Hard core science: in quantum mechanics, why does observation lead to collapse?

Scientists are not fully aware of this problem.

Scientists have a much clearer understanding of this problem than most people think.

If the bare theory is described in the simplest language, we can say that quantum mechanics describes how the quantum state of the system evolves and what results will be obtained by observing a system with a certain quantum state. In short, there are two things, one is evolution and the other is observation.

Corresponding to these two things, there are two concepts, one is quantum state and the other is observable.

Microscopic particles are different from macroscopic particles and cannot be described by definite momentum and position. In the basic postulate of quantum mechanics, the motion state of microscopic system can be completely described by quantum state. Quantum states are vectors ("state vectors") in Hilbert space. One of the most common expressions of this state vector is the wave function. In quantum mechanics, a wave function can completely define all the motion States of a microscopic particle: knowing the quantum state, we know all the information of the quantum system; On the contrary, all the information of a quantum system is combined to form a quantum state.

Relatively speaking, in an empirical sense, we are more concerned with the so-called observable measurement, that is, what results we will "see" when we observe the system. These considerable measures include position, momentum, angular momentum, energy and so on, which we can see in the classical world. We say that quantum states contain all measurable information.

Then, the formal theory of quantum mechanics revolves around two problems:

"Given the initial state, how to predict the quantum state of the system at a certain moment in the future?"

"Knowing the quantum state of a system, what possible observation results will we get when we observe it concretely, and what is the probability of getting this result?"

The former is a question of evolution, while the latter is a question of observation. In quantum mechanics, there is a postulate. The former is Schrodinger equation and the latter is Bonn rule.

In addition, there is a postulate that entangles the two problems, called projection postulate-this postulate also has a famous name, called wave function collapse.

We can draw these three hypotheses.

The first postulate is Schrodinger equation. The status of this equation, like Newton's second law in classical dynamics, is the most basic cornerstone. Its main function is to describe how this wave exists and changes: what is the shape of its wave packet? How fast does it spread? What is its amplitude? What is its frequency and wavelength? Wait a minute.

Quantum state is a definite and continuously changing state function, which is strictly predicted by deterministic equations.

The second assumption is the Bonn Rules. When observing, what we see is not a wave function, but a considerable measure. Each observable corresponds to a series of eigenstates and eigenvalues (that is, quantum states that can produce certain observations for this observable). The observation result can only be one of these eigenvalues. Usually these eigenvalues are discrete (but not always! ), this is the original origin of the word "quantum". So which eigenvalue will the specific result be? This is determined by the "overlap" between the quantum state of the particle and the eigenstate corresponding to the eigenvalue. Figuratively speaking, each eigenvalue corresponds to an eigenstate, which is also a quantum state and a vector in Hilbert space. The angle between the eigenstate and quantum state of a particle determines the possibility of its appearance. When the quantum state happens to be an eigenstate and their included angle is zero (completely coincident), then we have a probability of 100% to get the eigenvalue corresponding to this eigenstate. The greater the included angle, the lower the probability. When the included angle is 90 (orthogonal), the probability is zero. This is the Bonn rule.

The third postulate is the projection postulate, that is, the wave function collapses. So what is the collapse of this wave function? What's so strange about it?

Strangely, this is the tangled point of evolution and observation. According to the classical concept, observation can always objectively reflect a certain state of the system, and the state of the system is independent of observation. But the projection postulate tells us that the quantum state of the system suddenly becomes the eigenstate of the result when we observe it. There are two meanings here:

The first layer is related to observation, not independent of observation;

The second layer is the sudden wave function evolution contrary to Schrodinger equation.

Please note that the concept of wave function collapse was not put forward by Copenhagen scholars such as Bohr or Heisenberg, but by von Neumann. The strangest thing here is that the evolution of wave function seems to be divided into two different modes. When we ignore it, it satisfies Schrodinger equation and is deterministic, continuous and unitary (von Neumann named it U process). When we observe it, it will suddenly undergo random mutation-this mutation not only occurs at the moment of observation, but also depends on what you observe (von Neumann named it R process). When you observe, two things happen. First of all, according to the observable measurements you observe, a series of eigenstate options will be generated. Second, according to the Bonn rule, quantum states choose one of these options.

