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Are random errors necessarily gaussian? Errors are very often Gaussian, but not always. Here are some physical systems where random fluctuations (or "errors" if you're in a context with the thing that's varying constitutes an error) are not Gaussian: The distribution of times between clicks in a photodetector exposed to light is an exponential distribution....


51

Physics models rarely hint at ontological level. Throwing dice can be modelled as deterministic process, using initial conditions and equations of motion. Or it can be modelled as stochastic process, using assumptions about probability. Both are appropriate in different contexts. There is no proof of "the real" model.


49

You're right; the Schrödinger's equation induces a unitary time evolution, and it is deterministic. Indeterminism in Quantum Mechanics is given by another "evolution" that the wavefunction may experience: wavefunction collapse. This is the source of indeterminism in Quantum Mechanics, and is a mechanism that is still not well understood at a fundamental ...


36

An alternative way to generate random numbers, that truly is quantum, and also quite easy: put a small radioactive source near a Geiger counter. Radioactive decay is a truly random event in the quantum sense, and is basically not subject to thermal noise at all. For maximum visual impact, replace the Geiger counter with a cloud chamber. That way you can ...


34

Throwing dice is just throwing dice. That's all. It's not stochastic, nor deterministic. It's just throwing dice. Now we model throwing dice as a process, and that's where the stochastic or deterministic side starts to play in. It is the process that is stochastic or deterministic, not the throwing of the dice. It's how we think about the throwing of ...


33

The surprising answer is that nothing triggers it. In quantum mechanics all we can talk about is the probabilities of various events happening: whether they actually happen in a given period is truly random. There is no secret mechanism which we could find which controls whether an event happens or not. Well, there are, really, three-and-a-half ...


32

The decay phenomenon is a purely quantum mechanical property. This problem is equivalent to a particle in a finite potential well, and a lower potential state that is available outside the well. Classically if the energy of the particle in the well is lower than the potential barrier - it will never get to the lower state. By quantum mechanics, the particle ...


28

As noted in the comments this is a much studied question. Einstein, Podolsky and Rosen wrote a paper on it, "Can Quantum-Mechanical Description of Reality Be Considered Complete?", published in Physical Review in 1935, and universally known today as the EPR paper. They considered a particular situation, and their paper raised the question of "hidden ...


28

The fact is that there are two kind of things: 1) the wave function and 2) the physical observables. The evolution of the wave function is dictated by the Schrödinger equation and is deterministic meaning that if you know the wave function at some time, then you know it at any time just using Schrödinger equation $$ i \hbar \frac{d}{dt} \left \lvert \Psi (...


25

This is really a footnote to Chris' answer but it got a bit long for a comment. It sounds odd to claim that a particle has no position, but it's easier to understand if you appreciate that a particle is just an excitation in a quantum field. When Heisenberg was developing his ideas physicists still thought of particles as little billiard balls. With the ...


17

Speaking loosely, each individual atom has a desire to become stable, but that translates into a probability of decaying. This means, since there are billions and billions of atoms in a macroscopically significat chunk of material, that there are always going to be unlikely holdouts, and these holdouts are responsible for radiation that after the initial ...


16

In quantum mechanics, the solution of the equations (Schrodinger, Dirac...), called wave functions are deterministic, at each $\left(x,\,y,\,z,\,t\right)$ point, but the only prediction they give is a probability distribution, which depends on the boundary conditions of the problem. $Ψ$ is a complex valued function, and measurements are real numbers and this ...


15

Look up Diaconis's work on flipping coins. While it is technically deterministic, what happens is that extremely small changes in the initial conditions flip the outcome. The same would be true of dice. When you shake them in your hand and throw, small changes would give different outcomes. What makes it seem random is that we can't control our hands well ...


14

The reason is probably the central limit theorem: When you add lots of independent random variables, their sum will form a normal distribution, irrespective of their individual probability distributions. This makes normal distributions a pretty good guess if you do not have information about the origin of the error or if you have multiple sources of error. ...


