What Einstein and Bohr were arguing about was exactly 01 Uncertainty Principle 02 EPR paradox

Author: Amazon's Butterfly (Butterfly_of_Amazon)

The previous article "The Sword of Huashan in Quantum Mechanics" Talked about the problem of causality and objectivity in the Copenhagen interpretation, Einstein and Bohr launched a debate for more than twenty years, until the two giants of science died one after another, and the debate was still fruitless.

Today I'm going to talk in detail about what they're arguing about.

Before you start writing, let's say two sentences about why you wrote this article. Friends who are not interested can skip it directly, which does not affect the reading of the article.

Science is an important tool for us to understand the world, and religion, philosophy and science should ultimately be compatible rather than contradictory, so the most impactful quantum physics for understanding the world is worth everyone's time to understand. But there are many popular science articles on quantum mechanics on the Internet, is it meaningful for me to write such an article? Combined with my own experience, I think there is.

Non-professionals will encounter many difficulties in learning quantum physics. If you learn through professional books, due to the lack of a systematic theoretical foundation, coupled with no one to answer questions, the difficulty is undoubtedly huge, and there is no need; if you understand through popular science articles, you will generally encounter two situations, one is that the article is biased towards storytelling, very attractive but lack of in-depth analysis, after reading or not understanding, one is that the article is too professional, the reading is very difficult, and it will get stuck at many nouns and key points. Hopefully my article will improve in this regard, and I'm confident that I have the ability to try it out.

First of all, I think I have some scientific literacy and know how to respect science. Although I am not engaged in physics-related majors, the spirit and attitude of science have been integrated into my thinking and habits, and I have mastered some scientific methods, knowledge and abilities. These ensure that my article is rigorous and less prone to "civil science" self-talk.

Secondly, every time I write an article, I learn first with confusion and problems, think clearly and then write, so I know where the confusion of the general reader is and how to write clearly.

Finally, the positioning I gave to the article is "deeper than popular science, shallower than the paper". Physics and mathematics as a student are my strong points, and if necessary I will add some simple calculations and deductions, which may not be as interesting as popular science articles, but will be suitable for non-professional readers who want to learn more about the deep principles.

After all, it is written while learning, and if there is an error, it is also expected to include and correct.

The previous article mentioned: Bonn's probabilistic explanation, Heisenberg's uncertainty principle and Bohr's complementary principle together constitute the core of the quantum theory "Copenhagen Interpretation", the former two destroying the strict causality of the classical world, and the complementary principle and uncertainty principle destroying the absolute objectivity of the world.

The classical school represented by Einstein could not accept that the physical world did not have strict causality and objectivity, and they believed that the Copenhagen theory was "not necessarily wrong, but necessarily incomplete", and that it was necessary to find out where the problem was, replace it with a better theory, and pull physics back into a normal and understandable state.

So what are the specific aspects of the debate between the classical school and the Copenhagen school on causality and objectivity? Let me give two examples that are relatively easy to explain.

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01 Uncertainty principle</h1>

Heisenberg pointed out that the momentum of a particle (if the momentum is not understood, it can be understood as velocity) and position can not be accurately measured at the same time, the more accurate the momentum is measured, the greater the measurement error of the position, in turn, the more accurate the position is measured, the greater the measurement error of the momentum, and the product of the error of the two must be greater than h/4π (h is Planck's constant, the value is very small, 6.626× 10^-34 joules). This is the case with all pairs of physical quantities, such as energy and time. This is the uncertainty principle, originally translated as the uncertainty principle, proposed by Heisenberg in 1927.

Intuition tells the classical school that the error is caused by insufficient measurement methods, and with the improvement of the measurement level, the error will become smaller and smaller, and eventually it will be able to break through the limit of the uncertainty principle.

But Heisenberg said: "It is impossible, this limit is caused by theory, no matter how to improve the measurement method and improve the measurement method, it is impossible to break through."

Regarding the controversy over the measurement method, it is impossible to determine right or wrong in a short period of time, and it is considered that the principle of inaccuracy is correct.

The classical school goes on to say: "Although it is inaccurate, in fact particles have a definite momentum and position (i.e., objectivity, also called reality) at every moment, but they cannot be accurately measured at the same time."

But Heisenberg says, "No, particles have no definite momentum and position before measurement" (hence the "uncertainty principle" was later translated as the "uncertainty principle" because the new name better expresses the universality of the principle and reduces misunderstandings).

Classical school: "'Before the measurement, the electron has no definite momentum and position'? What does this sentence mean"?

Heisenberg: "I don't know what it means for specific electrons, probably... Maybe... possible... It means that multiple states are superimposed on top of each other."

Isn't that confusing? Our understanding of the world is based on analogies and reasoning, such as: we think that the line between two points is the shortest because we can measure it with a ruler to see which line requires the least scale, can walk to try, and see which line takes the shortest time. But we can't find an analogy to what Heisenberg is saying, and intuition and habit tell us that "momentum and position are there."

One might say, "It doesn't make sense to discuss the question 'whether momentum and position were there before measurement' because it is impossible to know anyway". Actually, no, it's not a metaphysical problem, science has ways to incorporate it into the system, different understandings can derive different conclusions, and these conclusions can be verified by observation. This will be described in detail in the next article.

