(A popular summary of the paper “Towards Futuristic Interpretation of Quantum Mechanics” by Alexander Poltorak being currently prepared for publication)
Quantum mechanics (QM) is one of the most successful theories of physics that withstood the test of time. Indeed, it is one of the best-tested theories known to science. Yet, we hardly advanced in our understanding of the meaning of QM since its inception almost a century ago. The indeterministic nature of the theory puts it at odds with both classical physics and our intuition, and continues to perplex physicists and philosophers of science today as it perplexed Einstein, who famously said, “God does not play dice with the universe!” Superposition and entanglement seem to defy common sense and, yet, they have been confirmed experimentally time and again.
The phenomenon known as the collapse of the wavefunction does not follow from the Schrödinger equation and is added ad hoc. This is called the Measurement Problem, which led some physicists to adopt such extravagant interpretations of QM as Many Worlds (Hugh Everett, 1956) (characterized by Bryce DeWitt as schizophrenia with a vengeance (DeWitt, 1970)), just because they do not have the Measurement Problem.
As I suggested earlier (Poltorak, 2003; and 2005), many enigmas and paradoxes of QM are easily understood from the perspective of the relativity of simultaneity, first introduced by Einstein in the context of the Special Theory of Relativity and extended in this interpretation to quantum physics.
Schrödinger Cat
Schrödinger cat was thought up by Ervin Schrödinger as a gedanken (i.e., thought) experiment demonstrating conceptual problems of quantum mechanics he helped formulate earlier (Schrödinger, 1935) as a follow-on discussion of the EPR paper (Einstein, Podolsky, & Rosen, 1935). Schrödinger focused on the paradoxical state of a macroscopic object—a cat—suspended between life and death in a blurred state of superposition of two quantum-mechanical states, alive and dead. He also zeroed in on the property he called entanglement, which he realized was at the center of quantum physics.
The paradox presented by the Schrödinger cat, however, is not its suspended state of animation—the superposition of state is well understood today. The paradox relates to the collapse of the wave function from the state of superposition into one of the defined classical states. Moreover, the profound contradiction revealed by this gedanken experiment is the irreconcilable clash between pre- and post-experiment predictions of quantum mechanics.
Before the observer opens the box, quantum mechanics predicts that the cat is not in any of the four classical states: it is neither alive, nor dead, nor both, nor neither. Rather, it is in the fifth state unique to quantum mechanics—the state of superposition of being alive and dead. What is important to us is that the Schrödinger equation definitively excludes at least two states: being alive or being dead, as the cat is neither alive nor dead. However, after an observer opens the box, he finds the cat in a definite state of being either alive or dead. Moreover, if the cat spent a considerable amount of time in the box, it will be found either very hungry or very smelly, depending on its fate. This finding is in stark contradiction to the prediction of the Schrödinger equation.
Let us say, we consider the state of the cat yesterday, at noon, without opening the box. We determined based on the Schrödinger equation that the cat is neither alive, nor dead, nor both, nor neither, but is in a state of superposition of two states—being alive and dead. When we opened the box today at noon, we found the cat dead. A post-mortem autopsy of the cat determined that the cat died of poisoning by prussic acid roughly 48 hours ago and was dead yesterday at noon. Here we have it: the Schrödinger equation predicted that the cat was not dead (neither dead nor alive) yesterday at noon, and yet, after we open the box and found a dead cat, we determined that the cat had died yesterday at noon. Herein lies the paradox—the predictions of quantum mechanics contradicts the experimental findings. (The Copenhagen interpretation doges this issue by claiming that the state of a quantum system is indeterminate between measurements, and it is impossible to say what state the system is in before measuring it.)
Further analysis of this paradox reveals that it has to do with the treatment of time in quantum physics. Although quantum mechanics (at least in the Copenhagen interpretation) insists that the state of the cat was fixed at the time the observation, the collapsed state comes with its history.
