The document discusses an experiment involving sending electrons through "color boxes" and "hardness boxes" to determine if color or hardness can be predicted. The results show that: 1) Sending electrons through a color box and then a hardness box results in a 50/50 chance of coming out hard or soft, showing color does not determine hardness. 2) Similarly, sending electrons through a hardness box and then a color box also results in a 50/50 chance of coming out the color, showing hardness does not determine color. 3) Reversing the order of the boxes still yields the same 50/50 results, demonstrating the color or hardness cannot be thought of as a persistent property of the electron.

2. Does White determine Hardness? So we can
answer this question by using our boxes

3. So –let’s send in some random electrons, and lets
send them into a color box, and lets take the
electrons that come out the white apparature

4. So –I am going to take a piece of metal, scrape off
some electrons, and then send them in

5. They come out about ½ and ½, and I take those
that come out the white apparature

6. I want to know does-white determine hardness ?
and I can do that-by sending the white electrons
into the hardness box-and seeing what comes out

7. Then I will find that 50% come on hard and 50%
come out soft

8. Then I will find that 50% come on hard and 50%
come out soft

9. And now –lets take the situation and reverse this

10. And now –lets take the situation and reverse this
You will again get 50/50

11. So if you take a white electron and send it in a
hardness box –you are at even odds

12. And If I send a soft electron into a color box- you
are still at even odds

13. So-now-what we are gonna do is run so pseudo
experiments –which will lead us to some more
complicated experiments

14. So for example-take this last experiment-take electons into color box –
coming out the white apparature
(some one behind you)

15. The send into a Hardness box-then send the soft
electron into a color box
And what do you expect to happen-

16. Well lets think about the logic here-anything into the hards box-must be measured
to be white And we just did the experiment that if we send the electron into the
hardness box 50% it comes out the hard apparature and 50% in comes out the soft
apparature

17. Since colors are repeatable-our prediction-is that
of the electrons that are incident upon the color
box-100% will come out white and 0% should
come out black

18. • Except that class is all wrong
• We said already knowing the color does not predict the hardness-but
this electron –which was previously measured to be white-is
subsequently measured and sometimes it comes out white –
sometimes it comes out black- 50/50 percent of the time

19. • What that tells you is that you can not think of an electron that is
“black” and “soft” written on it-because apparently that “black” and
“soft” Is not a persistent thing

20. What that tells you is that you can not think of an electron that is
“black” and “soft” written on it-because apparently that “black” and
“soft”Is not a persistent thing

21. Meaning that once it is “black” it stays “black”-so
what is going on here?

22. If i would had changed the experiment-the same
results would have been produced (23.28)

23. So the first natural move would be to say that “there is a property of the
electron that we have not measured yet?”-that determines weather it
comes out the second color box “black or white” (24.09)

24. So people have spent a tremendous amount of
time and energy looking at the initial electrons

25. And looking with great care

26. Some feature which determines which port –they
come out of-and the shocker is no one has every
found such a property

27. For Ms Walsh-the boxes are
• To measure electron spin
• And to measure Lx and Ly

28. • The Stern–Gerlach experiment demonstrated that the spatial orientation
of angular momentum is quantized. It demonstrated that atomic-scale
systems have intrinsically quantum properties, and that measurement in
quantum mechanics affects the system being measured. In the original
experiment, silver atoms were sent through a non-uniform magnetic field,
which deflected them before they struck a detector screen. Other kinds of
particles can be used. If the particles have a magnetic moment related to
their spin angular momentum, the magnetic field gradient deflects them
from a straight path. The screen reveals discrete points of accumulation
rather than a continuous distribution, owing to the quantum nature of
spin. Historically, this experiment was decisive in convincing physicists of
the reality of angular momentum quantization in all atomic-scale systems

30. • The Stern–Gerlach experiment involves sending a beam of particles
through an inhomogeneous magnetic field and observing their
deflection. The results show that particles possess an intrinsic angular
momentum that is closely analogous to the angular momentum of a
classically spinning object, but that takes only certain quantized
values. Another important result is that only one component of a
particle's spin can be measured at one time, meaning that the
measurement of the spin along the z-axis destroys information about
a particle's spin along the x and y axis

31. Spin up and spin down
• https://www.khanacademy.org/science/physics/quantum-
physics/quantum-numbers-and-orbitals/v/quantum-numbers

32. How To Understand Quantum Superposition
Yes!!!!!!!!!!!!!!!!
• https://www.youtube.com/watch?v=hkmoZ8e5Qn0
• The spin of the electron is 2 different axis
• So spin up (black) –in x direction (soft)
• And spin down (white) – in y direction (hard)

33. Goto the web site-then go to the video
• Since the Pauli matrices do not commute, measurements of spin
along the different axes are incompatible. This means that if, for
example, we know the spin along the x-axis, and we then measure
the spin along the y-axis, we have invalidated our previous knowledge
of the x-axis spin. This can be seen from the property of the
eigenvectors (i.e. eigenstates) of the Pauli matrices that:
• https://en.wikipedia.org/wiki/Spin_(physics)#Measurement_of_spin_
along_the_x-.2C_y-.2C_or_z-axes

34. https://en.wikipedia.org/wiki/Spin_(physics)#Mea
surement_of_spin_along_the_x-.2C_y-.2C_or_z-
axes

35. Heisenberg's Uncertainty Principle Explained
• https://www.youtube.com/watch?v=a8FTr2qMutA

36. https://www.youtube.com/watch?v=a8FTr2q
MutA

37. • Other things
• MIT22_02S12_midterm2010sol.pdf
• http://www.phys.ufl.edu/~pjh/teaching/phy4604/tests/test3solns.pd
f

38. Color-up spin or down spin
• Hardness- x axis or y axis