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Unexperienced experience: Profound Stories of quantum mechanics (2)

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Most know that the Copenhagen interpretation was accepted in the end. However, few know the profound meaning of the argument.

 

Debate over realism and locality

 

(Continued from the previous column) The Copenhagen interpretation of probabilistic determination by measurement and Einstein’s argument against it played a critical role in the development of physics in the 20th century. Most know that the Copenhagen interpretation was accepted in the end. However, few know the profound meaning of the argument. Let us talk about standard quantum theory and the major premise of physics prior to quantum physics.

 

Einstein–Podolsky–Rosen paradox (EPR paradox)

 

Let’s say that you and your friend are connected while holding each other’s hands. In other words, both of you put place different hands, right or left, over each of your heads. No one knows which hand is raised by each of you, thus exhibiting a 50-50 chance.

 

Imagine that you are on the moon, leaving your friend on the earth, and someone glances at your friend holding up the left hand. While on the moon, you are sure to hold the right hand up. Common sense suggests that both of you already gave a promise to each other before parting, i.e., your friend decided to raise his or her left hand before the observer saw him or her. However, the Copenhagen interpretation tells us a different story: the act of observation causes your friend to raise his left hand.

 

In addition, you, who are raising the left hand on the moon at the same time, are seen holding the right one up the moment your friend is observed. This means the end of coexistence between you who raised the left hand and you who raised the right one; the former (with the left hand put up) has disappeared. Of course, the opposite case could be observed. Note that neither of your hands is determined until observed and that the observation gets your hand determined.

 

The science had been built on the premises of realism and locality. From a perspective of the former, natural phenomena have already existed in certain states independent of the observer, and measurement is the work of confirming this regardless of the observer’s action or the decoherence of waves. Whether there is an observer or not, nature itself is “as it is.”

 

The occurrence of physical phenomena being local means that there is no faraway or remote influence on others. Any objects, forces, energy, information, and other physical entities cannot teleport but must change positions or propagate continuously. Even if the mass of the sun existing far away suddenly changes, it does not affect the earth at that moment, but the change in gravity must spread to the earth continuously, as do the waves detect the change in the sun.

 

Realism has been a premise agreed upon without any need for an explanation since the beginning of  science, while locality is the basis of relativity and electromagnetic theories. According to the Copenhagen interpretation, physical entities are determined only by measurement, and the effects of measurement are transmitted instantaneously faster than light. This is a denial of the theory of relativity, which cannot but arouse considerable controversy.

Figure 1. EPR pairs where spins are in two states: up-down (50%) and down-up (50%). If the left spin measures up, the right spins down in an instant, no matter how far it is apart. Because the two spin states are not independent of each other, they are said to be in an entangled state.

Figure 1. EPR pairs where spins are in two states: up-down (50%) and down-up (50%). If the left spin measures up, the right spins down in an instant, no matter how far it is apart. Because the two spin states are not independent of each other, they are said to be in an entangled state.

 

The illustration of left–right hands mentioned above is an example of the Einstein–Podolsky–Rosen paradox (EPR paradox). Some scientists, including Einstein, attempted to resolve the paradox by adjusting this quantum theory to the principles of locality and realism. However, in 1964, John Bell showed that a theory on the basis of the two simultaneously went against the outcome of the Copenhagen interpretation. In 1972, an EPR experiment with photons verified Bell’s theory, which revealed that the EPR paradox is not a paradox but a fact.

 

Standard quantum theory predicts and describes reality very accurately and serves as a common foundation for multiple disciplines and technologies, such as modern chemistry, electronic engineering, materials science, and molecular biology. A theory incompatible with those that explain reality so well is not easily acceptable. The battle was over, and the Copenhagen interpretation has become the standard quantum theory. Nature is non-local, and measurment is the final determinant.

 

Nonlocality that refers to the immediate delivery of measurement effects is not considered contrary to the theory of general relativity. Meanwhile, locality, the premise of general relativity, applies to observable physical entities, and the wave function of quantum mechanics is a virtual concept for the description of phenomena, not an observable physical entity. (No wave function is used in Heisenberg’s quantum mechanics, who also introduced the uncertainty principle first).

 

Therefore, even if the change in the wave function is faster than light, it does not violate the theory of relativity [1]. In the illustration of left and right hands, even if I am holding my right hand up on the moon, no one knows whether this is attributed either to my friend on the earth being observed or to someone observing me until they receive information on the measurement of my friend more slowly than light.

