# Tagged Questions

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 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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### 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 ...
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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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### Why do we have an elementary charge but no elementary mass?

Why do we have an elementary charge $e$ in physics but no elementary mass? Is an elementary mass ruled out by experiment or is an elementary mass forbidden by some theoretical reason?
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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Are voltages discrete when we zoom in enough?

Voltages are often thought of as continuous physical quantities. I was wondering whether by zooming in a lot, they are discrete. I feel like the answer to the above question is yes as voltages in the ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### Can physics get rid of the continuum?

Almost every physical equation I can think of (even though I don't actually feel comfortable beyond the scope of classical mechanics and macroscopic thermodynamics, as that's enough for dealing with ...
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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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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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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### 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? ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
318 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 ...
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### 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 ...
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### 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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### 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 $1.4×10^{32}$ ...
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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
1k views

### How can there be really any instantaneous velocity?

I have read about Zeno's arrow paradox that tells us there is no motion of the arrow at a particular instant of its flight. It can be inferred that there can be no velocity at any instant. Moreover we ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...