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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2answers
84 views

Space and time quanta? [closed]

Is there a possibility the space and the time are not continuous, but rather, quantified (only some positions in the space exist, and some instants in the arrow of time) ? Hopes my question is clear.
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0answers
18 views

Discrete translational invariance of lattice systems and conserved quantities [duplicate]

Imagine a crystal lattice with discrete translational symmetry. Is there any way to obtain local periodic conserved quantities by taking a derivative (deliberately left abstract)? The discretised ...
4
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2answers
90 views

How photons can emerge quantized if their cause is continuous?

I know that photons are quantized, they are not continuous. But they are created by an accelerated charge. So how is it possible to have a quantized outcome from a symmetric continuous event? I mean ...
2
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3answers
385 views

Difference between discretization and quantization in physics

I am just trying to understand the fundamental difference between these two concepts in physics: From discreteness of some quantity: one usually interprets it as a quantity being only able to take ...
0
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1answer
54 views

Time it takes for a single unit of movement [duplicate]

I've just been wondering, what is the time that passes between one moment to another. Lets take an example that we have a single light source, so small that it emits only a single, constant beam of ...
0
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0answers
23 views

How to compute remnant discrete charges?

When a $U(1)$ gauge symmetry is broken by Higgs field with $U(1)$ charge $g$, we have a remnant $\mathbb{Z}_q$ symmetry. How can I compute the corresponding charges under this remnant group for ...
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2answers
119 views

I have been thinking about the unification of general relativity and quantum mechanics [closed]

I have been thinking about the unification of general relativity and quantum mechanics. after giving it much thought I'm wondering if the problem is not in the formulas used but the numbering system. ...
3
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0answers
84 views

Do lattice gauge theories with discrete gauge groups have sensible continuum limits?

In lattice gauge theories the only gauge invariant observables are constructed from Wilson loops and local field strength observables are reconstructed as zero size limits of Wilson loops. Furthermore ...
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4answers
214 views

Why, fundamentally, are particles charged?

This is something that has long bothered me, and I have asked a few physicists and chemists and never gotten a very satisfying answer. Why are particles charged? And I'm not asking (and this is the ...
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1answer
137 views

Global symmetries in type IIB string theory vs type IIB supergravity

In the AdS/CFT correspondence I know that the mapping of global symmetries involves also the S duality that in the field theory side is $SL(2,Z)$. In Type IIB supegravity this duality is $SL(2,R)$. I ...
2
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3answers
27 views

Why do we assume differential coefficients of number of molecules?

In many portions of physics (like Maxwell's velocity distribution law) we assume statements like- Number of molecules having velocity between $c$ to $c+dc$ is $dn$. But number of molecules $n$ ...
1
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2answers
116 views

Does calculus work on the quantum scale [duplicate]

I have read somewhere that Leibniz championed the idea that the world is continuous as this was needed for his (or maybe Newtons) new invention (or discovery?) of calculus. But if I am not mistaken a ...
0
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0answers
40 views

Does quantum chromodynamics imply continuous space? [duplicate]

I am thinking it does. That's because a pillar of quantum chromodynamics is renormalization, which is itself due to the assumption that electrons are point particles (having no extent). A point ...
0
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1answer
93 views

What's Wrong With This Quantum Analogy?

"Sometimes the idea of the quantum is compared to the units we use for money. A dollar can be divided into smaller units, where the cent is the smallest possible unit." A question I came across ...
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2answers
138 views

Modelling discrete spacetime

Supposed space and time were to be discrete, then how would i go about modelling this inside a computer simulation? In a simple 2D world, taking a square for example with side length $A$, then if ...
0
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2answers
114 views

Finding the action of a discretized Lagrangian

I am trying to find the action associated with the Lagrangian density $$ \mathcal{L} = \frac{1}{2}\left( \frac{\partial\phi}{\partial x} \right)^2 + \frac{1}{2}m^2\phi^2. \tag{1} $$ I am supposed to ...
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1answer
1k views

Does the universe update time in some finite interval? [duplicate]

I was listening to a lecture by leonard susskind and one of the analogies he used was a coin having two states and he "broke" time into intervals. He continued to say that at each interval of time, if ...
2
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3answers
203 views

Why do electrons occupy in discrete energy states?

Why can't there be any continuous energy band in an atom?
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7answers
2k views

Quantization vs. continuous energy levels

I still don't get what it means for atomic energy levels to be continuous or quantitized (incontinuous). Clearing this up will really help me. Also, can anyone tell me why energy levels in solids are ...
1
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0answers
54 views

In discrete models of spacetime, what are some implications of the Einstein equation

We have several models of discrete spacetime. Sorkin has a causal growth dynamics, there's spin foams, Panangaden showed a correspondence between interval domains and spacetimes. I am looking for ...
0
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0answers
57 views

The relation between commutation and quanta

This question discusses discretization in some sense, and this question talks about how quantization and Hilbert Spaces are related (the answer seems to to be not at all), but what I'm curious about ...
2
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1answer
139 views

Conserved quantity corresponding to reflection symmetry

I know about Noether's theorem, but I don't actually know how to use it myself. Suppose our universe were symmetric with respect to reflections about planes. What conserved quantity would then exist ...
1
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1answer
225 views

How is quantization related to commutation? [duplicate]

How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence non-...
0
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0answers
28 views

Discrete time like a computer program [duplicate]

Has anybody thought about the effects of discretizing time in the way most computers do? In computer programming; collision detection for example, or updating a trajectory of a particle, everything is ...
0
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1answer
91 views

Problem with momentum values in a QM problem

I have the following equation of $Ψ$ around a ring (the particle is bound to move only on the ring): To visualize the state(it dies before L/2 if L=2πR): We can see from the first picture that ...
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0answers
47 views

If you have two Planck lengths extended from one point forming a right angle, whats the length of the hypotenuse? [duplicate]

Can we do measurements at this scale seeing that the length of the hypotenuse would have a value at a length that cant exist (1.4 Planck lengths)? Or is my interpretation of the Planck length ...
39
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3answers
9k views

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 ...
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1answer
100 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 $e^{ikja}=e^{...
4
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0answers
56 views

Conservation Laws and time-reversal symmetry [duplicate]

In most dynamics books I've read they refer to conservation laws and their associated symmetries, cf. Noether's theorem. I know that the conservation of momentum is a result of the homogenity of ...
2
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4answers
71 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 ...
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1answer
226 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 ...
4
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3answers
2k 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 ...
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1answer
71 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.
2
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2answers
251 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 ...
2
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0answers
80 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 ...
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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
143 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 ...
3
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1answer
91 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): \mathbb{...
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2answers
327 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 ...
31
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4answers
5k 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
52 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 ...
0
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0answers
97 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
148 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 ...
23
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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 ...
6
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2answers
246 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 ...
3
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0answers
118 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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1answer
168 views

Why is the density of states in $k$-space constant?

Why are the allowed states in $k$-space equidistant in every direction? As a consequence of this, the density of states for phonons in 3D is $$\frac{V}{(2\pi)^3}$$ while for electrons it is $$2 \frac{...
1
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0answers
101 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
214 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 ...
1
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2answers
544 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?