(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 0o or 90o 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.
“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.”
I’m not sure I agree with this statement. At the time that Copernicus and Galileo developed their heliocentric models, the Ptolemaic model gave more accurate predictions (because C & G didn’t consider elliptical orbits, and assumed the sun was the center.) By your argument, the heliocentric alternative would have had to be thrown out from the start.
A “bad” but simpler model might be a stepping stone to an eventually good model.
That said, there is a difference in whether you predict with slightly worse accuracy, or whether you predict something completely different.
Mano, you’re talking about ‘quantum contextuality‘;
As I’ve already said, this was established by the proof of the Kochen-Specker theorem (aka the Bell-Kochen-Specker theorem), which came out a couple of years after Bell’s 1964 paper;
From the OP;
Bell himself considered the ‘steep price’ to be worthwhile. He favoured Bohmian mechanics (a hidden-variable theory). See here;
https://sites.math.rutgers.edu/~oldstein/papers/bb.pdf
Greetings from the peanut gallery!
A recent theory published in the Journal of Cosmology and Astroparticle Physics, according to space.com, posits that “the matter of the massive star that births a black hole would become dark energy during its complete gravitational collapse.”
Sliding past a lot of hand-wavium, doesn’t this imply that if one party had a means of forming a big black hole, and another party had a precise Dark Energy-ometer, that the first could signal to the other instantaneously over any distance?
robert79 @#1,
It is a fact that the heliocentric model was rejected at the beginning by most astronomers and took a long time to gain acceptance. When one looks at the history of science, one sees that new theories always have a very difficult time challenging established ones.
What happens is that a new theory that eventually becomes successful initially usually agrees with just a few of the results that the old theory explains, says nothing about most of the rest, but does explain a few results that the old theory disagreed with or found difficult to explain. But this is usually not enough to overthrow the old theory.
But if, over time, the new theory attracts adherents who are able to expand its range of applications, resolve some of its deficiencies, and expose more flaws with the old theory, there may come a time when the community of scientists switches allegiance to the new theory and a scientific revolution is born. But these revolutions usually are slow and invisible to the people living through it. It is only in hindsight that they appear dramatic.
This is a question that I look at in great depth in my book The Great Paradox of Science.
Clarification to #2: Bell’s theorem did not exclude spin as a possible hidden variable (see the quote from the OP in #2). The K-S theorem did. So, position can still be a hidden variable in Bohmian mechanics, but spin can’t.
I’m sure this has been thought and discussed but whatever experiment is done and prepared, the experimenter is part of the experiment and local to it when preparing the experiment. So the locality should be a non-issue because everything is part of the same universe. The non-locality issue only makes sense if you accept that free will exists and cannot be accounted for by natural (as opposed to supernatural) phenomenon.
Pierce @#3
The gravitational collapse of matter into a black hole is different from the collapse of the wave function and does not imply instantaneity. Gravitational waves travel at the speed of light.
Mano Singham @ # 7 -- I didn’t mean to imply that all “collapses” are equal -- maybe if I understood the math I’d have a clue why they don’t say “resolve” or something without such a physical analog.
But if the formation of a black hole, a local event as experienced for several lightyears around, somehow increases the level of dark energy, a non-local phenomenon as presently understood, that might bring the cosmic cops running to cite a violation of Einstein’s rules & regulations (something not addressed by the “cosmological coupling hypothesis” article I read, which also describes a cosmological scenario of a dark energy surge ~5BYA which I don’t think I’ve heard mention of before either).
The only scientist named is “team member Gregory Tarlé, professor of physics at the University of Michigan”. Does the Journal of Cosmology and Astroparticle Physics have a rep worth heeding?
Journal of Cosmology and Astroparticle Physics is a reputable journal.
The issue of “objective reality” seems to me to arise because some people take mathematical operations too literally. Quantum mechanics is a very nice mathematical model that allows us to make measurements and predict subsequent measurements. While doing that it introduces a bunch of intermediate mathematical objects, like the wave function, or Hilbert spaces. Wave function is NOT a real object, which should be self evident from the fact that it’s complex, yet people insist on talking about wave function collapse as if talking about a real physical object.
