Why position and momentum cannot be determined at the same time in an uncertain relationship

It's like asking why 1+1 equals 2The question you ask is a law that people have summed up based on a phenomenon, and then this law is universally applicable and has not been overturned by other theories, and then people write it down like a theorem formula. If you come up with a scientific hypothesis based on a certain phenomenon one day, and it is repeatedly verified to be correct, then your hypothesis can become a theorem and be listed in the textbook, and that's how science develops.

The position and velocity of microscopic particles cannot be determined at the same time, and we can explain the uncertainty principle of quantum mechanics with degrees of freedom and resolution.

Let's start by understanding what degrees of freedom are:

Statistically, degrees of freedom refers to the number of independent or freely variable data in a sample when the parameters of a population are estimated by the statistics of the sample, which is called the degree of freedom of the statistic.

For example, if there are two variables, a and b, and a+b = 6, then its degrees of freedom are 1. Because in fact, only A can really change freely, and B will be limited by the difference in the value of A.

Next, in the psychology of degree, degree and logic are combined and interrelated. We might as well imagine that in the universe, degree and logic may be combined and related to each other, because this is also more in line with the principle of logical simplicity in nature.

Degree and logic are interrelated and interrelated. The more certain the degree, the more limited the value of the logic is. The more certain the logic, the more limited the value of the degree is. The more certain the velocity, the more limited the value of the final position is, and their degrees of freedom are 1.

For example, the more certain the velocity, the more possible the position in nature changes from the original 3 possibilities to 2 possibilities, and the resolution changes from 3 to 2, the more inaccurate the position, and when the velocity is completely determined and the position resolution is 1, the particle may appear at any position. Therefore, the more certain the speed, the less accurate the position. In the same way, when the position is fully determined and the velocity resolution is 1, any speed is possible.

That is, the more certain the position, the less accurate the speed.

The degree and logic are combined and correlated with each other, resulting in the two variables interfering with each other and cannot be independently and freely valued.

The world is so incomprehensible that God is the only one to blame. God shouted "Who can be lazier than me", and the whole world fell silent.

Because when one of the quantities is measured, it must have an effect on the magnitude and direction of the other quantity, and the measurement must be sequential, so it is impossible for the two quantities to be measured at the same time.

Because the physical quality of motion is changing.

Here's a "slide" for reference.

This formula is derived in detail in the book of quantum mechanics, which is difficult to write here, so it is recommended to check the textbook on quantum mechanics.

I recommend a thinner copy of "Quantum Mechanics" written by Zhou Shixun.

Both momentum and position are uncertain, and if the uncertainty of one is >0, the uncertainty of the other is > infinity. The product of the uncertainty of the two is not less than h

The physical meaning of the Heisenberg coordinates and momentum uncertainty relationship is that microscopic particles cannot have both definite coordinates and corresponding momentum.

Both are uncertain because if one is determined, then the other is infinity and impossible.

According to the uncertainty relationship (uncertainty principle):

x*δp h 4 ==> δp h (4 *δx) = i.e., the momentum uncertainty of the electron is about .

h is Planck constant.

According to the uncertainty principle, the momentum of microscopic particles cannot be accurately determined ......

To reduce the error, it is necessary to measure the electron using high-frequency electromagnetic waves (more accurate position) and low-frequency electromagnetic waves (more accurate velocity) to find the average momentum reduction error ......

It is also possible to calculate according to the state of the electron (except for individual electrons).

These two ... I don't understand, I have the impression that the first volume is solved separately by using the Schrodinger equation, and you can also use the Herminian Wide Imperial Operator to make Changyan integrals, but they are all mathematically calculated, I want to ask them if they are really related?

The commonly used relation is δxδp h, where the approximately equal sign instead of the greater than equal sign, is a commonly used means to estimate one of the uncertainties at the other time.

What follows requires some statistical knowledge.

Mathematically, the strictest statement is:

x 2> >=(h 4) 2 (yes 4 not 2 ) where < δx 2> and < δp 2 > are the statistical variance of x,y, and then you take the root number (standard deviation) of the variance as the estimation of δx,δp, then you have δxδp>=h 4

But this is only the so-called mathematically rigorous statement, except for some distributions, the deviation of using standard deviation to describe a statistical distribution is not necessarily meaningful, so in fact, when using the uncertainty relationship, we often only make magnitude estimates, and also use some more arbitrary estimates for δx and δp (for example, using the half-height and width of the distribution to estimate), various different methods may be several times different, and in fact, the general quantum state will not reach the minimum uncertainty. However, a typical quantum state does not deviate much, so we often use the δxδp h relation to estimate a certain uncertainty. (When this equation is taken as an equal sign, it is actually based on de Broglie's relation to the matter wave).