Motion Is Discontinuous and Random Shan Gao @ ECUQ Project To those people who have been plagued by the quantum puzzle
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|Everyone Can Understand Quantum> |
Double-slit Experiment
It contains the only mystery of quantum mechanics.
------ Feynman, 1963
Double-slit experiment has been widely discussed since the founding of quantum mechanics. Nearly all textbooks of quantum mechanics illustrate the weirdness of quantum world using the experiment. As Feynman (1963) said, it contains the only mystery of quantum mechanics. But have we disclosed the mystery and understood the double-slit experiment? As we think, the answer is definitely negative. The realists have been asking, “how on earth does the single particle pass through the two slits?[1]” In this section, we will present a clear realistic picture of the particle passing through the two slits to form the double-slit interference pattern, and demonstrate that the double-slit interference is just the natural display of quantum motion.
The left figure is a simple sketch map of double-slit experiment. The single particle (e.g. electrons) is emitted from the source S one after the other, then passes through the two slits to arrive at the screen B. In this way, when a large number of particles arrive at the screen, they collectively form a double-slit interference pattern.
Let's first see whether or not the familiar continuous motion of particles can account for the formation of the double-slit interference pattern. According to the definition of continuous motion, the single particle can only pass through one of the two slits in each experiment. Then it is evident that the double-slit interference pattern will be the same as the direct mixture of two one-slit patterns, each of which is formed by opening each of the two slits. The passing process of each particle in double-slit experiment is exactly the same as that in one of these two one-slit experiments. However, all known experiments show that the interference patterns for the above two situations are evidently different. This is an inevitable dilemma when using continuous motion to explain the formation of the double-slit interference pattern. In fact, we can see where the perplexity lies more easily from the following fact, i.e., that when one of the two slits is shut, the particle can reach some position on the screen, but when the shut slit is opened, it will prevent the particle from reaching the above position on the screen.
No way out but reject continuous motion. The orthodox interpretation of quantum mechanics indeed rejects continuous motion, but at the same time, it also rejects all possible forms of motion, and proves that the rejection is inevitable. Thus the orthodox interpretation not only fails to give the realistic motion picture of the particle passing through the two slits, but also surprisingly asserts that this is not due to its inability, but because the motion picture does not exist at all in reality. In the following, we will see how the orthodox interpretation "practises deception", and where it "gives the show away".
The orthodox interpretation first implicitly assumes that continuous motion is the only possible form of motion, and then proves that continuous motion cannot account for the double-slit interference pattern by employing the similar demonstration as the above. Thus the orthodox interpretation rejects continuous motion, and owing to the uniqueness of continuous motion, it also rejects all possible forms of motion for the microscopic particles. It asserts that when people talk about any property of particles, they must measure the property, in other words, there exists no microscopic reality independent of observation. Furthermore, the orthodox interpretation explains the double-slit experiment in the sense of measurement, and regards such an explanation as the only possible one. This explanation can be simply expressed as follows. If you want to know how the single particle passes through the two slits to form the double-slit interference pattern, you must detect which slit the particle passes through by taking a position measurement. But according to quantum mechanics, this kind of position measurement will inevitably destroy the double-slit interference pattern. Then on condition that the double-slit interference pattern is not influenced, we cannot detect which slit the single particle passes through, and thus we cannot know how the single particle passes through the two slits to form the double-slit interference pattern. Accordingly the realistic motion picture of the particle passing through the two slits does not exist in the sense of observation. Moreover, since there exists no microscopic reality independent of observation, the realistic motion picture of the particle passing through the two slits does not exist in essence.
The above demonstration of the orthodox interpretation seems to be flawless, and it indeed "dusts the eyes of" nearly all great men in the 20th century [2]. However, there exist two unnoticed deadly flaws in the demonstration. One is that the orthodox interpretation implicitly assumes continuous motion is the only possible form of motion, but it never gives a justifiable argument. The other is that the orthodox interpretation only employs the position measurement to detect how the particle passes through the two slits in individual experiment.
Concerning the first flaw, the implicit assumption of the uniqueness of continuous motion has never been seriously examined and disbelieved. Even we can say, no one has ever noticed that it is an assumption, since nearly all people including those arguing against the orthodox interpretation religiously believe in it. The validity of this assumption appears to be evident, but as we will see, it is an ingrained prejudice. It was fed to grow up by the successful experience and the edification of great men, but it instead fetters the thoughts of the great men, and tries to obliterate the reality behind experience. It finally becomes a terrible demon under the cosher of people, and even wants to devour the whole real world. Now only reason can tame it, and help it get back the lily-white heart and the naive temperament. Indeed, there exist many reasons to lead people to unconditionally accept the above assumption, and the reasons from experience and history may play a decisive role. But we must note that people seldom consider the rationality of this assumption, and never seriously study whether there exist other possible even more fundamental forms of motion, even though they cannot help but reject continuous motion in the face of quantum mechanics. Why do people believe in it so religiously? An interesting fact may be that it is unnecessary for people to doubt this assumption before the appearance of quantum mechanics, while the orthodox interpretation prohibits people from doubting it again after the founding of quantum mechanics. But then, we had better leave this question to the philosophers.
