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Some history here might be useful; one of the oldest cosmological theories that we have was developed by Ionian philosophers which was an atomic theory; in that theory uncertainty as in random motion was taken as something fundamental (they called it the clinamen which is usually translated as swerve). This shows that pure determinism, physically, is ...

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The Heisenberg Uncertainty Principle (HUP) holds for special observables, as energy and time, space and momentum, .. To every observable there corresponds a quantum mechanical operator. Quantum mechanical operators either commute or not commute, and are seen in the commutation relationships. Observables that do not commute are what the HUP is about. Is ...

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First and foremost we have to understand that if we are deriving laws of nature then our primary assumption is that the natural phenomenons are not random. If they are random, it would be impossible to say anything about them. Now let's come back to Quantum Mechanics. There is nothing random about the motion of electrons or any other subatomic particles ...

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There is something going on. Which is that certain observables are fundamentally incompatible. That means firstly that you can do an experiment for one observable or for another observable, but you can't do an experiment for both observables at the same time. And what's worse if you did an experiment for A then one for A again and then one for B the two ...

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For the angular momentum there is no lower bound for the product $(\Delta L_a)_\psi (\Delta L_b)_\psi$ differently from $x$ and $p$. Indeed there are states $\psi$ such that $L_a\psi =0$ for $a=x,y,z$ simultaneously. I am referring to the states with $L^2\psi =0$ which imply $$(\Delta L_a)_\psi (\Delta L_b)_\psi=0$$ So you cannot write something like $$... 0 Plotting that probability distribution is what my wave function ψ(x) is. No the ψ(x) is a complex valued function. The probability density is given by ψ(x)ψ(x)^* , i.e. the complex conjugate squared with the original. For the second point, this P and its square roots are meaningless; there are no two independent probabilities; there is one ... 1 To me it seems you are a little confused on the basics, so I think going over some of the basics will do more to help you than trying to answer your question directly. As a result, first I am going to make a few statements about the basics of quantum mechanics, then I am going to comment on your two statements, and lastly I'll come to your question. OK, ... 1 A photon is both a particle and a wave is utterly incorrect. A photon is the carrier of the electromagnetic interaction and does not appear in the description of quantum mechanics until you introduce quantum field theory. a particle doesn't have both speed and momentum defined values at the same time Maybe you mean position and momentum (velocity ... 1 The uncertainty principle of quantum mechanics is neither a statement about Fourier transforms, nor is it a statement about the "precision" of measurements as such (although the experimental measurement of the standard deviation is of course only accessible by repeated experiments). For any quantum state \lvert \psi \rangle and any observable A, we ... 1 The average vector momentum of an electron bound to an atom is exactly zero. (Otherwise, the electron would leave the atom!) The average magnitude of the momentum can't be zero, because of the uncertainty principle. So Feynman is using the approximation \vec p = \vec 0 + \Delta p \hat p, where the magnitude \Delta p comes from the uncertainty ... 0 In QM that electron would need more and more kinetic energy when it closes to nucleus, so at some point Coulombic force becomes too weak. The result is an equilibrium position with nucleus, i.e. hydrogen atom. Heisenberg's uncertainty principle is useless when it comes to hydrogenic 1/r potential, but for harmonic oscillator r^2 potential we can use ... 0 We all know about the discrepancy between relativity and quantum physics at the scale relative to particles. No, we do not, at least those of us who have studied particle physics for decades. Special relativity and quantum mechanics describe particle data with great accuracy. General relativity, due to the extreme weakness of the gravitational constant ... 0 Start with two particles in the state UD+DU, where U and D are the "up" and "down" eigenstates of the measurement Alice plans to make. Put u=U+D and d=U-D, and suppose Bob makes a measurement with these eigenstates. Note that UD+DU=ud+du. (The factor of 2 doesn't matter). Alice makes her measurement and finds her electron is in state, ... 1 Under your assumption of simultaneously well-defined x and z value, you reach predictions which are inconsistent with quantum theory. This is exactly what leads to Bell's inequality which is (experimentally!) violated by quantum theory, see https://en.wikipedia.org/wiki/Bell%27s_theorem or the explanation in Preskill's lecture notes ... 1 It's all about orders of magnitude. Heisenberg's uncertainity principal is really given by:$$\Delta x \Delta p \geq \frac{h}{4\pi}=\frac{\hbar}{2}$$Where \hbar=\frac{h}{2\pi}. But sometimes the right hand side is replaced by h or \hbar, this is simply an approximation, just to make our lives easier. So formally you should always use \Delta x \Delta ... 3 The Heisenberg uncertainty principle applies to dimensions commensurate to h_bar, i.e. at the level of particles ( atoms, molecules, elementary particles). Temperature is a classical observable appearing in thermodynamics as a variable, but when analyzed from the emergent statistical ensemble it is not a variable but a statistical average of the kinetic ... 1 Say the unperturbed Hamiltonian is H_0 = \hbar \omega \left( a^\dagger a + \frac{1}{2} \right), the perturbed one is H_1 = \hbar \omega \left( \alpha^\dagger \alpha + \frac{1}{2} \right) = U_0^\dagger H_0 U_0 and the state at time t=T reads$$ |T\rangle = e^{-\frac{i}{\hbar}H_1 T} |0\rangle = U_0^\dagger e^{-\frac{i}{\hbar}H_0 T} U_0 |0\rangle  The ...

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Let's say Heisenberg was right that we can't measure both location and velocity of a small particle at the same time, So doesn't it say that the observations of any experiment that we have done in all these years wasn't actually the exact outcome of those phenomenons? Outcome of what observation to what degree of precision? And because we ...

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You can't measure location and velocity at the same time because they require different equipment to have exclusive access to the object. But that isn't what the uncertainty principle is about, not in the slightest. Take sound. You can make sounds that have a really precise pitch, or sounds that happen for a very short duration. But when you choose to make ...

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If by 'we' you mean 'you and the box' then travelling at relativistic speeds will change nothing for you, you wouldn't notice anything. Only if you kept the box stationary and accelerated the particle to relativistic speeds would it maybe be able to break out of the box, depending on the potential barrier of the box.

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The no cloning theorem (which follows directly from linearity of time evolution) says you can't make a copy so you can't do that. But that is not the point. The point is that you can make a state and even of you made a thousands states just like, the state itself will not give good results for position and good results for velocity. There are states that ...

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