Thread: Spins

Though particles have..same properties..Let they differ in their orientation...which means they differ in properties associated with their orientions...is it possible ??!..

The spin of an electron precesses. However when measured it is always up or down spin and nothing in between. The spin may have been purposely oriented at 45 degrees it will be measured as straight up or down when measured.

Originally Posted by pikpobedy

The spin of an electron precesses. However when measured it is always up or down spin and nothing in between. The spin may have been purposely oriented at 45 degrees it will be measured as straight up or down when measured.

This is potentially misleading. The electron spin can be measured in any direction, and the spin will either be in that direction or the opposite direction. There is nothing special about the up or down directions. Also, although the measurement of spin of a single electron in any particular direction gives only a "yes" or "no" answer, a large collection of identically prepared elections can have the direction of spin determined by an appropriate sampling from the collection.

Agreed.
Would I be correct in speculating that the required sample size to get an acceptable margin of error depends on the prepared orientation?
For example electrons prepared at zero, zero would require a smaller sample size than those oriented at +30, -45?
I am basically asking questions related to statistical variance in the up-down counts and statistical variance of the infered orientation?

Why do I ask you ask? If I were to state "quantum theory is the most accurate" this would be me parroting / quoting what I have read.
Unlike many things, I have done no experiments nor perused any raw or refined data showing that electron spin of can be determined to astonishing resolution, precision accuracy, exactitude, confidence levels (whatever terms are used) .
All I have read is if it is straight up you always measure up. If it is in between up and down depending on what it is you have to deal with probabilities of up or down. I have not had the opportunity to peruse test data of that type.

Originally Posted by KJW

This is potentially misleading. The electron spin can be measured in any direction, and the spin will either be in that direction or the opposite direction. There is nothing special about the up or down directions. Also, although the measurement of spin of a single electron in any particular direction gives only a "yes" or "no" answer, a large collection of identically prepared elections can have the direction of spin determined by an appropriate sampling from the collection.

Is this right? How can the spin ever be measured to be a certain direction as J^2=j(j+1)= 3/4 and Jz^2 =1/4 for a spin 1/2 particle?

Originally Posted by Jilan

Is this right? How can the spin ever be measured to be a certain direction as J^2=j(j+1)= 3/4 and Jz^2 =1/4 for a spin 1/2 particle?

By measuring samples from the collection in various directions, one can eventually locate the particular direction in which an entire sample yields "yes" upon measurement.

Originally Posted by pikpobedy

Agreed.
Would I be correct in speculating that the required sample size to get an acceptable margin of error depends on the prepared orientation?
For example electrons prepared at zero, zero would require a smaller sample size than those oriented at +30, -45?
I am basically asking questions related to statistical variance in the up-down counts and statistical variance of the infered orientation?

Why do I ask you ask? If I were to state "quantum theory is the most accurate" this would be me parroting / quoting what I have read.
Unlike many things, I have done no experiments nor perused any raw or refined data showing that electron spin of can be determined to astonishing resolution, precision accuracy, exactitude, confidence levels (whatever terms are used) .
All I have read is if it is straight up you always measure up. If it is in between up and down depending on what it is you have to deal with probabilities of up or down. I have not had the opportunity to peruse test data of that type.

You still appear to be regarding the up-down direction as preferred.

Preferred? As opposed to what? As far as I have been informed is that when electron spin is measured a single photon of unique energy is expelled. It's energy is not proportional to the angle of the spin as it would be in a classical system. Can you elaborate on this.

What about my query on the probabilities? Actual numbers. It's a serious sincere question. Not a challenge.

You've been in this sandbox a bit longer than me. My intention is not to stump people.

Originally Posted by pikpobedy

Preferred? As opposed to what? As far as I have been informed is that when electron spin is measured a single photon of unique energy is expelled. It's energy is not proportional to the angle of the spin as it would be in a classical system. Can you elaborate on this.

What about my query on the probabilities? Actual numbers. It's a serious sincere question. Not a challenge.

You've been in this sandbox a bit longer than me. My intention is not to stump people.

