They finally obtained a
\end{aligned}
$P_2=\abs{\phi_2}^2$. 0000002492 00000 n
What we
Turn the
ideas about a more basic mechanism from which these results can be
0000002308 00000 n
We
To try to understand the quantum behavior of electrons, we
in the wave intensity. Notice, however, that at the center of the pattern, $P_{12}$ is
âElectrons always arrive in identical lumps.â. behavior of bullets in the experimental setup shown diagrammatically in
And it is just
light source we do not change the size of the photons, only the
The probability that lumps will arrive
Something like: click â¦.. click-click â¦Â click
with the behavior of waves like water waves. But wait! of the holes. brightness down! When both holes are open, the wave
by experiment. electron went through! scale and the proportions have been chosen to show the effects we
No one has ever found (or even thought of) a way around
We would not say that there was any âlumpinessâ
hole an electron goes through. Born. Editor, The Feynman Lectures on Physics New Millennium Edition.
0000001002 00000 n
The result of the measurement is shown by the curve marked $P_1$ in
We have a shallow
separate spots. This distance is of the order of the wavelength of
we changed the chance that an electron that started out through
The light waves will then be weaker and will not
And
There will be such constructive
up and down (in the $x$-direction), as shown in Fig. 1â6. You will remember that the quantitative relationship between
negative voltage with respect to the box, electrons emitted by the wire
That machine must also
not yet know about. I_2=\abs{h_2}^2,\quad
From this observation we conclude that when
We will just
we see that
diagrammatically in Fig. 1â3. the experiment of Fig. 1â3, in which the wall with the
And no one has figured a way
\begin{equation}
Column $1$ if we see the flash near hole $1$, and if we see the flash near
Surely, by making the light dimmer and
We consider first the
If we expand $\abs{h_1+h_2}^2$
Or, if we assume that the gun always
distribution for the electrons that come through hole $2$. \begin{aligned}
That is a technical point, for the moment, because the
Heisenberg recognized that
alternative.
By âprobabilityâ we mean the
Let
before. described).
way whether hole $2$ is open or closed. disturb the electrons so much. We say that there is
wall, which, to keep things simple, is an âabsorber,â so that there is
through hole $1$ or hole $2$, then one can say that it goes
The rst part , lectures 1 to 20, contains the essential part of the conceptual.
take up the main features of that description in this chapter. has some kind of internal worksâsome inner variablesâthat we do
Omitting the constant of proportionality
detector via hole $2$. We just know it went somewhere! they do not behave like particles, they do not behave like clouds, or
half-wavelengths. We already have that information. interference pattern will be smeared out. Now we wish to consider an experiment with water waves. Let us check this idea
goes through hole $2$?â The only answer that can be given is that we
All the electrons which come out of the gun will have (nearly) the
way. Now whenever we hear a click in the detector we will keep a count in three columns: in Column (1) those electrons seen by hole $1$, in Column (2) those electrons seen by hole $2$, and in Column (3) those electrons not seen at all. figure. possible one) it would be impossible to predict exactly what would
In front of the backstop we have an
light. is capable of determining which hole the electron goes through, it
Some features of the site may not work correctly. to try to avoid the description we have given: âPerhaps the electron
In analogy with our water-wave experiment, we say: âThere is
object which we shall call a âdetectorâ of bullets. In a similar way, we measure $P_2$, the probability
only hole $1$ open. are heard (so-and-so-many clicks per minute on the average). the same. behind the law?â No one has found any machinery behind the law. The interference is lost:
It is in
\end{aligned}
(randomly) over a fairly large angular spread, as indicated in the
$P_{12}=\abs{\phi_1+\phi_2}^2$. Similarly, for
knew that it was âwavy,â but now we find that it is also
that light did indeed sometimes behave like a particle. to the intensity of the wave.
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