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State reduction due to a fluorescent screen
Volume 141, number 3,4
PHYSICS LETTERS A
30 October 1989
STATE REDUCTION DUE TO A FLUORESCENT SCREEN Euan SQUIRES Centrefor Particle Theory, Department of Mathematical Sciences, University ofDurham, Science Laboratories, South Road, Durham, Dill 3LE, UK Received 28 August 1989; accepted for publication 8 September 1989 Communicated by J.P. Vigier
A recent claim that the GRW state vector reduction will not occur whenparticles aredetected at a fluorescent screen is disputed.
In a recent article Albert and Vaidman [11 have claimed that wavefunction collapse to a (near) position eigenstate, as in the theory of Ghirardi et a!. [21, is not adequate to describe all measurements. Whilst this might be true, the example they give is inadequate to provide evidence for such a claim. Albert and Vaidman consider the usual Stern— Gerlach experiment for measuring an electron’s spin along some axis. According to whether this is + or the electron is deflected up or down, and so strikes a fluorescent screen at point A or point B, thereby exciting atomic states in the neighbourhood of one or the other of these positions. They point out that the two components of the wavefunction give rise to different energy levels of the atoms in the two neighbourhoods, but that there is no significant spatial separation between one component and the other. At this stage they are surely correct and hence, in a GRW type of model, no measurement has taken place. The next thing that happens is that the excited atoms decay by emitting photons. Albert and Vaidman assert, again correctly, that photons emitted from the region of A and photons emitted from the region of B (one set emitted in one component of the wavefunction and one in the other) occupy significantly different regions of space only for a very short time (~AB/c), certainly not for a sufficient time to permit the GRW collapse mechanism to operate. This argument, however, is surely incorrect, or at least irrelevant. The reason is that the photons emitted from —
region A or region B are, from the point of view of GRW, different photons. In fact, of course, the GRW mechanism only applies to non-relativistic quantum theory (see, however, ref. [31)where particle creation is impossible. Hence the only reasonable way to describe the above experiment is to assume that the photons are already present in the atoms at A and B and that their detection occurs when they are knocked out by the electron. Then clearly there are macroscopic separations in both the “A-photons” and the “B-photons” between the two components of the wavefunction, so the GRW mechanism will indeed cause the wavefunction to collapse. We can see all this more easily if we note that the measurement can be made even if the screen is only present at A (say). The presence of a flash from A would indicate + spin and its absence spin. Clearly in the former component the photons are moving away from the region ofA, whereas in the latterthey are not. Any reasonable generalisation of the GRW mechanism would su~estthat this is a situation in which collapse would occur. —
References [1] D.Z. Albert and L. Vaidman, Phys. Lett. A 139 (1989) 1. [2] G.C. Ghirardi, A. Rimini and T. Weber, Phys. Rev. D 34 (1986) 470. [3] P. Pearle, in: Proc. Erice School “62 years of uncertainty” (1989).
0375-960l/89/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
95
PHYSICS LETTERS A
30 October 1989
STATE REDUCTION DUE TO A FLUORESCENT SCREEN Euan SQUIRES Centrefor Particle Theory, Department of Mathematical Sciences, University ofDurham, Science Laboratories, South Road, Durham, Dill 3LE, UK Received 28 August 1989; accepted for publication 8 September 1989 Communicated by J.P. Vigier
A recent claim that the GRW state vector reduction will not occur whenparticles aredetected at a fluorescent screen is disputed.
In a recent article Albert and Vaidman [11 have claimed that wavefunction collapse to a (near) position eigenstate, as in the theory of Ghirardi et a!. [21, is not adequate to describe all measurements. Whilst this might be true, the example they give is inadequate to provide evidence for such a claim. Albert and Vaidman consider the usual Stern— Gerlach experiment for measuring an electron’s spin along some axis. According to whether this is + or the electron is deflected up or down, and so strikes a fluorescent screen at point A or point B, thereby exciting atomic states in the neighbourhood of one or the other of these positions. They point out that the two components of the wavefunction give rise to different energy levels of the atoms in the two neighbourhoods, but that there is no significant spatial separation between one component and the other. At this stage they are surely correct and hence, in a GRW type of model, no measurement has taken place. The next thing that happens is that the excited atoms decay by emitting photons. Albert and Vaidman assert, again correctly, that photons emitted from the region of A and photons emitted from the region of B (one set emitted in one component of the wavefunction and one in the other) occupy significantly different regions of space only for a very short time (~AB/c), certainly not for a sufficient time to permit the GRW collapse mechanism to operate. This argument, however, is surely incorrect, or at least irrelevant. The reason is that the photons emitted from —
region A or region B are, from the point of view of GRW, different photons. In fact, of course, the GRW mechanism only applies to non-relativistic quantum theory (see, however, ref. [31)where particle creation is impossible. Hence the only reasonable way to describe the above experiment is to assume that the photons are already present in the atoms at A and B and that their detection occurs when they are knocked out by the electron. Then clearly there are macroscopic separations in both the “A-photons” and the “B-photons” between the two components of the wavefunction, so the GRW mechanism will indeed cause the wavefunction to collapse. We can see all this more easily if we note that the measurement can be made even if the screen is only present at A (say). The presence of a flash from A would indicate + spin and its absence spin. Clearly in the former component the photons are moving away from the region ofA, whereas in the latterthey are not. Any reasonable generalisation of the GRW mechanism would su~estthat this is a situation in which collapse would occur. —
References [1] D.Z. Albert and L. Vaidman, Phys. Lett. A 139 (1989) 1. [2] G.C. Ghirardi, A. Rimini and T. Weber, Phys. Rev. D 34 (1986) 470. [3] P. Pearle, in: Proc. Erice School “62 years of uncertainty” (1989).
0375-960l/89/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
95