Volume of Electrons -2 Particles in Motion

[limitkiller]

Assume that in an imaginary space there are only two electrons.
Now if we spin one of those around itself, without moving its pivot , what would happen to the other one?(I think it would keep moving normally because if it starts turning around the first electron it means we can have "smaller electrons ",and if it is so what is "the smallest electron"?

 

[Bloodthunder]

wut? "spin one of those around itself"?

 

[limitkiller]

wut? "spin one of those around itself"?

um... yes,what do you mean?

 

[toombs]

The whole idea of matter occupying a volume is a macroscopic idea only. It breaks down on the scale of individual particles. It's not that particles occupy an infinitely small volume. It's more that volume is not a valid physical property of subatomic particles. Electrons do not have volume. They do not have size. They behave nothing like ordinary particles like ball bearings do.

It is exactly like trying to ask what colour the electrons are. Colour is also only a macroscopic property applying to macroscopic amounts of matter. Electrons, or any other subatomic particle, do not have colour.

So what properties do they have? To name a few, electrons have mass, position, momentum, energy, and another property called spin. The first four are basically the same as their macroscopic counterparts with a few caveats, but the last one is not a valid property of macroscopic matter. So this works both ways: just as electrons do not have a size or colour, ball bearings do not have spin. Spin is a property of subatomic particles only.

 

[limitkiller]

The whole idea of matter occupying a volume is a macroscopic idea only. It breaks down on the scale of individual particles. It's not that particles occupy an infinitely small volume. It's more that volume is not a valid physical property of subatomic particles. Electrons do not have volume. They do not have size. They behave nothing like ordinary particles like ball bearings do.

It is exactly like trying to ask what colour the electrons are. Colour is also only a macroscopic property applying to macroscopic amounts of matter. Electrons, or any other subatomic particle, do not have colour.

So what properties do they have? To name a few, electrons have mass, position, momentum, energy, and another property called spin. The first four are basically the same as their macroscopic counterparts with a few caveats, but the last one is not a valid property of macroscopic matter. So this works both ways: just as electrons do not have a size or colour, ball bearings do not have spin. Spin is a property of subatomic particles only.

I meant "turn it around its pivot" by "spin one of those around itself"...
well,I said there are nothing but two electrons. I think I should add a magical force that keeps one of the electrons and turns it around it self...

 

[toombs]

What I meant to say is that to understand how subatomic particles behave, you need to discard almost all analogies to the macroscopic matter everybody is already familiar with. Electrons don't "spin around pivots" like spinning balls in space. They don't have angular velocity. They don't have a size either. So your scenario is invalid, as are your two questions about the electrons' behaviour and size.

 

[limitkiller]

Thank you...

 

[Drakkith]

Just adding in that all particles have intrinsic "Spin". For an electron its spin is equal to 1/2. This means that it must "spin" around two times in order to have one full revolution. See how confusing this is? Quantum spin is NOT like the spin of a basketball. One could say that the spin of a macroscopic object is a poor representation of what actually happens. This is similar to waves. Waves that make up a subatomic particle are NOT like the normal wave you see on the ocean or hear through the air. Both the waves and spins of macroscopic objects are a result of the combined movement of many many many subatomic particles.

Because we use similar terms to describe these effects between such vast scale differences, there is MUCH confusion when people are first introduced to quantum mechanics. This is even more prevalent when you talk to someone like my roomate who REFUSES to accept quantum spin because it doesn't make any sense.

Spin as defined by Wikipedia:

Spin is a type of angular momentum, where angular momentum is defined in the modern way (as the "generator of rotations", see Noether's theorem).[1][2] This modern definition of angular momentum is not the same as the historical classical mechanics definition, L = r × p. (The historical definition, which does not include spin, is more specifically called "orbital angular momentum".)

Look up the full article at: http://en.wikipedia.org/wiki/Spin_(physics)

Now here's a question. Can you introduce MORE "spin" of some type on a single fundamental particle? I actually don't know.

 

[limitkiller]

Just adding in that all particles have intrinsic "Spin". For an electron its spin is equal to 1/2. This means that it must "spin" around two times in order to have one full revolution. See how confusing this is? Quantum spin is NOT like the spin of a basketball. One could say that the spin of a macroscopic object is a poor representation of what actually happens. This is similar to waves. Waves that make up a subatomic particle are NOT like the normal wave you see on the ocean or hear through the air. Both the waves and spins of macroscopic objects are a result of the combined movement of many many many subatomic particles.

Because we use similar terms to describe these effects between such vast scale differences, there is MUCH confusion when people are first introduced to quantum mechanics. This is even more prevalent when you talk to someone like my roomate who REFUSES to accept quantum spin because it doesn't make any sense.

Spin as defined by Wikipedia:


Look up the full article at: http://en.wikipedia.org/wiki/Spin_(physics)

Now here's a question. Can you introduce MORE "spin" of some type on a single fundamental particle? I actually don't know.

