Without it, you can't even play with your phone.

Regardless of whether they have actually come into contact with quantum mechanics, many people will use the phrase "When in doubt, use quantum mechanics" to make jokes about difficult problems. In fact, in real quantum mechanics, there are also some "uncertainties", such as the "uncertainty principle" that you may have heard of. However, "uncertainty principle" is an incorrect name and will cause misunderstanding of the nature of this principle. Its real name is " uncertainty principle ".

01

Suggested explanation of the principle

The uncertainty principle means that the position and momentum of a particle cannot be determined at the same time . The clearer its position, the less certain it is about how fast it is running. Vice versa, the more certain its speed is, the more vague its position is. Moreover, this uncertainty is a quantified specific value, not a philosophical concept that comes up on a whim. We just said that the name "uncertainty principle" is wrong. However, starting from the meaning of this wrong name to understand the uncertainty principle is a quick and easy way for many popular science books (including Hawking's works) and basic university physics teaching, and even Heisenberg's original understanding. Let's start from here. Imagine that we measure the state of a particle. Before the measurement, we know nothing about it - just like there is a black cat in a dark room, we have to shine a light on it to know where it is.

However, if the cat is weak and is knocked away by the light when the light is turned on, then we cannot tell whether it was originally flying or was knocked away by the light. So we have to lower the energy of the light so as not to interfere with our observation object.

The energy of light is not determined by brightness, but by its frequency . In the visible light band, it is expressed as the color of light: purple light has higher energy than green light, and green light has higher energy than red light. This may be a bit counterintuitive, but think about an X-ray chest X-ray: the X-rays used for chest X-rays are actually very weak, but the frequency of X-rays is very high, even stronger than ultraviolet rays. The energy of each photon is at the level of ionizing radiation, and too much exposure is enough to cause health problems.

Back to the point, lowering the energy means lowering the frequency of light. For example, if the original illumination is purple light, and it is changed to red light, the fragile black cat will not be hit too hard, and we can know its original state of motion. However, after changing to red light, a new problem arises: the wavelength of red light is too long, exceeding the size of the black cat, and it goes around it . Or, even if reflection occurs, the position we detect is within a wavelength range, and the error is quite large.

Therefore, either we cannot see clearly where the black cat is, or we do not know the movement state of the black cat. If the accuracy of one increases, the accuracy of the other will decrease, and the "uncertainty principle" will appear.

Although this explanation is relatively easy to understand, it gives people the feeling that human technological capabilities are insufficient. If we find a new method, we may be able to obtain the state of the observed object without disturbing it.

In fact, the uncertainty principle says that uncertainty is the inherent property of a particle. Whether you measure it or not, its position and momentum cannot be determined at the same time .

Please note that it is “impossible to determine at the same time”, not “impossible to be determined at the same time”.

02

Two simple inferences and other implications

We once thought that if we could measure the state of all particles, then based on a set of physical laws, we could deduce their future states, and the future evolution of the world would be clear. This even includes our thoughts, because the material basis of thinking is also the electrical impulses of neurons.

But the uncertainty principle directly negates the entire premise. If the state of a particle itself is uncertain, no matter how many physical laws there are, they are useless. The development of quantum mechanics has revealed more facts, such as the uncertainty of the state itself, which is not "either black or white, but we don't know whether it is black or white". Later, the superposition state (randomness of quantum state measurement) of "both black and white can only be given to you with a glance" has pushed scientific determinism to a dead end.

From a purely classical perspective, the third law of thermodynamics states that absolute zero cannot be reached. From the uncertainty principle, it is also a straightforward inference: the so-called absolute zero is when the molecular atoms that make up a substance are in a fixed position and no longer move. This simultaneously determines the position and motion state of each particle, which is contrary to the uncertainty principle and therefore cannot be reached.