This is a debate between the Classical School and the Copenhagen School about the objectivity of the quantum world. The following leads to the debate on the localization of the quantum world.

02 EPR paradox</h1>

In 1935, Einstein, along with Podolsky and Rosen, published a paper titled "Is Quantum Mechanics' Description of Physical Reality Possiblely Complete", proposing a thought experiment: two particles in a quantum entangled state fly in two opposite directions from the origin. When the coordinates of particle 1 are measured to be x0, the coordinates of particle 2 can be inferred to be -x0, and the momentum of particle 1 can be measured to be p0, and the momentum of particle 2 can be inferred to be -p0. This is determined by the characteristics of the quantum entanglement state, which has been confirmed experimentally (although the experiment does not use continuous quantities such as momentum and position, which are inconvenient to measure, but discrete quantities such as spin and polarization direction), and there is no dispute between the classical and Copenhagen schools, the controversy lies in its interpretation.

Einstein believed that the moment two entangled particles fly out, they have "agreed" on the behavior after that, including the momentum and position of each moment. After measuring the momentum or position of particle 1, the momentum or position of particle 2 can be known based on the entangled state property of "particle 2 and particle 1 have the same speed and magnitude and opposite direction". The Copenhagen School believes that before the measurement, the particle has no definite momentum and position, only at the moment of measurement is determined by the measurement, while completing the measurement of particle 1, based on the entangled state property of "particle 2 and particle 1 speed is equal, opposite direction", the momentum or position of particle 2 can be inferred.

Paying attention to the description "determined by measurement", the paper grasps this point and further proposes: according to Einstein's theory of relativity, any information can not travel faster than the speed of light (i.e., localization), and in this experiment, according to Copenhagen theory, when two particles fly out for a long time and are far enough apart, because the momentum or position of particle 1 is determined by the measurement, how can particle 2 know what its momentum or position should be valued at the moment particle 1 is measured? Unless there is a hyperlated action between two particles that violates the locality to communicate information. If the Copenhagen theory is not to violate locality, it must abandon uncertainty and accept reality, that is, whether measured or not, particles have a definite momentum and position at every moment, which is the EPR paradox.

Bohr wrote a rebuttal paper of the same name, published in the Physical Review. To summarize Bohr's answer, it roughly means that due to quantum entanglement, some physical property of the whole system is indivisible, and this indivisibility has nothing to do with space. Before measurement, two entangled particles, no matter how far apart they are, must be an interconnected whole, and even two independent particles do not exist, let alone the objective physical state of a single particle. Because they are one and the same, there is no need to transmit any signals to each other.

Judging from Bohr's answer, while insisting on denying reality, he implies the existence of a hyperactivity, because he says that "indivisibility has nothing to do with space." Note, however, that he is not denying locality. The locality required by the theory of relativity limits the transmission of classical information faster than the speed of light, and Bohr believes that the transmission of classical information does not exist in this experimental process, because the particles in quantum entanglement "are originally coordinated and do not need to transmit signals to each other." But what determines the indivisibility of cross-space is unknown.

Regarding the transmission of information, it is necessary to write a separate paragraph:

Classical information transmission refers to the transmission of messages or the transmission of substances, one party wants to obtain originally unknown messages or substances that were not originally available from the other party, and localization limits the speed of such transmission. Bohr believed that the entangled two particles were a whole, and that measuring the speed or position of particle 1 was not the cause of determining the speed or position of particle 2, all of which were just the state of the overall system, and the two particles did not need to communicate with each other.

To give an example:

There is a couple whose husband does not return home for many years, and the wife files for divorce in anger. In order to avoid divorce, the husband fled to Sagittarius, 4.3 light-years away from Earth. The court awarded divorce in absentia. The moment the verdict was handed down, the husband changed from married to unmarried, and although it would be 4.3 years before he could get the news of the court's verdict at the earliest, it did not prevent him from becoming a bachelor, and his entanglement with his ex-wife ended here.

Here, the transmission of the court's judgment is the classic transmission of information, subject to the limitation of localization, and it takes 4.3 years to reach Sagittarius at the earliest. The change in the marital status of the husband and wife is beyond the distance, reaching both parties in an instant, but there is no actual message transmission.

In Liu Cixin's novel "Three-Body Problem", the three-body people who are 4 light-years away from the earth deploy "zhizi" on the earth and use quantum entanglement to achieve real-time monitoring of the earth, which is actually impossible.

Bohr's answer apparently did not satisfy Einstein, who mocked Bohr's description of quantum behavior as "ghostly hyper-action" and commented on the probabilistic explanation, arguing that it was only a statistical approximation theory, and that there might be some yet-to-be-discovered complete theory describing nature that could give variables to correspond to each element of physical reality. This complete theory is called hidden variable theory.

With time to elaborate on the theory of hidden variables later, we will return to the debate. The explanations of the two men in the EPR paradox seem to be indistinguishable from right from wrong, because both agree on the final result, but the interpretation of the process is different, but no one can insert a checkpoint in the process to make a judgment. Will this controversy become an unsolved case that will never be decided?

The next article, "Einstein and Bohr's Argument, Who Won in the End?" will be recounted.