How do they spin without having angular velocity ?
According to what Wiki said, it isn't possible(probable ) for an electron to have no spin.Is it the same thing outside atoms?

 

[Drakkith]

How do they spin without having angular velocity ?
According to what Wiki said, it isn't possible(probable ) for an electron to have no spin.Is it the same thing outside atoms?

Spin is intrinsic angular momentum. Is there a velocity? I don't know. Is the electron actually spinning itself around? I don't know. As far as I can tell, spin is a fundamental property of particles and cannot be changed in any way. We can change the direction, but not the actual spin itself. And yes, it is the same whether the electron is inside or outside an atom.

 

[danR]

physics often borrows terms from everyday experience for a new use. The 'spins' of quantum entities (1, 1/2, 0, etc.) is a tip-off that they really don't relate to the spinning of planet or ball around its own axis. I guess it was easier to call it 'spin' than, say 'glerp'.

The glerp of a photon is 0. The glerp of an electron is 1/2.

OK, but what is the spin of electron?

Electrons don't have a spin. They don't spin at all. They are like 'time', or 'love', or 'bimetallism economic theory'. These things don't have spin.

 

[Polyrhythmic]

physics often borrows terms from everyday experience for a new use. The 'spins' of quantum entities (1, 1/2, 0, etc.) is a tip-off that they really don't relate to the spinning of planet or ball around its own axis. I guess it was easier to call it 'spin' than, say 'glerp'.

The glerp of a photon is 0. The glerp of an electron is 1/2.

OK, but what is the spin of electron?

Electrons don't have a spin. They don't spin at all. They are like 'time', or 'love', or 'bimetallism economic theory'. These things don't have spin.

The concept of spin is not totally unlike classical angular momentum. At least it obeys the same algebra, so to say it is something totally different would be inaccurate. However, the analogy of a spinning object clearly breaks down at the quantum level. It is best to view it just as some additional feature of a quantum particle which obeys certain rules, and leave it at this. I don't get your comparison of clearly different concepts, it makes no sense to me. To assign something like angular momentum (around its own axis) to some elementary particle like an electron is not too far-fetched, even though we know that quantum mechanically, things are different. I wouldn't compare this to assign angular momentum to concepts like love or some theory...

PS: The spin of a photon is 1.

 

[coelho]

Could I say that spin is something that has the units of angular momentum, but that nobody actually knows what it is, and that was assigned to the subatomic particles so the calculations (like conservation of angular momentum) would add up?

 

[toombs]

Could I say that spin is something that has the units of angular momentum, but that nobody actually knows what it is, and that was assigned to the subatomic particles so the calculations (like conservation of angular momentum) would add up?

Spin has a mathematical description that completely explains the results of certain experiments. Thus we know exactly what spin is. Its mathematical description defines it.

Now, if you are going to ask what is "really" going on underneath the mathematical description, I have this to say: probably nothing. There is no need to elaborate any further, as no experiment has given us reason to doubt the description's completeness. Now, if you are about to ask if there isn't a simpler way of defining spin to predict the same observed behaviour, the answer is we've looked for many years and it seems we already have the simplest description. You are of course welcome to look for one. Such searches have often led to amazing discoveries and predictions. Just keep in mind that it must agree with all of the previously executed experiments.

And finally, if you ask, why is it so strange and difficult to understand? Well, it's strange, but true. Like Feynman said, "If you don't like our universe, just go somewhere else."

 

[danR]

The concept of spin is not totally unlike classical angular momentum. At least it obeys the same algebra, so to say it is something totally different would be inaccurate. However, the analogy of a spinning object clearly breaks down at the quantum level. It is best to view it just as some additional feature of a quantum particle which obeys certain rules, and leave it at this. I don't get your comparison of clearly different concepts, it makes no sense to me. To assign something like angular momentum (around its own axis) to some elementary particle like an electron is not too far-fetched, even though we know that quantum mechanically, things are different. I wouldn't compare this to assign angular momentum to concepts like love or some theory...

PS: The spin of a photon is 1.

The spin is 1 or -1, correct. What I'm saying is the idea of 'spin' is so far removed from laypersons' gut-feeling and experience of the idea as to cause confusion. But for physicists it was the best choice without making up an entirely new word. This is what I mean by 'don't really' etc., in the sense of everyday 'realism'.

A term like 'tensor', on the other hand, carries so little of its root baggage to the layperson, that it's in no danger of being misunderstood, whereas it can convey its full meaning only to a physics postgraduate.

It is the macroscopic realist baggage that laypersons always try to fit on the quantum (or relativistic) procrustean bed that must be eliminated, and the idea of everyday spin applied to everyday abstractions, that is most suitable.