13

Although the uncertainty principle stems from the mathematical structure of QM, i.e., originates from the noncommutivity of some observable letting them behave as fourier transform pair as explained in another answer, I still think it is a statement on measurements, (i.e., imposes fundamental limits on measurements) since QM itself seems to be a theory of ...


13

The easy answer is "no one knows". The Schrödinger equation is just an equation that old Erwin threw together that happened to fit the experimental data. It is not even consistent with relativity theory (second derivative of space but only first of time) so clearly something is wrong with it. It just happens to work real well for engineering.


12

I believe spontaneous means it happens on its own. You don't need any outside influence to get the isotope to decay. This term is sometimes used in contrast to stimulated. Random means one cannot know precisely when the next decay will happen, though one can predict the probability of such events occurring in some time interval. A decay process can be both ...


11

The magnet has a finite moment of inertia. What would happen when the magnet with "wrong" orientation enters Stern-Gerlach apparatus? Of course, the magnetic field will exert torque on it. The magnet starts rotating. After it comes to the equilibrium orientation, i.e. is oriented along the field, the torque is zero, but angular velocity is at maximum, and ...


11

If I understood correctly, what you are trying to build is a hardware based random number generator, where you want to use some quantum mechanics-based mechanism to supply the randomness. I'm no experimentalist, thus, take my comments with a grain of salt. Your suggestion is to use Schottky noise from a illuminated photodiode. I believe that it's a pretty ...


11

Answers here have generally addressed the different question of whether empirical variables should be Gaussian, but 21joanna12 asked about experimental errors, which admit a completely different analysis. The best resource on that question I can recommend is Chapter 7 of Probability Theory: The Logic of Science by E T Jaynes. In short, there are good reasons ...


11

If you look at the actual equations governing quantum mechanics, there is no randomness at all. The nucleus starts out in a state where it hasn't decayed. Over time, it evolves into a mixture of the undecayed state and the decayed state. It's like Schrodinger's cat. Gradually the mixture shifts more and more toward decay. If an observer watches the nucleus ...


10

To add to Nathaniel's Answer because (1) it is a good answer and (2) I get nervous recommending radioactive materials handling to anybody I don't know: I would really think about the cloud chamber idea, especially since you're a software guy with a math background. It would need to be inside a darkened container, but you could run a webcam to show what is ...


10

In the standard interpretation of quantum mechanics the time-evolution of the system and what we observe are separated (unlike Newtonian mechanics). The system, while unobserved exists in a superposition of states (all the states that satisfy the Schrödinger equation). These states (while unobserved) evolve in time according to the Schrödinger equation. This ...


9

I've never heard about a non deterministic theory in physics, classical physics is, quantum theory is (if I take the wave function of the universe its evolution is deterministic), general relativity is ... And about the wave function collapse, it means that something not well understood happens when a system interact with another one which posses much more ...


9

The experimental result that the rate of decay is measured to be proportional to the amount of undecayed particles actually confirms memorylessness. This is because this result, together with the assumptions that the particles are not "communicating" with one another and that they are identical confirms that the probability density of the time to decay for ...


8

Today, in my physics class my teacher was talking about how we can never predict the outcome of a coin flip Your teacher was most likely not talking about this from a QM perspective of how experiments have probabilistic outcomes due to the inherent nature of QM (as we currently understand it). Your teacher was most likely making a comment about how it is ...


7

In the sense of "Copenhagen Interpretation", what exactly is an interpretation? What purpose does an interpretation serve? I would describe interpretations of quantum mechanics as part of the philosophy of physics. Here is a well-known quote by Bertrand Russell: "As soon as definite knowledge concerning any subject becomes possible, this subject ceases to ...


7

Understanding the uncertainty principle really only involves accepting the idea that, at small scales, elementary particles behave like waves. The uncertainty principle is a well-known property of waves. One of the consequences of this idea is that position and wavelength cannot be measured to an infinite precision simultaneously with one another. Imagine, ...


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