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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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25 views

Max Planck and energy quantization idea [migrated]

Did Planck have an intuition behind the idea of energy quantization of atomic oscillators and radiation, or it was just a mathematical trick to drive his distribution law?
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0answers
20 views

Does our universe has a limited decimal precision? [duplicate]

This question may be a bit strange but I was wondering if our universe has a kind of limit in precision. For example: A particle can be in coordinates a or ...
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4answers
74 views

In $E=hf$, can $f$ assume any positive value? (Beginner) [duplicate]

The energy of photon is given by the equation $E=hf$, where $h=$ Planck's constant, and f=frequency of radiation. Is f quantized, or can it assume any value? If it can assume any value, then wouldn'...
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2answers
45 views

Why position and momentum operators are both continuous spectrum while angular momentum is discrete? [duplicate]

We know that position $\hat{r}$ and momentum $\hat{p}$ are both continuous spectrum operators, i.e. $$\hat{r}|r'\rangle=r'|r'\rangle, \quad \hat{p}|p'\rangle=p'|p'\rangle.$$ But the angular operator $\...
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27 views

Quantized time wow

I have not been able to find enough bibliographical material related to the quantization of time. I would like to know more about this topic because recently it is believed that the concept of space ...
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3answers
91 views

What was shocking in Einstein's partcile theory of light?

I know that when Einstein proposed the particle theory of light it was revolutionary and shocking for most of physicists and it took years to accept that view. Particle theory had been proposed in the ...
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2answers
76 views

Do we know, or at least have a strong argument for the fact that for a given time interval, we can always find a smaller time interval? [duplicate]

Motivation: In Biology, when, for example, biologists try to model the population dynamics of a population, they say: Let $N: \mathbb{R}^{nn} \to \mathbb{R}^{nn}$ be a function that represents ...
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2answers
66 views

Could spacetime have crystalline properties?

Space-time is currently modeled as a continuous manifold. However, space-time shares many features in general relativity that mimic a fluid-like thing. Fluids are certain states of matter and under ...
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0answers
34 views

Non-vanishing matrix elements in QFT after discretization

In QFT, introducing the lattice size $L$ implies that the momentum of plane wave solutions is discretized as $$\vec{p}_\vec{n} = \dfrac{2\pi}{L}\vec{n}\quad,\qquad \vec{n}\in\mathbb{Z}^D$$ I would ...
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2answers
110 views

Is Bohmian mechanics wrong in the case that space and time are quantized?

Bohmian mechanics assumes that particle trajectories are continuous. Also, it claims the random outcome of certain experiments (like the double-slit experiment) to be due to the random initial ...
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0answers
13 views

Why the eigenvalues of hamiltonian are discrete in bounded systems (only discrete energy levels)? [duplicate]

In one dimensional motion the general potential is given as in the figure above When energy is between V min and V 1 the energy levels are discrete like in the potential barrier and well example or ...
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2answers
94 views

Why atom has the straight discrete energy levels? [duplicate]

Interaction between a nucleus and electrons is in gravity(not considering) and electrostatics. Due to electrostatics nucleus attracts electrons. The force that describes this process is $$F=k\dfrac{...
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0answers
20 views

Pairwise additivity of numerical potentials

Surely this is a trivial problem, but I'm very much confused on how to approach so please bear with me. Say I have a two-dimensional evenly-spaced 16x16 grid centered at the point (x1,y1). I also ...
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1answer
104 views

Is any particle's energy quantized?

In the above picture, the author is trying to summarize the correlation between particle and wave packet. In doing so, he assumes that frequency is related to energy as: $E=h\nu$. Is this apparent ...
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0answers
18 views

Representing a system of particles being mapped from two to three space [duplicate]

Let's say you have a grid with nodes at the intersections of the grid which represent particles. Noether's theorem says that any differentiable symmetry of the action of a physical system has a ...
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1answer
32 views

What is a finite cellular automaton?

I found this paper: https://arxiv.org/abs/1606.08764 There, it is said "We realize constant-space quantum computation by measure-many two-way quantum finite automata" What are "finite automata"? ...
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76 views

Is simulating quantum field theoretical equations in the continuous limit the same as simulating really quantum continuous processes?

