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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44
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9answers
4k views

Is time continuous?

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 ...
31
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8answers
2k 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 ...
27
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5answers
2k views

If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons?

If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons? The probability of a photon having just the right amount of energy for an atomic transition is ...
20
votes
7answers
3k views

Is (rest) mass quantized?

I learned today in class that photons and light are quantized. I also remember that electric charge is quantized as well. I was thinking about these implications, and I was wondering if (rest) mass ...
18
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2answers
2k views

Does the Planck scale imply that spacetime is discrete?

On a quantum scale the smallest unit is the Planck scale, which is a discrete measure. There several question that come to mind: Does that mean that particles can only live in a discrete grid-like ...
16
votes
4answers
493 views

Is the electromagnetic spectrum discrete?

I'm just starting to learn physics and I have a question (that is probably stupid.) I learned that energy levels that the bound electron can have are discrete. I also learned that when an electron ...
14
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1answer
434 views

Discreteness of set of energy eigenvalues

Given some potential $V$, we have the eigenvalue problem $$ -\frac{\hbar^2}{2m}\Delta \psi + V\psi = E\psi $$ with the boundary condition $$ \lim_{|x|\rightarrow \infty} \psi(x) = 0 $$ If we ...
13
votes
4answers
780 views

Reason for the discreteness arising in quantum mechanics?

What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
12
votes
3answers
681 views

Space-time in String Theory

I would like to understand how Physicists think of space-time in the context of String Theory. I understand that there are $3$ large space dimensions, a time dimension, and $6$ or $7$ (or $22$) extra ...
11
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5answers
2k 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 ...
8
votes
3answers
517 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?
7
votes
1answer
127 views

Theoretical reasons for charge quantization

I'm aware of Millikan's oil drop experiment and I've read that quarks have fractional eletric charge, but I was wondering if there's any theoretical argument that makes us believe charge is quantized. ...
7
votes
2answers
610 views

Bounded and Unbounded (Scattering) States in Quantum Mechanics

I understand that bounded states in quantum mechanics imply that the total energy of the state, $E$, is less than the potential $V_0$ at + or - spatial infinity. Similarly, the scattering state ...
6
votes
3answers
518 views

Are there any quantities in the physical world that are inherently rational/algebraic?

Whenever we measure something, it is usually inexact. For example, the mass of a baseball will never be measured exactly on a scale in any unit of measurement besides "mass in baseballs that are ...
6
votes
3answers
850 views

Is space infinitely divisible?

As a child I remember hearing the popular paradox presented by Zeno proposing that Achilles could never catch a tortoise in a race since he would have to traverse the infinite space between himself ...
6
votes
0answers
121 views

Do semiclassical GR and charge quantisation imply magnetic monopoles?

Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how? (I am not ...
5
votes
2answers
200 views

Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)

It seems to me that Hamiltonian formalism does not suit well for problems involving instantaneous change of momentum, like particle collisions with hard wall or hard sphere gas model. At least I could ...
5
votes
1answer
94 views

Gauging discrete symmetries

I read somewhere what performing an orbifolding (i.e. imposing a discrete symmetry on what would otherwise be a compactification torus) is equivalent to "gauging the discrete symmetry". Can anybody ...
5
votes
2answers
191 views

Integer physics

Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
5
votes
0answers
95 views

If time isn't continuous, what is the best-known upper bound on the length of time intervals?

There have been several questions about whether time is continuous or not and it seems like the answer isn't currently known. I know quantum mechanics treats time as continuous and any mathematics ...
4
votes
3answers
739 views

What are some approaches to discrete space-time used in modern physics?

This thought gave rise to some new questions in my mind. What are the consequences for: How would it affect duality i.e. particle, wave property of photons? How does this statement affect the ...
4
votes
1answer
429 views

Dirac magnetic monopoles and electric charge quantization

Wikipedia describes how assuming the existence of a single magnetic monopole leads to electric charge quantization. But what if there's more than one? The same argument would apply to each of them ...
4
votes
1answer
207 views

What fundamental reasons imply quantization?

In classical wave mechanics, quantization can occur simply from a finite potential well. In quantum mechanics, the quantization is obtained from the Schrödinger equation, which is, to my knowledge, a ...
4
votes
2answers
703 views

How could spacetime become discretised at the Planck scale?

I didn't have much luck getting a response to this question before so I have tried to reword and expand it a little: In early 2010 I attended this inaugural lecture by string theorist- Prof. ...
4
votes
2answers
345 views

Derivation of the Lagrangian method using discretized time axis

I'm watching this video lecture by Leonard Susskind of Stanford: http://www.youtube.com/watch?v=3apIZCpmdls After some preliminaries, at 34 minutes he jumps into a discretization of the time axis ...
3
votes
3answers
559 views

Does the Opera result hint to a discrete spacetime?

Could the Opera result be interpreted as some kind of hint to a discrete spacetime that is only seen for high enough energy neutrinos? I think I've read (some time ago) something like this in a ...
3
votes
3answers
218 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 ...
3
votes
3answers
380 views

Is velocity quantized?

