A thought experiment illustrating microcosmic research
(Physicist with a hangover)
I
Suppose that a certain physicist-experimenter has the task of determining the coordinates of a certain microparticle on the X-axis at a certain moment T1 with arbitrary precision. Can this be achieved?
In general, it can be said that there are certain limitations in the act of measuring in the microcosm expressed by Heisenberg's indeterminacy, or the uncertainty principle. These limitations affect some combinations of microparticle parameters that cannot be measured simultaneously with arbitrary accuracy. But in this case, it is only one act of measuring a simple parameter on only one axis. So even the most rigorous physicist will say that it is possible without limitation. This work is quite doable.
So our experimenter begins. If at the allotted time T1 presses the red button starting the measurement experiment, it will determine the coordinate of the microparticle X1 with arbitrary precision. What will it be? It is important to underline that there will be no fuzzy spatial cloud of probability values, no abstract mathematical matrix, no transformation of some mysterious function ?, but a specific point on the x-axis. It is a precise measurement result localized in time and along one spatial coordinate axis.
However, this situation is complicated by the fact that the experimenter began his work with a severe hangover after yesterday's big party. He found it hard to hit the red start button, so he missed and didn't start the experiment. The act of measurement did not take place.
There are no problems. The measurement can be done a little later. Suppose our physicist decides to postpone the act of measurement for a time T2 = T1 + t, where t = 1 minute. Since the first measurement did not take place, the situation has essentially not changed. Limits have not been set. A new admissible measurement was made with arbitrary precision. If all is well, the experimenter will get the exact coordinate of the microparticle X2. It will also be a point on the x-axis, but in a different location. Some have already guessed that our physicist missed the red start button again. The measurement did not take place again. He tries again and misses again at X3.
So we will interpret the situation. Our experimenter had a number of opportunities to perform the act of measurement at moments T1, T2, T3 … T(n) … with an intermediate space t. In any of them he can get the exact coordinate of the microparticle on the axis x1, X2, X3 … X (n) …. Taking advantage of the fact that it is possible to allow some fun things to happen in thought experiments, we force the time interval t to decrease to zero. In total, we will get an infinite series of points on the axis, the spacing of which will be close to zero. The points actually connect to one curve.
What is this curve? It is a diagram of the exact coordinates of a microparticle along the x-axis at a certain time interval. Thus, at any instant in this space there will be a point on the curve with an exact coordinate on the x-axis. In other words, every point on this curve can be found if the experimenter begins the measurement at the appropriate moment. There is evidently a rigid determinism going on here; there are no gaps for randomness and probability.
But that is not all. We will assume that our physicist was so clumsy that he touched the instrument and inadvertently changed the arm of the measuring instrument from the X-axis to the Y-axis. Now all measurements will be valid for the ordinate axis. In total, a specific curve with potentially measurable coordinates of the microparticle will be obtained again. All axes are the same in our case, so as a result of the same mental trick, we can get an exact coordinate curve along the Z axis.
So we have determined three curves along three axes. They can be integrated into a single spatial curve, which can be safely called a "trajectory". If the experimenter performs only one act of measurement on any of the three axes at any given moment in the given space, he establishes a point on that curve (and nowhere else!). On the other hand, every point on this spatial curve can be found if, at an appropriate moment, we measure any of the three coordinate axes we choose. There is a complete unique correspondence that does not allow for different interpretations.
As a result of this thought experiment, we concluded that the motion curve of a microparticle does exist, is precisely localized in space and time, and can easily be found with arbitrary precision at any point on any chosen axis. This is a pretty deterministic routine.
II
Problems arise when we set the task of getting, say, the exact coordinates of two or more points at once. This is where the key limitation characterizing the nature of our relationships with the microcosm begins to operate. We called this the “second measurement problem”. Twentieth-century physicists described this using Heisenberg's indeterminacy or indeterminacy principle.
In the human experience of the macrocosm there are events; events occur in microcosm. And there is a process of transmission, a presentation of the events of the microcosm in our macrocosm. It is important to emphasize that the above-mentioned problem does not concern the happenings in the human macrocosm and microcosm. It only affects the translation process. Here, on the border of two worlds, there are key difficulties, which we have already written about in the article "Circular Determinism and Probability".
One can primitively describe how difficult it is to transfer more than one precise (with arbitrary precision) measured value from the microcosm to the human macrocosm. What will happen with other necessary values? Now that a defect in our usual deterministic research methodology is detected, it inevitably opens the floodgates of indeterminacy and randomness. In capacitive compensation, it is necessary to resort to the use of indirect descriptive-calculation procedures: blurred spatial clouds of probability values, abstract templates and refined transformations of the mysterious function ?.
It is important to emphasize once again that all these indirect procedures have no direct connection with the real events and processes in the microcosm. They are only computational - descriptive procedures that are simply convenient for physicists and allow in some way to solve the problem of presenting events in one pattern to another. In the above thought experiment, it was proved that the curve of movement of a microparticle (trajectory) really exists. Each point can also be found experimentally with arbitrary precision. However, it is not possible for us to map this curve on a diagram with any accuracy (although roughly it can be done in a bubble chamber or expansion (cloud) chamber).
Positivists (physicists and philosophers) in this situation come to the amusing conclusion that the trajectory in the microcosm does not exist, that the microparticle is not a point object precisely located in space, but represents a cloud of probability, blurring space and time, and other nonsense.
Materialists, physicists and philosophers should respond to this ugliness in a rigorously scientific way with a differentiated approach: separating current descriptive-computational models of reality from physical reality itself. Finally, it will enable its removal from modern microcosmic physics, already confused by the dominance of superficial descriptive-calculation methodology, and will achieve success in a deeper understanding of the nature of the relevant physical processes.
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