Time-dependent neutron interferometry: Evidence against wave packet collapse?

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  • Foundations of Physics, Vol. 15, No. 10, 1985

    Time-Dependent Neutron Interferometry: Evidence against Wave Packet Collapse?

    C. Dewdney, J A. Garuccio, 2 Ph. Gueret, 3 A. Kyprianidis, 4 and J. P. Vigier 5

    Received January 25, 1985

    [f the energy-absorbing radio-frequency spin-flipping device used in perfect crystal neutron interferometry is an intermediate measuring device, then the experimental results contradict the associated wave packet collapse and support the real existence of the de Broglie pilot waves in both arms while the neutron travels in only one.

    Recent experiments performed with perfect single crystal neutron inter- ferometers confirm the statistical predictions of the usual quantum formalism, I~) but raise again questions concerning its proper interpretation.(2)

    1. SPATIAL NEUTRON INTERFERENCE

    Consider first the basic experiment presented in Fig. 1. With ~'J = Oii = ~o and Io +I,, = const, the intensity is

    I o=2 [00I 2 (1 +cos)~) (1)

    1 European Exchange Fellow temporarily at Institut Henri Poincar6, Laboratoire de Physique Th6orique, 11, Rue P. et M. Curie, 75231 Paris Cedex 05, France.

    2 Istituto di Fisica, Universit/~ di Bari. 3 Institut de Math6matiques Pures et Appliqu6es, Universit6 P. et M. Curie 4, Place Jussieu,

    75230 Paris Cedex 05, France. 4 On leave from the University of Crete, Physics Department, Heraklion, Crete, Greece, at

    Institut Henri Poincar6, Laboratoire de Physique Th~orique, 11, Rue P. et M. Curie, 75231 Paris Cedex 05, France.

    5 Institut Henri Poincar6, Laboratoire de Physique Th~orique, 11, Rue P. et M. Curie, 75231 Paris Cedex 05, France.

    1031

    0015-9018/85/100o-1031504.50/0 1985 Plenum Publishing Corporation

    825/I5/10-3 ~

  • 1032 Dewdney et al.

    Fig. 1. Neutron interferometry scheme.

    By varying the thickness of the phase-shifting material in the beam I, the optical path difference of the beams can be altered and interference observed at the detectors as a modulated intensity given by Eq. (1). The neutrons can be continuously switched from a maximum in Io, zero in Ih to zero in Io and a maximum in lb. The neutron flux from the source is such that each neutron is detected before the next is emitted in the source.

    (a) The Copenhagen Interpretation: What can be said about these results in the Copenhagen interpretation of quantum mechanics (CIQM)? As in the two-slit experiments, the intensity modulation is interpreted in terms of the wave aspect of matter, and the individual records of the detec- tor in terms of the particle aspect. Following Bohr, (3~ any attempts to sub- divide the experiment to reveal the particle between source and detector induces a wave packet collapse, i.e., localizes the particle in one beam, and interference effects disappear. The wave and particle nature of matter are complementary aspects requiring mutually exclusive experimental arrangements for their manifestation. Since in this view the neutron is not to be conceived of as a particle before detection localizes it, questions con- cerning which beam a given neutron enters at the region of superposition cannot be formulated and the question of interpretation is summarily closed.

    (b) The Causal Stochastic Interpretation: If, contrary to the Copenhagen interpretation, we believe with Einstein (4~ and de Broglie (5) that neutrons are particles that really exist in space and time, then Rauch's statement below, ruled out in the CIQM, can be made:

  • Neutron Interferometry and Wave Packet Collapse 1033

    "At the place of superposition, every neutron has the information that there have been two equivalent paths through the interferometer, which have a certain phase difference causbN the neutron to join the beam in the forward or deviated direction. "(6)

    It is then possible to suggest physical models to explain the causation of individual events, a nonexistent option in CIQM. That such a model exists which provides a consistent causal determinate description of individual events in quantum theory may not be widely known. (7 9) In the causal stochastic interpretation of quantum mechanics (SIQM), neutrons are par- tMes and waves simultaneously, the particle traveling one path through the interferometer whilest its real wave is split and travels along both. The waves interfere in the region of superposition and give rise to a quantum potential Q = -(h2/2m)(V2R/R), with ~b = R e ;s/h) in the scalar case, which carries information concerning the whole apparatus and determines the particle trajectories according to p=VS. The changing phase relations between the waves in I and II lead to a changing quantum potential struc- ture that determines which beam each individual neutron enters according to its initial position in the wave packet. A detailed explanation of this type has been provided for the two-slit experiment and square potential phenomena, which may be easily extended to this case. (1)

