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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45
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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 ...
33
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8answers
3k 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 ...
28
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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 ...
22
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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 ...
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 ...
17
votes
4answers
521 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 ...
15
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4answers
859 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 ...
14
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1answer
524 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
3answers
755 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 ...
13
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1answer
183 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 ...
12
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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
547 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?
8
votes
3answers
308 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 ...
7
votes
1answer
145 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
4answers
807 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
548 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
976 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
3answers
75 views

Units of a discrete Fourier transform

Normally a Fourier transform (FT) of a function of one variable is defined as $$f_k=\int^\infty_{-\infty}f(x)\exp\left(-2\pi i k x\right) dx.$$ This means that $f_k$ gets the units of $f$ times the ...
6
votes
0answers
128 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
1answer
100 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
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2answers
216 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.
4
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3answers
776 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
66 views

Discretizing the Wave Equation in polar coordinates

I want to discretize the wave equation $$\frac{1}{c^2}\frac{\partial^2\psi\left(\vec{r},t\right)}{\partial t^2}=\triangle\psi\left(\vec{r},t\right)$$ in polar coordinates. I find the following ...
4
votes
1answer
242 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
1answer
510 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
99 views

Is temperature discrete

Because an object's temperature is inversely proportional to the wavelength of blackbody radiation which it emits, physicists have theorized the existence of Planck temperature at around $1.4×10^{32}$ ...
4
votes
2answers
737 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
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2answers
354 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
566 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
249 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
426 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
360 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
143 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
81 views

Is there an absolute minimum scale to the universe? If so, why?

Based on my rather circumscribed understanding of modern physics, one of the key insights of quantum mechanics over previous scientific theories is the prediction that there exists an absolute limit ...
3
votes
2answers
142 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 ...
3
votes
1answer
62 views

Justification of discrete spectrum for V(x) unbounded at $\pm \infty$ in Pauling and Wilson

In Pauling and Wilson, Introduction to Quantum Mechanics, they offer the following intuitive reason for the discrete spectrum of a potential which is unbounded at $\pm \infty$: This is ...
3
votes
1answer
993 views

Is time quantized? Is there a fundamental time unit that cannot be divided? [duplicate]

Is the present just a sharp line between the past and the future with no time at all, or is the present a short frozen unit of time? Could time be quantized into a fundamental units? Like Planck ...
3
votes
1answer
104 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
3answers
149 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 ...
3
votes
1answer
178 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
355 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
700 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
4answers
135 views

I don't get band structure of solids

If the energy levels of bound electrons are discrete, why do band structures in solids arise?
2
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3answers
123 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
351 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
1k 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
125 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
105 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
181 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
0answers
84 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 ...