# Is SPIN a calculated or physically measureable characteristic?

Regarding the term "Spin"...

I've see a number of different descriptions. In the book I'm currently reading it says it is "loosely" the measure of the strength of rotational motion, and "technically" the measure of the quantity called angular momentum.

It also states we consider the spin of an photon to be 1, and electron to be 1/2, etc. My question is: Were these values (1, 1/2, 1-1/2, etc.) arrived at by some type of mathematical calculation, or were they arrived at by some type of physical measurement (using some type of measuring device)? And what does the number "1", as it relates to "Spin", mean? Does it have anything to do with the quantity of the number "1"?

Drakkith
Staff Emeritus
I would say it was both calculated and observed. For example, the way an electron behaves when bound to an atom wasn't accurate until the concept of spin was thought of, after which the math started working and explained the observed measurements exactly.

Fredrik
Staff Emeritus
Gold Member
Physical terms like "spin", "force", "electric field" etc. are always defined by some theory, so yes, there's a mathematical definition. In this case, the relevant definition is a part of the standard way to add the assumption that space is isotropic (the same in every direction) to quantum mechanics.

Of course, a given theory's definition isn't going to be used by anyone unless the theory's predictions agree with experiments pretty well. So experiments are important too.

The meaning of the term is pretty hard to explain. It's mainly about how you would have to change your description of the particle if you rotate your laboratory around it.

dextercioby
Homework Helper
Spin is the name a theory uses to describe certain effects at quantum level. As these effects can be measured, there are 2 ways a theory can contain the results of the measurements: either as input data, or as consequence of some mathematical calculations. The qm spin would rather be a result of the theory, and not one of its hypothesis.

I am hearing that Spin is a property whose value is determined by calculation after measuring the effect it has on another directly measurable property of that same particle, and that Spin cannot be directly measured.

f95toli
Gold Member
I am hearing that Spin is a property whose value is determined by calculation after measuring the effect it has on another directly measurable property of that same particle, and that Spin cannot be directly measured.

We can capture say spin 1/2 particles in traps and then flip them using external magnetic fields; you can see the flips by e.g. using spectroscopy.

This is the whole basis for NMR/MRI and ESR.

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...This is the whole basis for NMR/MRI and ESR.

That is interesting

Am I correct in assuming that "1" and "1/2" are only a description of the relationship of the magnitude of Spins?

DrChinese
Gold Member
That is interesting

Am I correct in assuming that "1" and "1/2" are only a description of the relationship of the magnitude of Spins?

Somewhat. A spin 1 particle's wave function returns to the original form after being rotated 360 degrees. A spin 1/2 particle's wave function returns to the original form only after being rotated 720 degrees, so a 360 degree rotation only gets it half way there. Hence the spin 1/2 designation.

I don't have the book in front of me, but I believe I remember reading (I paraphrase) the Photon's actual Spin was originally determined to be "2", and the Electron's "1". And for some reason they wanted to use the Photon's Spin as the baseline for comparison, so they "labeled" the Photon's Spin 1, and the Electron's Spin 1/2 (maintaining the original relative ratio). I apologize if I've misquoted something, but if that were true, how then does one complete circular rotation (360 degrees) now directly relate to the Photon's Spin 2 as explained above?

DrChinese
Gold Member
I don't have the book in front of me, but I believe I remember reading (I paraphrase) the Photon's actual Spin was originally determined to be "2", and the Electron's "1". And for some reason they wanted to use the Photon's Spin as the baseline for comparison, so they "labeled" the Photon's Spin 1, and the Electron's Spin 1/2 (maintaining the original relative ratio). I apologize if I've misquoted something, but if that were true, how then does one complete circular rotation (360 degrees) now directly relate to the Photon's Spin 2 as explained above?

Of course some where or another you set a baseline of what 1 means. Really no change in the explanation. There is a certain convenience for using 1 for a photon, which you can probably see.

Drakkith
Staff Emeritus
Somewhat. A spin 1 particle's wave function returns to the original form after being rotated 360 degrees. A spin 1/2 particle's wave function returns to the original form only after being rotated 720 degrees, so a 360 degree rotation only gets it half way there. Hence the spin 1/2 designation.

Do you have a link to something that explains this a little more?

DrChinese
Gold Member
Do you have a link to something that explains this a little more?

Sorry, I don't have anything more useful than this, which is probably more basic than you are asking for a reference on:

"The conventional definition of the spin quantum number s is s = n/2, where n can be any non-negative integer. ...

