In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat space and time on an equal footing and there are many approaches to the problem how to introduce time operator. In order to support these approaches we propose the experiment that will clearly expose the equivalence of space and time regarding the relation towards quantum interference. The proposed experiment can show that it is possible to have superposition of being created in two different moments in time, and by measuring standard interference pattern, it will be shown that there is interference in time. It is similar to the case of verification of the possibility of single quantum system to be in the state that is superposition of two different positions in space. If so, this would mean that there should be exactly the same formal approach to the space coordinates and time in quantum mechanics since they are all quantum in their nature.
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat space and time on an equal footing and there are many approaches to the problem how to introduce time operator. In order to support these approaches we propose the experiment that will clearly expose the equivalence of space and time regarding the relation towards quantum interference. The proposed experiment can show that it is possible to have superposition of being created in two different moments in time, and by measuring standard interference pattern, it will be shown that there is interference in time. It is similar to the case of verification of the possibility of single quantum system to be in the state that is superposition of two different positions in space. If so, this would mean that there should be exactly the same formal approach to the space coordinates and time in quantum mechanics since they are all quantum in their nature.
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states.
Abstract: Since the very begining of quantum theory there started a debate on the proper role of space and time in it. Some authors assumed that space and time have their own algebraic operators. On that basis they supposed that quantum particles had “coordinates of position”, even though those coordinates were not possible to determine with infinite precision. Furthermore, time in quantum physics was taken to be on an equal foot, by means of a so-called “Heisenberg’s fourth relation of indeterminacy ” concerning time and energy. In this paper, the proper role of space and time in the core of non-relativistic quantum phsysics is analyzed. We will find that, rigorously, that relation for time and energy shows a different root. For the role of space, it will be discussed that there is no “coordinate of position ” in the conceptual structure of quantum physics because quantum particles are not point-like objects. 1.
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
This paper proposes that time behaves not as a continuous stream but as a quantum superposition of possible moments that collapse into a single present through observation. The theory draws from quantum field models and wavefunction-based mathematics to argue that time carries amplitudes and interference effects much like spatial quantum states. Instead of treating time as a passive background, the model treats it as a measurable quantity that reacts to attention and resolution. Moreover, it integrates thought experiments, proposed physical tests using time-bin qubits and optical clocks, and theoretical links to entropy, consciousness, and metaphysics. It stays within the framework of relativity and standard quantum mechanics while offering a shift in how time is involved in measurement and reality formation. It suggests that the “now” does not exist until something observes it, and each observation activates one real version of time while excluding all others. Because of this, the paper calls for a new view of time—not as something flowing on its own but as a quantum variable that becomes real only through interaction.
In (1), it is stated that “time flows continuously like a river’ … and is treated like a classical variable in Quantum Mechanics.” Here, we wish to consider the behaviour of time in quantum situations. We argue that a 4-space sense of time appears in quantum mechanics through exp(-iEt+ipx), but only intertwined with E (energy) and p (momentum), i.e. interactions involving these variables. Furthermore, there suggest that there must be a clear measure of t as well as an interaction changing E to use exp(-iEt) and a clear measure of x and an interaction changing p to use exp(ipx). In particular, we note that the classical equation x/t = v ensures that time and x are not on the same footing and this same equation holds in special relativity, so -Et+px = constant ((1)) which has the appearance of x and t being on the same footing (as well as (x,ct)) is subject to x/t=v (for xo=0, to=0). Thus, if x/t=v governs x and t information, then x and t are not independent. It seems that one would require fluctuations from these values. The fluctuations ranges could be linked, but actual t and values within the fluctuations would be independent. . We suggest it is possible to find a formalism which treats x and t independently from ((1)), but this formalism must be intertwined with E and p. In particular, one has free particle quantum mechanics in which delta t = hbar/E and delta x = hbar/p. X and t are decoupled in this scenario and so appear as independent because there is no notion of x/t=v when dealing with quantum type interactions. When dealing with such interactions, one uses the probability exp(-iEt+ipx), but this begs the question: How is this factor really used? We suggest that one must consider the following. Given exp(ipx), one uses it if p changes and there is a distinct measure of changing x in the problem. This scenario applies to two-slit interference, bound states with V(x) and one dimensional reflection-refraction at a point x=0. Given exp(-iEt), one uses it if there is a distinct interaction involving E, i.e. it changes and there is a distinct measure in time. Thus, two-slit interference, one dimensional reflection-refraction and elastic scattering from a V(x) are out because they don’t involve changes in E. A bound state with V(x) certainly involves changes in E, but does not have a direct measure of time t (independent of x). A bound state with V(x,t), however, does have a direct measure of t (being independent of x) and also involves energy changing and so exp(-iEt) may be used in this case, as will be shown.
Following homogeneous canonical formalism where the time is treated on an equal footing with the space coordinates, we propose an alternative formulation of quantum mechanics in which the time is considered as a dynamical variable. The basic equation corresponding to and being equivalent to the ordinary Schrödinger equation is obtained when we consider the space coordinates x as a parameter corresponding to the time t in the ordinary formulation. The formal solution of this equation is given and examined. By making use of this solution the scattering theory is formulated in our formalism. It is shown that observables corresponding to the time and space coordinates can be defined. A short comment on the energy-time uncertainty relation is also given.