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Questions tagged [discrete]

Discrete means as opposed to continuous. For, instance, people may ask questions about discrete electric charges, discrete spacetime, discrete energies, etc. If discretization is vital/essential to the question then tag it with the [tag:discrete] tag.

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Planck theory of discrete energy of photons and electromagnetic spectrum

Planck said that "energy of photon is quantized. That means energy of a photon cannot be any random value but a certain values only". If this is true how electromagnetic spectrum is continuous. For ...
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64 views

Does gravity need to be explained by quantum mechanics if spacetime is discrete?

I have read that Einstein‘s theory of general relativity, explaining gravity as a warping of space time, is inconsistent with quantum mechanical theories attempting to explain gravity. My question is ...
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Any nice solutions to this kinematics problem? [closed]

So I made a mock F=ma exam with a couple of my friends on AoPS. Here is one of the problems (problem 21) Bob lives in the universe $\Omega$, which happens to be a physics simulation. In $\Omega$,...
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47 views

Are all lengths multiples of the Planck length? [duplicate]

If the Planck length is the smallest unit of length that has any physical meaning then is it true to think that all the lengths are multiple of the Planck length?
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What led Bohr to come up with the idea of quantization of angular momentum? How Bohr Proved this idea? [duplicate]

How did Bohr come up with the idea of quantization of angular momentum? In the proof of quantization of angular momentum we use de Broglie wavelength concept and de Broglie wavelength concept was ...
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48 views

Is every kind of energy quantised?

I know this is been asked on this site before but I felt unsatisfied by its one answer. I’m familiar with the concept of quantisation, I keep reading that “energy is quantised” but what do they mean ...
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2answers
72 views

Does the “Particle in a box” mean space & motion are quantized?

Recently I had a conversation with someone about quantum mechanics, I was asking if it meant everything was quantised. If space and our ability to move through it and the positions matter could take ...
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1answer
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Feynman Lectures on Physics: Vol 1, 11-6: acceleration vector

I’m trying to get through 11-6 section of Feynman’s Lectures on Physics, Vol 1, particularly explanation of acceleration vector calculation in his example: It’s clear that acceleration ...
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2answers
64 views

Infinite square well discrete energies meaning

In the problem of infinite square well we come out with quantized energies that an electron can have. And each energy level has its own wave function. The general solution is a linear combination of ...
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36 views

Is the acceleration produced by electrostatic repulsion quantized?

Say the universe at time $t_0=0$ consists of two electrons at rest, both of charge $q$, separated by some distance $r$. The repulsive force $F$ between them is $F = C q^2/r^2$ where $C$ is Coulumb's ...
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1answer
51 views

Different energy levels in quantum mechanics

I have a doubt regarding energy levels. I saw that translational energy levels are quasi-continuous, rotational energy levels are discrete and vibrational energy levels are more discrete. I want to ...
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2answers
196 views

If an atom can have only discrete energy values, why it can move on any speed?

Atom, as a quantum system can have only certain energies. Also, energy, specifically kinetic energy depends on velocity, which should mean, that an atom should move only on some strict velocities, and ...
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1answer
67 views

How can a continuous spacetime look discrete on a larger scale?

Referring to Arnold Neumaiers answer here, where he states that: "If time appears discrete (or continuous) at some level, it could still be continuous (or discrete) at higher resolution" This ...
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How does angular momentum get quantized? [duplicate]

We know that the magnitude and direction of angular momentum is quantized in quantum mechanics. We can explain the quantization with the help of quantum numbers. But actually who is responsible for ...
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893 views

Generator for parity?

The unitary translation operator, $\hat{T}(\lambda) = e^{i\hat{p}\lambda/\hbar}$, is generated from the Hermitian operator $\hat{p}$. The unitary rotation operator, $\hat{R}_z(\alpha)=e^{-i\hat{L_z}\...
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26 views

Is the Planck length a minimum or a unit of discrete distance? [duplicate]

Can 2 things, or 2 measured distances be 1.2 planck lengths away from each other? Or must they be 2 planck lengths away?
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Why is the optimum window length for a discrete fourier transform of a signal less than 100%?

