# 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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### 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 ...
13k 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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### 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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### 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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### 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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### 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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### 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. ...
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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 $0$...
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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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### 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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### 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 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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### 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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### 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 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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### 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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### 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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### 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 were,...
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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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### 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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### The Quantization of Photon Energies [duplicate]

Despite Planck's constant being in $E=hf$, it would appear to me that energy is still not discrete, as frequency can be an fraction of a Hertz that one wants. How does this imply that electromagnetic ...
4k 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 ...
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### 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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### 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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### 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 ...
680 views

### 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 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 ...
742 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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### 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? ...
725 views

### Quantization of Electron Spin

Why is electron spin quantized? I've seen the derivation for the Hydrogen atom's energy levels, but my professor jumped to electrons having spin 1/2 or -1/2 as experimental. Why do electrons obey the ...
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### 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 ...
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### 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-...
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### Mapping between numbers and symbolic representations

I am not a physicist but applying symbolic dynamics for information coding in signal processing. Is there any mapping between symbols and numbers?
569 views

### 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: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
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### 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 ...
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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 ...
441 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 ...
208 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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### Wannier Functions as Discrete Basis

In solid state physics, using Bloch's theorem we know that the one-electron energy eigen-function can be written as $\psi_{\lambda,\vec{k}}(\vec{r})$ where $\lambda$ indexes eigenvalues of $\hat{H}$ ...
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### 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 ...
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### 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 ...