of the physics.

In the 19th century the lines in the hydrogen spectrum was found to be defined by the Balmer formula which is a purely empirical function.
Scientists of the time had very little understanding of the significance of the function let alone the physical nature of the spectrum.
Fast forward to the 1920s and the Balmer formula was found to be based on a class of functions known as Laguerre polynomials which are solutions of a particle in a central Coulomb potential.
From the Laguerre polynomials comes our understanding regarding energy and angular momentum levels for the hydrogen atom.

Another example is the concept of spin in quantum mechanics.
Spin was introduced ad-hoc into quantum mechanics to explain the Stern-Gerlach experiment.
It wasn't until the Dirac equation which was an early application of Special Relativity to Quantum Mechanics that spin was found to have a physical nature.

Incidentally the Dirac equation predicted the existence of antimatter.

 

[Subduction Zone]

Yeah, after giving it more thought, I don't want to go there.



Instead, I want to back up to this statement. The OP was whether an electron is in an inertial frame when in an orbital about a nucleus. Now that we've clarified a few things, I want to ask the question again in two different ways:

1) My simplified example made it obvious the particle was not in an inertial frame because the way I phrased it essentially begged the question. However, if we can't say anything about how the electron is moving, how do we know whether it is or isn't in an inertial frame? Isn't a body's motion important to determining the answer?

2) What is the probability of an electron's position in the absence of a nucleus, i.e. a free electron? Is it a straight line with constant velocity?

(FYI, I have a freighter's worth of questions to unpack that have been raised from reading through Carroll's book. This is only the first one, and there are so many I think I'm starting to forget them. I appreciate everyone's patience and hope I'm not wasting your time.)

I do not think that you understand what a frame of reference is. A frame of reference is a point of observation. For example anywhere on the surface of the Earth can be a frame of reference, but since the Earth is constantly accelerating it cannot be an inertial frame of reference. On an atomic scale the motion of an electron is not well defined so one cannot even begin to form a frame of reference from the electron's point of view.

 

[essentialsaltes]

1) My simplified example made it obvious the particle was not in an inertial frame because the way I phrased it essentially begged the question. However, if we can't say anything about how the electron is moving, how do we know whether it is or isn't in an inertial frame? Isn't a body's motion important to determining the answer?

Well, the electron is subject to a nonzero force, so I don't see how it could be.

[I like Subduction Zone's answer possibly (possibly, mind you) better than my own. If Einstein carried out thought experiments where he rode on a photon (adopting its frame of reference) that's one thing. But you can't do a similar thing with quantum particles, because they are not like rocks you can sit on, even in imagination.]

2) What is the probability of an electron's position in the absence of a nucleus, i.e. a free electron? Is it a straight line with constant velocity?

In the absence of everything and anything at all? Something like that. Even then, the state is not uniquely determined. Most of the wavefunctions will look something like this:

Subject to the Heisenberg Uncertainty Principle, the uncertainty in position (how long the wave packet is) is inversely proportional to the uncertainty in momentum (how well defined the 'frequency' is). In the extreme limit where you know exactly where you are (as in the Heisenberg pulled over for speeding joke) the wavefuction is like a delta function, and in the extreme limit where you know its momentum perfectly, it's a plane wave of a single frequency filling the universe.