I'm trying to determine the best settings for a discrete Fourier transform on a signal with noise. Now I've stumbled on something that I can't seem to explain, I'm hoping someone can give me some ...
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2answers
67 views

Density Of states derivation

In the aspect of density of state derivation or simply assuming the frequency of a solid as a continuous distribution we have to come up with an equation expressing the density of states. Its derived ...
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1answer
28 views

Partition Function when the Energy States are Both Discrete and Continuous

Normally for statistical mechanics (in this example I will be only refering to the canonical formalism to keep things simple) we generally have a system that we solved the equations of motion for and ...
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2answers
99 views

Is force quantised?

Things like charge, distance, energy, etc are quantised , Are all the phenomenon around us also quantised ?? Like time or say Force !? I was reading this question which goes about seeing the effect ...
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22 views

Update: Does the Planck scale imply that spacetime is discrete? [duplicate]

This question has already been asked Does the Planck scale imply that spacetime is discrete? however I'm wondering if there has been any change in the community since it was asked roughly 8 years ...
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31 views

Why is photon quantized in vacuum? [duplicate]

Apparition of quantized energy levels in quantum physics is usually explained in analogy with sound waves in a box (like in music instruments): the wave has to satisfy the boundary conditions and ...
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21 views

Fourier transform of some discrete, finite, non-uniform signal

Suppose I have some finite signal $x(t)$ of $N$ data points. This signal is produced by some program or some experiment and so is discrete and the difference in time between each data point $\delta t$ ...
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1answer
70 views

Problem in the continuum limit of a Kronecker delta

I am having troubles in understanding how to correctly perform the continuum limit of a double sum containing a Kronecker delta. Imagine to integrate a function depending on $t$ and $t'$, both ...
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1answer
29 views

Discrete energy rounding

If energy is only found in discrete amounts what happens when the amount of energy falls below the minimum individual unit? does it have a floor or ceiling function or does it matter what type it is?
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2answers
105 views

Discrete energy levels of electrons in isolated atom

My question is a duplicate of this. Please consider the equation $\nabla^2\psi + (2m/\hbar^2)[E-V]\psi=0$ (1) Potential of electron revolving hydrogen atom is given as $V=\frac{-e}{4\pi\...
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86 views

Is the whole electromagnetic spectrum made of quanta?

My question is probably stupid (and maybe has already been answered on other posts), but I just started investigating quantum physics and I am struggling to understand the real meaning of "quantum". ...
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Why light coming from distant stars is not discrete? [duplicate]

Imaging the light racing out from distant sun, as beam of light shoots aways is a circular pattern (spherical actually), remembering that, light comes in photons or packets of energy. so how come is ...
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1answer
78 views

Where exactly does energy quantisation come in for light?

Planck quantised the energy of light in order to solve the black body radiation problem. However, I am confused as to exactly what he quantised. On one hand, I have seen that he quantised the energy ...
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45 views

Discrete time evolution in a non-Euclidean space?

The time independent schrödinger equation can be written as $$i\frac{\partial \psi}{ \partial t}=H\psi$$ if we consider the case of a 1D particle we can evolve it in time by discretising the ...
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50 views

Can Noether's theorem be applied to cyclic time symmetries? [duplicate]

Noether's theorem relates continuous symmetries in the time evolution of a system to a conserved value. Many conserved values, such as conservation of momentum, can be described via this theorem. I'...
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1answer
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Is the answer to the question “How many moments in time exist between any two particular moments?”, infinitely many? [duplicate]

This question is related to Xeno's paradox, and to the discrete/continuous time debate, but it comes from a slightly different angle. If the answer is infinitely many, why would this not be a ...
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25 views

Geometrical way to view discretization of energy in quantum mechanics. How commutation relation implies discreteness?

The relation from which discreteness in eigenvalue of the energy of bound state arises is $[x, p]=i\hbar$ followed by the rule that wavefunction should be normalizable. So my question is there a ...
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1answer
54 views

Would any continuous model of the universe have/be based on hypercomputational laws?

