encyclopedia

Bohr-Einstein debates

The Bohr-Einstein debates on foundational aspects on quantum mechanics happened during the Solvay conferences . They consisted of analyses of thought experiments. Put simply, they were an attempt by Einstein to explain away the aspects of Bohr's interpretation of Quantum Mechanics that he disliked. Bohr attempted (and, most scholars agree, largely succeeded) to rebut these challenges. The Bohr-Einstein debates remain among the most important in the history of the philosophy of physics, and are certainly the most influential of their kind in the Twentieth Century.

On the side of Niels Bohr, we have the Copenhagen interpretation. This can be described as syncretic, with basic concepts the collapse of the wavefunction, nondeterminism given by the Born probability, and the correspondence principle. On the side of Albert Einstein, we have realism, determinism, causality, and locality.

Bohr's form of correspondence principle states that when doing experiments with quantum states, the results of experiments can only be described in classical terms (Heisenberg cut ); while at the same time, the experimental apparatus obey the uncertainty principles. He also invoked: complementarity, which states that an object is both a wave and a particle but yet that any particular experiment can only detect one of the two aspects; the uncertainty principle; positivism in that the results of experiments are all there is; the claim that any experiment, no matter how cleverly designed is doomed to affect the state of the system being observed unpredictably; action at a distance; and nonlocality.

Contents

1 Diffraction (the single slit experiment)

2 Interference (the double slit experiment)

3 Photon in a box

4 EPR paradox

5 Modern critique of Bohr's analysis

Diffraction (the single slit experiment)

Suppose a wave-particle (e.g. photon, electron) passes through an opaque plane with a tiny hole with a size comparable to its wavelength and there is a screen placed behind the hole measuring the position of the wave-particle (e.g. photographic plate). The wavefunction spreads out after passing through the hole and so, the final position of the particle is indeterminate. Supposedly, if the wavefunction collapses at a given point, it would have to be instantaneous everywhere because otherwise, we might have the bizarre situation where the particle is detected at one point and then simultaneously (lightlike separation) the same partice is detected at another point simply because the wave function at the other point still isn't in causal contact with the collapse at the other point!

Bohr's point: Complementarity: Diffraction gives the explanation in the wave picture. But he claims there is also a particle explanation. The particle is deflected unpredictably by the hole, in effect gaining a transverse momentum. Why? Because the hole measures the transverse position of the particle and we have the energy-momentum uncertainty principle.

Bohr's modification: Replace the hole by a shutter which only remains open for a brief period of time. In the wave picture, working out the wave partial differential equations, we find the diffracted wave has a spread in frequencies. In the particle picture? The uncertainty principle plus the relation between energy and frequency. Why? Because the shutter moves and so, if you works out the dynamics using the conservation of momentum and energy, there will be a significant energy transfer.

Einstein's point: Using the conservation of momentum and energy, can we measure the momentum and energy transfer imparted to the opaque plane/shutter system and use that to predict in advance (the screen can be placed arbitrarily far from the opaque plane, giving us as much time as we need to delay the final measurement) we the particle will be detected?

Bohr's point: The opaque plane/shutter has a finite mass. This means the uncertainty in the position of the hole multiplied by the uncertainty in its momentum is of the order of Plank's constant. So this can't be done. Also, the uncertainty of the shutter time and the energy transfer.

Interference (the double slit experiment)

Bohr: If we know which slit the particle went through, we won't see an interference pattern because measuring which slit the particle went through picks out its particle aspects. If we don't know which slit the particle went though, then the wave aspects come to the fore and we observe an interference pattern, which means the particle passes through BOTH slits. (This will still happen if only one particle passes through the double slits at a time).

Einstein: We know the initial position of the particle and because of the screen, we also know the final position of the particle. So, since the particle could only have passed through one of the two holes, using dynamics, we can figure out how much energy/momentum is transferred to the opaque plane containing the double slits, we can figure out which trajectory (i.e. which hole) the particle goes through AT THE SAME TIME as we are getting a statistical interference pattern.

Bohr: More case by case analyses of concrete implementations of Einstein's idea

Photon in a box

Einstein: Suppose we have a box with a shutter with a couple of photons in it. Let the shutter open for a brief period time, enough for a photon to escape. So, we know when the photon left to an accuracy of Δt. But can't we also measure the energy of the photon with an arbitrary accuracy by comparing the mass of the box both before and after the photon left?

Bohr: Even though Einstein referred to the mass, we need a way to measure it. So let's assume we are in a gravitational field and weigh the box. (Aren't there other ways of measuring mass? Bohr claims that any other method would "miraculously" involve some saving explanation, just of the sort of his explanation for his particular implementation of it) But how are we going to measure its weight? Use a spring scale balance and find out what conterweight is necessary to bring the box back to its original position. But according to the uncertainty principle, the momentum of the box will be uncertain which means the more accurate we wish the mass measurement to be, the longer the period of time we have to spend measuring it. But according to general relativity, clocks run at different rates at different altitudes and if we're not sure of the position of the box, there would be an uncertainty in the proper time of the box as well.

EPR paradox

This is not really a "paradox". See EPR paradox for the main article.