"Mathematically, quantum mechanical spin is not described by vectors as in classical angular momentum, but by objects known as spinors. There are subtle differences between the behavior of spinors and vectors under coordinate rotations. For example, rotating a spin-1/2 particle by 360 degrees does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720 degree rotation. A spin-zero particle can only have a single quantum state, even after torque is applied. Rotating a spin-2 particle 180 degrees can bring it back to the same quantum state and a spin-4 particle should be rotated 90 degrees to bring it back to the same quantum state. The spin 2 particle can be analogous to a straight stick that looks the same even after it is rotated 180 degrees and a spin 0 particle can be imagined as sphere which looks the same after whatever angle it is turned through."

http://en.wikipedia.org/wiki/Spin_(physics)

Hi.

Let me quote this article: http://physicsworld.com/cws/article/news/2006/nov/10/spin-measured-without-destruction. It captures many aspects of spin, both theoretical and experimental.

"Spin measured without destruction

Nov 10, 2006

The spin state of a single electron in a quantum dot has been measured for the first time without destroying the state. David Awschalom and colleagues at University of California, Santa Barbara, determined the spin by reflecting polarized laser light from a quantum dot. The development could lead to the exploitation of the quantum properties of single electrons in quantum computers (Sciencexpress 9 November 2006).

Quantum computers could exploit the fact that a quantum particle can be in two states at the same time – spin up or spin down in the case of an electron. With the two states representing a one or a zero, N such particles – or quantum bits (qubits) – could be combined or “entangled” to represent $2^N$ values simultaneously. This could lead to the parallel processing of information on a massive scale. However, the realization of a quantum computer involves fundamental challenges such as how to read the logical state of a qubit without destroying the state, and how to entangle the qubits.

Semiconductor quantum dots are nanoscale structures that contain as few as one electron and show great promise for use as qubits. Information can be stored in the spin state of a single electron and while several optical and electronic schemes exist for reading the spin state, they all destroy the state as part of the process.

The Santa Barbara group shone plane-polarized laser light on a gallium-arsenide quantum dot. The spin state of the electron was determined from the direction of rotation of the polarization of the reflected light – the so-called Kerr rotation. According to Awschalom, a Kerr rotation measurement is inherently non-destructive because it involves photons that have reflected from the sample without absorption. “If a photon was absorbed by the dot (thereby disturbing the system), then Kerr rotation would not be observed”, he explained. The researchers minimized the chances of absorption occurring by using photons with energy sufficiently far from any optical transitions in the quantum dot.

Awschalom explained that the Santa Barbara work represents an important step towards the optical entanglement of single-electron quantum dots. Upon reflection, photon and dot are entangled in the same quantum state. If the photon is then reflected from a second dot, all three are entangled. If the polarization of the photon is then measured, the two quantum dots remain entangled."

Cheers.

Hi.

Let me briefly sketch how spinors got introduced.

Consider mass-shell relation from special theory of relativity,
$E^2 - p^2 = m^2$
This is a quadratic equation. Suppose we are not really happy with having to calculate with squares such as $E^2$ and $p^2$. For instance, we expect that a system of 2 objects has energy exactly the same as both objects do together. If objects have energies $E_1$ and $E_2$, the system of just these two objects should have energy $E_1 + E_2$. Well, that's what we'd like to see and what we'd expect. But, in special theory of relativity, one has $E=\sqrt{m^2 + p^2}$, so energy of 2 objects is in relativity $E_1 +E_2 =\sqrt{m_1^2 + p_1^2} + \sqrt{m_2^2 + p_2^2}$. It doesn't look nice.

So, can we have some other equation instead of this ugly looking quadratic equation? We would like to have an equation without squares!
We live in a world with 3 spatial dimensions $x,y,z$ and with 1 temporal dimension $t$. So, the ugly equation is really even uglier:

$\;\;\;\;\;\; \mathcal{T}$his is one ugly equation:
$$E^2 - p_x^2 - p_y^2 - p_z^2 = m^2$$
Can we somehow drop squares?

How about like this: $E - p_x - p_y - p_z = m$? This is a nice looking equation! Will this do? Well, if we take square of this equation, we arrive at an equation that is even uglier than the ugly looking one... Not good... And there's nothing that can be done about it, too.

