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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1answer
53 views

What makes things move in a universe with blocktime? [on hold]

In a universe with blocktime the past, present and future all exist at the same time. But what makes it appear that for example my body is going from one movement ...
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1answer
36 views

Decoupling of double discrete Fourier transform

I have a problem with a double Fourier transform I encountered: $$\sum_{j=1}^L \sum_{l=1}^L e^{-i\pi \frac{n_1}{L} (j+l)}e^{-i\pi \frac{n_2}{L} (j-l)}V(j-l)$$ where $n_1,n_2$ are integer. If the ...
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3answers
87 views

Energy equation in Quantum Mechanics

We know that total energy of the system is classically continuous, but in quantum mecanics (QM) it is quantised. My question is: How can we use the conservation of energy equation to derive ...
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2answers
151 views

Is Bekenstein entropy limit inconsistent with universal continuity?

It is unknown whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Can universal continuity be experimentally falsified? Is the universe finite ...
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0answers
24 views

Snyder's Lorentz invariant discrete space-time

Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous? I'm sure this has been ...
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1answer
338 views

Can universal continuity be experimentally falsified?

It is an unresolved question whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Is the universe finite and discrete? How could spacetime become ...
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1answer
22 views

Is the hypothesis “at some level, spacetime becomes discrete” falsifiable?

Suppose I conjectured that, at some length scale, spacetime was discretized into "cells", Minecraft-style. For simplicity, I guess let's say they're cubes with side length $n$. Presumably we can put ...
3
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1answer
111 views

Is the energy always discrete?

In the von Neumann axioms for quantum mechanics, the first postulate states that a quantum state is a vector in a separable Hilbert space. It means it is assumed the Hilbert space has a basis with at ...
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0answers
32 views

Is there a fundamental frequency of time? [duplicate]

Our eyes and brains can only perceive frequencies as individual frames up to some limit, after which we perceive the motion to be "continuous." Is there such a frequency of time? Along the same ...
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0answers
134 views

If spacetime is discrete: what would space expansion mean? [closed]

How is space expansion explained in physical theories where spacetime is quantized? Discrete spacetime is claimed in some candidate theories of quantum gravity like loop quantum gravity and algebraic ...
0
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0answers
37 views

Angular momentum $J_z$, how do we get eigenvalue of $m\hbar$?

If we have angular orbital momentum for $z$-direction, we assume that for state $|j,m>$ that eigenvalue is $m\hbar$. Similarly for $J^2$, we assume $j(j+1)\hbar^2$ Can I get reference of ...
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10answers
11k views

Is time continuous or discrete?

While working on physical system simulation software, I noticed that I had implemented discrete time, which means that there was an update mechanism advancing the simulation for a fixed amount of time ...
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1answer
81 views

Does limiting to infinity violate laws of physics?

It is noteworthy that one cannot simply divide any length more than the Planck-length. If so, one cannot simply divide any volume more than the $(Planck-length)^3$. So if I want to find the limit of ...
2
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1answer
75 views

Why are harmonic oscillators quantized? [closed]

What physical reason is there for a mass on a spring to have discrete energy levels? And why are those energy levels equally spaced, i.e. why is $E \ \alpha \ f$? Personal background and ...
0
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1answer
79 views

Proof for quantized angular momentum [duplicate]

In Bohr's model, Bohr stated that the angular momentum of the electron is quantized and stated that $$L=\frac{nh}{2\pi}$$ So what is the proof for that equation or, in other words, how did he derive ...
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1answer
936 views

Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...
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4answers
323 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 ...
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2answers
598 views

What is the 'resolution' of the reality in pixel terms?

What resolution should a TV screen have so that its image were so faithful as reality as if the TV were a window? Also what would happen if Physics could reproduce a 'pixel' of the size $ l_{p}^{2} $ ...
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0answers
21 views

Is the position of matter discrete in universe? [duplicate]

In computer, for example, if we use integer to represent position of objects, position can be (0,0) , (3,5), but not in (1.5,3.5). In real world, there are something that is discrete, such as atomic ...
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2answers
92 views

How does quantum mechanics and quantum field theory explains discrete energy levels of particles?

Please give me a brief explanation as to how qm and qft describe and explain the energy level that exist in an atom. I understand that in QM energy state is quantized but does not offer an ...
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0answers
54 views

Trying to understand why energy must be quantized/discrete

So I'm reading about bound systems right now in my quantum text. It is beginning to explain why energy must be quantized, and is doing so by introducing the reader to the one dimensional "quanton in a ...
0
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1answer
71 views

Is there a minimum distance?

I would imagine there is no limit to how small space can get. Is this correct? I am aware of planck's constant, but cannot objects be closer than Planck's constant is short? Perhaps this question is ...
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2answers
87 views

If the Universe is going to last infinitely long, what is the type of this infinity?

Let's say we've built a machine, that prints a sequence of all natural numbers from 0 to $\infty$. We "could" do this in a Universe with an infinite amount time (if we also make many other assumptions ...
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0answers
27 views

Minimum amount of space [duplicate]

I always believed that there were no limits in the world and then I learned that a minimum temperature exists, and maybe a maximum speed. And now I am wondering about the boundaries of the world. Is ...
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0answers
18 views

Resources on the discreteness of space and time

Does anyone know any books or other sources of information on the discreteness of space and time? The only ones I've managed to find require graduate level physics knowledge, which sadly I do not ...
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1answer
256 views

Must bounded operators have normalisable eigenfunctions and discrete eigenvalues?

When we have bound states, to my knowledge, we have states that are normalisable and a discrete energy spectrum. However, in the case of scattering states that have a continuous energy spectrum, the ...
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10answers
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Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
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4answers
82 views

Where is the fallacy in this issue related to electric charge quantization? [closed]

Suppose there are two identical conducting objects; one with 5 units of positive charge and the other is uncharged. Initially these are separated and later these are brought into contact. I guess net ...
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1answer
55 views

Intuitive way to think about discrete energy levels

I'm currently taking an introductory quantum mechanics course and we just finished learning about the infinite square square well scenario. I understand all the maths used for calculating the ...
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0answers
39 views

Discrete Fourier transform for periodic signal?

From the Signal and System textbook, by Oppenheim, I learned that the discrete-time Fourier transform can be written as $$ x[n]=\frac{1}{2\pi}\int_{2\pi}X(e^{j\omega})e^{j\omega n}d\omega $$ $$ ...
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2answers
81 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. ...
0
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0answers
17 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 ...
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2answers
88 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 ...
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3answers
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What causes a black-body radiation curve to be continuous?

The ideal black-body radiation curve (unlike the quantized emission seen from atomic spectra), is continuous over all frequencies. Many objects approximate ideal blackbodies and have radiation curves ...
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2answers
109 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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3answers
203 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
53 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 ...
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1answer
199 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 ...
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0answers
22 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
110 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. ...
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4answers
164 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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0answers
58 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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5answers
3k views

Why position is not quantized in quantum mechanics?

Usually in all the standard examples in quantum mechanics textbooks the spectrum of the position operator is continuous. Are there (nontrivial) examples where position is quantized? or position ...
1
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1answer
111 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 ...
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3answers
25 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 $n$ ...
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2answers
86 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 ...
5
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2answers
332 views

Is the assumption that space-time has to be a continuum just a matter of mathematical taste?

Is the assumption that space-time has to be a continuum just a matter of mathematical taste? Isn't there any physical significance associated with it?
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0answers
39 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 ...
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5answers
758 views

When is energy discrete/quantized for a potential well?

Specifically, my question is: Should one expect energy quantization for a particle in the following potential well? More generally, how can one tell whether or not energy should be ...