# Heisenberg's uncertainty principle [duplicate]

Can anyone explain Heisenberg's uncertainty principle and it's derivation. Im a 12th standard student.Please make it simple enough for me to understand.

• Why put it on hold? the question is valid. Very briefly. For some operations Ab = BA (sum, product, max value, etc) Other operations are not. ("Then" in cooking recipe). Quantum mechanics has Measure_Energy (M_E) and Measure_Time. Interestingly "M_E than M_T" is not the same as "M_T then M_E". So, AB-BA is not zero. Heisenberg's uncertainty is directly related to that. Now, you can also Measure_Impulse (M_I). Interestingly "M_E then M_I" = "M_I then M_E". Thus you can simultaneously measure energy and impulse, but not energy and time of the system. You need to know matrix algebra. – sixtytrees Jul 14 '16 at 22:21
• @sixtytrees Quantum mechanics does not have a time operator. There is no action called "measure time" in QM. physics.stackexchange.com/questions/6584/… The energy-time uncertainty principle, unlike the position-momentum one, is more subtle and nuanced. The question was put on hold neither because of the sentiment in my initial comment, nor because it was too difficult to answer. If you read the close reason, you would see that it was because there was no or little effort put into the question. Also, please do not spam comments. – orthocresol Jul 15 '16 at 8:39
• – Mithoron Jul 15 '16 at 14:41
• – Mithoron Jul 15 '16 at 17:18
• There is a complete derivation in Atkins & Friedmann "Molecular Quantum Mechanics', ed 3, p25 – porphyrin Aug 3 '16 at 8:50

## 1 Answer

It is a basic postulate of quantum mechanics. It states that it is impossible simultaneously to measure the position of a particle, say an electron, an atom or a molecule, and its momentum. It places limits on these measurements such that uncertainty in position $\Delta x$ and momentum $\Delta p$ is given by $\Delta x\Delta p \ge \hbar/2$ where (hbar) $\hbar =h/2\pi$ and $h$ is the Planck constant $6.626 \times 10^{-34}~\mathrm{J~s}$. In a classical world no such restriction occurs, but this is not what is observed experimentally.

The important part is simultaneous measurement. We can measure where an atom is to whatever precision an instrument will allow, (e.g. by xray crystallography) but we cannot in the same measurement (i.e. at same time) know what its momentum is. We can measure an atom's speed v as accurately as we like and hence momentum mv. We note its position in two places a and b, say 10 m apart, and divide distance by time to cover this distance.

The uncertainty principle places limits on the measurement of momentum mv and position that allows us to know both the position and momentum an atom (particle) has at any given instance. Ask again if this is not clear