Heisenberg's Uncertainty Principle: The More You Know, The Less You Know.
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- เผยแพร่เมื่อ 11 ก.ค. 2017
- What is Heisenberg's Uncertainty Principle?
This strange concept is at the heart of quantum Physics.
In this video, I explain, using simple terms, what it means
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Heisenberg's uncertainty principle: Δх * Δр ≥ ħ/2
The Heisenberg's uncertainty principle is correct, moreover, it is fundamental. If the uncertainty principle is incorrect, then all quantum mechanics is incorrect. Heisenberg's justified the ncertainty principle in order to save quantum mechanics. He understood that if it is possible to measure with every accuracy both the coordinate and momentum of a microparticle, then quantum mechanics will collapse, and therefore further justification was already a technical issue. It is the uncertainty principle that prohibits microparticles in quantum mechanics from having a trajectory. If the coordinates of the electron are measured at definite time intervals Δt, then their results do not lie on some smooth curve. On the contrary, the more accurately the measurements are made, the more "jumpy", chaotic the results will be. A smooth trajectory can only be obtained if the measurement accuracy is small, for example, the trajectory of an electron in a Wilson chamber (the width of the trajectory is enormous compared to the microworld, so the accuracy is small).
Heisenberg's formulated the uncertainty principle thus:
if you are studying a body and you are able to determine the x-component of a pulse with an uncertainty Δp, then you can not simultaneously determine the coordinate x of the body with an accuracy greater than Δx = h / Δp.
Here is a more general formulation of the principle of uncertainty: it is impossible to arrange in any way an instrument that determines which of the two mutually exclusive events has occurred, without the interference pattern being destroyed.
It should be immediately said that the Heisenberg uncertainty principle inevitably follows from the particle-wave nature of microparticles (there is a corpuscular-wave dualism is the principle of uncertainty, there is no corpuscle-wave dualism - there is no uncertainty principle, and in principle quantum mechanics, too). Therefore, there is an exact quantitative analogy between the Heisenberg uncertainty relation and the properties of waves.
Consider a time-varying signal, for example, a sound wave. It is pointless to talk about the frequency spectrum of the signal at any point in time. To accurately determine the frequency, it is necessary to observe the signal for some time, thus losing the accuracy of time determination. In other words, sound can not simultaneously have the exact value of its fixation time, as it has a very short pulse, and the exact frequency value, as it is for a continuous (and, in principle, infinitely long) pure tone (pure sine wave). The time position and frequency of the wave are mathematically completely analogous to the coordinate and (quantum-mechanical) momentum of the particle.
We also need to clearly understand that the Heisenberg's uncertainty principle practically prohibits predicting behavior (in the classical sense, since Newton was able to predict the position of the planets), for example, an electron in the future. This means that if the electron is in a state described by the most complete way possible in quantum mechanics, then its behavior at the following moments is fundamentally ambiguous. Therefore, quantum mechanics can not make strict predictions (in the classical sense). The task of quantum mechanics consists only in determining the probability of obtaining a particular result in the measurement, and this is fundamental. That is why the uncertainty principle has such a fundamental meaning (there is no uncertainty principle - there is no quantum mechanics). But this does not mean that we do not know any "laws or variables that are hidden from us", etc. No. It's just the reality. This is analogous to how a particle can exhibit corpuscular and wave properties - just this is reality and nothing more. And even if we know the "hidden parameters" (compare, understand why the wave properties and corpuscular ones are manifested), this reality will not change, and the uncertainty principle will also work, but we will understand it more fully.
It must be added that not all physical quantities in quantum mechanics are measurable simultaneously, that is, they can have simultaneously definite values. If physical quantities can simultaneously have definite values, then in quantum mechanics they say that their operators commute. The sets of such physical quantities (complete sets) that have simultaneously defined values are remarkable in that no other physical quantity (not being their function) can have a definite value in this state. The fully described states (for example, the description of the electron state) in quantum mechanics arise as a result of the simultaneous measurement of a complete set of physical quantities. By results of such measurement it is possible to determine the probability of the results of subsequent measurements, regardless of what happened with the electron before the first measurement.