 

Considering that semiconductor circuits were already developed using quantum mechanics in the 1950s, it may seem that the debate over the foundation of quantum mechanics even in the 1970s was just an idle intellectual argument. However, the profound insights gained from this debate are utilized for the development of today’s quantum information and communication technologies. Left/right-handed pairs of photons are used as basic materials for quantum communication that ensures absolute security against eavesdropping.

 

Imagine two persons dividing up an EPR pair entangled in an up–down state, as shown in Figure 1, to communicate with each other. If someone secretly steals communication information, the owners of EPR pair can notice it as the act of reading information to steal changes the EPR pair. In quantum communication, a third party cannot secretly extract information.

 

An unfinished story

 

The standard quantum theory has been recognized as an undoubtedly right theory through every verification procedure. However, this does not mean that there are no other quantum theories. Let me briefly introduce one of them, the de Broglie–Bohm Theory. This theory, also known as Bohmian mechanics, was first proposed by Louis de Broglie, the proponent of the matter wave, in the early 20th century, and developed by David Bohm, who observed the Aharonov-Bohm effect first. For more detailed information on Bohm’s interpretation, see Physics and High Technology [2,3].

 

While the standard theory is built on both nonlocality and nonrealism (nonlocal nonrealism), the de Broglie–Bohm Theory presupposes nonlocal realism. This interpretation accepts quantum nonlocality, where a wave function can be transmitted far away in an instant, but it adheres to realism that a physical entity has already existed regardless of observation.

 

The EPR and double-slit experiments aforementioned are to prove that the local realism, which presupposes locality and reality at the same time, is wrong and not that the nonlocal realism is wrong. Regarding the pathway of particles passing through the slits to the screen in the double-slit experiments, the standard theory states that there is no trajectory of single particles—the trajectory indicates the particle positions—while the de Broglie–Bohm theory, which sticks to realism, says that each particle has a well-defined wavy trajectory irrelevant to measurement [4].

 

Bohmian mechanics does not distinguish between quantum and classical measurement and has restored realism by invoking again the interpretation that measurement is to confirm what is predetermined. Moreover, it describes and predicts what standard theory describes and predicts, including the uncertainty principle.

Yet, it is premature to judge which theory is right or wrong now [5]. Note that you can just choose the one you prefer in terms of usefulness, aesthetic beauty, or psychological comfort. The two theories have different views on whether physical entities exist in the unobservable realm, but what exists and how it does in this realm are not subject to scientific verification.

 

Figure 2. Average trajectories of groups of photons passing through a double-slit (left) and the probability distribution of photons found in the space between the slit and the screen. Not the trajectories of single photons. A weak measurement, which extracts some information about photons so that they can reach the screen without losing all of their quantum properties.

 

Figure 2. Average trajectories of groups of photons passing through a double-slit (left) and the probability distribution of photons found in the space between the slit and the screen. Not the trajectories of single photons. A weak measurement, which extracts some information about photons so that they can reach the screen without losing all of their quantum properties [5].

 

Conclusions

 

In the current curriculum, only standard theories are taught, while other theories and interpretations are not even mentioned in class. The former is better and more useful than others. I will also continue to utilize standard theories.

 

However, it is not desirable to stick to the attitude that says, “Shut up and calculate,” without questioning the standard theories just because the others are wrong. Different from other disciplines, science has empowered rigorous observation not through great scholars, theories, or sensible major premises. A logical or concise description of observations and measurements sometimes requires the use of a notion without a physical entity, but whether the nonobserverble notion is right or wrong cannot be judged. Any logical system that can consistently explain phenomena and be verified through observation is a valid theory, whatever it is. There should not necessarily be a single right theory.

 

[References]

[1] Some think this explanation is intended to circumvent the problem. Theories have been proposed to integrate quantum theory and the general relativity, but there is still a way to go.

[2] Roh Jae-Woo, “Weak Measurement, Strong Measurement, and Quantum Theory,” Kwon O-dae, “New Trends in Studies of the Copenhagen Interpretation of Quantum Theory,” Physics and High Technology Vol. 22, No. 5 (2013).

[3] Kim Myung-seok, “Bohm’s interpretation of Ontology and the Quantum Theory of Motion,” Physics and High Technology Vol. 21, No. 4 (2012).

[4] It is an assumption of classical mechanics that particles move in a straight line at a constant velocity when no external force is applied to them, so we do not need to hold on to this.

[5] Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, L. Krister Shalm, Aephraim M. Steinberg, “Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer,” Science, vol. 332, p. 1170 (2011).

 

 Author

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

 sckim@kist.re.kr 


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