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Unexperienced experience: Profound Stories of quantum mechanics (1)

Viewed : 434 times,  2021-09-09 02:03:18

Is Schrödinger’s cat in a mixed state of being either dead and alive? You may have heard of these questions at least once when learning quantum mechanics.

 

Perspectives and linguistic misconceptions of mainstream theories about quantum measurements

 

“Is Schrödinger’s cat in a mixed state of being either dead and alive?”

“If a state is determined only by measurements, has the moon appeared there just because I see it?”

 

You may have heard of these questions at least once when learning quantum mechanics, which are mainly used to describe quantum mechanics as an esoteric and mysterious discipline. What about the uncertainty principle and some statements, such as the state of an object that is determined only by measurements or the cat is simultaneously alive and dead? All of these combined with Albert Einstein’s denial of them and conflicts among scientists, sound perfect for the beginning of a thriller film that fascinates movie-goers.

 

Such films develop a story of particle-wave duality and uncertainty but then fizzles out, not telling whether the cat is alive or dead. Let us look into the answer. This article is intended for those who have insights into quantum mechanics.

 

“Red Light, Green Light” played by electrons—here they are at the moment of observation

 

Figure 1. An electron that exists as if it’s distributed in a wide space before observation (left) and an electron that appears at a point at the moment of observation (right) 

Figure 1. An electron that exists as if it’s distributed in a wide space before observation (left) and an electron that appears at a point at the moment of observation (right) 

 

In the Copenhagen interpretation, the mainstream interpretation of quantum mechanics, an object exists in several states simultaneously, and it then exists in one state when being measured, which is determined by probabilities. Take, for example, an electron present in multiple places at the same time. When someone finds where it is, it only appears in one place.

 

Note that it does not mean that an observer becomes aware of the location of the electron, which is unknown to the observer, at the moment of measurement. You can say that when the electron is alone, it fills the entire space like a hazy mist, but when being looked at, it seems to be sucked into one point for a moment. In other words, electrons play the game called Red Light, Green Light. The point of convergence depends on the probabilities each time.

 

Figure 2. Schrödinger’s cat: A thought experiment in quantum mechanics[1]

Figure 2. Schrödinger’s cat: A thought experiment in quantum mechanics[1]

 

Let us look at a thought experiment called Schrödinger’s cat. Inside a box, there is a radioactive atom with a 50% chance of decaying in an hour, a device that releases poison gas if the atom decays, and a living cat. According to standard quantum theory, the atom is in the mixed state of decaying and intact. This means the device is in two states of releasing poison gas and not releasing poison gas, and the cat is also in the state of being dead by poison gas and alive simultaneously.

 

Is the cat dead or alive when you open the box and see the cat? Is the cat dead or alive just because you saw it after opening the box? The radioactive atom is in a microscopic world in which the measurement makes the final decision, whereas both the device and the cat are in the macroscopic world. Schrödinger’s cat links these two different worlds, noting that measurement was not well defined in the Copenhagen interpretation.

Figure 3. Double-slit experiment with electrons; measurement by the double-slit (left) and measurement only on the screen (right) [2]

Figure 3. Double-slit experiment with electrons; measurement by the double-slit (left) and measurement only on the screen (right) [2]

 

There are also experiments that have verified that measurements determine phenomena. Consider the double-slit experiment with electrons. As shown in the figure above, the double-slit has two narrow and long gaps in parallel. Most of the electrons fired by an electron gun are filtered, but some pass through the slits, making dots on the screen. If you keep firing electrons, chances are, more electrons pass through the slits and reach the screen, making more dots on it. Now, look at the screen, and you will find several interference fringes formed on the screen as if two waves from the two slits met.

 

Consider two light waves passing through both slits. If the crests of each wave meet and add together at a certain point, the resultant amplitude is larger. Meanwhile, if a crest of one wave meets a trough of another wave, then the amplitude is smaller. As a result, bright and dark bands are repeatedly produced on the screen. This is true of the electron experiment.

 

However, if you put a measure by the slits and see the electrons instead of the screen, the interference fringes disappear, and two slit-shaped lines are formed on the screen. Why? Is it because you’ve seen electrons that haven’t reached the screen yet? Then, what is measurement?

 

What is measurement?

 

In textbooks, the contact of the microworld, such as electrons with the macroworld (e.g., equipment, people, the earth, stones, etc.), is called measurement. The subject of measurement is not a person but a macroscopic system.

 

How big is the macro-world? Are 100 atoms big enough? Is quantum mechanics an incomplete theory that only applies to the microscopic world? If a theory applies only to half of the world, can it be a principle of physics? Measurement is also a physical phenomenon, but why is it so different?

 

The quantum measurement is an ambiguous concept because it assumes that the world is divided in a dichotomous manner when nature is not. This measurement problem has not been resolved at all for decades, and when asked about it, people would reject any arguments and instead say, “Shut up and calculate!” [3].