If physical quantities can not simultaneously have definite values, then their operators do not commute. The Heisenberg uncertainty principle establishes the limit of the accuracy of the simultaneous determination of a pair of physical quantities that are not described by commuting operators (for example, coordinates and momentum, current and voltage, electric and magnetic fields).
Let's add a little history. A. Einstein assumed that there are hidden variables in quantum mechanics that underlie the observed probabilities. He did not like the principle of uncertainty, and his discussions with N. Bohr and W. Heisenberg greatly influenced quantum mechanics and science as a whole.
In the Copenhagen interpretation of quantum mechanics (N. Bohr and followers), the uncertainty principle is adopted at the elementary level, and it is in this interpretation that it is believed that this can not be predicted at all by any method. And it was this interpretation that Einstein questioned when he wrote to Max Born: "God does not play dice." To which Niels Bohr, answered: "Einstein, do not tell to God what to do." Einstein was convinced that this interpretation was erroneous. His reasoning was based on the fact that all the already known probability distributions were the result of deterministic events. The distribution of the tossed coin or rolling bone can be described by the probability distribution (50% eagle, 50% tails). But this does not mean that their physical movements are unpredictable. Conventional mechanics can calculate exactly how each coin will land, if the forces acting on it are known, and the eagles / tails will still be randomly distributed (with random initial forces). But it is unlikely that this experience can be extended to quantum mechanics.
The position of Bohr and Einstein must be viewed as views from different angles of view on one phenomenon (problem), and in the end it may turn out that they are right together. This can be demonstrated by lottery. Despite the fact that theoretically the results of the lottery can be predicted uniquely by the laws of classical mechanics, knowing all the initial conditions (it is necessary only to determine all the forces and perturbations, and to make the necessary calculations), in practice the lottery results are always probabilistic, and only in theory they can be predicted (try win the jackpot :). Even in this simplest case, we will be "inaccessible" to all the initial data for calculations. It is logical to assume that the quantum system will be incomparably more complicated than the lottery, and therefore, if we master the "true" laws of the quantum world, the probabilistic picture will remain, since the microworld is such in essence. Moreover, if you think about it, then our world is also probabilistic. It is deterministic only in theory, and practically, in everyday life, we can only predict, for example, tomorrow (or a second, or a year, or 10 years) with a certain probability (who can guarantee the event of tomorrow with 100% probability?). And what is interesting is that only after having lived it (by making a measurement), we can say what probability was realized. Quantum mechanics in action :).
More see by link: www.quora.com/Is-Heisenbergs-principle-of-uncertainty-wrong/answer/Volodymyr-Bezverkhniy?share=b4884212
Benzene on the basis of the three-electron bond:
REVIEW. Benzene on the basis of the three-electron bond (full version, 93 p.).
vixra.org/pdf/1612.0018v5.pdf
1. Structure of the benzene molecule on the basis of the three-electron bond.
vixra.org/pdf/1606.0152v1.pdf
2. Experimental confirmation of the existence of the three-electron bond and theoretical basis ot its existence.
vixra.org/pdf/1606.0151v2.pdf
3. A short analysis of chemical bonds.
vixra.org/pdf/1606.0149v2.pdf
4. Supplement to the theoretical justification of existence of the three-electron bond.
vixra.org/pdf/1606.0150v2.pdf
5. Theory of three-electrone bond in the four works with brief comments.
vixra.org/pdf/1607.0022v2.pdf
6. REVIEW. Benzene on the basis of the three-electron bond (full version, 93 p.). vixra.org/pdf/1612.0018v5.pdf
7. Quantum-mechanical aspects of the L. Pauling's resonance theory.
vixra.org/pdf/1702.0333v2.pdf
8. Quantum-mechanical analysis of the MO method and VB method from the position of PQS.
vixra.org/pdf/1704.0068v1.pdf
Bezverkhniy Volodymyr (viXra):vixra.org/author/bezverkhniy_volodymyr_dmytrovych
Thanks man.... I appreciate it👍
Hi Sir.
For this syllabus (New HSC Physics) must we be able to derive Heisenberg's uncertainty principle.
Thanks
No. In fact heisenberg isn’t even in the syllabus anymore
lets go vihan