At the end of this article: https://hal.archives-ouvertes.fr/hal-00542373/document it is said that: "For example, several works simulate quantum field theoretical equations in the continuous limit of ...
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0answers
61 views

Are there any proved consistent quantum continuous cellular automata/game of life model?

There are quantum cellular automata (continuous game of life, which is a type of cellular automata): https://hal.archives-ouvertes.fr/hal-00542373/document There are continuous cellular automata (...
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1answer
70 views

Mechanism for light generation

Is all observable light caused by electrons dropping to a lower discrete energy level while bound in an atom? If so, how can a continuum of frequencies be generated? Is the thermal radiation ...
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3answers
117 views

Quantum mechanics calculations - must they always output a rational number?

If space is quantized, and particles are quantized, then the chance of a particle showing up in a specific unit of space must be a rational fraction? Could a quantum mechanics calculation ever output ...
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0answers
70 views

Is the universe a lattice?

My understanding is that cause and effect create a partial order of events in the universe (and that relatively prevents anything stronger). My understanding is also that it’s generally useless to ...
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2answers
41 views

Quantisation of States in QM

In the orthodox interpretation, the eigenvalues are the only measurable values of the corresponding operation, i.e., if the total energy of a particle is measured, the only numbers (as outcomes) are ...
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3answers
116 views

Is there a basic/elementary mass in the universe? [duplicate]

When speaking about electrical charges, it seems every particle either has a charge $+1$ or $-1$, in units of the electron charge. Therefore, we have a fundamental charge. But what about mass? Is ...
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49 views

Why is $x(t) = \frac {x_n + x_{n+1}}{2}$ when proving the Euler-Lagrange Equation?

When proving the Euler-Lagrange Equation for a single degree of freedom, we replace continuous time with stroboscopic time. We replace $$\dot x=\frac{x_{n+1}-x_n}{\Delta t}$$ but why do we replace $$...
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16 views

How to obtain boundary effects in the eigenmode analysis of a discretized WLC?

I'm currently working on the eigenmodes of a worm-like chain (WLC) polymer in the discretized version. We have the overdamped Langevin equation $\zeta\dot{r}(s,t)=-\kappa r''''(s,t)+\xi(s,t)$ for a ...
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29 views

Why are physical systems continuous?

To my (very limited) knowledge, physical systems (fluids, for example) can't have jump discontinuities. Why? Which fundamental laws can this be derived from, if any? This question is related to ...
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0answers
26 views

DFT of a non-continuous discrete time series

I am looking for a periodic signal in a time series $x_i, \quad i=1, \, ...,\, N-1 , \, N , \, N+P , \, N+P+1 , \, ... , \, N+P+M$ where $P$ is an unkwnown gap in time, for which I have no ...
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1answer
114 views

Is light a discrete or continuous phenomena?

Image a light bulb. In it the filament with a simple metallic composition, copper or other metals. At the precise instant, say $t=0$, where the first copper atom will be shining. In which direction ...
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0answers
14 views

What about space, what can we assume [duplicate]

Keeping it simple, is space infinitely divisible? Of course I realize the answer is no simple task. Regardless, keep it simple enough that in a sense, a common understanding amongst the average person ...
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0answers
60 views

What are common methods to remove discretization on experimental measures?

I have some experimental data, and since the measurements are digital, the data is discretized/quantized/rounded/truncated. I need to know if there are general methods, or common methods, to "smooth" ...
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2answers
386 views

Feynman's path integral and energy discretization?

Feynman’s path integral formulation of quantum mechanics is based on the following two postulates: If an ideal measurement is performed to determine whether a particle has a path lying in a region of ...
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2answers
120 views

Path Integral analogue for discrete systems

What is the analogue for path integral formulation for a discrete system? e.g. chain of typical 2-level excitonic systems: \begin{equation} H=\sum_k \sigma^+_k\sigma^-_k+\sum_{k<l}(\sigma_k^+\...
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2answers
98 views

Is the space of possible positions of a particle in QM discrete?

I recently updated my understanding about quantum mechanics from popular science level to basic undergraduate level. What surprised me is that for the quantum state of a particle, the wave function ...
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1answer
256 views

Classical Mechanics: Continuous or Discrete universe? [duplicate]

The question of the "continuous" or "discrete" nature of the universe is the subject of diatribe among the greatest physicists in the world. I would like to discuss the same topic, but asking a ...
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1answer
163 views

How is particle in a ring is in bound state?