 

An important experiment on the measurement problem took place in 1999 at the end of the 20th century. In a double-slit experiment with sufficiently large fullerene molecules (C60), interference fringes were formed, as seen in the experiment with electrons [4]. In principle, interference fringes can appear even if they were fired with a cannon rather than C60.

 

Noticeably, there is a condition where interference fringes disappear even when you see only the screen and not the slits. In a double-slit experiment carried out in a vacuum, the interference fringes disappear when the degree of vacuum is low enough for the fired fullerene molecules to collide with gas molecules while flying or spreading to the screen.

 

In other words, even when you do not see the slits with a measure, the interference fringes disappear as if the collision with gas molecules were equivalent to measurement. The same is true at high temperatures. Ever since then, double-slit experiments with increasingly larger molecules have been reported [5].

 

Description of decoherence

 

The wave function Ψ(x,t) = |Ψ(x,t)|exp[iθ(x,t)] , which represents the state of an object, consists of an amplitude (|Ψ|), along with a phase (θ). The amplitude indicates the probability that an object will be found there, and the phase shows when and where a crest and a trough on a wave appear. In the double-slit experiment, if the waves passing through the two slits are coherent, bands (interference infringes) are always produced at certain points as the crest and trough meet together.

 

If the gas density exceeds a critical value, fullerene molecules can collide with gas molecules anytime and anywhere while spreading to the screen. As both waves collide here and there, scattering each other’s phases, the positions of the crest and trough are randomly changed, causing decoherence of waves. This causes the interference fringes to disappear. As the temperature increases, photons from all directions give rise to decoherence.

 

When even a microscopic object with the well-defined phase of a wave function comes in contact with another physical system, the wave functions of the two are hardly coherent. Ultimately, their coherence is lost, which causes the quantum characteristics to disappear. A perfect quantum system should be completely isolated.

 

A description of decoherence resolves the ambiguity of categorizing the world into the microworld and macroworld. Quantum mechanics applies to all physical systems, regardless of their size, but as they get larger, isolating themselves is more difficult, so they gradually fall under the realm of classical mechanics, with decoherence continuing to happen.

 

From this point of view, the particle-wave duality is not a real sense of duality but becomes a natural phenomenon. Quantum measurement can be viewed as a temporary expression used in a period when quantum mechanics was not well-established, referring to a phenomenon in which the divided physical systems exhibit decoherence while interacting with each other[6].

 

The cat’s life or death has already been determined before you open the box. The phase of the cat’s wave function cannot be maintained because of the collision with numerous air molecules and the exchange of photons with the surroundings. The act of opening the box doesn’t change anything. This is true of the moon. Whoever sees the moon does not affect its existence.

 

Conclusions

 

In the Doctor Who episode “Blink,” which was produced as a science fiction TV series for BBC, Weeping Angels and quantum measurement-derived characters were introduced. The Weeping Angels stand still when you look at them but come next to you in a blink when you look away. They are originally formless but turn into winged angel statues when being witnessed. As such, quantum mechanics is often adopted to justify the esoteric settings of films.

 

Verbal expressions for quantum mechanics have provoked humanities scholars into philosophical debates on existence and cognition. In addition, those who interpret an argument that human observations determine the world as scientifically proven have said that there is a universe only when humans exist. Furthermore, there is a stance that free will in humans, which seems to be contrary to deterministic classical mechanics, can be present just because of quantum mechanics.

 

In my opinion, the attempt to connect those unreasonable ideas with quantum mechanics is because of early linguistic expressions. At a time when this field was still unknown, “a phenomenon (decoherence) in which an isolated physical system cannot maintain the phase of its wave function as it is connected to the outside” was named “measurement” to imply human acts. Coexistence between this and that was expressed in our dichotomous language, along with the term “determination” that has a meaning of disconnection and discontinuation. Most of the confusion will be resolved if we stop using the words “measurement” and “determination.” (to be continued)

 

[References]

[1] wikimedia commons / Schrodingers cat / CC BY-SA 3.0ctor=1

[2] https://blog.naver.com/msnayana/221374970924

[3] “Shut up and calculate!” This is a traditional answer to the question about the measurement or realism of standard quantum theory. It could be the viewpoint where there is no problem if it works, or it could be a reaction when the argument is boring.

[4] Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller, Gerbrand van der Zouw & Anton Zeilinger, “Wave–particle duality of C 60 molecules,” Nature, vol. 401, p. 680 (1999).

[5] Markus Arndt & Klaus Hornberger, “Testing the limits of quantum mechanical superpositions,” Nature Physics, vol. 10, p. 271 (2014).

[6] Wave–particle duality can be seen as a linguistic problem. “Particles” and “waves,” which are the terminology of binary classification, are used to explain natural phenomena, but when this classification turned out not to work in some phenomena, the word “duality” began to be used. 

 

 Author

 Seungchul Kim |  Principle Research Scientist, Computational Science Research Center of KIST 

 sckim@kist.re.kr 


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