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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Is the Planck length the smallest length that exists in the universe or is it the smallest length that can be observed?

I have heard both that Planck length is the smallest length that there is in the universe (whatever this means) and that it is the smallest thing that can be observed because if we wanted to observe ...
0
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1answer
34 views

The proof of a discrete Fourier identity in quantum field theory

On page 25, in the book Quantum Field Theory for the Gifted Amateur by Tom Lancaster and Stephen. J Blundell, it states the following: We impose periodic boundary conditions forcing ...
2
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4answers
53 views

Is there a maximum accuracy for positions in the universe?

I was thinking how, since an object in our universe can move from one position to another, it must have passed through all the positions between those two positions. (I am thinking it moved it a ...
1
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1answer
100 views

Planck length paradox [closed]

This is a paradox I thought of a few days ago, and I wanted to ask whether it makes any sense and where the mistake is. We know that the nothing but light can move faster than light itself. So in a ...
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3answers
1k views

Do quarks violate quantization of charge?

Does existence of various kinds of quarks like up, down, strange, charm, top, bottom violate the quantisation of charge or just redefine it as up quark have charge +2/3 and have -1/3. Or do things get ...
-1
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1answer
57 views

Is the concept of infinity valid in physics, beyond its convenience? [duplicate]

Is infinity a meaningful concept in physics, apart from making some of the maths easier? Especially since reality seems to be discrete.
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9answers
4k views

Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
2
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2answers
173 views

Considering this hypothesis…is charge really quantized? [closed]

[If anything goes against any mathematical or physical rules please let me know. I am a first year undergraduate student perusing a joint major in mathematics and physics so I do not have a complete ...
0
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0answers
31 views

Dirac quantization condition for magnetic monopoles how is obtained? [duplicate]

assuming we have a magnetic monopole charge on the origin with magnetic field given by $$ D= \frac{q.dr}{r^{2}} $$ how is the quantization of the charge for a monopole obtained in this case ?? i ...
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7answers
6k views

Is there a maximum frames per second (FPS)?

Take a video camera and crank up the frames per second rate. Disregarding current technological advancements, could a camera's FPS go so fast that any two captured images be identical? Would ...
2
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0answers
64 views

Antimatter universe and Noether's theorem

I am studying Feynman's "symmetry in physical laws", where he talks about conservation laws for corresponding symmetries. (I know this is Noether's theorem, I am studying this from David Tong's ...
0
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0answers
20 views

Is energy discrete [duplicate]

It is often stated that because the energy in an em wave is $E=hf$, the energy comes only as multiples of $h$, ie quantized. But we know that $f$ is a real number, and you could have fractions of one ...
0
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1answer
58 views

Infinite halving of a distance

If an object is, say, 100 cm. from a wall, and I move the object halfway to the wall and stop, then the distance is reduced to 50 cm. If I continually move the object by one half of the remaining ...
2
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1answer
37 views

Is there a sensible fully-discretized Hamilton's principle?

In computational physics it is common to formulate Hamilton's principle in a semi-discrete way, where space is continuous but time is discrete: in other words the Lagrangian $$L(q, \dot q, t): ...
1
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2answers
122 views

Does each photon have a unique wavelength?

Since the frequencies (or inversely, wavelengths) of photons are part of a continuous realm, doesn't this mean that no photon has exactly the same frequency? Two photons might have the same apparent ...
29
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4answers
4k views

Is there an infinite amount of wavelengths of light? Is the EM spectrum continuous?

The electromagnetic spectrum is a continuum of wavelengths of light, and we have labels for some ranges of these and numerical measurements for many. Question: Is the EM spectrum continuous such that ...
0
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1answer
44 views

Quantum physics and constructable numbers [duplicate]

I do not know much about quantum physics. However, I do know it believes the world is discrete ( has quanta). This seems to contradicts the fact that we can create an object of length root 2 since you ...
1
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4answers
200 views

Is nature quantized?

I was reading Planck's postulate the other day on Wikipedia and couldn't help but noticing the sentence: "...is the postulate that the energy of oscillators in a black body is quantized..." ...
0
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0answers
62 views

Is the elementary charge really a constant of nature? - Accuracy of QED

There are a couple of natural constants; examples are Planck's constant or the Speed of light in vacuum. The elementary Charge is the coupling factor to all Kind of electromagnetic interactions; this ...
2
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2answers
67 views

Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
6
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2answers
194 views

Can the momentum eigenstates be non-orthogonal?

Consider the Hilbert space of a particle, whose position domain is confined to $q\in[0,1]$ (e.g. a particle in a box with unit width). Using $$ 1=\int_0 ^1 dq |q\rangle\langle q| $$ and the position ...
9
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2answers
1k views

Is frequency quantized in the black body spectrum?

I'm aware that there're some questions posted here with respect to this subject on this site, but I still want to make sure, is frequency quantized? Do very fine discontinuities exist in a continuous ...
2
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0answers
79 views

In string-net condensation, what does the quantized charge means? [closed]

The electrical charge is quantized strictly for elementary particles. What kind constraints does this fact applied to string-net theory? For the this question, I want to understand why electrical ...
1
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0answers
30 views

Discrete Laplacian with geodesic distances

Normally, I have a a scalar function f(x,y), sampled on a two dimensional, regularly spaced grid in Cartesian coordinates. Evaluating the Laplacian of this function just requires the standard ...
0
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0answers
74 views

Trace part of Hamiltonian

Given an electron in one discrete dimension, the Hamiltonian is given by $H_{n,n'}\in Mat_{N\times N}\left(\mathbb{C}\right)$ acting on $l^2\left(\mathbb{C}^N\right)$ where $N$ is some integer ...
0
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1answer
82 views

Are there more reasons why we can not be part of an $n$ dimensional Game Of Life?