 

[Polyrhythmic]

I see what you mean, and I agree. In physics, there are concepts which cannot be explained correctly to laypersons by analogy to objects they are familiar with. One good example is magnetism: The magnetic field is unlike anything a normal person is familiar with, it is what it is, a magnetic field which has certain physical properties.

 

[Drakkith]

I see what you mean, and I agree. In physics, there are concepts which cannot be explained correctly to laypersons by analogy to objects they are familiar with. One good example is magnetism: The magnetic field is unlike anything a normal person is familiar with, it is what it is, a magnetic field which has certain physical properties.

I see where you are going, but I think magnetism is FAR more accepted by the average person than most things. Probably because you can take two magnets and see immediately what happens. We cannot do the same thing to spin and other properties.

 

[Polyrhythmic]

I see where you are going, but I think magnetism is FAR more accepted by the average person than most things. Probably because you can take two magnets and see immediately what happens. We cannot do the same thing to spin and other properties.

I guess that's true. Most people don't know about spin, but everybody knows magnetism.

 

[Drakkith]

I guess that's true. Most people don't know about spin, but everybody knows magnetism.

In my experience people generally will not have a problem with common day things until you explain HOW it works in a way they've never heard of. It is 100% correct to say that the north pole of two magnets repel each other. People see it happen all the time and will readily agree. However, if you say that the magnetic moments of the electrons and atoms in the magnet are aligned the same way and produce the magnetic field which causes the repulsion, you suddenly get a blank stare at best.

 

[Polyrhythmic]

In my experience people generally will not have a problem with common day things until you explain HOW it works in a way they've never heard of. It is 100% correct to say that the north pole of two magnets repel each other. People see it happen all the time and will readily agree. However, if you say that the magnetic moments of the electrons and atoms in the magnet are aligned the same way and produce the magnetic field which causes the repulsion, you suddenly get a blank stare at best.

Exactly, that's what I meant in the first post you quoted me on. You can't properly explain this concept in simple terms which a layman could relate to.

 

[Drakkith]

Exactly, that's what I meant in the first post you quoted me on. You can't properly explain this concept in simple terms which a layman could relate to.

Ah ok.

 

[limitkiller]

But if electrons do not have volume,then how do we define their coordinations in the space?

 

[danR]

But if electrons do not have volume,then how do we define their coordinations in the space?

That's the very problem of quantum uncertainty that came up in the early 20th century. And it wouldn't matter if they have volume or not. H₂ molecule has a certain (uncertain) volume. But the very nature of the quantum beast is that the x,y,z,t coordinates of its centre of 'mass' cannot be determined, and I gather from the experts, not even defined.

In other words, some seem to say that the exact simultaneous positions and momenta of quantum objects do not exist. Perhaps not even a 'meaning'.

 

[DrClapeyron]

I searched wikipedia for "electron spin" and it directed me toward a page titled "Electron Magnetic Dipole Moment". I remember that "moments" in physics are usually the difference between two points and the product of some force or charge, and I remember magnetic dipole moments from an example used to discribe how food is heated in a microwave. So I think I have a good intuitive sense of what is going on.

Spin is defined as an intrinsic value and to me intrinsic pretty much means mysterious. So is there some sort of mechanism controlling electron spin? Is it just a change in the domain of all the points on the surface of an electron just because the electron exists?

Follow up: Does anyone have a website where I can go and find out how properties like spin and magnetic moments were discovered? I have my old college text at home but I am so used to reading things off the internet.

But if electrons do not have volume,then how do we define their coordinations in the space?

That almost sounds like a smart *** response, brilliant. Maybe we should just treat electrons as a line or a point?

 

[toombs]

Follow up: Does anyone have a website where I can go and find out how properties like spin and magnetic moments were discovered? I have my old college text at home but I am so used to reading things off the internet.

I believe the first experiment confirming some of the properties of particle spin was the Stern-Gerlach experiment. Wikipedia, with any luck, should give a good description of what happened.

 

[Drakkith]

But if electrons do not have volume,then how do we define their coordinations in the space?

You can treat the electron as a point particle in space with an increasing strength in its field as you move closer to it, but that is not the most accurate I believe. Quantum Mechanics treats it and all other particles as waves and wavepackets that don't have a defined position in space, only probabilities of being somewhere compared to being somewhere else.

That's the very problem of quantum uncertainty that came up in the early 20th century. And it wouldn't matter if they have volume or not. H₂ molecule has a certain (uncertain) volume. But the very nature of the quantum beast is that the x,y,z,t coordinates of its centre of 'mass' cannot be determined, and I gather from the experts, not even defined.

In other words, some seem to say that the exact simultaneous positions and momenta of quantum objects do not exist. Perhaps not even a 'meaning'.

That is correct. It is believed that at the quantum level nothing has an exact position or momentum. I think experiments verify this pretty accurately.

