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This article comes from the official account of Wechat: ID:fanpu2019, author: Ethan Siegel

Physicists have not completely ruled out the existence of hidden variables. is there anything inherent that we don't know yet? We don't know, we just know-- quantum mechanics is really amazing.

Write article | Ethan Siegel

Translation | Hardon

In addition to the variables we already know and know how to measure, there may be other variables. But they still can't get us out of quantum weirdness.

It is well known that light is both volatile and particle, as shown in this 2015 photo. What is not well understood is that matter particles exhibit similar fluctuations. Even objects as large as people are volatile, although it is extremely difficult to measure them. Photo Source: Fabrizio Carbone / EPFL since people discovered the strange behavior of quantum systems, we have been forced to deal with a seemingly disturbing fact. Whatever the reason, the reality we perceive, such as where objects are and what attributes they have, is not fundamentally determined. As long as you do not measure or interact with other systems, it is in an uncertain state, and we can only talk about its properties and the results of any potential measurements in the sense of statistics and probability.

Is this caused by the basic limitations of nature? Is there any inherent uncertainty in the system before the measurement is completed or the quantum interaction occurs? Or is there a "hidden reality" that is completely predictable, understandable, and determines what we see at a deeper level? This possibility is fascinating, and it is favored by scientists who can compete with Einstein. This is also the question of William Blair, a supporter of Patreon, who said:

"Simon Kochen and Ernst Specker demonstrated from pure logical reasoning that there are no so-called hidden variables in quantum mechanics. I checked the data, but the mathematics and physics in these articles are beyond my understanding. Can you enlighten us?"

Reality is very complex, especially when it comes to quantum phenomena. Let's start with the most famous example of quantum uncertainty, which is the Heisenberg uncertainty principle.

The figure illustrates the inherent uncertain relationship between position and momentum. The more we know about one of the two, it is fundamentally impossible to know exactly about the other. Other pairs of conjugate variables, including energy and time, spin in two vertical directions, angular position and angular momentum, also show the same uncertainty. Photo Source: Maschen / Wikimedia Commons in the classic macro world, there is no so-called measurement problem. For example, if you take any object you like, such as a jet plane, a car, a tennis ball, a pebble, or even a grain of dust, you can not only measure any attribute you want to know about it, but also infer what these properties will look like in the distant future according to the laws of physics that we already know. Newton's laws of motion, Einstein's equations and Maxwell's equations are all deterministic, and if you can tell me the position and motion of each particle in your designated system or universe, I can tell you exactly where they will appear and how they will move at any time in the future. Our only uncertainty comes from the limitations of the equipment we use to make measurements.

But in the quantum world, this is no longer the case. There is an inherent uncertainty in the quantum world, and it is uncertain to what extent you can understand the various properties of objects at the same time. For example, if you try to measure the value of a particle:

Position and momentum

Energy and lifespan

Spin in any two vertical directions

Or angular position and angular momentum.

You will find that knowing that these two quantities are limited at the same time, the product of their uncertainty cannot be less than a certain basic value, and is proportional to the Planck constant.

The particle beam passing through the magnet may produce quantized-discrete results caused by particle spin angular momentum (5), or classical-continuous results (4). This experiment, called the Stern-Grah experiment, shows some important quantum phenomena. Photo Source: Tatoute / Wikimedia Commons in fact, when you measure one of the quantities very accurately, the uncertainty of the other complementary quantity automatically increases, and their product is always greater than a certain value. The Stern-Grah experiment shown above is an example. Quantum particles such as electrons, protons and nuclei all have an intrinsic angular momentum, which we call quantum "spin", although these particles do not have any actual spin. In the simplest case, the spin of these particles is 1 stroke 2, and no matter which direction you measure it, it can be positive (+ half) or negative (- half).

Now, here comes the strange place. Suppose we emit these particles (silver atoms were used in the initial experiment) through a magnetic field in a particular direction. Half of the particles will deflect in one direction (in the case of spin = +), and half of the particles will deflect in the other direction (in the case of spin =-half). If you let these particles pass through the Stern-Grah device in the same direction in the other direction, there will be no further splitting, which means that the + and-half particles will "remember" the direction in which they split.

But if you let them pass through a magnetic field perpendicular to the first direction, they will split again in the positive direction and the negative direction, as if in this new direction, there is still uncertainty-- which is + 1max 2 and which is-1max 2. Now, if you go back to the original direction and apply another magnetic field, they will split again in the positive and negative directions. To some extent, measuring their spins vertically not only "determines" these spins, but also destroys to some extent what you previously knew about the direction of the initial split.

