Beamsplitting Interference phenomena are certainly among the most exciting phenomena in the whole of physics. In the following we will concentrate mainly on interference of weak fields; i.e. the beams contain, on average, only a few photons. The principle of classical interference is as follows: a light beam is split by an optical element, for example by a semitransparent mirror or a screen with several very small apertures, into two or more partial beams. These beams will take different paths and are then reunited and form interference patterns. The first step, the splitting of the beam into partial beams, plays a decisive role; light beams coming from different sources (or from different spatial areas of the same source) do not interfere with each other! We start our discussion of interference with an analysis of the action of a beamsplitter. To form a realistic idea of this device, let us imagine a semitransparent mirror. (Our considerations apply equally well to a screen with two apertures. We could also generalize to cases of unbalanced mirrors, with reflectivity different from 1/2, or screens with apertures of different size.) The classical wave picture can describe interference phenomena without any great effort: the incoming beam is split into the reflected and the transmitted partial wave, and each of these waves contains half of the energy. The process of splitting becomes conceptually difficult only when we think of the beam as consisting of spatially localized energy packets, or photons.
Recent experiments have shown that fullerene and fluorofullerene molecules can produce interference patterns. These molecules have both rotational and vibrational degrees of freedom. This leads one to ask whether these internal motions can play a role in degrading the interference pattern. We study this by means of a simple model. Our molecule consists of two masses a fixed distance apart. It scatters from a potential with two or several peaks, thereby mimicking two or several slit interference. We find that in some parameter regimes the entanglement between the internal states and the translational degrees of freedom produced by the potential can decrease the visibility of the interference pattern. In particular, different internal states correspond to different outgoing wave vectors, so that if several internal states are excited, the total interference pattern will be the sum of a number of patterns, each with a different periodicity. The overall pattern is consequently smeared out. In the case of two different peaks, the scattering from the different peaks will excite different internal states so that the path the molecule takes becomes entangled with its internal state. This will also lead to degradation of the interference pattern. How these mechanisms might lead to the emergence of classical behavior is discussed.
We investigate the relationship between phase interference associated with action, the relativistic dynamics of proper time, and the structural origin of action quantization. We start from the general principle of interferential compatibility of action introduced in previous works, in which the dynamic phase of a system is given by
ϕ=S/ℏ and phase coincidences between distinct evolutions occur only when
ΔS=2πnℏ. We show that when this formalism is specialized to the relativistic action of a free particle
S=−mc2τ, the phase evolution naturally implies an internal frequency
ωC=mc2/ℏ, corresponding to the Compton clock. When two systems evolve with distinct proper times, their Compton phases diverge, producing a relativistic phase beating. We demonstrate that the interferential coherence condition
Δϕ=2πn defines a discrete sequence of synchronization instants and directly implies the relation
mc2Δτ=nh, showing that discrete action increments emerge as a geometric consequence of the relativistic periodicity of the phase. We also show that the used phase coincides exactly with the rest phase of the Dirac equation solutions, establishing the connection with the relativistic dynamics of fields. The beating between Compton clocks defines an operational discretization of the action that can be interpreted as a discrete sum, whose continuous form is recovered in the limit of almost perfect synchronization between reference frames. We also discuss the relationship of this formalism with the notion of the internal clock introduced by de Broglie and with the interferential structure of relativistic matter interferometry. In this framework, Planck's constant emerges as the geometric invariant associated with the first closure of the relativistic beating between Compton clocks. Quantization can then be interpreted as a coherence condition between relativistic phases, establishing a direct bridge between quantum interference, proper time relativistic dynamics, and the variational principle of stationary action.