I may have misrepresented what you meant. When you talk about the up-down direction, I am regarding this literally whereas you may be regarding this generically. The point is that one can measure spin in any direction, and the electron will respond to indicate that its spin is either in that direction or in the opposite direction, with a probability that depends on the direction of spin in which the electron was previously prepared. Though the measurement of spin for a single electron can only yield a "yes" or "no" answer for a single chosen direction, the electron does have a definite direction of spin.

Without invoking Pauli spin matrices, I think the probability that an electron with a specified spin direction will be measured to have spin in some other direction is:



where is the angle between the prepared direction and the measured direction.

OK. I created a table of angles versus probabilities. This gives waht I expected results for 0, 90 and 180 degrees and such. As for in between I was surprised at the nice round number at 60 and 120. Well when I saw the surprise 75% at 60, then of course the 25% at 120 was not surprising.

Anyway I have some small grunt work to peruse my references on how to determine the sample size considering yes or no counts (ie discrete counts).
My background in appied stats and probabilities is in quality assurance and reliability. So I tend to work with defective probabilities that are in PPM or small percentages.
I deal with them with variables measurement (gaussian distributions) or counts (pass-fail, poisson or binomial distributions).

I'm just getting some insight coming into this from a direction that I am familiar.
I'm also looking at Susskind lectures on this. At present the abstract symbology is killing me because it does not automatically talk to me like I am used to in other maths and maths applications.

pikbobedy, it was not clear from your last post what if anything you find surprising . Please can you restate?

I knew from a Susskind lecture that a spin prepared at zero degrees will always be measured up. Similarly a spin at 180 degrees will always be measured down. I was told this by Susskind. A spin at 90 degrees had to obviously be 50%. I do know that at 90 degrees to the measuring method the spin axis could be north-south, east-west, and anything in between depending on the prepartion. I do know than electron spin is more about angular momentum explanations than classical spin.
It was the neat 75% and 25% at 60 and 120 degrees respectively that surprised me. Easy to remember milestones.
Remember I have no basic understanding on how that probability relationship was proven. Was it a best fit to the correlation of experiments or is it derived from fundamental mechanisms involved.

Look my background goes back to university level chemistry, chemistry of the solid state and electricity and magnetism physics. Spin flip of electrons was but a useless banality to cram about in a prequisite courses for an engineering degree. I was in a demanding school.

The formula KJW stated is derived from quantum mechanics and the experiments agreed with it. Here are lots of equations!
http://www.uvm.edu/~kspartal/EPR_Sim...AboutSpins.pdf

It is incorrect the say the spin actually points in a given direction. The best that can be said is that is has a component that is quantised in a given direction. The actual spin processes around that direction at roughly 35 degrees for a spin 1/2 particle. Here is a nice diagram.
Spin

Jilan: I disliked the article you referred to. It says this:

"Spin is intrinsic angular momentum associated with elementary particles. It is a purely quantum mechanical phenomenon without any analog in classical physics. Spin is not associated with any rotating internal parts of elementary particles; it is intrinsic to the particle itself. An electron has spin, even though it is believed to be a point particle, possessing no internal structure. The concept of spin was introduced in 1925 by Ralph Kronig, and independently by George Uhlenbeck and Samuel Goudsmit".

But see The discovery of the electron spin by Samuel Goudsmit and note this:

"When the day came I had to tell Uhlenbeck about the Pauli principle - of course using my own quantum numbers - then he said to me: "But don't you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates".

IMHO it's a modern myth that the electron intrinsic spin is nothing to do with rotation. See the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". I don't know where this myth comes from, but it seems to be connected to the non-sequitur you can find in older versions of the Wikipedia Stern-Gerlach article:

"If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. Even if the electron radius were as large as 2.8 fm (the classical electron radius), its surface would have to be rotating at 2.3×10^11 m/s. The speed of rotation at the surface would be in excess of the speed of light, 2.998×10^8 m/s, and is thus impossible.[2] Instead, the spin angular momentum is a purely quantum mechanical phenomenon."