$\;\;\;\;\;\; \mathcal{T}$his is one pretty equation:
$$a_t p_t + a_x p_x + a_y p_y + a_z p_z = a_m m$$
This is not bad. No squares here! Can this do? Well, lets take a square of it and see if we can relate it then to the original ugly looking equation. When squared, the better looking equation with $a$s and $p$s turns out a bit nasty... Like this: $a_t^2 p_t^2 + a_x^2 p_x^2 + a_y^2 p_y^2 + a_z^2 p_z^2 = a_m^2 m^2 + More$.

OK, if we compare
$\;\;E^2 \;\;\;\;- p_x^2 \;\;\;\;- p_y^2 \;\;\;\;- p_z^2 = \;\;\;\;m^2$
with
$a_t^2 p_t^2 + a_x^2 p_x^2 + a_y^2 p_y^2 + a_z^2 p_z^2 = a_m^2 m^2 + More$
we see that all we need is to have most of $a$s obey this simple rule:

$\;\;\;\;\;\; \mathcal{T}$his is one simple rule:
$$a^2 =-1$$
And then, ugly and pretty equation have the same physical meaning and look the same when squared. Err... there's one more thing, though. We have to take care of $More$. There should be no $More$. What exactly is $More$? It is $More = (a_x a_y +a_y a_x) p_x p_y + \dots$. So we must also have $a_x a_y +a_y a_x = 0$ and so on. This can be better re-written as:

$\;\;\;\;\;\; \mathcal{T}$his is one better written rule:
$$a_x a_y = -a_y a_x$$
OK, check this last equation: $a_x$ and $a_y$ can't be ordinary numbers.

So $a$s are not ordinary numbers. However, if we define them like this, then there is no $More$ and we have our pretty equation the way we wanted it.

Yes, extraordinary objects $a$s are spinors. To be precise, they are spin operators. This is how it was done back in 1928. Today we use a bit different notation. However, the principles are the same: one can turn squares into vectors - ugly equation into pretty one.

And how come vectors in spin space rotate slower than vectors in physical space-time? Well, that is a bit complicated to demonstrate and to comprehend.

So what's the use of pretty equation? We know particles obey ugly equation. How about pretty one?

It turns out that most particles that obey ugly equation are in fact composite particles. Particles that are ruled by ugly equation are made of two particles held together.

And what is the equation governing those two, more fundamental, particles?

Yep, You got it right: $\mathcal{The \;\; Pretty \;\; Equation!}$

I certainly hope someone had a good laugh today

Cheers.

Drakkith
Staff Emeritus
Kraflyn, I actually think I understood most of that. Thanks!

Hello.

You're most welcome.

Cheers.

Of course, a given theory's definition isn't going to be used by anyone unless the theory's predictions agree with experiments pretty well. So experiments are important too.

The meaning of the term is pretty hard to explain. It's mainly about how you would have to change your description of the particle if you rotate your laboratory around it.

Experiments are important, too?

Experiments are everything in science and engineering. Theory is important too.
Facts before theory.

Meaning of the term is pretty easy to explain. Just check simple "Stern-Gerlach" experiment for the facts. Then we can talk about the isotropy of the space to "model" spin.

OP: Ask yourself how you understand charge, and you will get the answer for spin. Of course with relevant experimental facts.

Fredrik
Staff Emeritus
Gold Member
Experiments are important, too?
Yes, they are. Perhaps I could have elaborated, but it seemed unnecessary to turn a short post into an essay, after I had already made my point.

Experiments are everything in science and engineering.
This statement is much less accurate than mine.

Meaning of the term is pretty easy to explain. Just check simple "Stern-Gerlach" experiment for the facts.
A description of a Stern-Gerlach device can be taken as the definition of what it means to measure a spin component of an uncharged spin-1/2 particle. But this isn't a good way to define the term "spin".

Yeah I think I have made my point. I do research professionally, so I don't worry about accuracy when I post on PF in my free time.
To tell beginners that to understand spin, they need to dig their heads in a physics book is far from inaccurate, it's very misleading.
The term "spin" can be defined experimentally as well (and it can be directly measured ... incidentally, judging from the responses it looks like nobody is actually working on spin here; but rather everybody seems to be "studying" spin), I don't see a point why theory (with all its imperfections) should hold a dominance as to how phenomenology is defined. And yes, I am a theorist.

I don't see the difference in "measuring" something and definining it, since in physics everything is measured before they are defined. You measure it; figure out the truth and then muddy it with as much Math as you wish, spin - still goes back to a simple SG apparatus for people who actually manufactured the hard-drive of the computer you are reading this note at this minute.
For people who spend years on definitions, it may not be the case.

