Yann LeCunShared publicly - Aug 24, 2013

This gives an entirely new meaning to nondestructive measurement.John Baez originally shared: How To Know What Would Have Happened, But Didn't

Suppose you have a bunch of bombs. Some have a sensor that will absorb a photon you shine on it, and make the bomb explode! Others have a broken sensor, that won't interact with the photon at all.

Can you choose some working bombs? You can tell if a bomb works by shining a photon on it... but if it works, it blows up - so it doesn't work anymore!

So, it sounds impossible. But with quantum mechanics you can do it. You can find some bombs that would have exploded if you had shone photons at them!

Here's how. Put a light that emits a single photon at A. Have the photon hit the half-silvered mirror at lower left, so it has a 50% chance of going through to the right, and a 50% chance of reflecting and going up. But in quantum mechanics, it sort of does both!

Put a bomb at B. Recombine the photon's paths using two more mirrors. Have the two paths meet at a second half-silvered mirror at upper right. You can make it so that if the bomb doesn't work, the photon interferes with itself and definitely goes to C, not D.

But if the bomb works, it absorbs the photon and explodes unless the photon takes the top route... in which case, when it hits the second half-silvered mirror, it has a 50% chance of going to C and a 50% chance of going to D.

So:

• If the bomb doesn't work, the photon has a 100% chance of going toC.

• If the bomb works, there's a 50% chance that it absorbs the photon and explodes. There's also a 50% chance that the bomb does not explode - and then the photon is equally likely to go to either C or D. So, the photon has a 25% chance of reaching C and a 25% chance of reaching D.

So: if you see a photon at D, you know you have a working bomb... but the bomb has not exploded!

This is the Elitzur–Vaidman bomb-testing method. It was invented by Avshalom Elitzur and Lev Vaidman in 1993. One year later, physicists actually did an experiment to show this idea works... but alas, not using actual bombs!

For details, read these:

• A. Elitzur and L. Vaidman, Quantum mechanical interaction-free measurements, Found. Phys. 23 (1993), 987-997.http://arxiv.org/abs/hep-th/9305002

• Paul G. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. Kasevich, Experimental realization of "interaction-free" measurements,http://www.univie.ac.at/qfp/publications3/pdffiles/1994-08.pdf.

The picture is from the Wikipedia article:

http://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester

This gives an entirely new meaning to nondestructive measurement.John Baez originally shared: How To Know What Would Have Happened, But Didn't

Suppose you have a bunch of bombs. Some have a sensor that will absorb a photon you shine on it, and make the bomb explode! Others have a broken sensor, that won't interact with the photon at all.

Can you choose some working bombs? You can tell if a bomb works by shining a photon on it... but if it works, it blows up - so it doesn't work anymore!

So, it sounds impossible. But with quantum mechanics you can do it. You can find some bombs that would have exploded if you had shone photons at them!

Here's how. Put a light that emits a single photon at A. Have the photon hit the half-silvered mirror at lower left, so it has a 50% chance of going through to the right, and a 50% chance of reflecting and going up. But in quantum mechanics, it sort of does both!

Put a bomb at B. Recombine the photon's paths using two more mirrors. Have the two paths meet at a second half-silvered mirror at upper right. You can make it so that if the bomb doesn't work, the photon interferes with itself and definitely goes to C, not D.

But if the bomb works, it absorbs the photon and explodes unless the photon takes the top route... in which case, when it hits the second half-silvered mirror, it has a 50% chance of going to C and a 50% chance of going to D.

So:

• If the bomb doesn't work, the photon has a 100% chance of going toC.

• If the bomb works, there's a 50% chance that it absorbs the photon and explodes. There's also a 50% chance that the bomb does not explode - and then the photon is equally likely to go to either C or D. So, the photon has a 25% chance of reaching C and a 25% chance of reaching D.

So: if you see a photon at D, you know you have a working bomb... but the bomb has not exploded!

This is the Elitzur–Vaidman bomb-testing method. It was invented by Avshalom Elitzur and Lev Vaidman in 1993. One year later, physicists actually did an experiment to show this idea works... but alas, not using actual bombs!

For details, read these:

• A. Elitzur and L. Vaidman, Quantum mechanical interaction-free measurements, Found. Phys. 23 (1993), 987-997.http://arxiv.org/abs/hep-th/9305002

• Paul G. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. Kasevich, Experimental realization of "interaction-free" measurements,http://www.univie.ac.at/qfp/publications3/pdffiles/1994-08.pdf.

The picture is from the Wikipedia article:

http://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester

- 2013-09-15 07:36:15Z
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After being emitted, the photon 'probability wave' will both pass through the 1st half-silvered mirror (take the lower-route) and ... Read morebe reflected (take the upper-route).

If the bomb is a dud:

The bomb will not absorb a photon, and so the wave continues along the lower route to the second half silvered mirror (where it will encounter the upper wave and cause self-interference).

The system reduces to the basic Mach–Zehnder apparatus with no sample bomb, in which constructive interference occurs along the path horizontally exiting towards (D) and destructive interference occurs along the path vertically exiting towards (C).

Therefore, the detector at (D) will detect a photon, and the detector at (C) will not.

If the bomb is usable:

Upon meeting the observer (the bomb), the wave function collapses and the photon must be either on the lower route or on the upper route, but not both.

If the photon is measured on the lower route:

Because the bomb is usable, the photon is absorbed and triggers the bomb which explodes.

If the photon is measured on the upper route:

It will not encounter the bomb - but since the lower route can not have been taken, there will be no interference effect at the 2nd half-silvered mirror.

The photon on the upper route now both (i) passes through the 2nd half-silvered mirror and (ii) is reflected.

Upon meeting further observers (detector C and D), the wave function collapses again and the photon must be either at detector C or at detector D, but not both.

Thus we can state that if any photons are detected at (C), there must have been a working detector at (B) – the bomb position.

With this process, 25% of the usable bombs can be identified as usable without being consumed.[1] whilst 50% of the usable bombs will be consumed and 25% remain 'unknown'. By repeating the process with the 'unknowns', the ratio of surviving, identified, usable bombs approaches 33% of the initial population of usable bombs. See Experiments section below for a modified experiment that can identify the usable bombs with a yield rate approaching 100%.