If the observation result is determined by observation means, it is easy to accept (classical theory can't even accept this because observation is objective); But it is puzzling that the evolution of the system is also determined by observation means. This is the most controversial part of wave function collapse.

Some textbooks say that this is because observation will inevitably interfere with the system, so observation will inevitably change the state of the system. This explanation is very common and easy to understand, but it is a typical classic thinking and wrong.

If the observation "disturbed and changed the state of the system", it means that the system had a definite "state" before the observation. What quantum mechanics tells us is that observation changes the "quantum state". Quantum mechanics uses the concept of quantum state, but it doesn't explain what quantum state is-is it the state of the system? I don't know if the quantum state is the state of the system. What does "superposition state" mean? From the point of view of state vector, it is not only superposition, but also arbitrary superposition. According to our calculation convenience, it can be regarded as the superposition of any different states. Will the state of a system change with our will?

Moreover, Bell's experiment also clearly shows that there can be no definite state under the premise of localization. The so-called "observing the state of the jamming system" is untenable.

In the basic assumptions of quantum mechanics, observation, "collapse" and "R process" are all primitive concepts. As an axiom, it is basic and needs no explanation. Without changing the formal theory of quantum mechanics, we cannot know what observation is. Is it consciousness that makes reality? Or is it a purely physical process? Stop it, stop it.

From the point of view of pure closed calculation, quantum state is a tool for us to predict the observation results, and the manual of quantum mechanics is only a part of the tool manual. It is useful, but we only know it is useful, and we don't know anything else.

Von Neumann was the first person to analyze the observation process in detail by physical mechanism. He tried to explain observation by physical process-trying to dispel the mysterious process of "collapse" by some certain physical process. However, from the starting point of the system's "superposition state composed of eigenstates", through the interaction between the system and the instrument, the observer's intervention and acceptance of the instrument's instructions, to the final end point "we know a specific result in consciousness", he found that this process could not be completely solved, because the linear nature of Schrodinger equation can be used to deduce the physics between the system and the instrument, and between the instrument and the observer. However, in the end, what we realize is a clear and single result. Therefore, after analyzing the observation process in detail, he can only digest the material part, and those parts that have not been digested are classified as "immaterial", that is, consciousness. He said that the collapse was probably related to consciousness. This is the origin of "collapse of consciousness".

Many people categorically say that "observation is a purely physical process" and basically have not thought about what this sentence means. This is a casual language. If observation is a purely physical process, it means that quantum mechanics is incomplete. Because the observation process exists as an axiom in quantum mechanics. If the observation process is a physical process, as a complete physical theory, it should be described rather than postulated. Mandatory provisions are made in the form of postulate, that is to say, quantum mechanics is powerless to these physical processes.

A large number of people, led by Copenhagen School, explained that the state vector represents not the physical state, but our cognitive state-because we can't directly obtain the physical state of microscopic particles. Therefore, quantum mechanics does not describe the physical change process of the system, but describes the renewal process of our cognition of the system. This is the so-called "epistemological wave function", abbreviated as. As for the "objective state" of the system independent of our cognition, it is meaningless. Superposition as a description of cognitive state is nothing strange. "Collapse" is a Bayesian update after we get observation information from the outside world. The most influential explanation here is Copenhagen, which holds that the microscopic world is different from the classical world, and the state vector is applicable to and only applies to the microscopic system. When microscopic particles transmit information to observers through classical instruments, they will inevitably "collapse" into a classical state at a certain moment. In other words, there is a classical instrument between the microscopic particles described by quantum state and those of us who can only accept the information of classical state. When crossing the quantum classical boundary, the wave function will collapse.

In contrast, it is an ontology wave function.

