A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
The Worldview of Relative Simultaneity (MURAYAMA Akira)
CHAPTER I
Relativity and Four-dimensional spacetime
[The Latter half] ---- Philosophical Examination ----8. Problems in the Quantum Theory
(2) Observation Problem
As discussed, quantum mechanics has shown notable development and achievements. However, it has also been affected by problems about its theoretical significance. This fundamental challenge is called the observation problem.
Unless electrons are observed when they pass through the double slits, they are regarded as quantum-based probability waves passing through the slits. In this case, it is impossible to specify in principle which slit they have traveled through. Those electrons play a role in being distributed in interference check patterns. However, if the electrons are observed when they pass through the double slits, it is possible to specify which slit they went through, but they are no longer probability waves and they just play a role in being distributed as simple particles.
In response to this situation, the following interpretation was made. When an electron is observed, its wave function as an electron collapses and transforms into a complicated quantum system that interacts with observation devices. Depending on how to observe, the wave function showing an equal chance of which slit electrons will pass through momentarily transforms into the wave function identifying a particular slit. This phenomenon is termed "collapse of the wave function" or "reduction of the wave packet."
As long as observations are not conducted, the object remains purely in an ambiguous state. However, observation causes specification of either state.
In response to this interpretation, Schrödinger, who was not satisfied with the probability interpretation of quantum mechanics, presented the following thought experiment.
Imagine a situation in which a cat is confined in a closed box. Inside the box are radioactive elements. When an atom of the element splits and gives out radiation, a bottle containing poison gases opens, which will kill the cat. The fission of radioactive atoms is a quantum phenomenon, which means that both states exist. Both with and without collapse of wave function have a 50 percent probability. It is impossible to know when radioactive atoms will split as long as the radioactive phenomenon is observed.
In addition, the detection device for the radioactive phenomenon is also made from atoms and each atom acts in accord with the principles of quantum mechanics. Therefore, it is conceivable that the very complicated quantum system involving the device can be expressed by a kind of wave function. In accordance with this reasoning, this wave function exists as a superposition of two types of states in which it detects or does not detect radioactive phenomena. Both the part of the device to emit poison gases and the cat, which may die if breathing the gas, are made from atoms and molecules in principle. With this reasoning, both states in which the cat is alive and dead can be considered to superpose depending on the probability of fission of radioactive atoms.
The observer observes inside the box by opening it. Through this process, the interpretation is that the wave function of the superposed states collapses to be focused on the wave function representing specific state whether the cat is alive or dead. The cat's condition is determined whether it is alive or dead only after the cat is observed.
These stories probably sound foolish. Then, suppose that the observer himself (or herself) is confined in the box instead of the cat. For the observer in the box, with the radioactive atoms in superposed states, the question is which state the observer exists in. At least, as long as the observer can observe the situation without any problem, the person will definitely stay alive. The next question is what if another observer is looking at the situation outside the box. It is the wave function of two superposed states for the outside observer until that person sees if the observer in the box is alive or not. The probability of the observer in the box being alive or dead is equal. Only when the box is opened and the wave function collapses can the outside observer know if radioactive atoms have split and if the person in the box is dead or alive. However, close consideration shows that the outside observer is also a certain quantum system in principle as well as wave function. If the outside observer is surrounded by a larger box and another observer is looking at this box from outside, for the observer outside the larger box, the person in the larger box may exist with the superposed states of confirming the alive or dead state of the observer inside the original small box. This hypothetical story continues endlessly.
Essentially, what does a determined condition mean? Does it have anything to do with self-consciousness? The heart of the matter goes deep into this subject.
In response to these questions, Niels Bohr (1885-1962) argued that pursuing micro worlds inevitably leads to such situation and that you should readily accept statistical laws without metaphysically exploring profound existences. He was from Copenhagen and was appointed as the founding director of the theoretical physics institute (Niels Bohr Institute) at the University of Copenhagen. The institute was the magnet for many bright theoretical physicists from all around the world in the 1920s. This group of physicists, who supported Bohr's ideas about observation problems in quantum mechanics, is often called the Copenhagen school.
In the meantime, Einstein suspected that quantum mechanics involving such mysterious observation problems was imperfect. He considered that many people could conduct only statistical predictions because they were still unaware of hidden variables. Based on these ideas, Einstein frequently debated with Bohr, the leading physicist in quantum mechanics, over the observation problems. Bohr examined Einstein's argument honestly and continued to respond to his counter arguments. Bohr ended up winning this famous debate. After all, Einstein's hypothesis that there would be some hidden variables proved wrong.
During the process of those debates, the EPR paradox was presented. Einstein presented this paradox about non-local relationship with Boris Podolsky (1896-1966) and Nathan Rosen (1909-1995).
There are two kinds of particles: Particle A and Particle B. Their attributes involve just the value of either a or b (For example, the direction of a spin and photons' polarization attributes). In addition, these two particles constitute a dynamic system in which when one has an attribute of a, the other always has an attribute of b, and vice versa. This assumption can be realistic. (For instance, when one side of a spin is in one direction, the other side is in the opposite direction.) The probability of these particles showing an attribute of a or b has an equal chance. According to quantum mechanics, these two particles can exist in the superposed states of two conditions unless they are observed.
However, if you observe Particle A, the wave function collapses and its attribute will also be determined to be a or b. At the same time, this also determines the attribute of Particle B even if you do not conduct an observation. This theory is completely valid even if the two particles are hundreds of millions of light years away. Then, information about A's reduction of the wave packet travels to B at superluminal velocity. However it is impossible that energy and information travel at a speed faster than light velocity. No non-local relationship (action at a distance) is conceivable. Many physicists firmly believed so for a long period of time. They thought that quantum mechanics must be imperfect if it was contradictory to their long-cherished belief. It was Einstein's last resistance in his late years. He had long objected to the probability interpretation of quantum mechanics, arguing that God does not play dice.