I've read that when Turing-Church thesis is applied to the universe and physics, one of the three interpretations that we can use and is defended by some important physicists is that: "The universe ...
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1answer
87 views

Discretization of Hamiltonian with first derivative

In a particular 1D system, the Hamiltonian can be writen as $$H=\mathrm{i}\left(f(r)\frac{\partial}{\partial r}+\frac{1}{2}f'(r)\right)\; ,$$ wher $\mathrm{i}$ is the imaginary unit, and $f(r)$ is a ...
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3answers
173 views

Superposition principle forbids quantisation?

Apparently bound states in quantum mechanics require energy states to be discrete. That means energy in such systems is quantized, right? However, say that we have a superposition of energy ...
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1answer
119 views

Is entropy quantized in Loop Quantum Gravity?

From the Beckenstein-Hawking formula, we know that entropy is proportional to the area of the event horizon of a black-hole: $S\propto A$. From Loop Quantum Gravity, we know that length, area and ...
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3answers
115 views

Quantization of electrons' angular momentum in atoms and molecules

It is known that the Schrödinger's equation of the electron's wave function in atoms can be solved analitically only when a single electron is present (the "hydrogenlike atom"). In that case, the ...
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1answer
107 views

How to Find Jerk from Discrete Velocity Data?

I have measured the velocity of an object at discrete intervals. I want to find the corresponding acceleration and jerk of the object. How do I do this with discrete values rather than continuous ...
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1answer
108 views

Is space continuous? [duplicate]

Take a particle, it has a position $(x, y, z)$ maybe it is $(0.231, 8.962, 10.567)$. Is there a maximum precision to this? Is the space discrete or continuous? If it is discrete, how thin the ...
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1answer
23 views

What is the flux $\Phi$ enclosed by cyclotron orbit, which can express the quantization rule?

Suppose an electron (mass $m$, charge $e$) in the xy-plane with $B=(0,0,B)$ (The classical EOM result in circular orbit). Using the Bohr-Sommerfeld quantization rule we can find that $E_n = (n+1/2)\...
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0answers
71 views

Compactness and Quantization

So I was thinking today about when observables become "quantized", and came to the conclusion that every instance of quantization I've ever come across has come about from solving the Schrödinger ...
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3answers
71 views

What are wave-functions in QM. corresponding to?

I was learning about a particle trapped in a double well potential $$V(0) = \infty, V(x1)=\infty$$ which can be described by $\psi_n$ for n=0,1,...,$\infty$ with corresponding Energies $E_n$. Just ...
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0answers
23 views

Aggregation phenomena : How to get from a discrete to a continuous point of view

I'm studying a diffusion limited aggregation phenomenon. The $N$ particles diffuse in a box and when there is a contact they stick with a probability $p$, and let's say to simplify $p=1$. Meaning that ...
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1answer
57 views

Minimal Requirements for Space and Time

I read recently that to consider the Planck length of less than 1.6 x 10 exp -34 meters the smallest unit that can manifest 4 coordinate space time to be incorrect in its interpretation. The reason ...
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0answers
25 views

Is it possible to define background independent fluid dynamics equations?

Imagine a lake, and you measured the distance from each molecule to it's neighbours for molecules to within say 3 molecular radii. Taking this data you could reconstruct the positions of the ...
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4answers
172 views

Is it possible to have non-integral multiple of $e$ as charge?

We have 2 similar balls. On one ball there is charge $e$ and on other no charge. I connect the balls using a metal wire. We know that the charge gets shared until they have the same charges. Thus we ...
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0answers
100 views

Why any theory of spacetime atoms would be wrong from start? What about causal sets?

After watching this public talk by Nina Arkani-Hamed titled "The doom of spacetime", I can't fully understand what he said in the answer to an audience question about gravity. He said we can't simply ...
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106 views

Can Probability be quantized? [duplicate]

There are conjectures that quantities like space, time, energy, etc. are quantized and can only get some discrete values. I was wondering if there is any relationship in physics that interrelates ...