I constantly keep having to explain my views about quantum mechanics to people on the internet. My views are simple, but they need developing a bit of development to explain. For the longest time, people used ‘interpretations’, approximate pictures that expressed the unfamiliar quantum ideas in terms of familiar classical ideas, to simplify the exposition. The infidelity of the interpretations unfortunately seems to have created more confusion for many people than the interpretations are worth, hence this attempt to explain it without those crutches.
But, what is this article? It is not physics, since it is not cocerned here about the experimental evidence in favor or against quantum mechanics. Physics ultimately explains our world in terms of theories, compressed representations of our experiences, but they are useless if they are not faithful compressions. There is no guarantee that quantum mechanics is actually correct, but this discussion attempts to explain only what the theoretical framework of quantum mechanics is, irrespective of whether and to what extent that comports with the experimental evidence.
At the same time, it is not a research paper. Yes, it does have my ideas, ideas that I feel will be useful to some to understand quantum mechanics, and some of it I haven't seen elsewhere. But, stylistically, it is all wrong for a research paper; for one, it does not credit prior work—work that has certainly influenced me, and some that didn't, but should have, but for my lack of scholarship and familiarity with the literature. It is a position paper describing my current understanding of the subject, disconnected from how I got to it.
Neither it is a pedagogical piece on the subject. For one, I have no familiarity with teaching: partly unfamiliarity with teaching and partly a sufficiently different worldview making communication difficult. Second, I assume complete familiarity with the mathematics of quantum mechanics, and the ability to transform my stilted prose into the beautiful algebra that underlies introductory quantum mechanics. I also drop the reader into complex notions abruptly, without the usual gentle introduction that is the hallmark of pedagogical writing.
So then what is it? I will call it a blog post, so a blog post it shall be!
Most confusion about quantum mechanics arises from a very simple place: it is the status of the observer in quantum mechanics. To step back, in physics till the beginning of the 20th century, we got into the habit of describing physical systems by writing down ‘laws’ that described the change or constancy of some properties of the system. These properties, like position, velocity, acceleration and were supposed to be absolute, as were quantities like force that measured the interaction of the system with all other systems in the universe. One could, separately, ask the question about what one actually saw: to the extent that measurement is a change of state of the measuring device, it is also a concern of physics. But, in this set of theories we lived in, the two pieces were separable: we did not need to be concerned about the measuring system when talking about the measured system, since the concepts in terms of which we described the system were absolute. Note that this does not mean there was no concept of relativity: a moving observer did observe a different speed. But, one could always choose to do the calculation in some Machian frame of reference and transform the results to what other observers would see, no conceptual change was needed.
At the beginning of the 20th century, this began changing. As was said, there were only two unsolved problems: one was the puzzle of the velocity of light brought into focus with the Michaelson Morley experiments of 1887, and another was the puzzle of black body radiation following from Planck's formula from 1900. As it turns out, the solution of the first one came with the development of the special theory of relativity, whereas the second led to the development of quantum mechanics.
But the story is more interesting than that. The two developments had something more in common: both of them struck hard against the absoluteness of the concepts of observer-independent system properties. In the case of special theory of relativity, this is not strictly necessary: after all Lorentz transformations explained the Michaelson-Morley experiments and, also, the Fizeau's 1851 experiments supporting ‘partial ether drag’, without invoking any conceptual change in one's worldview. But, when Einstein came along, he reinterpreted these as an observer dependent definition of space and time, changing, for the first time the absolute nature of some concepts like space, time and simultaneity, though not of others like the inertial nature of a frame. This observer dependence of the notions of space and time turn out to be more than mere conveniences they appear to be in the special theory of relativity: they soon allowed great progress. The crown jewel, called the general theory of relativity, could not have been framed using the hack of, physical Lorentz transformation of absolute space and time. Instead of that, one truly needed to move away from absolute separation of time and space since, in principle, the entirety space-time region ‘accessible’ to different observers were overlapping but different, so no transformation was possible that would describe the system. Moreover, the very concept of distance on a scale set by the gravitational field became problematic to define.
Quantum mechanics took this even further: it challenged the very notion of properties when applied to subsystems. Since the separation of observer from the observed is a separation into subsystems, this fundamentally changes the way we need to think of describing systems. In stead of making some properties of the system non-absolute, or observer dependent, it now disavowed the guarantee of ascribing any property to an observed system: not by some miraculous property of observation as often implied in the popular literature, but because observation implies a separation of the observed from the observer, and subsystems cannot hold properties.