Now we will further analyze the first flaw in the demonstration of the orthodox interpretation. As we know, when discussing the double-slit experiment, people always ask the following question, i.e., that which slit the single particle passes through in individual experiment. The orthodox view asserts that this question is meaningless, since we cannot measure which slit the particle passes through on condition that the interference pattern is not destroyed. In fact, this question is indeed meaningless, and as it happens the orthodox answer is right. But as we have seen above, its reason is by no means right. The actual reason should be that if the particle passes through only one slit in each experiment, the interference pattern will not be formed at all[3] . Thus it is obviously wrong to ask which slit the single particle passes through in individual experiment. The particle must pass through more than one slit, otherwise the double-slit interference pattern cannot be formed.
On the other hand, we can still ask the following question, i.e., that how the single particle passes through the two slits to form the interference pattern. It is just this question that clearly unveils the first deadly flaw of the orthodox interpretation. Then what is the answer of the orthodox interpretation? As we know, it concludes that there exists no any realistic motion picture of the particle passing through the two slits, and the above question is still meaningless. But how can it arrive at this conclusion? It cannot do, and no one can do. What the orthodox interpretation bases on is only the above prejudice, i.e., that continuous motion is the only possible form of motion. Once the prejudice is rejected, and the realistic motion picture of the particle may exist, we can actually find it by using a logical microscope. The reasoning is very simple. Since the particle does not pass through only one slit in individual double-slit experiment, it must pass through both slits when passing through the two slits. The particle has no other choices in logic! This kind of bizarre motion is not impossible in principle. Since it will take a period of time, not one instant, for the particle to pass through the slits, what the particle needs to do is just moving discontinuously in the two slits. In reality, this is just the display of quantum motion.
Now we will turn to the second flaw in the demonstration of the orthodox interpretation, i.e., that the orthodox interpretation only uses the position measurement to detect how the particle passes through the two slits in individual experiment. This flaw is a technical flaw, and actually results from the first flaw. The validity of position measurement relies on the absolute validity of the implicit assumption in the first flaw, according to which continuous motion is the only possible form of motion. When this assumption is no longer valid, and the realistic motion of particles does exist and is not continuous motion, the single particle will pass through both slits in a discontinuous way. Then the position measurement may be incapable to detect how the particle passes through both slits in individual experiment, and thus it may be invalid. The orthodox interpretation always pertinaciously takes the position measurement, but it just swallows the bait of quantum mechanics. Quantum mechanics can easily meet such position measurement by using the wavefunction collapse, and thus it successfully conceals the real face of the microscopic reality. According to quantum mechanics, the position measurement will destroy the real motion state of the particle, and collapse it to the region near one slit. As a result, the position measurement not only destroys the double-slit interference pattern, but also is incapable to detect the real motion picture of the particle passing through the two slits.
Once we realize the above technical flaw in the demonstration of orthodox interpretation, we can try to use a new kind of measurement. It can meet the situation where the particle passes through both slits in individual experiment, and can detect the real motion state of the particle passing through the two slits while not destroying the interference pattern. Fortunately, this kind of measurement has been found (cf. Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993). It is called protective measurement. According to the theory of protective measurement[4] , since we know the wave function of the particle beforehand in double-slit experiment, we can protectively measure the real motion state of the particle when it passes through the two slits. At the same time, the wave function of the particle will not be destroyed after such protective measurement, and the interference pattern will not be destroyed either. Thus by using protective measurement we can find the realistic motion picture of the particle passing through the two slits while not destroying the interference pattern, and the measurement results will reveal that the single particle indeed passes through both slits in a discontinuous way.
From the above analysis we can see, the first flaw in the demonstration of orthodox interpretation prevents people from assuming a new form of motion which is different from continuous motion in theory, while the second flaw further prevents people from detecting this kind of motion in experiment. Now we have remedied these two flaws, and accordingly the realistic motion picture of particles naturally appears. It is just the quantum motion of particles. As a result, the mystery of the double-slit experiment is finally unveiled.
In the double-slit experiment, the real process is that the single particle discontinuously passes through both slits. Concretely speaking, the particle is still in one of the two slits at each instant, but during a very small time interval the particle discontinuously moves throughout both slits and passes through them. Since the particle can pass through both slits in such a way, it will not only contain the information of one slit, but contain the information of both slits when arriving at the screen. Then it is intelligible that the double-slit interference pattern is not a simple mixture of two one-slit interference patterns. Certainly, in order to form the double-slit interference pattern, it not only requires that the particle passes through both slits, but also requires that the wave functions passing through the two slits superpose and interfere with each other. The latter is fulfilled by the law of quantum motion.
[2] The underlying reason, as we think, is that they all had the following prejudice, i.e., that continuous motion is the only possible form of motion.
[3] Here we assume the particle is the only existence as the orthodox interpretation does. Thus Bohm (1952)'s hidden-variable theory is not considered.
[4] See Section 4.3 of Quantum Motion for a detailed introduction of protective measurement.