But maybe this isn't the right place for this discussion, I apologize for the "noise".

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Hi.

Why leave? Everyone can say anything related to physics. Right? Right.

Besides, You are both right. Sometimes experiment leads the way, sometimes theory. Well, most of the time experiment leads the way. When did theory lead? General relativity predicted some peculiar details not experimentally known at the date. Then, Bohm and Aharonov predicted an effect, experimentally verified a year later.

Yes, what would a theory be without experiments? A fairytale at best. Insanity at worst. However, if people didn't start to conceptualize practical things, we would still herd cattle and hit each other with sticks. If theory of evolution is correct, that is...

So it's even now: theory vs. experiment latest result is 1:1

By the way, Penzias and Wilson discovered cosmic microwave background radiation only when they stopped ignoring noise from their instruments and got courage to check their antennas! It turned out the noise brought them Nobel...

Cheers.

Fredrik
Staff Emeritus
Gold Member
To tell beginners that to understand spin, they need to dig their heads in a physics book is far from inaccurate, it's very misleading.
The term "spin" can be defined experimentally as well (and it can be directly measured ...
First of all, what the OP has in mind when he said "spin" isn't what corresponds to the spin component operators ##S_1,S_2,S_3##, but what corresponds to the squared operator ##\mathbf{S}^2##. I'm not aware of any way to measure that directly, other than to determine which one of the particle species defined by the theory we're dealing with. This can't be done without a theory that tells you how each particle species will behave in experiments.

Second, even if we had been talking about spin components, you wouldn't use a Stern-Gerlach apparatus to measure one of them, unless the particle is an uncharged spin-1/2 particle. Wouldn't you have to use a different device for each particle species? Yes, knowing these devices would certainly add to your understanding of spin, but so would an understanding of how spin is defined in the theory. Theories are what helps us understand experimental results, so it seems very strange to be so dismissive of theory.

...in physics everything is measured before they are defined.
This is clearly not true. Kraflyn already gave you a couple of examples.

You measure it; figure out the truth and then muddy it with as much Math as you wish,
"Find out the truth and muddy it with math"... I agree with the first part, that what we find out when we do experiments can be considered "the truth". In fact, I would go so far as to say that experimental results are the only things in physics that should be considered "facts". In particular, theories of physics should never be considered "facts", no matter how accurate their predictions are. But "muddy it with math"? Seriously? As if theories only obscure the facts, rather than give us a way to understand them better. This goes against everything that science is about.

Hi.

And... here we go again. Theory vs. experiment: round 2

Cheers.

First of all, what the OP has in mind when he said "spin" isn't what corresponds to the spin component operators ##S_1,S_2,S_3##, but what corresponds to the squared operator ##\mathbf{S}^2##. I'm not aware of any way to measure that directly, other than to determine which one of the particle species defined by the theory we're dealing with. This can't be done without a theory that tells you how each particle species will behave in experiments.

Second, even if we had been talking about spin components, you wouldn't use a Stern-Gerlach apparatus to measure one of them, unless the particle is an uncharged spin-1/2 particle. Wouldn't you have to use a different device for each particle species? Yes, knowing these devices would certainly add to your understanding of spin, but so would an understanding of how spin is defined in the theory. Theories are what helps us understand experimental results, so it seems very strange to be so dismissive of theory.

This is clearly not true. Kraflyn already gave you a couple of examples.

"Find out the truth and muddy it with math"... I agree with the first part, that what we find out when we do experiments can be considered "the truth". In fact, I would go so far as to say that experimental results are the only things in physics that should be considered "facts". In particular, theories of physics should never be considered "facts", no matter how accurate their predictions are. But "muddy it with math"? Seriously? As if theories only obscure the facts, rather than give us a way to understand them better. This goes against everything that science is about.

Fredrik, I agree with you %99 percent. No question. Whether or not we can measure S^2 , we can discuss separately. I can think of, admitedly hypothetical, spin-functional devices to do the deed but that's another point.

I think I have to agree that I was too dismissive, theories certainly help us, in fact sometimes more than experiments.

But I just want to stress; there are sometimes theoretical trainwrecks (as the legendary Anderson calls the current state of the High-Tc superconductivity situation) that are caused due to lack of adequate experimentation. My point is; theory doesn't obscure the facts always, but without experiment; this can happen.

Two serious examples are as I said

1) String theory
2) and High Tc superconductivity.

Lots of debates and no real practical achievement. Common point?
Not enough experiments in both cases.

Fredrik
Staff Emeritus