# What does the Heisenberg principle actually mean? [duplicate]

As far as I can understand, the Heisenberg principle limits the possibility of calculating the exact position and momentum of electrons, as the light we use to observe it changes it's velocity.

But isn't this just our inability to calculate the position and momentum? Doesn't an electron exactly exist at one place at a given time? So why the concept of "probability of finding an electron" or "electron clouds"? Doesn't the electron have a clear path around the nucleus every time similar to the Bohr model? Isn't it just that we do not know where or what that path is?

So what is the flaw in my argument? ('cause I know there has to be something,😀)

## marked as duplicate by WillO, Qmechanic♦Apr 6 at 18:22

• Possible duplicate of Is uncertainty principle a technical difficulty in measurement? – Thomas Fritsch Apr 6 at 16:58
• If electrons had “clear paths”, the double-slit experiment would not show an interference pattern. Atoms are not little solar systems. – G. Smith Apr 6 at 17:21
• "So what is the flaw in my argument?" What argument? – WillO Apr 6 at 17:40
• As far as I can understand, 7+3 = 10. But isn't this just our inability to add 7+3 and get 9? Isn't 7+3 actually 9? So why the concept of "adding 7 plus 3 to get 10"? Isn't 7+3 really 9? Isn't it just that we don't know how to compute this? So what is the flaw in my argument? How would you attempt to pinpoint the flaw in such an "argument"? – WillO Apr 6 at 17:45

What you are asking for is a world that is fundamentally classical, with limits to our understanding.

There exists a cooperative game for a team of three people. We ask them to go into rooms that will be completely isolated, and they won't be able to communicate with each other. They can come up with any strategy that they want to in advance. Once they are in their separate rooms, we will ask each of the three of them to hit buttons labeled 0 or 1 to make the sum of their three chosen numbers even or odd, we will collect the numbers and add them and determine if they win.

One fourth of the time, we run what's called a control experiment, where we ask them all to make the sum of their numbers even: and the team wins if their sum is even. The rest of the time, we choose one of the three at random to “betray” the other two: we ask the traitor to make the sum even, and we ask the other two to make the sum odd, and the team wins if the sum of their three chosen numbers is odd. So the two nontraitors know that there is a traitor but do not know who it is, while the traitor doesn't know they are operating at cross-purposes to their team.

In the classical world this puzzle can only be answered 75% correct: you have to choose one of the four situations to get wrong each time.

In the quantum world answering this puzzle depends on your ability to preserve and manipulate these delicate quantum states when you bring them into the communication-less room, but in principle nothing in physics stops a team from winning 100% of the time: it is purely an engineering challenge.

Somewhere within that space of what you don't know, in other words, can be hidden strange correlations that cannot be explained in the classical world. If you postulate hypothetical hidden information in this Heisenberg uncertainty then you have to also postulate that there is no way to truly make these rooms unable to communicate between each other, as the hidden information can travel instantaneously between two points no matter what stands between them. In our relativistic universe it must also be able to go backwards in time, if you go down that path. Most of us do not really like that approach, but it does have some adherents among the pilot wave enthusiasts.

The Heisenberg uncertainty principle is an envelope of quantum mechanics. You cannot understand it using classical mechanics, which is what the Bohr model is. It can be shown that the classical equations emerge from the underlying quantum mechanical level when the variables are such that the HUP is fulfilled trivially.

The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. There is a minimum for the product of the uncertainties of these two measurements. There is likewise a minimum for the product of the uncertainties of the energy and time.

This is not a statement about the inaccuracy of measurement instruments, nor a reflection on the quality of experimental methods; it arises from the wave properties inherent in the quantum mechanical description of nature. Even with perfect instruments and technique, the uncertainty is inherent in the nature of things.

The quantum mechanical wave functions which describe at the particle level the interactions, and the operators representing variables that act on these wavefunctions are new mathematical tools for modeling reality at the microscopic level quantum mechanically. Commutators are the ones on which the HUP is based, and one has to study quantum mechanics to see how that happens.

What you are missing is that the HUP is a quantum mechanical principle and cannot be "explained" with classical mechanics.

Why quantum mechanics became necessary to describe nature is a different question.