On 10/16/2019 2:50 PM, John Clark wrote:
On Wed, Oct 16, 2019 at 4:49 PM 'Brent Meeker'
<[email protected]
<mailto:[email protected]>> wrote:
/> I thought you read Carroll's book. His example shows in what
sense you can erase the information after the photon has hit the
screen./
If you wait to erase the which way information until after the photon
has hit the screen then the experiment would be much easier to
perform, but the results of it are obvious and rather dull, you would
see interference bands because there would be ambiguity over which
slit the photon went through.
Here's Carroll's description from his blog...which is more interesting
that just erase or not erase:
When we measured the recording spin in the vertical direction, the
result we obtained was entangled with a definite path for the traveling
electron: [↑] was entangled with (*L*), and [↓] was entangled with
(*R*). So by performing that measurement, we knew that the electron had
traveled through one slit or the other. But now when we measure the
recording spin along the horizontal axis, that’s no longer true. After
we do each measurement, we are again in a branch of the wave function
where the traveling electron passes through both slits. If we measured
spin-left, the traveling electron passing through the right slit picks
up a minus sign in its contribution to the wave function, but that’s
just math.
By choosing to do our measurement in this way, we have erased the
information about which slit the electron went through. This is
therefore known as a “quantum eraser experiment.” This erasure doesn’t
affect the overall distribution of flashes on the detector screen. It
remains smooth and interference-free.
But we not only have the overall distribution of electrons hitting the
detector screen; for each impact we know whether the recording electron
was measured as spin-left or spin- right. So, instructs our professor
with a flourish, let’s go to our computers and separate the flashes on
the detector screen into these two groups — those that are associated
with spin- left recording electrons, and those that are associated with
spin-right. What do we see now?
Interestingly, the interference pattern reappears. The traveling
electrons associated with spin-left recording electrons form an
interference pattern, as do the ones associated with spin-right.
(Remember that we don’t see the pattern all at once, it appears
gradually as we detect many individual flashes.) But the two
interference patterns are slightly shifted from each other, so that the
peaks in one match up with the valleys in the other. There was secretly
interference hidden in what initially looked like a featureless smudge.
Adapted fromWikipedia
<https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser>
In retrospect this isn’t that surprising. From looking at how our
quantum state Ψ was written with respect to the spin-left and -right
recording electrons, each measurement was entangled with a traveling
electron going through both slits, so of course it could interfere. And
that innocent-seeming minus sign shifted one of the patterns just a bit,
so that when combined together the two patterns could add up to a smooth
distribution.
You professor seems more amazed by this than you are. “Don’t you see,”
she exclaims excitedly. “If we didn’t measure the recording photons at
all, or if we measured them along the vertical axis, there was no
interference anywhere. But if we measured them along the horizontal
axis, there secretly was interference, which we could discover by
separating out what happens at the screen when the recording spin was
left or right.”
You and your classmates nod their heads, cautiously but with some degree
of confusion.
“Think about what that means! The choice about whether to measure our
recording spins vertically or horizontally could have been made long
after the traveling photons splashed on the recording screen. As long as
we stored our recording spins carefully and protected them from becoming
entangled with the environment, we could have delayed that choice until
years later.”
Sure, the class mumbles to themselves. That sounds right.
“But interference only happens when the traveling electron goes through
both slits, and the smooth distribution happens when it goes through
only one slit. That decision — go through both slits, or just through
one — happens long before we measure the recording electrons! So
obviously, our choice to measure them horizontally rather than
vertically had to/send a signal backward in time/to tell the traveling
electrons to go through both slits rather than just one!”
After a short, befuddled pause, the class erupts with objections.
Decisions? Backwards in time? What are we talking about? The electron
doesn’t make a choice to travel through one slit or the other. Its wave
function (and that of whatever it’s entangled with) evolves according to
the Schrödinger equation, just like always. The electron doesn’t make
choices, it unambiguously goes through both slits, but it becomes
entangled along the way. By measuring the recording photons along
different directions, we can pick out different parts of that entangled
wave function, some of which exhibit interference and others do not.
Nothing really went backwards in time. It’s kind of a cool result, but
it’s not like we’re building a frickin’ time machine here.
The more interesting thing to do is to make the decision on whether to
erase the which way information or not to erase it until after the
photon passes the slits but before it hits the screen; it turns out
that if you decide to not erase the information then you don't get a
interference pattern, but if you decide to erase it then you do get a
interference pattern. And that exparament has already been performed
and yes the results are weird because the decision to erase or not to
erase the information was made long after, even billions of years
after, the photon passed the slits so you might think it would make no
difference as far as the picture on the screen is concerned, but it does.
And I think all of this is super interesting, *_but_* it is *_not_*
the experiment Deutsch proposed. And you still haven't told me what
your best guess is that Deutsch will find when he develops that all
important photographic plate; will he see interference bands or no
interference bands? I've already told you how I'd place my money.
I haven't because I'd have to re-read Deutsch's thought experiment, I
don't remember how he proposed to erase the which-way.
Brent
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/c4dcab42-aec5-4794-8cab-612827c454a4%40verizon.net.