Particle in a potential well forms a bound state which gives rise to discrete energy levels. But states for particle in a ring also have discrete energy levels even where there is no potential well. ...
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1answer
107 views

Is space-time quantised? [duplicate]

i was reading and a question popped into my head and i could not find the answer anywhere if photon destruction is instantaneous doesn't it mean that space-time is quantised? here is my problem: ...
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2answers
207 views

Fourier Transform and Lattices

I've been always confused Fourier transforms on lattices because some times a continuous version is used and others a discrete version is used. I don't understand well when should use one or the other....
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1answer
51 views

Continuous limit of discrete position basis

Say we have a $1D$ lattice with spacing $a$ between two sites. How does one formally map the discrete position basis of the lattice to a continuous one in the limit $a\to 0$. For instance how does ...
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1answer
102 views

Is there a proposed minimum amount of energy?

I've read that "The Planck length is believed to be the shortest meaningful length (...)"(1). Regardless of the factual accuracy of this claim, I'm wondering if: is there a related concept regarding ...
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0answers
96 views

Planck length, planck time, and planck rotation? [duplicate]

given that there is a fastest speed at which anything can travel in our universe,299,792,458 meters per second, that seems to imply there may be a smallest distance in our universe, so first of all, ...
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0answers
68 views

Lorentz Symmetry Group as continuous symmetry for limit of discrete spacetime

There is a variety of models of quantum field theory, where discrete spacetime is used as technical support, or even suggested as physical reality. As far as I know, all of such models faced serious ...
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1answer
60 views

Do discrete symmetries in molecules leave statistical “artifacts” like the Equipartition Theorem?

In statistical mechanics we have the equipartition theorem which can derive heat capacity simply from degrees of freedom. For example, diatomic gases have an increase heat capacity of $ \frac{7}{2} N ...
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0answers
48 views

Is discrete energy spectrum a result of representing external systems as a potential?

A quantum harmonic oscillator, or a quantum model of the hydrogen atom, have discrete energy spectrum. However, both models involve a potential, which means that the system is not isolated. One could ...
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0answers
43 views

Relation of the Heat kernel and the solution of the discrete diffusion equation

As is well known, the solution to the continuous 1D diffusion equation $\partial_t f=D\,\partial_x^2 f$ is given by the Heat kernel $$f(x,t)=\frac{\mathrm{e}^{-x^2/4Dt}}{\sqrt{4\pi Dt}} \ .$$ On the ...
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0answers
20 views

How is energy quantized? [duplicate]

I'm at the moment studying quantum physics and I came across $$E=hf.$$ My question is: how come there are only certain energies allowed if in this formula $f$ can be any number, and therefore, energy ...
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2answers
174 views

Is $Y: (t,x,y,z)\to(t,x,-y,z)$ a Lorentz transformation?

A question from the book "Quantum Field Theory and the Standard Model" by Matthew D. Schwartz. Is the transformation $Y: (t,x,y,z)\to (t,x,-y,z)$ a Lorentz transformation? If so, why is it not ...
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0answers
32 views

Confusions in discretizing a momentum delta integral

I have an integral of the following form: $$\int dk_{x}dk_{y}dk_{z}\frac{1}{(2\pi)^{3}}\delta\left(\sqrt{k_{x}^{2}+k_{y}^{2}+k_{z}^{2}}-p\right)f(k)$$ There are two ways to convert it into discrete ...
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2answers
109 views

Is there a conserved quantity for Parity Symmetry?

I've recently read about the Cobalt-60 experiment and Parity violation on weak interactions, what says the parity is not a symmetry on weak interactions. But if I did not understand wrong EM and ...
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1answer
64 views

How can there be instantaneous rate of change? [duplicate]

To find rate of change you need two instants. how is the rate of change calculated at a particular instant when at least two instants are needed to find it?
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3answers
300 views

How does anything move through a physical distance? [duplicate]

I was wondering and came across a thought: if an object is moving at a particular speed, say 5 m/s, it is equivalent to say that the object is moving at 500 cm/s, or 5000 mm/s and so on; clearly, you ...