While, according to the Special Theory of Relativity, the distinction between past and future is not absolute, within a given frame of reference, we can define the past as fixed and the future as uncertain. The state of the cat at noon yesterday was uncertain to the observer and, consequently, in the observer’s (relative) future. Today, however, after opening the box and collapsing the wave function, the observer collapsed the state of the cat into a certain state (say, dead), thereby moving it into the observer’s (relative) past. We see that before opening the box, the state of the cat at noon yesterday was in the future of the observer, whereas after opening the box, the cat at noon yesterday is in the observer’s past. The paradox is, therefore, the conflicting characterization of time (past or future) before and after the experiment. It is as if the collapse of the wave function instantaneously flips the future into the past. Luckily, the nature of the paradox points to its resolution. It is all about time, after all.
Relativity of Time
Following Newton, time was believed to be absolute. In 1895, Lorentz was the first to distinguish “local” time, as it is measured in a particular frame of reference, from the proper time in a preferred reference frame, which he associated with aether. He was the first to describe mathematically the correlation between local times using what came to be known as Lorentz transformations. From 1898 to 1905, Poincaré published a series of papers in which he explained Lorentz transformations by a synchronization error between the local times (Poincaré, The Measure of Time, 1898/1913) (Galison, 2003) (Poincaré, The Theory of Lorentz and The Principle of Reaction, 1900).
In 1905, Einstein did away with aether and its preferred frame of reference considering all inertial frames of reference on equal footing. Most importantly, he demoted time from its absolute status and the pedestal, on which Newton had placed it, and considered the local time to be relative to the frame of reference in which it is measured. Einstein recognized that to compare time intervals between events and evaluate the simultaneity of events in different frames of reference, clocks in these frames of reference had to be synchronized by exchanging a light signal.
While Lorentz, Poincaré, and Einstein were primarily focused on the relativity of motion, with the relativity of time being a consequence of the relativity of motion, it is the relativity of time that is the primary focus of my Futuristic interpretation of QM. The fact that time flows differently in different frames of reference is independent of the relative motion of these reference frames. We cannot compare intervals of time between events in different frames of reference before clocks in the respective frames of reference are synchronized. It is the exchange of information that synchronizes the clocks. Since light is the fastest way to exchange information, in the Special Theory of Relativity (STR), we usually speak of synchronizing the clocks by sending a light signal. How it is done is not important. What is important is that to synchronize clocks the information has to flow from one frame of reference to another. The relative motion of these frames is irrelevant to the need for the synchronization of clocks, albeit the relative motion affects the transformation of time intervals from one frame to another—time dilation. I contend that the relativity of time is a fundamental property of time and is not an accident of the relativity of motion.
In extending the notion of the relativity of time on quantum physics, I proposed to generalize the definition of a frame of reference to mean an information processing system with a reference clock.
The relativity of time requires synchronization of clocks in different frames of reference, which, in turn, requires the exchange of information. Until clocks are synchronized, the events in one frame of reference are in the future of the observer in another frame of reference, who lacks any knowledge of these events. Our intuitive conception of time naturally splits time into past and future, wherein the past is fixed, and the future is not. Therefore, the lack of meaningful information about events in another frame of reference before clock synchronization places these events in the future of the observer.
Synchronization of Clocks in Quantum Mechanics
It has been my contention that the collapse of the wavefunction has to do with the synchronization of clocks in two reference frames, not unlike in the special theory of relativity. Before we can compare time intervals in two frames of reference in the STR, we need to synchronize the clocks. A similar situation occurs in QM. A quantum-mechanical system and an observer, each represent a distinct frame of reference with its own clock and timeline. Before clocks are synchronized, the timeline of the quantum-mechanical system is in the future of the observer who lacks information about this system. Clock synchronization accomplished by the process of measurement collapses the wave function and brings the quantum-mechanical system’s timeline into the present time of the observer.
The transition from the future into the past is the process of collapsing a plurality of possibilities into a single actuality, similar to the collapse of the wave function which reduces a plurality of possible states into a single state we find as a result of the measurement.