The electron isn't spinning like a planet. It's a spin half particle, akin to Dirac's belt, which you might call a "bispinor" with two orthogonal rotations. It spins thisaway AND it spins thataway. Imagine you've got a spinning disk in front of you. It's standing on its edge and it's rotating clockwise. Now spin it like a coin with your left hand. It now has two orthogonal spins. Which way is it spinning? Every which way. You can't say. But you can start again, get it standing on edge rotating clockwise, then spin it like a coin with your right hand. Which way is it spinning now? Every which way. You still can't say. But you can say that this compound rotation has the opposite chirality to the first.

Originally Posted by Farsight

The electron isn't spinning like a planet. It's a spin half particle, akin to Dirac's belt, which you might call a "bispinor" with two orthogonal rotations. It spins thisaway AND it spins thataway. Imagine you've got a spinning disk in front of you. It's standing on its edge and it's rotating clockwise. Now spin it like a coin with your left hand. It now has two orthogonal spins. Which way is it spinning? Every which way. You can't say. But you can start again, get it standing on edge rotating clockwise, then spin it like a coin with your right hand. Which way is it spinning now? Every which way. You still can't say. But you can say that this compound rotation has the opposite chirality to the first.

Can you recover any of the behavior seen in electrons with such rotations? Can we see how, with the mathematics?

Originally Posted by KJW

Though the measurement of spin for a single electron can only yield a "yes" or "no" answer for a single chosen direction, the electron does have a definite direction of spin.

Originally Posted by Jilan

It is incorrect the say the spin actually points in a given direction. The best that can be said is that is has a component that is quantised in a given direction. The actual spin processes around that direction at roughly 35 degrees for a spin 1/2 particle. Here is a nice diagram.Spin

I stand corrected. However, for a single electron, there exists a direction in which the measurement of spin will produce a "yes" result with 100% certainty.

Originally Posted by Jilan

The actual spin processes around that direction at roughly 35 degrees for a spin 1/2 particle.

I looked at the precession sketch. It is a bit rough. Is the 35 degrees the angle subtended by the vertical line h/2 and that arrow (root3/2)h.
Reason I ask is that the 35 degrees appears to be more like 50 since the precession subtended angle is obviously less than 90.





Susskind states a strong magnetic field will quickly align a spin within a short half-life. It was also my understanding that the precession is minimized in this strong magnetic field. The stronger the field the quicker the effect.

Upon removal of the strong field the precession will reappear and the alignment will decay also.

Originally Posted by Jilan

The formula KJW stated is derived from quantum mechanics and the experiments agreed with it. Here are lots of equations!
http://www.uvm.edu/~kspartal/EPR_Sim...AboutSpins.pdf

Excellent. Can I count on a very low error rate in there? Zero errors? This is important. Otherwise I can work this.

Originally Posted by PhysBang

Can you recover any of the behavior seen in electrons with such rotations?

Not per se, but IMHO you can get the gist of the Stern-Gerlach experiment via an analogy. This was performed with silver atoms, which have an unpaired electron but are neutral. Each silver atom is something like a football on the penalty spot with an initial backspin. You come along and kick it, giving it either left or right sidespin. The ball goes into the top left corner or the top right corner, akin to the two spots on the Stern-Gerlach target. See this in the wiki article: "If the particles were classical spinning objects, one would expect the distribution of their spin angular momentum vectors to be random and continuous". They aren't spinning like a planet, they're spinning like Dirac's belt. Their angular momentum vectors are compound, and have either one chirality or the other.

Originally Posted by PhysBang

Can we see how, with the mathematics?

No, sorry, I don't know how to even approach the mathematics for this.

Pickpobedy, it might be wrong, I'm not at a computer, but you should be evaluate it for the cosine easily enough.

Good question about the alignment in the field. I've asked this question before and been told it's not actually strong enough to realign the spins. Still I'm not 100% convinced though!

Pinko, wrt to the maths. It's just maths. I'm not sure there would be an error?

Hey..can u tell me ..For the research field BSc phy or BSc che is better???..
Thank u..

You are on a Physics forum, what do you think the answer will be?

Yes ..I know that answer will be Bsc physics...but I have a question that chemistry too deals with this quantum field...chemistry is my field..so is there any scope that after completing Bsc chemistry...If I am able to enter this quantum field??..