In physics, Mermin's device[1] [2] or Mermin's machine[3] is a thought experiment intended to illustrate the non-classical features of nature without making a direct reference to quantum mechanics. The challenge is to reproduce the results of the thought experiment in terms of classical physics. The input of the experiment are particles, starting from a common origin, that reach detectors of a device that are independent from each other, the output are the lights of the device that turn on following a specific set of statistics depending on the configuration of the device.
The results of the thought experiment are constructed in such a way to reproduce the result of a Bell test using quantum entangled particles, which demonstrate how quantum mechanics cannot be explained using a local hidden variable theory. In this way Mermin's device is a pedagogical tool to introduce the unconventional features of quantum mechanics to a larger public.
The original version with two particles and three settings per detector, was first devised in a paper called "Bringing home the atomic world: Quantum mysteries for anybody" authored by the physicist N. David Mermin in 1981.[4] Richard Feynman told Mermin that it was "One of the most beautiful papers in physics".[5] Mermin later described this accolade as "the finest reward of my entire career in physics". Ed Purcell shared Mermin's article with Willard Van Orman Quine, who then asked Mermin to write a version intended for philosophers, which he then produced.[6] [7] Mermin also published a second version of the thought experiment in 1990 based on the GHZ experiment, with three particles and detectors with only two configurations.[8] In 1993, Lucien Hardy devised a paradox that can be made into a Mermin-device-type thought experiment with two detectors and two settings.[9] [10]
In Mermin's original thought experiment, he considers a device consisting of three parts: two detectors A and B, and a source C. The source emits two particles whenever a button is pushed, one particle reaches detector A and the other reaches detector B. The three parts A, B and C are isolated from each other (no connecting pipes, no wires, no antennas) in such a way that the detectors are not signaled when the button of the source has been pushed nor when the other detector has received a particle.
Each detector (A and B) has a switch with three configurations labeled (1,2 and 3) and a red and a green light bulb. Either the green or the red light will turn on (never both) when a particle enters the device after a given period of time. The light bulbs only emit light in the direction of the observer working on the device.
Additional barriers or instrument can be put in place to check that there is no interference between the three parts (A,B,C), as the parts should remain as independent as possible. Only allowing for a single particle to go from C to A and a single particle from C to B, and nothing else between A and B (no vibrations, no electromagnetic radiation).
The experiment runs in the following way. The button of the source C is pushed, particles take some time to travel to the detectors and the detectors flash a light with a color determined by the switch configuration. There are nine total possible configuration of the switches (three for A, three for B).
The switches can be changed at any moment during the experiment, even if the particles are still traveling to reach the detectors, but not after the detectors flash a light. The distance between the detectors can be changed so that the detectors flash a light at the same time or at different times. If detector A is set to flash a light first, the configuration of the switch of detector B can be changed after A has already flashed (similarly if B set to flash first, the settings of A can be change before A flashes).
The results of the experiment are given in this table in percentages:
| 1 | 1 | 100 | 0 |
| 2 | 2 | ||
| 3 | 3 | ||
| 1 | 2 | 25 | 75 |
| 1 | 3 | ||
| 2 | 1 | ||
| 2 | 3 | ||
| 3 | 1 | ||
| 3 | 2 |
In order to make sense of the data using classical mechanics, one can consider the existence of three variables per particle that are measured by the detectors and follow the percentages above. Particle that goes into detector A has variables
(a1,a2,a3)
(b1,b2,b3)
We have 8 possible states:
| (G,G,G) | (G,G,G) | |
| (G,G,R) | (G,G,R) | |
| (G,R,G) | (G,R,G) | |
| (G,R,R) | (G,R,R) | |
| (R,G,G) | (R,G,G) | |
| (R,G,R) | (R,G,R) | |
| (R,R,G) | (R,R,G) | |
| (R,R,R) | (R,R,R) |
(b1,b2,b3)=(a1,a2,a3)
For any given configuration, if the detector settings were chosen randomly, when the settings of the devices are different (12,13,21,23,31,32), the color of their lights would agree 100% of the time for the states (GGG) and (RRR) and for the other states the results would agree 1/3 of the time.
Thus we reach an impossibility: there is no possible distribution of these states that would allow for the system to flash the same colors 1/4 of the time when the settings are not the same. Thereby, it is not possible to reproduce the results provided in Table 1.
Table 1 can be reproduced using quantum mechanics using quantum entanglement. Mermin reveals a possible construction of his device based on David Bohm's version of the Einstein–Podolsky–Rosen paradox.
One can set two spin-1/2 particles in the maximally entangled singlet Bell state:
| ||||
| |\Psi |
to leave the experiment, where
|\uparrow\downarrow\rangle
|\downarrow\uparrow\rangle
Quantum mechanics predicts a probability of measuring opposite spin projections given by
P(\theta)=\cos2(\theta/2)
where
\theta
\theta=0
\theta=\pm120\circ