

Electron Spin and Quantum Mechanics
Name: Ben
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
Although I am familiar with quantum physics and know about
only being able to calculate the probability of an electron's
position in space, I do not quite understand how this one works. If
two electrons with coherent spins and all are traveling in opposite
directions and you do some research and you find whether one is
spinning up, you have to know, faster than the speed of light that
the other electron spins down. My question is basically, people say
that before you know the particle's spin, you have the probability
of its spin, and so it spins both up and down, but this is
confusing, because knowing the probability should not mean it is in
both states, it should only mean that you have not found out for
sure which state it is in. This is the definition of probability,
right? If you role a die, but do not look at it, you can figure it
has a 1/6 chance for landing on each side, but this does not mean it
has landed on all six sides. Please help me understand.
Replies:
Ben,
This is a fun and fascinating, but very confusing and complicated subject
indeed. I think the thing that might be confusing you is the nature of the
particle *before* you measure its property. It is not quite right to say the
particle has a 'probability' of having a property  that implies that the
property is already set, but that you just do not know it. Instead, prior to
measuring it, the particle is a mix of all the possible properties. It is
all of them at once, and only becomes one once you measure it. This is known
as 'quantum superposition'. The particle would be in a limbo of all of the
possibilities until it 'collapses' into a single possible state when you
measure it. After the measurement, you still get a distribution of states,
and you can calculate probabilities based on that, but that distribution
only takes shape after the measurement  before that each particle is a
smear of all the possibilities. This sounds counterintuitive, but
experiments have been performed that confirm this strange behavior.
This concept is very confusing, and perhaps unsatisfying. In fact, many
scientists have historically disliked this explanation too. A famous thought
experiment was proposed by Erwin Schroedinger (of the Schroedinger equation)
where a cat would be both alive and dead at the same time until a separate
measurement would be made, and then the cat would 'collapse' into being
either dead or alive. (this is a *thought* experiment only  no cats were
harmed!) The question Schroedinger tried to ask is *when* and *why* and *how*
a particle transitions from all the possibilities into just one result.
Unfortunately, those details are still very much being worked out.
Another interesting aspect is known as quantum entanglement  where the
state of two particles are related, not independent. By measuring the
property of one particle, you constrain the other particle to a smaller set
of possibilities.
So this is just a taste of this fascinating (or perhaps frustrating) field
of study. I recommend you start reading on the following topics: quantum
entanglement, quantum superposition, Copenhagen interpretation, and the EPR
Paradox. Once you have these in mind, you can start reading about the
experiments that led to them.
Hope this helps,
Burr Zimmerman
Ben,
Two factors of modern physics are needed to understand this situation.
First, fast velocity: When an object appears to move close to the speed of
light, distances and times shift in such a way that the object's velocity
measures to always be less than the speed of light. If Albert and Barney
can move in opposite directions, both at threefourths of the speed of light.
If Albert measures Barney's velocity, it will be less than the speed of light
as Albert sees the universe. This is called Relativity.
Second, states of a particle: Spinup and spindown are the only two measurable
states of an electron, but not the only states. When the spin of an electron is
actually measured, it becomes either spinup or spindown, pointing along the
direction that spin is actually measured. If you measure vertical spin, then
the spin becomes either up or down in the vertical direction. If you measure
spin along the north/south direction, then the spin becomes either toward the
north or toward the south. Measurement does not show you what the state is.
Measurement forces the particle to become one of the measurable states.
The act of measuring something can affect what you are measuring.
Dr. Ken Mellendorf
Physics Professor
Illinois Central College
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Update: June 2012

