(See Part 1, Part 2, Part 3, Part 4, and Part 5. Also I am going to suspend the limit of three comments per post for this series of posts because it is a topic that benefits from back and forth discussions.)

As promised, here is a follow-up post to discuss how we know whether an ‘objective reality’ exists in the quantum world or not. It took me longer to write than I anticipated because the issues are subtle and I had to be careful in how I try to explain them. It is also a little long.

To refresh some ideas, ‘objective reality’ means that a measured quantity exists before we measure it. i.e., the measurement merely tells us what already existed. By contrast, the standard interpretation of quantum theory says that for certain properties of a particle, the measured value only comes into existence upon measurement and does not exist before. Hence the quantum world does not demonstrate objective reality. The problem is that since we seem to need the measurement in order to know what the value of the quantity is, it looks like we cannot say whether it existed before the measurement or not.

So how can we know something without in fact measuring it? Einstein suggested that if we can predict the outcome of a measurement with 100% accuracy, then that property has an objective reality, in that it exists before the measurement. i.e., it is as good as having been measured even though it has not been directly measured.

Let us now look at the scenario described by bluerizlagirl in a comment to Part 4 in this series.

How is this different from taking a red card and a black card from a deck; having someone select one at random, climb in a spaceship and travel halfway across the universe; and as soon as I look at my card, say it happens to be red, I know at once that their card is black? They have always been opposites from the outset, so as soon as you know the state of either one, then you automatically know the state of the other one, by the property of oppositeness.

This is a statement that the cards have objective reality. The problem with it is that the way that it is set up begs the question: it assumes that each card had to be either red or black right from the beginning, and hence that the second card was known to be black once the first card was looked at and seen to be red. This differs from the quantum case in that the two cards were never in a superposition of states, even at the beginning. Each card was either red or black, as is the case with macroscopic classical objects. We should not confuse the lack of knowledge of what state an object is in with it being in a superposition of states. Those are two different things. Creating a superposition of states is very hard and while possible for microscopic entities like electrons and photons, almost impossible for macroscopic things.

To make it a better analog of what quantum theory says, we would have to set it up so that the two cards A and B were initially created in a superposition of red and black cards (if you can imagine it), and then each one put in a separate sealed envelope without being looked at (i.e., measured) before one was sent off. When we looked at one card A halfway across the universe, we forced that card to shift from being in a superposition to being in just one or the other color and that measurement immediately caused the other card B back home to also collapse, but into the other color. In other words, the opening of the envelope containing card A resulted in a collapse of the superposed state and that collapse occurred instantaneously at both locations. This way of looking at it may sound preposterous but there is no logical reason to reject it. And indeed that is what is said to happen in the standard interpretation of quantum theory.

Objection: Doesn’t the instantaneous collapse of the wave function everywhere (even halfway across the universe) violate the fundamental tenet of relativity that nothing can travel faster than the speed of light?

Response: No. The relativity limitation is on information being transmitted faster that the speed of light because allowing that is what can lead to all manner of paradoxes. The instantaneous collapse of the wave function cannot be used to send information instantaneously. People have tried hard to find a way to use this collapse to send information faster than the speed of light but have consistently failed and have pretty much given up the effort.

Note that the person holding envelope B would not know what color their card was until they received a signal sent by A at the speed of light or slower, telling them what color their card was. The resulting prediction would be 100% correct but that only tells us that the color of card B had objective reality after A had observed their card. It tells us nothing about whether it would have been that color if it had been looked before A looked at their card. So we seem to be stymied.

The problem with classical macroscopic analogies like cards is that it is impossible to create them experimentally to be in a superposition of states. The cards were always red and black before any observation and so the phenomenon cannot be tested with such objects.

Question: So how do we test this in the quantum world?

Response: The analog experiment in quantum mechanics consists of creating a pair of electrons (or photons) A and B such that their total spin is zero. Thus all that we know is that the two spins must be in opposite directions to give a total of zero. The two electrons are said to be in an entangled state. We then send them off in opposite directions while still remaining entangled, which means that neither electron can come into contact with any macroscopic object that will cause the wave function to collapse. (This is not easy to do experimentally but can and has been done repeatedly.) Then if we measure the spin of one electron A and we find that it is spin up, then since the total spin is zero, we can be 100% sure that the other electron B will be spin down even before we measure it.