When you pass a group of particles through a Stern-Grah magnet, they deflect according to spin. If you let them pass through the second vertical magnet, they will split again in the new direction. If a third magnet is added in the same direction as the first, the beam will split again, proving that the previously determined information will be randomized by the most recent measurements. Photo Source: MJasK / Wikimedia Commons's reflection on this problem makes us realize that there is an inherent uncertainty in the quantum world that can never be completely eliminated. When you accurately determine the spin of a particle in a certain dimension, the corresponding uncertainty in its vertical dimension must become infinitely large to compensate, otherwise it will violate Heisenberg's inequality. We can not "deceive" the uncertainty principle, we can only obtain information about the actual results of the system through measurement.

But for a long time, people have been trying to explain this with another idea, which is the theory of hidden variables. In the latent variable theory, the universe is decisive and the quantum has intrinsic properties, which enables us to predict exactly where they will eventually appear and what the result of any quantum experiment will be. But in our current real world, some of the variables that control the behavior of the system cannot be measured by us. If we can measure, we will understand that the "uncertain" behavior we observe is only because we are ignorant of the real situation; if we can find, identify and understand the behavior of these variables that form the basis of reality, the quantum universe would not seem so mysterious.

Although at the quantum level, reality seems to be fickle, uncertain, and essentially unascertained, many people firmly believe that there may be properties that we cannot see, which determine the reality independent of the objective reality of the observer. By the end of 2022, we had not found any such evidence. My idea of hidden variables is to imagine that the universe on a quantum scale has dynamics that we don't understand but can observe. It's like connecting a vibrating plate at the bottom of our reality, and we can only observe the sand on the board.

If all you can see is sand, then in your opinion, the vibration of each grain of sand has a certain inherent randomness, and there may even be large-scale patterns or correlations between sand grains. However, because you cannot observe or measure the vibrating plate under the particles, you cannot know the complete dynamics of the control system. The information you can learn is incomplete, and what seems random actually has a fundamental explanation, even though we don't fully understand it.

This is an interesting idea worth exploring, but like everything in our physical universe, we must always confirm our ideas through measurements, experiments, and observations of actual matter.

The results of the "masked" double-slit experiment. Note that when the first slit (P1), the second slit (P2), or both slits (P12) are opened, the pattern you see will be very different, depending on whether one or both slits are open. Image source: R. Bach et al., New J. Phys., 2013 in my opinion, there is one such experiment, which is the most important experiment in all quantum physics-- the double-slit interference experiment. When you take a quantum particle and fire it into a double slit, you can measure where the particle falls on the background screen. If you do this hundreds, thousands, or even millions of times, you will eventually be able to see what the pattern looks like.

Then the strangest place appeared.

1. If you don't measure which of the two slits the particles pass through, you get an interference pattern where particles tend to appear in places where particles are highly unlikely to appear between them. Even if you let these particles pass through one at a time, the interference effect still exists, as if each particle were interfering with itself.

two。 However, if you measure which slit each particle passes through, such as using a photon counter, marker, or any other mechanism, the interference pattern will not appear. At this point you can only see two clumps, one corresponding to the particle passing through the first slit and the other corresponding to the particle passing through the second slit.

If we want to further determine what's going on in the universe, we can do another type of experiment, the quantum delay selection experiment.

This picture illustrates the Wheeler delayed selection experiment. In the image above, the photon first passes through the beam splitter, where it will choose the red or blue path and reach one of the two detectors. In the following illustration, a second beam splitter is placed at the end, and the paths are combined to produce an interference pattern. The choice of delay configuration has no effect on the experimental results. Photo: Patrick Edwin Moran / Wikimedia Commons John Wheeler is one of the greatest physicists of the 20th century. Wheeler has been thinking about quantum "weird" behaviors, such as how they behave sometimes as particles and sometimes as waves. When he began to design experiments to capture quanta that were expected to behave as particles, they behaved as waves, and vice versa. Perhaps the most telling of these experiments is the one shown above, which allows photons to enter the interferometer through a beam splitter, which has two possible configurations, "on" and "off".

The interferometer works by dividing the light into two different directions and then recombining them at last to produce an interference pattern according to the difference in path length (or light propagation time) between the two routes.

1. If configured to "open" (above), you can simply distinguish photons from two paths without getting a combined interference pattern.

two。 If the configuration is "off" (below), you will see a similar wave effect on the screen.

In classical mechanics (a) and quantum mechanics (Bmurf), the trajectory of a particle in a box (also known as an infinite square potential well). In (A), the particles move at a uniform speed and bounce back and forth. (BMY F) is the wave function solution of the time-dependent Schrodinger equation, and the geometric shape and intensity of the potential field in each graph are the same. The horizontal axis is the position, and the longitudinal axis is the real part (blue) or imaginary part (red) of the wave function. These steady states (B, C, D) and unsteady states (E, F) can only represent the probability of the occurrence of particles, not the specific results of particles at a particular time. What Wheeler wants to know is whether the photons "know" in advance how they must act. He imagines starting the experiment with a certain configuration and then "turning on" or "off" the instrument at the end of the experiment before the photons reach the end of the experiment. If light knows what it is going to do, you can capture it as it becomes a wave or particle.