The uncanny similarity between the collapse of the wave function caused by clock synchronization and the transition from the future into the past would suggest calling this approach time-relativistic interpretation of QM, as it is based on the generalization of the concept of relativity of time (as I improvidently called it when we first presented this interpretation at a conference in 2003). However, not to cause confusion with relativistic QM developed by Paul Dirac in late 1920s, I subsequently renamed this interpretation as the “Futurist” interpretation, because, as you will see later, many of the events causing paradoxes in QM can be explained as simply happening in the future of the observer. This interpretation of QM is generally based on the Lorentz-Poincaré-Einstein’s idea of relativity of time, i.e., the lack of simultaneity in different frames of reference. Unlike in Special Relativity, I do not consider here the relativity of motion, but rather the relativity of time itself. In fact, the concept of relativity of time is broader than the relativity of motion. In two frames of reference at rest with respect to each other, there is no time dilation. However, the notion of simultaneity does not necessarily translate from one frame of reference to another. For example, an observer in one frame may experiences two events as simultaneous while they may not appear simultaneous to an observer in another frame of reference if these events are not equidistant to the observer.
Although Lorentz, Poincaré, and Einstein only considered classical reference frames moving relative to each other, I proposed to extrapolate this notion to a quantum-mechanical system and its observer, regardless of their relative movement. In my definition, a quantum-mechanical frame of reference is a closed information processing system with a clock. The common thread with the STR is the realization that clocks will show different times in different frames of reference; and an exchange of information, i.e., an act of measurement, is necessary to synchronize the clocks in different reference frames.
A quantum-mechanical system represents one frame of reference that has its own timeline. An observer is in another frame of reference with its own clock and timeline. Thus, a quantum-mechanical system, which is the object of measurement, and the observer are in two different frames of reference. Before their clocks can be synchronized, information exchange between the two frames of reference must take place—this is the act of measurement.
The Collapse of the Wave Function
Physicists do not like the collapse of the wave function because it does not follow from the Schrödinger equation and is added ad hoc. Mathematicians do not like it because it makes the wavefunction a discontinuous function—something difficult to deal with. We somehow forget that we deal with a fairly similar situation every moment of our lives without making a fuss about it. The transition between the future and the past that we experience every moment of our waking lives behaves in exactly the same way.
Indeed, there is an uncanny similarity between the collapse of the wave function and the transition from the future into the present and the past. As explained above, the future time is characterized by a plurality of amorphous possibilities or, in the language of mathematics, by the distribution of probabilities of all possible events, just as a quantum mechanical system is characterized by the wave function that describes a distribution of probabilities of all possible states of the system.
While there is no accepted theory of time, the intuitive distinction between past and future is that the past is fixed, and the future is not. The present moment is the point on the timeline when the distribution of probabilities of future events collapses into a single value—one or zero—depending on whether the event in question happens or not.
This is very similar to the situation we find when conducting a quantum-mechanical experiment: from all possible quantum-mechanical states, we select only one state that we observe in the experiment—what is referred to as the collapse of the wave function. This similarity suggests that what we are dealing with in Quantum Mechanics is the transition from the future into the past.
This transition happens because for as long as there is no exchange of information between the reference frame associated with the quantum-mechanical system and the reference frame associated with the observer, the timeline of the quantum-mechanical system is in the future of the observer. Indeed, until the experiment is conducted, there is no information available about the state of the quantum-mechanical system, aside from what we can glean from the Schrödinger equation—a distribution of probabilities. As the future is characterized by the lack of information and, conversely, the past is characterized by the existence of the information, as far as the observer is concerned, the quantum-mechanical system is in the future of the observer, as the observer lacks the information about it. When the experiment is conducted, and the information about the system is obtained, the clocks are synchronized and, as far as the observer is concerned, the quantum-mechanical system has moved into the observer’s present time. This means, the timelines are aligned, and two frames now share past, present, and future.
Schrödinger cat revisited
Let us again reconsider the Schrödinger cat. Before an observer looks inside the box, the cat is in the future time relative to the observer. Therefore, there is nothing unusual about its state of superposition—it is neither dead nor alive because, as far as the observer is concerned, the event that determines the fate of the cat did not happen yet. Once the observer opens the box—the act that allows for the exchange of information, which synchronizes the clocks—the cat moves into the observer’s present time. No wonder, only one possibility is actualized—the cat is either dead or alive. The key to the solution of the Schrödinger cat paradox is the realization that time flows differently in different reference frames associated with the quantum-mechanical system and the observer: what is present in an isolated quantum system is still in the future for the observer until an experiment is conducted, which synchronizes the clocks and brings the quantum-mechanical system into the observer’s present—hence the collapse of the wavefunction, hardly a paradox at all. This illustrates how my Futurist interpretation demystifies quantum mechanics.