Spin is defined as an intrinsic value and to me intrinsic pretty much means mysterious. So is there some sort of mechanism controlling electron spin? Is it just a change in the domain of all the points on the surface of an electron just because the electron exists?

Spin is a fundamental quality of all subatomic particles. It is just as fundamental as mass or charge. Asking what controls it is like asking what controls charge or mass. The only answer is that we don't know what, if anything, is "controlling" it.

Follow up: Does anyone have a website where I can go and find out how properties like spin and magnetic moments were discovered? I have my old college text at home but I am so used to reading things off the internet.

I would try wikipedia. It might have sections on the history of these or have links to them. If all else fails just ask google "How was quantum spin discovered?"

That almost sounds like a smart *** response, brilliant. Maybe we should just treat electrons as a line or a point?

Not sure why you would say that. That seems like a perfectly fine question to me.

 

[toombs]

But if electrons do not have volume,then how do we define their coordinations in the space?

It is easy to give a particle coordinates in space and no volume. It is done all the time in classical physics as an approximation. Something like this:

V = 0, or the particle occupies no volume. The particle's mass is m. The position is (x(t), y(t), z(t)) where x, y, and z are the 3d Cartesian coordinates, all functions of time.

In fact, even for electrons, this is a good approximation on the right space and time scales (small time or large space).

With large time or small space scales, this approximation fails and the above simple and clean description of the electron's motion over time is replaced with something strange and complicated: the wave function.

psi(x, y, z, t)

Its inputs are x, y, z, and t (independent variables; not functions of time anymore) and the output is a complex number. In other words, it assigns each point in space a complex number. The magnitude squared of this number gives the probability density (probability per unit volume) that the electron would "jump" to a region in space containing that point upon an ideal measurement of the electron's position. In this way, the electron is spread out in space. I wouldn't want to say the electron occupies a volume, because such an analogy to the macroscopic property isn't helpful. Believe me, on this scale, particles like electrons behave almost nothing like you would expect them to behave. To understand things better, you'll need to read about this wave function and the equation that describes how it changes over time, called the Schrödinger equation. This will probably require you to read about calculus, complex numbers, partial differential equations, and probability theory as well.

Just to see how an electron moves though is easier. There are a lot of neat demos on the internet. http://www.youtube.com/watch?v=cV2fkDscwvY" one of them.

 

[limitkiller]

Thank you for answers.

But the very nature of the quantum beast is that the x,y,z,t coordinates of its centre of 'mass' cannot be determined, and I gather from the experts, not even defined.

Is that because they move very fast and there are many factors changing their movement?
Or their nature simply does not have a one to one relation to what we define in mathematics as the space?

V = 0, or the particle occupies no volume. The particle's mass is m. The position is (x(t), y(t), z(t)) where x, y, and z are the 3d Cartesian coordinates, all functions of time.

Does it mean two electrons can occupy a single point in the space?And if it is so, which direction they would go?
Are you sure "their volume is zero" is equavalent to "it has no volume"? I am not sure,but I think there are differences between those two (Wich I cann't describe).

To understand things better, you'll need to read about this wave function and the equation that describes how it changes over time, called the Schrödinger equation.

Good idea!

 

[hillzagold]

Remember that electrons were originally thought to travel in a set path or ring? It's the standard picture everyone thinks of. That model was eventually deemed inaccurate, in favor of putting electrons in "clouds" where you could only guess where they would be. Things can change dramatically from Newtonian physics to quantum physics. Why do you think we needed people like Einstein to figure all of this out? lol

 

[danR]

But the very nature of the quantum beast is that the x,y,z,t coordinates of its centre of 'mass' cannot be determined, and I gather from the experts, not even defined.

Is that because they move very fast and there are many factors changing their movement?
Or their nature simply does not have a one to one relation to what we define in mathematics as the space?

No, although, yes, there are many factors affecting them. They are constantly being buffeted by zero-point vacuum energy, a sort of nanoscopic Brownian movement so to speak.

Macroscopic objects move very fast, but their positions in time can be measured with very high precision, although there is still a tiny quantum uncertainty.

Your second option gets closer to the truth. But there are different schools of thought and severity. Some hold that not only can position and momentum not be measured, but that it does not exist. Or even that it has no meaning. This is so alien to everyday experience, that we balk at it.

At the other extreme, and it seems to be a growing option, is the de Broglie/Bohm model. The electron has a position and momentum, although not measurable, that it is real at all times as a little particle, although it cannot have its position and momentum measured at the same 'time', etc. In place of a mathematical wave function showing the probability that the electron may be here or there, it has wave-like field, or real wave function, sort of surrounding it, a 'pilot wave', like a pilot boat, and this pilot wave allows the electron to sense its surroundings, such as a double-slit apparatus. The electron really has a place, and it's going through one slit or the other, but the pilot wave also let's it pretend it's a wave.