If velocity is not quantized, then do moving objects have 'infinitely decimal place' velocities which we just can't measure to infinite decimal places? From my understanding the quantization of ...
3
votes
1answer
324 views

What is “charge discreteness”?

I assume it is some kind of quantity. Google only made things more confusing. I get that it has something to do with circuits. I also get what a discrete charge is. In fact, I thought charges ...
3
votes
1answer
129 views

Discretization of Hamiltonian using finite difference always justified?

I have this continuum version $$ H_{R}=\int dx\psi^{\dagger}(x)(\frac{p^{2}}{2}+V)\psi(x) $$ with $V$ as constant potential. Is it always justified to go from this to $$ \sum_{i}c_{i}^{ \dagger ...
3
votes
1answer
88 views

Is it possible that the universe in its entirety is discrete rather than continuous? [duplicate]

Since electric charge is comprised of discrete units and and mass is formed by discrete units is it possible that space-time itself is discrete as well?
3
votes
1answer
170 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 ...
2
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4answers
312 views

What entities in Quantum Mechanics are known to be “not quantized”?

Since all the traditional "continuous" quantities like time, energy, momentum, etc. are taken to be quantized implying that derived quantities will also be quantized, I was wondering if Quantum ...
2
votes
2answers
663 views

Applying velocity Verlet algorithm

I want to implement a simple particules system using the velocity form of the Verlet algorithm as integrator. Initial conditions at $t=0$ for a given particule $p$: mass: $ m $ position: ...
2
votes
3answers
107 views

Configuration space of particles in the box

The notion of entropy says that we can count microstates that correspond to macrostate. But, I do not understand how this can be done. Does it imply that the state space is discrete (finite or ...
2
votes
1answer
258 views

Planck time & length

Why is Planck time the shortest possible duration ever? It's defined as the duration needed by light to travel Planck's length, but surely, give me any number, I can give you a lower number than that? ...
2
votes
2answers
808 views

Application of Calculus in Physics

Why do we apply Calculus in Physics when most of the quantities are not continuous and are not symmetrical at all levels of magnification? Aren't most, if not all, forms of Matter and Energy discrete? ...
2
votes
1answer
121 views

At the smallest level, how do things move?

When we see something moving on a screen it's usually just pixels being turned off at one location and turned on at another. For example: This would render a dot moving from A to C. Turn on pixel ...
2
votes
1answer
96 views

Topological vs. non-topological noetherian charges

What (if any) is the relationship between the conserved (non-topological) noetherian charges and topological charges? Namely, is there any "generalization" of the Noether's first theorem that includes ...
2
votes
2answers
175 views

A universe of angular momentum?

I read this on Wikipedia: [...] That most tangible way of expressing the essence of quantum mechanics is that we live in a universe of quantized angular momentum and the Planck constant is the ...
2
votes
2answers
82 views

What is the “discrete” analogue to “continuum” mechanics?

If I wanted to explore a discrete mathematics approach to continuum mechanics, what textbooks should I look into? I suppose a ready answer to the question might be: "computational continuum ...
2
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0answers
82 views

Is everything in the universe discrete? [duplicate]

When beginning my education, I regarded nearly everything as continuous and analog in nature: Physical objects could have any mass on a continuous scale Light sources could emit any intensity of ...
2
votes
3answers
137 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 ...
2
votes
0answers
149 views

Discrete sum over an exponential with imaginary argument, considering only every second lattice site?

Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g., A-A-A-...-A-A (total of N sites) ...
1
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2answers
183 views

Oil drop experiment and quantization of charge

How to systematically show that the resulting charges in oil drop experiment are integers multiplied by $e$ in other word how to extract $e$ from the data?
1
vote
2answers
533 views

Continuous vs. Discrete Spectra in various materials

I read that the reason solids emit continuous spectra is that they don't have time to let their electrons decay-they are too close together. Given that electrons decay on the order of 100 nanoseconds ...
1
vote
1answer
70 views

How can we consider charge to be continuous? [duplicate]

In electrostatics, we usually consider charge to be continuous on any body, to calculate the electric field of the body. For eg. I had proved the Shell Theorem taking an infinitesimal charge of $dq$ ...
1
vote
1answer
285 views

Is Space-Time Quantisation necessary or even meaningful?

It is believed among people working on Quantum Gravity, that space-time must be quantised at the Planck scale. Although it is very hard to verify such proposition, it is interesting from a ...
1
vote
2answers
70 views

Discrete approximation of charge density

Given the electric potential $\Phi(r)$ and the Poisson's equation: $$ \nabla^2 \Phi(r) = - 4\pi \rho(r)$$ Consider the 2-dimensional case and let's say that I want to discretize this using a square ...
1
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0answers
24 views

How to get discretization coefficients of matrix $A$ in Finite Volume Method (FVM)? [closed]

First we have Discretization of the Transport Equation $$ \frac{\partial \rho \phi}{\partial t} + \nabla(\rho U \phi) - \nabla (\rho \Gamma_\phi \nabla \phi) = S_\phi (\phi) $$ In Finite Volume ...