The experimental set up is that the two electrons are sent off, one along the +z axis while the other is along the -z axis. The two detectors are oriented so as to measure the spins along axes in the plane perpendicular to the z-axis, i.e. along any direction in the x-y plane. If we set the detector at A along the x-axis and find the spin to be in the +x direction, we can be 100% sure that if we set the detector at B to also be along the x-axis, we will find that electron spin to be in the -x direction. If we set the detector at A to be along the y-axis and we find the spin to be in the +y direction, we can be 100% sure that if we set B to also be along the y-axis, we will find that electron spin to be in the -y direction. This is true for any direction that we choose for the detectors. As long as the two detectors measure spin along the same axis, if one result is up the other will be down.

But again, this does not tell us if the spin of the electron at B had its value before the detector at A recorded what that electron’s spin was. All we know is the direction of electron B’s spin after we measure the direction of spin of electron A, not before. Although unlike with the cards, we can actually do this experiment, like with the cards, there seemed to be no way of determining whether an objective reality exists at this microscopic scale. So we seem to be stymied again.

This is the way that people were thinking of the problem for a long time, from the beginning of quantum theory, and so the debate raged for decades about whether an objective reality existed.

This is where John Bell comes in. He proposed a setup where the two detectors were not aligned along the same axis, but instead were skewed. i.e., the axis of the detector at A was at an angle other than 0^o or 90^o to the axis of the detector at B, i.e., neither parallel nor perpendicular. In such an arrangement, even after we measure the spin at A, while we can be sure that the spin of B would be opposite to that of A, we would not get 100% predictability for the results for B because the detector there is not parallel or perpendicular to the axis as A. As a result, sometimes both detectors would register spin up, sometimes both would register spin down, and sometimes one would register spin up and the other spin down. The outcomes would be statistically distributed and that distribution can be calculated using the laws of quantum mechanics. (It should be noted that there is no debate as to whether experimentally observed quantities should agree with the predictions of quantum mechanics. The success of quantum theory in explaining measured quantities is unchallenged, and so whatever alternative is proposed, the calculated results have to agree with those obtained by quantum mechanics.)

What Bell was able to prove in 1964 was that irrespective of any specific form that the theory might take, if one assumed that the two electrons always had their spin properties before any measurement was made on either of them, then the statistical distribution one obtained would always disagree with the predictions of quantum mechanics. So finally we had a way to test experimentally whether the electron spins had objective reality because the measured distribution of results of the two detectors (inserted into an an inequality known as Bell’s inequality or Bell’s theorem) can be used be to distinguish between the two cases. If the distribution obtained agreed with the predictions of quantum mechanics, then there is no objective reality. If there is objective reality, then the distributions obtained would disagree.

These experiments are devilishly difficult to carry out because they have to counter the many loopholes that could be postulated to explain the results while retaining the notion of objective reality. It took decades for teams of experimenters in many laboratories around the world to set them up. Starting in the 1980s, these difficult and painstaking experiments finally started to produce results and we now have a preponderance of evidence in support of the idea that in the quantum world, there is no objective reality, that when we start with a superposition of observable states for two entangled entities, the observed quantities of each only come into existence upon measurement.

Hence the spin of each does not exist before the measurement and so there is no objective reality.

But wait! There may yet be a loophole!

Bell also showed that you could get agreement with the results of quantum mechanics while assuming that the electrons had their spin properties before measurement, if you allowed for the spin results at A to be dependent not only on the orientation of the detector at A but also on the orientation of the detector at B and vice versa. But there is a steep price to be paid to recover objective reality this way. By setting the two detectors to do their measurements within a time interval of L/c (where L is the distance between the detectors and c is the speed of light), and also by being able to change the orientations of each detector at the last moment, the information to be communicated between the two detectors about their orientations would require faster than light travel, instantaneous in fact. This means that this must be a non-local theory and that contradicts the laws of relativity. As Bell says in his 1964 paper:

In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.

Experimenters carefully looked for other possible loopholes that might trick them into thinking there was no objective reality when there really was and were able to close them.

So to reiterate, the only way to retain objective reality is to invent a non-local theory where information can be transmitted instantaneously, which is of course undesirable. Giving up objective reality, at least at the microscopic level, is more appealing to physicists than violating relativity. So the issue seems to be settled for most of them. It seems fair to say that we now have a pretty robust consensus that as long as we constrain ourselves to just local theories in order to retain Lorentz invariance, there is no objective reality, at least as far as the microscopic world goes.

While writing this, I felt that for the sake of completeness I needed to look at the consequences of objective reality and Heisenberg’s uncertainty principle and that will be the next (and final?) post in this series.