I need some examples of the Heisenberg uncertainty principle on a basic level, or if possible in daily life. Or maybe a simple explanation for validity of the principle in easier words. I cannot get any example except for the measurement of position and momentum of electrons with the help of photons so I decided to ask it here. Are there any simple examples?
[Physics] Heisenberg uncertainty principle in daily life
everyday-lifeheisenberg-uncertainty-principleobservablesoperatorsquantum mechanics
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The relation $p={h\over \lambda}$ applies to photons, it has nothing to do with the uncertainty principle. The issue is localizing the photons, finding out where the are at any given time.
The position operator for a photon is not well defined in any usual sense, because the photon position does not evolve causally, the photon can go back in time. The same issue occurs with any relativistic particle when you try to localize it in a region smaller than its Compton wavelength. The Schrodinger position representation is only valid for nonrelativistic massive particles.
There are two resolutions to this, which are complementary. The standard way out it to talk about quantum fields, and deal with photons as excitations of the quantum field. Then you never talk about localizing photons in space.
The second method is to redefine the position of a photon in space-time rather than in space at one time, and to define the photon trajectory as a sum over forward and backward in time paths. This definition is fine in perturbation theory, where it is an interpretation of Feynman's diagrams, but it is not clear that it is completely correct outside of perturbation theory. I tend to think it is fine outside of perturbation theory too, but others disagree, and the precise nonperturbative particle formalism is not completely worked out anywhere, and it is not certain that it is fully consistent (but I believe it is).
In the perturbative formalism, to create a space-time localized photon with polarization $\epsilon$, you apply the free photon field operator $\epsilon\cdot A$ at a given space time point. The propagator is then the sum over all space-time paths of a particle action. The coincidence between two point functions and particle-paths This is the Schwinger representation of Feynman's propagator, and it is also implicit in Feynman's original work. This point of view is downplayed in quantum field theory books, which tend to emphasize the field point of view.
Motion does not cease at absolute zero if the system you are looking at has a zero point energy.
In many systems, e.g. crystals, at low temperatures the atoms/molecules behave as harmonic oscillators, and the energy of a harmonic oscillator cannot be reduced to zero: there is always some minimum energy called the zero point energy. This means that at absolute zero the atoms in a crystal will not be stationary. There will be a small vibration corresponding to the zero point energy. This is most obvious for light atoms like Helium where the zero point energy is enough to keep the system liquid, so even at absolute zero Helium will not solidify unless it's put under pressure.
The situation is different for a free particle. In that case, at absolute zero the momentum is zero but then we have no knowledge about where the particle is (i.e. $\Delta x = \infty$). If we want to measure where the particle is we have to put some energy in, but then of course the system is no longer at absolute zero and the momentum is now non-zero.
Best Answer
If by "daily life" you mean things we experience on a day to day basis at the macroscopic level (as opposed to the microscopic level), while the principle applies it does so insignificantly.
The principle essentially states that you can never simultaneously know the exact position and speed (momentum) of an object because all objects behave like both a particle and a wave at the same time. If you know the exact position, there will be some error in determining the momentum, and vice versa. At the macroscopic levels of every day life the behavior of a ordinary object is overwhelmingly particulate in nature.
Consider a baseball of mass $0.145\ \mathrm{kg}$ moving at a velocity of about $40\ \mathrm{m/s}$ ($90\ \mathrm{mph}$). The De Broglie wavelength of the baseball is on the order of $10^{-34}\ \mathrm m$. The diameter of an ordinary atom is on the order of $10^{-10}\ \mathrm m$. Consequently, the wavelike behavior of the baseball is too small to observe, and therefore the error in determining the simultaneous position and momentum of the baseball is infinitesimally small.
OK, let me put it another way. First, the uncertainty principle is
$$\Delta x\Delta p \geq \frac{\hbar}{2}$$
or
$$\Delta x \geq \frac{\hbar}{2\Delta (mv)}$$
Where $\hbar$ is the reduced Plank's constant of $1.0546 \times 10^{-34}\ \mathrm{J\cdot s}$
Now our baseball has a mass of $0.145\ \mathrm{kg}$ and speed of $40\ \mathrm{m/s}$ as measured by a radar gun. Assume the radar gun has an accuracy of $1\ \%$. Therefore the uncertainty in our speed (and momentum given constant mass) is also $1\ \%$ or $0.4\ \mathrm{m/s}$. Given this uncertainty, the uncertainty in the position of our baseball, $\Delta x$, is about $9 \times 10^{-34}\ \mathrm m$, which would be many orders of magnitude smaller than the diameter of an ordinary atom. In other words, the uncertainty in the position of ordinary objects is essentially zero.
Compare this to the uncertainty in the position of an electron of mass $9.1 \times 10^{-31}\ \mathrm{kg}$ moving at the same speed with the same uncertainty, which would be about $1.4 \times 10^{-4}\ \mathrm m$. That is 6 orders of magnitude greater than the diameter of an ordinary atom.
A more practical example for an electron is determining the uncertainty in its speed when moving around the nucleus of an atom given that its position is confined to the diameter of the atom. For example, the diameter of a hydrogen atom is about $1 \times 10^{-10}\ \mathrm m$. That would make the uncertainty in the speed of the electron confined to the atom of about $0.6 \times 10^6\ \mathrm{m/s}$.
Bottom line: Although the uncertainty principle applies to all objects, its application is not relevant to the objects we encounter in daily life.
Hope this helps.