The argument ended in victory for quantum mechanics in the way of overturning the long-held belief. John Stewart Bell (1928-1990) presented a certain inequality (Bell's theorem) based on the assumed locality. Briefly, based on the assumption that information usually travels locally and its correlations beyond space and time would be impossible, he constructed the theorem that certain systematic correlations could not exceed particular levels of values. If this theorem contradicts experimental facts, it follows that the locality hypothesis itself was wrong. Soon after, John Crowther and Alain Aspect confirmed that this inequality was contradictory to their experimental facts. This led to a situation in which we had no choice but to give credit for non-local relationship. (Some people argue about quantum-based teleportation, but in fact, superluminal communication has not been realized.)
With regard to the proposition that a reduction of the wave packet travels simultaneously, I wondered about what system of coordinates this simultaneity means because I had long paid keen attention to the relativity of simultaneity. Based on this critical thinking, I devised the following thought experiment (See Figure 1-8-1).
I note the above-mentioned correlated two particles (A and B). Three different observers (S1, S2 and S3) are traveling at different speeds. The three observers encounter Particle A at a certain spot at a time. Then, they measure Particle A and obtain its attribute of a. This means that A's wave function has collapsed. At the same time, B's wave function has also collapsed and its attribute of b must have been determined. What time did this collapse of B's wave function occur?
Based on the same timing as the collapse of A's wave function, each observer reports B's time and measurement results of its attribute in his or her own coordinate system through magnetic wave signals to another observer S4 who is static relative to Particle B. Observer S4 receives the reports from the three persons at a time of t4 and knows B's attribute of b. Each observer's report has the same attributive value, but with respect to the time at which B's attribute was determined by the collapse of its wave function, each observer makes different judgments. Observer S1 claims that B's attribute was determined at a time of t1. By the same token, observer S2 argues that B's attribute was determined at a time of t2 and observer S3 argues that B's attribute was determined at a time of t3. When on earth did B's wave function collapse? Observer S4 was informed of B's attribute at the time of t4, so is it reasonable to think that B's wave function collapsed at the time of t4. This means that A's wave function collapsed slightly after measurements had been carried out, which hints that a certain period of time existed in which the collapse of wave function did not occur despite measurements. This is illogical. Or in the eyes of observer S4, did observers S1, S2 and S3 exist as the superposed wave function of two conditions where A's attribute is observed as a and observed as b? Did the wave functions of the three observers collapse and the state focus to the situation an attributive value a was observed at the very moment observer S4 received the reports? Should the timing be assessed from the vantage point of observer S4's simultaneity? In this scenario, the three observers who are vastly distant from each other are regarded as observation devices for examining Particle B's attribute in the eyes of observer S4.
In accordance with this reasoning, the argument over local relationship eventually converges on the same subject as Schrödinger's cat. The quantum mechanics interpretation of collapsed wave functions leads to the thought that observers' observations are the determinants of what the universe is. The question then is which observer determines the essence of the universe.
Of course, many physicists have pointed out that the interpretation of collapsed wave functions is incompatible with the special theory of relativity. (*3)
However, unexpectedly, the mainstream trend of modern physics is largely subjective idealism. At least, modern physics is skeptical of native realism, which espouses existences independent of human consciousness. This thinking is supported by experimental facts suggesting that observers' observations do determine the essence of the universe. (Even what types of attributes quanta have depends on the choice of observers' observation devices.)
In fact, however, many physicists are skeptical of subjective idealism. Some of them are supportive of Everett's many-worlds interpretation. If observers' observations determine the essence of the universe, it does matter which observer's observation is actually trustworthy. If there are innumerable universes equal to the possibilities of observer's observations, it is unnecessary to place a particular observer in the center of the universe, and theoretical objectivity can be secured.
Meanwhile, Hue Price (previously mentioned in note 3) presented in his above-referenced book how to devise the reverse direction of time in causal relationships. That is, the idea is that future interactions can control even what happened in the past. His theory based on an existing single four-dimensional space-time is the most compatible match with my examination. I will address the subject of time direction in the latter part of this book.
Probably, the largest majority group of modern physics is modest pragmatists who earnestly examine the relationships between phenomena and numerical formula and constantly seek essential knowledge and technology, without being involved in such matters. As a matter of fact, their hard, methodical activities contribute to developing practical science and technology for humankind. Their activities do not always need any particular effort to interpret what the universe is. This fact should be recognized as such.
(*3) For example, Michael Lockwood argues: “But what does ‘instantly’ mean here? We know from relativity that simultaneity is relative to frames of reference. Which frame of reference is to determine the simultaneity plane along which the collapse takes place? Again, there doesn't seem to be anything in quantum mechanics itself that is capable of providing an answer.” (Refer to Michael Lockwood (1989), Mind, Brain and the Quantum, p. 207, translated by Sakae Okuda (1992), Sangyotosho.)
As I have noted in this section regarding EPR, Hue Price, the philosopher who supports block universe theory, also indicates that consistently explaining the collapse of a state function requires considering a specific privileged coordinate system. (Refer to Hue Price, Time’s Arrow and Archimedes Point (1996), p. 204, Chapter 8 “EPR and Special Relativity: The Cost of Nonlocality,” translated by Takayuki Toyama and Katsumi Kushimoto, Kodansha Ltd. (2001)).