    2. TIME-DEPENDENT SPIN SUPERPOSITION

    Now, according to Badurek eta/. (11) a completely different physical situation arises in the case of the time-dependent superposition of linear spin states using the radio-frequency spin-flip coil described in Fig. 2. Indeed "in that case the total energy of the neutrons is not conserved. ''(1I) The experimental arrangement can be schematically represented as in Fig. 2. The incident neutron beam containing one neutron at a time (Fig. 2) is subsequently divided into beams I and II. On beam I there acts a nuclear phase shifter represented by the action of a unitary operator e ix on 0, with X = -N2bcD, where b

  • 1034 Dewdney et al.

    MAGN.PRISt", POLARIZER HEL#'4HOLTZ COIL

    PERfECt / ~ . , . I 8o ".... _~ CRYSTAL " ' .~ . . . / - \ H-e~J.."j,- - NONOC_.HR'OMATOP [J - ~rtt . PI4ASESHIFTER~:;, , , ,

    I ~ - " " . J I oA" II \~&~C, ) ) 1

    \ ..............

    LOOP ~ ~ / I . . . . . . . . . . . . v 7_'~'zv__ t ' - - . . _ _ 1 I TO COUNTE,qS I ~- -~ ~ n-DETECTO.q l,

    (0 - BEAM) I /~

    z"

    Fig. 2. Sketch of time-dependent neutron interferometry,

    between the two spin eigenstates of the neutron within the static field. Neutrons passing through such a device (a spin flipper) reverse their initial +z polarization into the - z direction, by transferring an energy AE= 2#B 0 to the coil, while maintaining their initial momentum. (~I)

    The wave function in beam I after passing through the phase shifter is

    ~, = e" {Tz) = e" (10) (2)

    The corresponding wave function in II after the coil should be written

    +,,=e '(~e'lh) , J.z) = e'(~"/h) 9 ) (3)

    since the rf-coil is shown to be almost 100% efficient. (12) Let the wave function of the coil initially be G and finally ~b F. Then the wave function of the total system (neutron plus coil) is initially

    ~ = ~be(aO~ + b0u) (4)

    and finally

    ~y- = q~aO~ + ~fb~/ii (5)

  • Neutron lnterferometry and Wave Packet Collapse 1035

    and the condition for the observation of interference is ~b~.~q~r, that is, the state of the coil is virtually unaltered and no measurement in the usual sense takes place. Then ~P/---~i(atpi+b~ttl), the intensity I= ~7 ~vs=2, arid the polarization is given by

    15 = (COS(O3rft - - Z) , sin(o)rr t - Z), 0) (6)

    i.e., a vector that lies entirely in the xy plane. These are the well-known results of Badurek et al.,(i~) which are experimentally verified.

    (a) The Copenhagen Interpretation: Now how are these results encompassed within the CIQM? The observation of interference implies a wave aspect, hence the particle cannot even be said to exist during the time be, tween emission and absorption in the detector. A particle cannot exist in one beam (or pass through one slit in the double-slit experiment) and take part in interference. However, in order to describe the functioning of the coil, we must use the complementary localized particle aspect. The energy transfer that takes place, giving rise to the change of 0~, is described by Rauch in terms of photon exchange between the neutron and the field in the coil. Thus the neutron is conceived of as a particle in one beam, to explain energy transfer, and simultaneously as a wave existing in both, to explain interference. The complementarity of wave and particle descriptions is broken; both aspects must be used simultaneously in one and the same experimental arrangement. The complementary description is thus incom- plete, or can energy be exchanged with a probability wave?

    (b) The Causal Stochastic' Interpretation: In the SIQM we use the Feynman Gell-Mann equation for spin-l/2 particles as a second-order stochastic equation for the collective excitations of the assumed underlying covariant random vacuum, Dirac's aether. (13) A spin-l/2 particle is regar- ded as a localized entity surrounded by a real spinor wave due to pertur- bation of the vacuum. While the particle really travels one way (path I or II), the spinor wave propagates in both paths. In path II the interaction with the rf spin flipper inverts the spinor symmetry of the wave, while in path I the initial state is maintained. What happens in the interference region can now be represented by the action of a spin-dependent quantum potential Q and/or quantum torque ~, which can be shown to produce a time-dependent spinor symmetry in the xy plane. The particle traveling, for example, in path I is constrained by the spinor symmetry in the inter- ference region and its + z spin is twisted into the xy plane by the quantum torque. If it travels along path II, it suffers an additional spin inversion due to the rfcoil, furnishing this energy to the coil, while in the intersection area its - z spin is twisted again in to the xy plane. Consequently, a coherent picture is established which accounts for both particle and wave