Let us provide an example of a quantum mechanical calculation. Let us set up an observer subsystem and an observed subsystem and seal them in a box. The set up is arranged so that the observer subsystem records what it sees about the observed subsystem in its memory. Of course, we do it without violating any fundamental laws of physics, so we do not invoke irreversible changes: a memory that is written to, can under suitable circumstances be unwritten to. But, we can certainly arrange it so that under normal dynamics of the coupled observer-observed system, that rarely happens: the memory stores an usually accurate history of the observations. Since the memory is required to capture the history of observations, it needs to have many more degrees of freedom than the observed system. To those who believe that macroscopic systems cannot be quantum, we can actually, in gedankenland, arrange this for small periods of time with small number of degrees of freedom (e.g., a few electromagnetic cavities as observers, one or two two-state ions as the observed systems). In any case, as I said in the beginning, I am not discussing whether quantum mechanics applies: only discussing what it predicts if it is true.
Now let us take than above sealed box, and put it in an eigenstate of the Hamiltonian governing the inside of the sealed box. By the laws of quantum mechanics, the state of the system, except for an irrelevant overall phase, is unchanging in time. So, if we open the box at any time and measure anything in it, we shall get the same probabilities of measuring different outcomes. Let us leave aside where probabilities came from, till the next section; for now we accept the fact that we set up many boxes like the above at the same time, and open them and measure them at the same time, we shall still see different outcomes. The probability distribution of the outcomes will however be the same at different times.
But what do we see if we look at the observation record in memory. Quantum mechanics is unambiguious about it: it contains a record that shows evolution of the observed system consistent with its laws of motion. All possible consistent records turn out to have a nonzero probability of observation: all records inconsistent with the dynamics are seen with probability less than that of record alterations due to residual imperfections of the recording device.
Here we see the crux of the non-attributability of the properties of subsystems. One can argue that since we find the same probabilities of observations no matter when we open the box, the system as a whole is not changing at all. Yet, a subsystem set up to observe and record another subsystem, does produce a record. The probabilities of the various histories being recorded are completely calculable from a theory of the observed subsystem—and, knowledge of what is being measured— alone. In fact, according to quantum mechanics, as the system becomes more complex, the records even start obeying laws of thermodynamics such as an observed increase of entropy is far more likely than an observed decrease of entropy. So, in some sense, the evolution is real and we are left with the conclusion that even the attribution of the property of nontrivial evolution differs between looking at the entire system, or looking at parts of it.
Let us now change the previous box somewhat by making it more complicated. Let us set up the dynamic inside the box such that it is possible for an array of atoms in the box to get excited by a bunch of photons that are jumping around and then are emitted and detected by the single detector. Let us set up the box in an eigenstate —all we need is that that the probability of the record indicating that the atoms started all unexcited is nonzero, but eigenstates make the argument intuitively clearer—and see what the record says when we open the box after some time.
Again quantum mechanics is unambiguous: in cases where the record starts with all unexcited atoms, different atoms typically get excited and emit the de-excitation photons at different times. Not only that, if we look at each individual record, it is completely consistent with a random set of emission times, in fact in a precise sense due to de Finetti, and the probabilities of emissions at different times is given by the Born rule!
Of course all the previous section shows is that Born rule on the outside—in deciding the set of records that are seen—are consistent with a Born rule on the inside—in what probability rule each individual trajectory plays. So, we change the example slightly.
Now instead of having two subsystems, an atom-photon one and a photon-measurement one, let us adjoin a third one; let us call it the introspector. This basically observes the previous observer and records whether or not its record deviates from the expectations using Born rule. We also change the dynamics: all allowed dynamical trajectories of the original two subsystem time-reverse themselves so that the actual record is erased.
Now, what happens when we open the box? It turns out that except for a small fraction of the time—a fraction that can be made smaller than any real number by changing the parameters of the setup—the record is of course completely erased when the box is opened. That, in itself is not surprising: that is exactly what the time reversal was setup to do. What is surprising, however, is that the Born-rule detector—the one that did not participate in the time reversal—almost always has a record of Born rule being satisfied.
In other words, we can devise systems with increasing fidelity with the system we wanted, and with increasingly large number of observations to verify the probability laws on each individual record with increasing precision, yet only dealing with systems that do not evolve and that give unique results when finally measured.
With this development, we are close to the end: what happens to quantum effects when the system is big. We can again set it up in the same way as before: but, this time the detector measures presence or absence of interference fringes in a two slit experiment. Not surprisingly, quantum mechanics predicts interference fringes are produced, observed, and recorded.
We can now set up the same as before, but put in some material with which the particles will interact with near certainty, kicking them away. This time the record shows that interference fringes are not observed, and the probabilities of the flight along the two paths seem to follow Born's rule.