After talking with a colleague about the possible nature of the limitation of information propagation to c, and how everything can be seen relative to it, we wondered if the nature to this could be ...
3
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3answers
343 views

Computation theory and the simulation argument

Can physical states be treated as information (strings over some alphabet)? If (1) is true, isn't this a trivial conclusion that the universe can be simulated by a Turing machine or a cellular ...
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2answers
154 views

Is time infinitely divisible? [duplicate]

Simple question (I think). Is time infinitely divisible? I heard that it was, although not from a particularly explanatory source. If so, are we sure that it is, without a shadow of a doubt?
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4answers
189 views

Particles scattering on fluids: breakdown of the effective continuum description

When does the macroscopic continuum description of a medium like a fluid break down? Say I'm interested in a scattering process of some particles with momentum $p$ and energy $E$ off a fluid of ...
1
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0answers
74 views

Alternate theories of space and time [closed]

Do mainstream theories in physics make implicit assumptions about the nature of space and time? In particular, are there any theories which implicitly assume that space and time are continuous, or is ...
1
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1answer
125 views

Is there an error in Susskinds' derivation of Euler-Lagrange equations?

http://imgur.com/kZO5C0V First, I believe there is a trivial error. The second equation should have another $\Delta t$ multiplying everything on the right. It is divided out later when the equation ...
1
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1answer
213 views

Discrete vs Continuous spectra of operators [duplicate]

Why is it that if an operator $Q$ has a discrete spectra, that the eigenfunctions are all in Hilbert space? Why is it that if the spectrum is continuous we automatically know that the eigenfunctions ...
12
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3answers
672 views

Why does spin have a discrete spectrum?

Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
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2answers
108 views

Will Quantum Computation fail if spacetime is discrete?

Will Quantum Computation fail if spacetime is discrete? Basically, would a discrete spacetime impose unexpected limits on how many Qubits could be used in calculations? Conversely, can quantum ...
2
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3answers
198 views

What is the physical intuition behind the fact that 'energy is not continuous'?

First of all I am a novice regarding my knowledge of quantum mechanics. But curiously I do want to know what is the problem if energy is continuous like spontaneously flowing tap water. In fact I ...
0
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1answer
54 views

Convergent series in the real world with equal time for each term

A few months ago someone was explaining a philosophical principle in Aikido (a martial art) which involved a convergent series. The analogy he used was that, say you have a pool, and each day the pool ...
1
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1answer
46 views

How to discretize a finite crystal?

I am trying to find a general method to discretize a finite crystal system. How I have been discretizing systems so far (using Wannier functions): When you have an infinite crystal, you may apply ...
2
votes
1answer
47 views

How did Planck use the concept of statistical entropy in trying to understand the meaning of his own law?

I was reading Introducing Quantum Theory: A graphic guide (by J.P.McEvoy & Oscar Zarate) and came across Planck's predicament of understanding his very own law that accurately explained the ...
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3answers
98 views

Is the world we are living in discretized? [duplicate]

I do not know how to use professional words to ask my question, so I will try to use a layman language. Please bear with me for a moment. A ROUGH GUESS The world our eyes are seeing every moment is ...
2
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0answers
42 views

Making An Energy Momentum Plot For A Rashba Model (Using Discretization)

I want to make a plot of the Energy versus the Momentum of the Rashba model, using discrete matrices. First Ill show how I did this for the free particle. Subsequently I will show what goes wrong for ...
0
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0answers
53 views

What lives in the Hilbert Space? [duplicate]

Consider the eigenvalue equation: $$\hat{Q}\Psi = q\Psi$$ where $q$ and $\Psi$ are eigenvalues and eigenfunctions of the hermitian operator $\hat{Q}$. If the spectrum of the hermitian operator is ...
1
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2answers
354 views

Quantization of Electron Spin

Why is electron spin quantized? I've seen the derivation for the Hydrogen atom's energy levels, but my professor jumped to electrons having spin 1/2 or -1/2 as experimental. Why do electrons obey the ...
54
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10answers
7k views

Is time continuous or discrete?

While working on physics simulation software, I noticed that I had implemented discrete time (the only type possible on computers). By that I mean that I had an update mechanism that advanced the ...
1
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1answer
66 views

Can time be Quantised? [duplicate]

Can time be quantised? Would it be the smallest distance between two photons moving in the same direction or the shortest wavelength?
0
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0answers
28 views

Is the continuity (discontinuity) one of the intrinsic properties of all physical objects?

Is the continuity (discontinuity) one of the intrinsic properties of all physical objects? How do we define continuity? Which of the definitions of continuity are used (and why) in physics? This ...
5
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1answer
357 views

Switching from sum to integral

I'm specifically asking about an equation in An Introduction to Quantum Field Theory, by Peskin and Schroeder. Example from page 374: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
2
votes
2answers
861 views

How many atoms exist within a continuum body?

Materials, such as solids, liquids and gases, are composed of molecules separated by "empty" space. On a microscopic scale, materials have cracks and discontinuities. However, certain physical ...
0
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0answers
44 views

Argument for the Smallest Division of Time? [duplicate]

Okay so a couple of months ago I was watch Vi Hart's video on how .999999... is equal to 1. Some really interesting arguments that I had never heard before. Yesterday, I came across an article on ...
1
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1answer
127 views

Wannier Functions as Discrete Basis

In solid state physics, using Bloch's theorem we know that the one-electron energy eigen-function can be written as $\psi_{\lambda,\vec{k}}(\vec{r})$ where $\lambda$ indexes eigenvalues of $\hat{H}$ ...
3
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2answers
308 views

1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...