  • 1036 Dewdney et al.

    aspects of the experimental facts. (14) A neutron emerging from the pile has energy E corresponding to its spin-up state in the guide field. In the region of superposition it has energy E- (AE/2)(AE = 2#Bo) since the spin lies in the xy plane. This represents a gain or loss of energy, depending on whether the neutron traveled along path II or I, respectively, and is accounted for by the action of the spin-dependent quantum potential. Of course, in the statistical average (including the coil's gain of energy), the energy gains and losses cancel since the relative frequencies of neutrons in both paths are the same. Consequently a time ensemble of neutrons satisfies, on the average, energy conservation, but a single neutron clearly does not, a fact that in ordinary quantum theory can be accounted for by means of the energy uncertainty c~E, which, in the present case, has to exceed the Zeeman energy splitting, i.e., AE= 2#B o.

    3. ON QUANTUM MEASUREMENT THEORY

    Beyond this, the question arises whether the functioning of the coil can be considered to be a measurement. Rauch (6) suggests that

    "This experiment has shown explicitly that the interference properties of beams can be preserved even when a real energy exchange occurs, which is intuitively a measuring process. ''(6)

    Now clearly if the functioning of the coil is a measurement in the quantum mechanical sense, then ~bi would be orthogonal to ~b i and inter- ference would disappear--described in CIQM as wave packet collapse. The reasons for considering such an interaction as a quantum measurement process are the following: First, there is an energy exchange taking place unidirectionally from the passing neutron to the rf circuit, since the energy of the initial state differs by dE from that of the final state. This energy exchange, if decoded and extracted from the resonator circuit, could reveal the passage of the neutron. Secondly, this energy transfer in the form of a photon transition establishes a one-to-one correspondence between the change of the neutron's spin state from spin up to spin down.

    Of course, counter arguments exist as well, and these can be due to objective ambiguities of the coupling neutron-rf resonator or due to well- known prejudices of the standard (Copenhagen) interpretation of quantum mechanics. One of the latter is the well-known "no-go theorem," which for- bids simultaneous detection of "particle" properties (such as energy trans- fer) and "wave" properties (such as interference phenomena); since inter- ference has been observed, no information about a neutron path should be possible. A measurement in the orthodox point of view projects the state

  • Neutron lnterferometry and Wave Packet Collapse 1037

    vector 0 of a system S onto an eigenvector la) of the operator .~ corresponding to an observable A. As a consequence, the interference effects due to superposition of the state vector vanish. But, apart from this, a serious argument exists against the possibility of detecting a single photon transfer due to the macroscopic character of the rf resonance cir- cuit. This objection depends both .on a theoretical and a practical reasoning, consisting mainly in the theoretical limitation due to the uncer- tainty principle and in the technical feasibility of a single-photon detection.

    Let us consider first the Copenhagen "no-go theorem." We wish to argue on this point along the lines of Cini's theory of measurement without wave packet collapse that the ad hoc projection postulate added to the QM formalism is not at all necessary for understanding the usual quantum measurement predictions. In fact, Cini has proved (15) that the pseudo- collapse is merely a feature of a macroscopic device with large quantum numbers that establish the equivalence between a pure state density matrix of the system "microobject + apparaturs" and the statistical mixture that cancels the interference term. What appears in ordinary quantum measurement as a collapse is in fact due to the coupling of the microsystem with a macrodevice which makes the (always existing) interference term vanishingly small [i.e., ~bi and ~b F of Eq. (4), (5) become almost orthogonal]. In fact, in our case, if we stick to this well-founded represen- tation that always works with pure states, we immediately realize that the situation is completely different. The passage of a neutron only creates a single photon transfer that insignificantly changes the quantum number of the field, and thus the induced change of the state of the measuring instrument is restricted to small quantum numbers (~bi~r). In this case, according to Cini, the interference terms remain relevant and no collapse occurs .

    The point to clarify now is whether the neutron/coil interaction can be described as a "good" measuring device, whether one can really distinguish tlhe old from the new "pointer" position (i from Cs), and, in the last instance, if this interaction is a measurement. This question is of a qualitatively different nature than the no-go postulate of the Copenhagen School, since the latter simply postulates the incommensurability of a "pro- jection" or "collapse" measurement with an existence of a pure state. Here we are only dealing with the overpassing of a technical obstacle in...

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