Now, as far as the outside observer is concerned, the entire system is clearly in a superposition: the internal dynamics was designed so thsat there are no eigenstates that are not superposed, and the observation of unchanging probabilties for all observations is inconsistent with the overall system not being in an eigenstate.
But equally, the inside recording device clearly sees absence of superposition, and emergence of Born's rule. The way out of the conundrum is again the same: a subsystem can ‘pass on’ its superposition to other subsystems in such a way that observationally, it seems like it has chosen one or the other path, in proportion according to Born's rule. The entire system, nevertheless, stays in a state of superposition; and this fact of it remaining in a superposition can be observed from outside the system.
As discussed above, interactions can destroy superpositions, but what does this have to do with our everyday observation that macroscopic objects, or space-time for that matter, do not seem to have superpositions, whereas tiny things do? The difference in our experience is not so much in interactions, but in size or complexity or mass or ...
Now is the time to clarify a white lie in all the above discussion: superposition and interference are not all-or-nothing. Fringes have a parameter called contrast that is a quantitative measure of interference. We have studied a bunch of this stuff analytically, and found something interesting. If we try to observe a system, we necessarily have to interact with it. In classical physics, we can make the observation increasingly precise without changing the isolated dynamics of the system too much. The same is not true in quantum mechanics: if we try to get too much information out of a system too fast, we disturb the system noticeably.
What we found playing with toy systems is that when the measurement strength is below a quantity that increases as the system becomes macroscopic, the disturbance is small. Amazingly, when the measurement strength is above the inverse of this same quantity, quantum effects in the evolution are not recorded by the measurement. Since this quantity is very large for macroscopic objects, any measurement strength larger than a calculable tiny number and smaller than a similarly calculable huge number just measures a classical result, whether or not the system is inherently quantum! As stated above, this is a statement about the measurement, the entire observer-observed system still stays in a superposition.
In other words, if we directly wanted to see the wavefunction of a chair spread out, we would have to measure it—or else we will not know it is spreading out—but, do it incredibly weakly. For example, we could do the double slit experiment with chairs, so that the turning of the chairs at the slits still produced very little measurement of its path: by arranging for the slits to be in just the right kind of coherent state. This, so far has not been possible, though it has been possible with quite large molecules.
There is only one thing left in all this: where is the real observer—the ego, the me—in all this. I believe that the observer machine in the box is me. Notice that machine can see a wave-function collapse, when the outside observer, let us call him God, sees no collapse. The inside observer sees probabilities when its memory is introspected, whereas quantum mechanics merely propagates the wave function of the box—call it the universe— without any randomness.
In the many worlds' interpretation, this is simplified by noticing that it is exceedingly difficult to reverse time and erase all entanglements that have left the system; and the mind of God is unknowable. So, for all practical purposes the fact that a measurement has been recorded and entangled into a myriad copies of the information, commits us to condition our later results on this record.
Note that quantum mechanics says that the record, if designed properly, will never show a superposition; though there be superposition in the entire system. It also says different records will be consistent with each other, even though again, the superposition of the full system holds all the values. Finally, it says that each record can be interpreted as a random trajectory whose probabilities are given by the Born rule, even though the system as a whole is evolving deterministically. All this is pictured as saying that at every measurement, we randomly choose a universe, a particular consistency set, and all future measurements will be consistent with that. But, this is a picture; not quantum mechanics, which allows a simple, but for enormous technical implausibility, time-reverse actuator to show that the universes don't actually exist: in the picture, instead of splitting, they can be made to unsplit again.
So have we now resolved all the mysteries of quantum mechanics? That is a resounding no. We still want to have an understanding of how quantum mechanics works: a succinct statement of the basis of quantum mechanics like the equivalence principle that encapsulates special theory of relativity. I believe this has been achieved in recent years, at least partially, but that should be a different post.
Then, there are the questions of technical details of how quantum mechanics relates to other fields like information theory or space-time geometry. It is likely that one will get laws—emergent like thermodynamic laws, or otherwise—as one studies these interfaces. Recent work in this field gives hope that progress will be made.
And, finally, there is the measurement problem: exactly what class of subsystems have the right properties so that they can interact and measure and record faithfully, and, yet, without their record itself behaving quantum mechanically in almost all circumstances. We do know gedanken examples of such subsystems, but we do not know a succinct characterization. Quantum mechanics is reversible in a deep sense, so there will exist circumstances that will allow quantum eraser experiments, but some property of these systems makes them immune to most eraser, and we need to find the property and how it works. Again, there is some recent work that may have solved the problem, but some more work is needed.