# Measurement of spin due to the force on a magnet

Can we measure the spin of a particle by measuring the force on a Magnet?

I wish to consider a modified stern gerlach like apparatus where a Magnet of mass M is attached to a spring. Can we measure Spin of the particle by studying the deflection of the magnet?

Even if it is possible, I can see No way to calculate the force on the magnetic.
I think the consideration that the spring is composed of several degrees of excitation becomes important to analyze this problem.

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ZapperZ
Staff Emeritus
How tiny of a magnet do you have to be able to detect that small force?

Whenever you want to figure out something like this, you have to do a back-of-the-envelope calculation on the quantitative aspect of it. Figure out what strength of force that something like this would produce, and then see if there is a realistic setup that will be able to detect it!

Zz.

My guess would be that
the Force of the particle = Force on the Magnet = μ∇B.
The change in momentum = μ∇B*δT = μ∇B L/P
where δT = L/P
Where L is the extension P is the momentum.

ZapperZ
Staff Emeritus
And what "numbers" do you get? The magnitude will determine what you will need to detect such a thing. This is what I mean by being quantitative! It is how physicists design experiments.

Zz.

Numbers and whether such an experiment is performable is not my focus. My main interest is to understand how such a setup must be treated in theory.

On one hand We have the measurement apparatus(The Spring+Magnet System) that is described by classical laws. On the Other Hand We have a Spin, whose state is described by a wave function.
I wish to undertake a an analysis of what measurement apparatus is using a simple system. I think It becomes very important to take into consideration that the spring is composed of many degrees of freedom.

ZapperZ
Staff Emeritus
Numbers and whether such an experiment is performable is not my focus. My main interest is to understand how such a setup must be treated in theory.

On one hand We have the measurement apparatus(The Spring+Magnet System) that is described by classical laws. On the Other Hand We have a Spin, whose state is described by a wave function.
I wish to undertake a an analysis of what measurement apparatus is using a simple system. I think It becomes very important to take into consideration that the spring is composed of many degrees of freedom.
Ah, but the devil is in the DETAILS!

What will kill your spring-magnet system is that you will NOT be able to find a magnet sensitive enough to measure such a thing. That's why a quantitative value is crucial! I'm trying to teach you how to think through something like this when you are trying to figure out what can and cannot be done. Your dismissal of any quantitative evaluation will turn your idea into something useless if you are not aware of what can be realistically done!

Why do you think we have SQUIDs, and why do you think these are the most common devices to measure magnetic flux?

Zz.

mfb
Mentor
Torsion balances can easily measure forces of ~10^(-8) N, which is equivalent to the gravitational force between two 1kg-masses at 10cm separation. This number is 200 years old, so you can probably add a lot of sensitivity now.
Stern and Gerlach used a magnetic field gradient of 10T/cm, multiplied by the magnetic moment of an electron this gives a force of 20^(-20)N per atom. This is 100 years old, so maybe you get better gradients now (or the same gradients with less mass). You should have multiple atoms in the field at the same, of course.
Can close the gap between both numbers?

ZapperZ
Staff Emeritus
Torsion balances can easily measure forces of ~10^(-8) N, which is equivalent to the gravitational force between two 1kg-masses at 10cm separation. This number is 200 years old, so you can probably add a lot of sensitivity now.
Stern and Gerlach used a magnetic field gradient of 10T/cm, multiplied by the magnetic moment of an electron this gives a force of 20^(-20)N per atom. This is 100 years old, so maybe you get better gradients now (or the same gradients with less mass). You should have multiple atoms in the field at the same, of course.
Can close the gap between both numbers?
But this doesn't measure the "spin of a particle", per the OP.

Putting a bunch of atoms together and measuring the collective magnetic moment isn't that straightforward. Anyone who has done NMR or EPR experiment (as in electron paramagnetic resonance) can tell you, the atom-atom interaction and temperature WILL affect the orientation of neighboring atoms. One can already see this in solids where the nature of the Heisenburg coupling, for example, can determine if something is ferromagnetic or antiferromagnetic.

Zz.

DrDu
Basically this is the classical Einstein de Haas experiment from 1915.

mfb
Mentor
Well, it would measure the spin of a lot of particles, preferably a polarized beam.

Anyone who has done NMR
Did that. But not with a beam of particles.

Torsion balances can easily measure forces of ~10^(-8) N, which is equivalent to the gravitational force between two 1kg-masses at 10cm separation. This number is 200 years old, so you can probably add a lot of sensitivity now.
Stern and Gerlach used a magnetic field gradient of 10T/cm, multiplied by the magnetic moment of an electron this gives a force of 20^(-20)N per atom. This is 100 years old, so maybe you get better gradients now (or the same gradients with less mass). You should have multiple atoms in the field at the same, of course.
Can close the gap between both numbers?
So It appears that sort of some classical version of this experiment can be performed where A Continuous stream of atoms are sent through the apparatus and we can measure the average force on the magnet. That should be directly related to average spin of the particles that enter the setup.
Though measurements for single spin would be difficult to perform.
Is it meaningful to ask the question what is the Impulse the magnet feels when a single atom passes through. How does a record of that Impulse correspond to measurement of the electron.

Basically this is the classical Einstein de Haas experiment from 1915.
The Einstein de Haas experiment involves several electrons, we are interested in the effect due to one spin.

mfb
Mentor
Prathyush said:
Is it meaningful to ask the question what is the Impulse the magnet feels when a single atom passes through. How does a record of that Impulse correspond to measurement of the electron.
It depends on the speed of the atom and the length of the setup. A thermal atom with ~1km/s and 10cm length of the setup would give 100µs, multiplied with the force this corresponds to 10^(-24) kg m/s.

mfb said:
20^(-20)N per atom
Typo, should be 10^(-20)

Is there any chance that this type of experiment could be adapted to provide a similar measurement, at least indirectly?

http://arstechnica.com/science/2012/07/researchers-control-reactions-between-just-two-atoms/
I am not sure, how do you intend to set it up?

It depends on the speed of the atom and the length of the setup. A thermal atom with ~1km/s and 10cm length of the setup would give 100µs, multiplied with the force this corresponds to 10^(-24) kg m/s.
It appears Such an impulse would be rather Difficult/Impossible to measure.

But say one can somehow construct an apparatus that is sensitive enough to measure The force applied by the spring. I am very to understand How to apply A formalism That deals with springs that are to be treated Classically and Spins that must be treated Quantum Mechanically. In specific How does One see that Impulse must be quantized.

mfb
Mentor
Interesting aspect with a spring. The energy corresponding to a momentum is given by $E=\frac{p^2}{2m}$. Using m=1kg and p from above, this corresponds to 5*10-49J or ~5*10-15Hz. The single atom could not excite the whole spring/magnet system for any reasonable setup.

Thank you ZapperZ and mfb,
I see this is a Highly impractical situation. I will try to look else. Maybe research up on SQUIDS.
Can some one please refer me to a lucid introduction to the subject.