Let us now compare the three possible explanations of what happens with the Schrödinger cat:
Before the box is opened | After the box is opened | |
Classical physics | The radioactive atom either decays and kills the cat, or it does not. At all times, the cat is either dead or alive. | Observer finds the cat either dead or alive. |
Copenhagen interpretation of QM | The radioactive atom exists in the state of superposition of two states: decayed and not-decayed; the cat, entangled with the atom, is also in the state of superposition of two states: dead and alive. | The observer collapses the wave function, retroactively “causing” the atom to decay or not to decay thereby killing the cat or not. |
Many-Worlds interpretation of QM | The radioactive atom causes the universe to branch out into two copies: in one, it decays and kills the cat; and in the other, it does not. The cat is alive in one branch of the universe and is dead in the other. | The observer is split into two carbon-copies. One observer finds the cat alive in one universe, and the other copy of the observer finds the cat dead in the other universe. |
Futurist interpretation of QM | Until the measurement, the observer’s clock is not synchronized with a clock in the box, each being in a separate frame of reference. From the observer’s vantage point, a possible decay of the atom and the resulting fate of the cat are indeterminate because they are in the observer’s future. From this point of view, the cat is neither dead nor alive simply because it did not have a chance to die or not to die yet, as the radioactive atom has not had a chance to decay and kill the car or not, as far as the observer is concerned. | The opening of the box results in the exchange of information, synchronizing the clocks in two reference frames, one associated with the observer, and another, associated with the quantum-mechanical system. This brings the quantum-mechanical system into the observer’s present, allowing the observer to decide whether the cat is dead or alive. The “collapse of the wave function” is nothing more than a transition from the observer’s future into the observer’s present and past. |
On the Nature of Time
A legitimate critique of my Futurist interpretation would be an objection to using such categories as past, present, and future in attempting to explain the measurement problem in quantum mechanics when such temporal concepts are not well defined and do not follow from any contemporary theory of physics. Fair enough. However, all signs tell us that the nature of time is inextricably entangled (no pun intended) with quantum reality. To explain one, we need to assume the nature of the other as they seem to be two sides of the same coin.
In my opinion, time exists and is naturally divided into two domains—the past that we can never revisit and the future that we cannot know, with the present as the transition point between the two. With this in mind, we can say that the collapse of the wave function is the transition from the future into the past with the measurement performed in the present.
Alternatively, we can assume the fact of the collapse of the wave function without explanation and define time in the context of quantum physics as follows:
- the future is the state of the system being in the superposition of all possible states described by the wave function, with the square amplitude of the wavefunction defining the probabilities of each state being realized (found when measured);
- the past is the state of the system in a defined state after the collapse of the wavefunction;
- the present is the moment of measurement; and
- the arrow of time arises out of the irreversibility of the collapse of the wavefunction.
Either approach appears legitimate and is a matter of taste.
The Futurist interpretation of quantum mechanics presents the indeterminism of quantum mechanics as a natural indeterminism of the future time. It interprets the collapse of the wavefunction as the synchronization of clocks bringing the timeline of the quantum-mechanical system into the present time of the observer.
Wow. So Futuristic interpretation gives a specific reason for Copenhagen interpretation of collapse of wavefunction, ie: syncing of clocks is what causes collapse? Explanation that was missing from Copenhagen interp?
Also, as this is Quantum Torah site, do you see any QM/Torah connection here? I have some thoughts on it regarding G-d and religion, but not specific Torah verse, etc.
That’s exactly right. Synchronization of clocks moves the quantum system in the present time if the observer, which appears as the collapse of the wave function, as one state is selected among many.
As far as the connection to Torah, please wait for my next post where I am going to explain it.