It is clear that quantum states are physical states, and quantum mechanics describes physical processes, not our cognitive processes. Then, this theory must face the problem that the superposition state is the real physical state, which is the multi-world theory. The multi-world theory holds that reality itself is pluralistic. Since the multi-world theory opposes the wave function of epistemology, it is bound to regard the observation process as a pure physical process. Then we need to make a physical explanation of Bonn rule and projection postulate. Many literatures have done pioneering work in this field (for example, the decision theory of Deutsch and Wallace, the post-measurement uncertainty of Carroll and despite, the quantum symmetry of Zurek and so on). ), but no decisive breakthrough has been made so far.

There is also a kind of audience that is less, that is, it recognizes the prediction of wave function, but thinks that wave function is only an epistemological description of deeper reality. This is the theory of hidden variables. But Bell's theorem tells us that hidden variables must be nonlocal and conflict with the theory of relativity.

Briefly sum up these three points:

Namely "non-reality", "multiple reality" and "single non-localized reality". The traditional unique, partial and definite reality cannot be established.

Why do scientists know this subject better than people think? This is due to people's understanding of quantum entanglement and the development of decoherence theory. Please note that many people have a great misunderstanding about the theory of decoherence, which is regarded as an interpretation. Actually, it is not. This is a pure kinetic theory. It analyzes the observation process within the framework of formal theory of quantum mechanics. In this process, many original ambiguities have been clarified, but things have not been solved from the root.

I'm here to talk about decoherence in a popular way. The core of decoherence theory is that observation is a process of quantum entanglement between observation instrument (or observer) and system and environment. This process is pure and unitary, which is only described by Schrodinger equation. For example, if we have a particle, it may have two states, namely "+"and "-"; Meanwhile, we have an instrument to measure it. The instrument has a dashboard reading. At first, it is ready, and the reading is 0. Then we use it to measure particles, and it interacts with particles. If the particle state is "+",its reading is 1, otherwise it is 2. That is to say, the interaction between particles and instruments is expressed as:

So for any particle in superposition state, after it interacts with the instrument, according to the linear property of Schrodinger equation, there are:

Here is another postulate of quantum mechanics: the Hilbert space of a composite system consists of tensor products of Hilbert spaces of subsystems. I won't explain this here. I just want to say that according to this postulate, there is a famous entangled state-in this state, the quantum state of the composite system can't be expressed as the tensor product of the quantum state of the subsystem. Generally speaking, entangled state is inseparable, and its state vector can not be divided into two subsystems: particle and instrument. After the particles superimposed with "+"and "-"interact with the instrument, the instrument will not enter the superposition of "1" and "2", but the particles and the instrument will enter the superposition of "+,1" and "-2" together. At this time, the quantum state of a single instrument or a single particle no longer has a mathematical definition.

At this time, when we observe the instrument, we are forcibly dividing the whole system (particle+instrument) into particle part and instrument part. As mentioned above, the quantum state is meaningless at this time, and mathematically it has changed from a "pure state" to a "mixed state", that is, from a superposition state to a probability.

Therefore, observation is not what influence the observer has on the system, but there is no independent definition after the observer is entangled with the system.

As we mentioned earlier, two things actually happened during the measurement:

1. The option to form a series of observations according to the observable eigenstates;

2. The system "collapses" to one of its eigenstates.

In decoherence, the first process is called "optimal basis problem", and the answer is, why are the results produced by observation always definite classical results? Why can't we see particles here and there, dead and alive cats, and even animals that are both cats and dogs?

The second process is called "result problem", and the answer is, why does observation produce a specific result, and why is the probability of producing this result stipulated by the Bonn Rules?

Decoherence can answer the first question, but it can't do anything about the second. In the final analysis, this question still depends on interpretation.

For all the explanations of the existence of "collapse", the answer to the second question is that this process is collapse. It is still a mysterious process (physical or non-physical).

The answer of the multi-world theory to the second question is that this is a purely physical process that conforms to unitary evolution, so observation will not only produce a specific result, but all possible results will be preserved, except for a copy of "I", which can only achieve one result on one branch.

This is the difference that still exists today.

Finally, back to this question, "Why does observation lead to collapse in quantum mechanics?" The answer is that scientists don't know whether observation leads to collapse. Let alone answer why. But scientists are approaching this answer from different directions.