Thinking of a superposition in terms of wave functions is also NOT real. It’s just a mathematical trick that happens to be very helpful. We don’t have a nice way of doing quantum mechanics without introducing these fictional concepts, and that’s the main problem with all of this.
now that is an interesting argument, ed, but i have trouble believing it. like, i get that the terms humans develop to describe things are easy for humans to mistake as the things they describe, that we imagine we have more power to apprehend reality than our senses and cognition could ever really achieve. but this math corresponds to physical effects, right? microscopic phenomenon is measured through interaction with macroscopic detector and we have physical evidence a real thing happened.
i’m open. please elaborate.
@ Mano:
Yes, this is the messy bit where the analogy is being stretched to (at least) its limits. We’re expecting a static state to substitute for a dynamic one; and it is not hard to find examples of systems which can be in equilibrium while moving but not while stationary. (She says, trying to shake the mental image of Mano riding a bicycle to the laboratory and placing some test tubes in a centrifuge …..)
I don’t think that is preposterous at all. If we assume that “oppositeness” is a fundamental property of entangled particles, such that both particles will always exit superposition into opposite states simultaneously when either one is observed, it’s exactly what’s expected.
An alternative analogy might be two oscillators with the same period and opposite phase. Here, there are all kinds of hairy issues where real life on the macroscopic scale can get in the way, so all you actually end up measuring if you try the experiment in real life is how well you can keep two oscillators in sync (compare, naïvely trying to measure the speed of light by having two people, each with a dark-lantern and a telescope, on mountain tops a few kilometres apart; the dominant term is going to be the time it takes between the second person seeing the light from the first lantern and drawing the shutter on their own, which will be a matter of tens or hundreds of milliseconds in itself and subject to a “give or take” a couple of prefixes greater than the time it takes for the light to travel from end to end). If we uncover pendulum A and observe it swinging to the left at some moment in time, we can know that, if it were not for real-world phenomena, pendulum B would be swinging to the right at the same moment. It still doesn’t require any information to travel from one to the other faster than light, because the oppositeness was baked into the system all along. It still falls a bit short, though, because the oscillators don’t stop changing state when they are observed. But then, the universe is hardly under any obligation to give us good analogies for every natural phenomenon, even although there is no shortage of places where half of one thing times something else squared gives Joules.
What’s the problem with “objective reality” being an emergent property of sufficiently-large systems? Isolated particles are going to behave probabilistically; but even if it looks like a nice, smooth Gaussian bell curve from close up, the probability distribution for one particle over the whole of space is just a tiny narrow spike. And once we start considering more particles, thus diminishing the influence any one of them in isolation can exert over the system considered in aggregate, our system asymptotically approaches deterministic behaviour.
This does have a real-life analogue, in the form of an old carnival game where multiple dice are rolled, or marbles thrown across a board to settle in numbered holes, with points being awarded for certain totals and the opportunity to accumulate enough points over several rounds to win fantastic prizes. However, none of the “winning” totals have a high probability of occurrence (the odds of achieving 48 from eight fair dice are 1679615:1 against; and the distribution of numbers across a matrix of holes in a board can be skewed even worse by the inclusion of more middle and fewer extreme values). The barker may initially bias the result artificially in the player’s favour, risking giving away a low-value prize; but the game usually terminates with the player’s reserve of cash (or sometimes, patience) becoming exhausted.
ed @#10,
Bébé Mélange @#11 in their response to you has the right idea. I want to just elaborate on it a bit.
The problem is that the word ‘real’ has a physical connotation as well as a mathematical one, and we need to keep them separate.
In the physical world, it means that any measured observable has to be a real number. In the mathematical world, all it means that a number lies on the real axis, with no component along the imaginary axis.