The proposal of the uncertainty principle has triggered more famous events, such as the debate between Einstein and Bohr at the Solvay Conference, "Schrödinger's cat", the EPR paradox, the Bell inequality that was secretly supported by Einstein, and the fact that the Bell inequality was proven to be invalid. The 2022 Nobel Prize in Physics was awarded to three scientists whose experiments overturned Bell's inequality, which is the aftermath of this series.

2022 Nobel Prize in Physics, for using entangled photons to prove that Bell's inequality does not hold.

03

Misunderstandings about Physics Buzzwords

The foundation of the material world revealed by quantum mechanics is so different from the performance of the macroscopic world and is very counterintuitive, so it has been questioned and misunderstood. This is normal. As the founders of quantum mechanics, even Einstein and Schrödinger had doubts. What is there for everyone to doubt?

However, there are many misunderstandings about Einstein and Schrödinger's doubts. Many people think that they are against quantum mechanics. In fact, they are not against quantum mechanics itself, but against the interpretation of quantum phenomena by the Copenhagen School where Heisenberg belongs . In other words, how to use the language of the macroscopic world to explain the phenomena seen in quantum mechanics research.

Just like the uncertainty principle mentioned above, if the "uncertainty principle" is explained, everyone will be more likely to accept it. However, if we say that the particles themselves are uncertain, we need to use mathematics to express it, and there is no specific analogy in the macroscopic world.

Another misunderstanding is that quantum mechanics is "this is uncertain, that is uncertain", which is not the case. Even if the uncertainty principle denies the possibility of accurately measuring the state of a particle, the probability distribution of the particle state and its evolution process can be precisely determined by the Schrödinger equation. Particles may be where they should be, and they will never be where they should not be . There is no ambiguity at all. It's just that when you observe and measure it, it will give you a random result according to a certain probability distribution.

Precisely because quantum mechanics is so counterintuitive, it has been severely scrutinized by physics greats including Einstein. It is the most rigorously reviewed theory in history, but (for now) it is really faultless and its predictions have been confirmed by experiments one by one. The theory of "this is uncertain, that is uncertain" is unlikely to make any predictions.

Here are two examples of quantum mechanics that are relevant to our lives: The first is semiconductor theory . The concept of semiconductor energy bands is an extension of quantum mechanics. If quantum mechanics does not hold or cannot make accurate predictions, then semiconductor physics cannot hold, and the mobile phones and computers we use to read this article will not exist. The second is the sun's light . Einstein's mass-energy equation only reveals one aspect, and the temperature of the sun is too low, far from the temperature required for hydrogen nuclear fusion. If there is no tunneling effect revealed by the Schrödinger equation, the sun cannot shine; or, even if the temperature required for nuclear fusion is reached, the fusion reaction will be a hydrogen bomb explosion, and the entire star will be instantly destroyed, instead of being able to react and ensure that the reaction rate is extremely low, like a compost, with stable production capacity.

Another misunderstanding is that quantum mechanics means "this is quantum, that is quantum", everything is given piece by piece, it is a discontinuous digital world, and then people imagine that "we are all programs, living in a huge operating system". In fact, the seemingly discontinuous quantum world is calculated by various continuous equations, and it is only constrained by the peaks and troughs of probability distribution that it seems discontinuous.

When many media mention concepts in quantum mechanics, they like to use headlines such as "How terrifying is the double-slit experiment?" "Is intelligent quantum communication going to be realized?" "Master quantum entanglement and you can teleport!" We should take a normal view of quantum mechanics. The microscopic world is the material basis of the entire world, and the scope of quantum mechanics' predictions also covers the macroscopic world. We might as well assume that its wonderful performance is the way the world should be, and then reflect on it carefully:

“Why is it so difficult to draw analogies to the macroscopic world when mathematics makes such natural calculations possible?”

Author: Qu Jiong, a popular science writer whose works have been published in the National Museum, the National Space Administration, etc.

Reviewer: Zhang Wenzhuo, CEO of Quantum, former associate researcher of the Micius team of the University of Science and Technology of China