![]() ![]() Too many theoretically based physicists are answering here, and in my opinion give a wrong standing to what physics theories are. This was going to be a comment and then I decided to make an answer by an experimentalist. Therefore, it is the commutation relation between the operators that should be seen as the origin of their quantum mechanical uncertainty relations. However, it is the description by commutation relations and not that by Fourier conjugacy that generalizes to all quantum states and all operators. That the canonical commutation relations are equivalent to such a description by Fourier conjugate variables is the content of the Stone-von Neumann theorem. The reason how "waves" enter is that the uncertainty relation for $x$ and $p$ is precisely that of the "widths" of functions in Fourier conjugate variables, and the Fourier relationship we are most familiar with is that between position and momentum space. The principle is just a consequence of the basic assumption of quantum mechanics that observables are well-modeled by operators on a Hilbert space. In particular, it also holds in finite-dimensional quantum systems (like a particle with spin that is somehow confined to a point) for observables like spin or angular momentum which have nothing to do with anything one might call "wavenature". It is, in my opinion, crucial to note that the uncertainty principle does not rely on any conception of "particles" or "waves". Yields the "famous" version of the uncertainty relation, namelyīut there is nothing special about position and momentum in this respect - every other operator pair likewise fulfills such an uncertainty relation. Plugging in the canonical commutation relation The standard deviation is, for instance, zero for eigenstates of the observable, since you always just measure the one eigenvalue that state has. Now, the standard deviation (or "uncertainty") of an observable on a state tells you how much the state "fluctuates" between different values of the observable. Berlin Heidelberg New-York: Springer-Verlag.$$\Delta x \Delta p_x \geq \frac\lvert \langle\rangle_\psi\lvert$$ An Open Systems Approach to Quantum Optics. "A new wave equation for a continuous non-demolition measurement". "On unitary evolution and collapse in quantum mechanics". "Decoherence, the measurement problem, and interpretations of quantum mechanics". ^ B.D'Espagnat, P.Eberhard, W.Schommers, F.Selleri.Quantum Mechanics: Non-Relativistic Theory. | v x ′ − v x | Δ p x ≈ ℏ / Δ t, : CS1 maint: location ( link)). A formula (one-dimensional for simplicity) relating involved quantities, due to Niels Bohr (1928) is given by In particular, a measurement of momentum is non-repeatable in short intervals of time. It is also necessary to distinguish clearly between the measured value of a quantity and the value resulting from the measurement process. It is possible for other, less direct means of measurement to affect the electron. Particle physics Īn electron is detected upon interaction with a photon this interaction will inevitably alter the velocity and momentum of that electron. However, the need for the "observer" to be conscious (versus merely existent, as in a unicellular microorganism) is not supported by scientific research, and has been pointed out as a misconception rooted in a poor understanding of the quantum wave function ψ and the quantum measurement process. ![]() Despite the "observer effect" in the double-slit experiment being caused by the presence of an electronic detector, the experiment's results have been interpreted by some to suggest that a conscious mind can directly affect reality. Physicists have found that observation of quantum phenomena by a detector or an instrument can change the measured results of this experiment. This effect can be found in many domains of physics, but can usually be reduced to insignificance by using different instruments or observation techniques.Ī notable example of the observer effect occurs in quantum mechanics, as demonstrated by the double-slit experiment. While the effects of observation are often negligible, the object still experiences a change (leading to the Schrödinger's cat thought experiment). Similarly, seeing non-luminous objects requires light hitting the object to cause it to reflect that light. A common example is checking the pressure in an automobile tire, which causes some of the air to escape, thereby changing the pressure to observe it. This is often the result of utilizing instruments that, by necessity, alter the state of what they measure in some manner. In physics, the observer effect is the disturbance of an observed system by the act of observation. ![]()
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