For the longest time, there was a debate about the meaning of the wave function, with some insisting that any quantity that had physical relevance also had to be a mathematically real number. Hence there were attempts to have the wave function be real (in the mathematical sense) and represent something like the particle density. But those attempts did not bear fruit and the wave function was conceded to be a complex number whose absolute value (which is a mathematically real number) is what can be compared to observations in the physical world. The fact that the wave function is not ‘real’ in the mathematical sense seems irrelevant since we never measure the wave function directly.
Of course imaginary numbers (and complex numbers that have a component that lies along the imaginary axis) cannot be real in the physical sense but have great value in the mathematical sense. Hence they occupy an intermediate space and are ‘real’ in that we cannot seem to do without them while not being ‘real’ in the mathematical sense. Calling them a ‘mathematical trick’ seems to suggest that they somehow have less value and can be dispensed with. It is not just that they happen to be ‘very helpful’, they seem to be indispensable.
Surely something that seems to be indispensable to our understanding of the physical world has some claim to be ‘real’ even if not in the mathematical sense?
Occasionally I have wondered if positive and negative values represent entirely different qualities which shouldn’t be mathematically treated as part of the same number line, even if they can cancel out under some circumstances. Kind of like how assets and debts are often represented as positive and negative values respectively, but “$1 million assets and $2 million debts” is a very different situation than “$0 assets and $1 million debts” even if both cases can be represented as -$1M total wealth. Or maybe debt is simply imaginary and we can mostly ignore it like some rich people do. /jk
I haven’t had the inclination to try and figure out what the consequences for math would be if that were true (or if it’s even a viable and useful way of manipulating values), let alone how we would frame physics under that, so no idea.
“Surely something that seems to be indispensable to our understanding of the physical world has some claim to be ‘real’ even if not in the mathematical sense?”
No, it doesn’t. At all. It’s just a neat math trick, and moreover I’m completely comfortable with there not being a better math trick that only deals with real, i.e. physical quantities. Nature doesn’t owe us such simplicity.
@bébé some things in the math correspond to physical things, and some don’t. The wave function is emphatically not physical. So any talk about its collapse is .. not physical. Any talk about the wave function being a superposition is .. not physical. That doesn’t mean that these are not useful math tools, but that is all they are -- tools.
I should add that when they were first introduced, all the deviations from positive integers, including negative numbers and irrational numbers, were thought to be not ‘real’.
For avoidance of any confusion, I’ve so far only used the word “real”, to mean physical, aka measurable. If I post again and need to use “real” in the math sense, I’ll make sure to be explicit about it.
Why can’t we say that a pre-measurement microscopic quantum-mechanical system is objectively in a superposition of states? After all, this seems to be true independently of anyone’s opinion.
KG @18: Welcome to the quagmire of language about quantum physics!
‘objective reality’ is a term of art with the meaning of ‘having definite values even before measurement’. So, not a superposition, even though the superposition can be called objective, and ‘real’ in some sense.
Mano, have you seen this?
If they are right that the universe ‘remembers’ does this mean the universe itself is an observer? Or are the kind of quantum phenomena that can be unobserved for a while those that can fit into a single quantum cell?
anat @#20,
I have not seen this particular model butI have seen other models that claim that information is the fundamental constituent of the universe. Also theories that space and time are not continuous but discrete.
The problem for me is that there are so many variations and they are not easy to understand. As a result, I have not put much effort into each and am waiting for at least a partial consensus to emerge in favor of a particular model before I invest a lot of time and effort to understanding it.
Sorry that I cannot be of more help!
Mano @21: It is indeed difficult to keep up with all the ‘breakthrough du jour!s’. It sometimes seems they are daily.
Rob @22
That’s so deadpan that I can’t tell if you’re serious or not
file thirteen @23: Serious. There have been so many pop sci articles reporting on “possible breakthroughs” that reading the relevant papers would be a full-time job and then some. The papers usually end with something like “much work remains to be done, etc”.
Rob @24
I was just amused at your use of “du jour” (literal translation “of the day”) and adding it sometimes seems to be daily. If it isn’t daily, it’s not du jour. 🙂
Rob Grigjanis@19,
I suggest that “term of art” be changed. I suspect it’s partially responsible for all the quantum woo-woo.