In all cases, however, when the quantum reaches the end of the experiment, they behave exactly as you expected. In the double-slit experiment, when they pass through a slit, if you interact with them, they behave as particles, and if you don't interact with them, they behave as waves. In the delay selection experiment, if the final device for reorganizing the photon path appears before the photon arrives, you will get a wave-like interference pattern; in another case, you can only get a single photon without interference. As Niels Bohr (Einstein's main argument on the uncertainty of quantum mechanics) said:

". In terms of the observable effects that can be achieved by a clear experimental setting, whether our plan to construct or operate the instrument is determined in advance, or whether we choose to postpone the plan, there should be no difference between the two when the particles are in the process of moving from one instrument to another."

But does this rule out the idea that hidden variables may dominate the quantum universe? Not exactly. What it does is to make important constraints on the properties of these hidden variables. Starting with John Stewart Bell (John Stewart Bell) in 1964, many people have shown over the years that if you try to preserve a "hidden variable" explanation for our quantum reality, you must give something else important.

A variety of quantum interpretations and the matching of various properties. Despite the differences, there are no known experiments to distinguish these different interpretations, although some interpretations, such as those with locality, reality and deterministic hidden variables, can be excluded. Photo Source: English Wikipedia page on Interpretations of Quantum Mechanics in physics, we have the concept of locality, that is, no signal can travel faster than the speed of light, and information can only travel between two quanta at the speed of light or lower. Bell first showed that if you want to develop a theory of hidden variables in quantum mechanics, and it is consistent with all the experimental results we have done, then the theory must be nonlocalized. some information must be exchanged at a speed greater than the speed of light. According to experience, signals can only be transmitted at a limited speed, and locality is something we have to give up if we ask to develop the "hidden variable" theory of quantum mechanics.

What about Kochen-Specker 's theorem? This theorem appeared a few years after Bell's theory was put forward. It points out that you have to give up not only locality, but also so-called quantum non-intertextuality (quantum noncontextuality). Simply put, this means that any experiment you do gives measurements of any quantum properties of the system, which is not just a pre-determined "revealing pre-existing values".

On the contrary, when you measure a quantum observable, the value you get depends on what we call the "measurement context", that is, other observables that are measured at the same time as the amount you are concerned about. Kochen-Specker 's theorem is the first to show that quantum intertextuality (that is, the result of any observable measurement depends on all other observables in the system) is an intrinsic property of quantum mechanics. In other words, you cannot assign values to the basic physical quantities revealed by quantum experiments without destroying their relationships, which are essential to the operation of the quantum universe.

Quantum erasure experimental device. The two entangled particles are separated and measured respectively. The change of one particle at the end point does not affect the result of another particle. You can combine principles such as quantum erasure with double-slit experiments to see what happens to the information itself that is measured through the slit if you retain or destroy, observe or not observe. Photo Source: Patrick Edwin Moran / Wikimedia Commons when it comes to the physical universe, one of the things we always keep in mind is that no matter how certain we are of our own logical reasoning and mathematical rationality, the ultimate arbiter of reality is in the form of experimental results. When you understand our experiments and try to deduce the rules that govern them, you must get a self-consistent framework. Although there are countless interpretations of quantum mechanics that can describe reality equally successfully, no one has ever disagreed with the predictions of the most original (Copenhagen) interpretation. The preference for a certain interpretation, which many people have for reasons I cannot explain, is just a difference in ideology.

Nothing can stop you from assuming that there is an additional, potential set of hidden variables that really dominate reality. However, what Kochen-Specker Theorem tells us is that if these variables do exist, they will not predetermine the values revealed by the experimental results and are independent of the known quantum rules. This kind of experimental realization, which is called quantum intertextuality, is now a wide range of research fields in the field of quantum foundation, which has an impact on quantum computing, especially in the field of accelerating computing and pursuing quantum hegemony. This is not to say that hidden variables do not exist, but this theorem tells us that if you want to call them, you have to play such tricks.

No matter how much we dislike it, there is something "weird" inherent in quantum mechanics that we cannot easily get rid of. You may be uncomfortable with a fundamentally uncertain theory of the universe, but other interpretations, including those with hidden variables, are equally strange.

The writer introduces Ethan Siegel, an astrophysicist, writer and science communicator, teaching physics and astronomy. Since 2008, its blog "from the Big Bang" (Starts With A Bang!) He has won many science writing awards, including the best science blogger award from the Institute of Physics. The author is also the author of Treknology:The Science of Star Trek from Tricorders to Warp Drive and Beyond the Galaxy.

This article is published in "back to Park" authorized by the author, and the original article is published in https://bigthink.com/ starts-with-a-bang / hidden-variable-quantum/.

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