Let’s say I write a paper logically showing why the fragments of a detonating nuclear bomb cannot exceed the speed of light. Would that be interesting? Perhaps the nuclear bomb aspect might make the paper a little sexier, but clearly the paper wouldn’t add anything new to our understanding of special relativity (SR). Nobody who understood SR would be surprised by the paper. In the unlikely event that I managed to get the paper published, nobody would cite it, right? And anyone who did cite it as a “surprising” result clearly doesn’t understand SR. Right? Having said that...

Quantum mechanics is all about one thing: negative probabilities. Everything about it, particularly why it’s weird, can be summarized in the following very simple point about double-slit interference experiments. It was found, empirically, that when we send a certain kind of stuff (“particles,” such as photons or electrons) through a very narrow slit in a plate, and we detect them on a screen that is parallel to and far away from the plate (called the far-field approximation), we find that individual particles are detected, and if we detect enough of them, their distribution forms what is called the Fraunhofer diffraction approximation:

(Please ignore the axis units.) In the above example, the probability of
detecting a particle at, for example, location A is relatively high. It was also found, empirically, that if we
redo the experiment using *two* closely-spaced narrow slits (say, a left slit
and a right slit), we find that the detected particles form what is called an
interference pattern:

Notice that the interference pattern seems like it could fit inside the diffraction pattern shown earlier; we call this the diffraction envelope. In the above example, the distance between the slits is about four times the slit width, and the greater this ratio, the narrower the distance between peaks inside the diffraction envelope. Notice also that the likelihood of detecting a particle at location A is now zero.

That’s right. If
only *one* slit had been open, the probability of detecting a particle at
this point would have been nonzero. So
how is it that by *adding* another slit – by adding another possible path
through which a particle could reach location A – we *decrease* its
likelihood to reach location A? The
answer, mathematically, is that by adding probability amplitudes of waves prior
to taking their magnitude, terms that are out of phase can cancel each other,
resulting in a negative probability. The
answer, conceptually, is that the “particle” isn’t really a particle until it
is actually detected. It is only by
assuming that there is a particle that traversed *either* the left slit or
the right slit that we run into trouble.

And that’s it. That’s the very essence of quantum mechanics.

Now, let’s say that you’re about to do a double-slit interference experiment on electrons. Just before you start, you have to use the bathroom so you put your lab partner in charge. When you return, your lab partner says, “I was messing around with the double-slit plate and a foreign object – maybe a speck of dust – might have gotten stuck in the right slit. But the left slit is fine.” You go ahead with the experiment and send a single electron through, which you happen to detect at location A. What does this tell you?

It tells you that an object *must be in the right slit*,
because if they were both fully open, then interference would have prevented
the detection of the electron at location A on the screen. It also tells you that because the electron
was in fact detected on the screen, it was not absorbed (or scattered) by the object
in the right slit. In that sense, you
have managed to figure out that an object is in the right slit without actually
hitting the object with an electron.

There is absolutely nothing interesting or surprising
about the above point. In other words,
once you’ve accepted that quantum mechanics allows negative probabilities, then
of course you can set up a quantum mechanical interference experiment in which
the detection of a particle in a particular place (or by a particular detector)
renders information about the presence or absence of another object that
obviously did *not* absorb or scatter that particle.

In 1993, a famous paper was published in which the above example was characterized as an “interaction-free measurement.” (The Wikipedia entry on it is terribly written but at least gives the general idea.) It described what came to be known as the Elitzur-Vaidman bomb tester, in which a bomb would go off if its sensor absorbs a single photon, but defective sensors (of defective bombs) would allow photons to pass through unaffected. The general idea is nothing more than what I described above – you can set up the experiment so that detection of a photon in a particular place (such as location A) tells you that the sensor/bomb is operational even though the sensor did not absorb the photon.

The whole “bomb detection” notion was just a way to make
the paper a little bit sexier but didn’t add anything to our understanding of
quantum mechanics. To be fair, the paper
wasn’t completely useless... it did explain how to increase the efficiency of
detection to 50%. (A paper
published in 1995 showed how to push the efficiency much higher.) In my example above, the likelihood of
detecting an electron at location A is of course very low, yielding a very low
efficiency, but the fact that it is *nonzero* is what clearly demonstrates
that an object can be “measured” in the right slit without it absorbing or
scattering the electron.

*And there is nothing interesting or surprising
about that fact over and above the fact that quantum mechanics allows negative
probabilities. *

So why did I write this post about a 1993 paper whose conclusion should have been obvious to anyone who understood quantum mechanics? Because it has been cited over 800 times by publications, many of which continue to characterize “interaction-free measurement” as some kind of inexplicable paradox within quantum mechanics. What might that tell us about the credibility of those papers or their authors as experts on quantum mechanics?

Part of the confusion is the incorrect notion that an
“interaction” only occurs if the object being detected (bomb sensor, speck of
dust, etc.) actually absorbs or scatters a particle. Quantum mechanical waves are *constantly*
interacting with other objects. In the
double-slit interference experiment above, the waves emanating from only the
left slit (when the right slit is clogged with a dust speck) are different from
waves that would emanate from *both* the left and right slits, which is
why the screen detection distributions differ.
Therefore, the electron wave *did* interact with the speck of dust
in the right slit even if the entirety of the electron wave ultimately collapses
onto the screen and not the speck of dust.
In other words, to say that the electron didn’t interact with the right
slit presupposes that the electron is a particle, but it does not assume a
particle form until it is detected! The
entire misnomer of “interaction-free measurement” assumes that only “particles”
can interact, but photons and electrons do not take on particle-like qualities
until they are measured! (Specifically,
the particle- and wave-like characteristics of an object are complementary.)

Some of this confusion is clarified by Vaidman himself
(such as here)
and by other papers (such as this). I am not criticizing the discussion. I am simply pointing out that
“interaction-free measurements” should never have been surprising in the first
place.

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