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 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 ...
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1answer
130 views

Explicit solutions to 2-d Dirac Equation

The 2-d Dirac equation without any constants is represented usually as $$i*dt (\phi) = D (\phi)$$ where $D = m\sigma_2-i\sigma_1dx-i\sigma_3dy$. Where can I find explicit closed form solutions to ...
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1answer
281 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 ...
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1answer
483 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? ...
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2answers
1k 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 ...
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2answers
215 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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4answers
563 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 ...
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2answers
483 views

The Quantization of Photon Energies

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 ...
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4answers
1k 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 ...
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0answers
101 views

Wave Particle duality because of discrete time?

If time is discrete, such as the Planck's length, would the transition from one frame of time to the next explain why it appears matter changes from a particle to a wave? During that infinitely small ...
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3answers
290 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 ...
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1answer
182 views

What is the smallest increment of space and the smallest increment of time? [closed]

I believe that every point in space is a surface point. And if it was possible to break through or tear a point in space, it will create a black hole. I believe that's why a black hole can exist ...
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1answer
183 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 ...
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1answer
75 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 $dq$ ...
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0answers
116 views

What about continuity of Space and possible discreteness of Time? [duplicate]

Is time continuous or discrete? Is even this question a valid question? If you say, it all depends on resolution then assume the best possible resolution achievable. If it is discrete, then what about ...
4
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1answer
1k 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 ...
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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? ...
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0answers
175 views

Does a point exist in the real world [duplicate]

In mathematics we can have an infinite number of points between two integers. This is really circular logic since a point is defined as infinitely small. Does a point exist anywhere in the physical ...
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1answer
627 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 ...
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1answer
102 views

How do we know that time and distance are not discrete?

I know that it is believed that energy is discrete, in that it travels in quanta. I was wondering if there is any evidence which either proves or disproves something similar with both time and ...
2
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1answer
115 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 ...
5
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1answer
117 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
258 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.
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0answers
54 views

Has Time in the Universe been found to be Discrete or Continuous? [duplicate]

I have a question, has the Universe been found to come in Discrete Quantum, like Quantum Physics or is it Continuous in Nature? I was wondering if time was like a Continuum, like the fluid in a soft ...
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0answers
73 views

What were Feynman's objection(s) to a cubic lattice universe? [duplicate]

In this video of Feynman discussing the scientific method, starting at around eight minutes and 30 seconds, Feynman describes the proposition that space consists of a cubic lattice of points (as ...
2
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1answer
128 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 ...
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0answers
139 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 ...
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1answer
631 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 ...
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2answers
186 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 ...
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1answer
374 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 ...
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3answers
507 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 ...
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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 ...
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1answer
137 views

Is there a finite unit of distance that we cannot divide past?

If distance could be divided into an infinite no of units or points, then it seems to me that motion would be impossible since a meter for instance, having an infinite no of points within it (and the ...
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4answers
496 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 ...
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90 views

Division algebras $(\mathbb{R,C,H,O})$ and discrete symmetry [closed]

I once saw a statement about the relation between division algebra(which means you can define a division in this algebra, there is a theorem saying we only have 4 kinds of division algebra, real R, ...
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4answers
179 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 ...
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4answers
945 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 ...
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10answers
5k views

Is time continuous or discrete?

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 ...
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1answer
85 views

Vehicle acceleration

What I'm essentially doing is Kalman Filter. If anyone is familiar with (but it doesn't really matter in this case). Consider the following formulas: $$x_k=x_{k-1}+v_{k-1}dt+a_{k-1}\frac{dt^2}{2}$$ ...
2
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2answers
754 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: ...
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4answers
604 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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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 ...
2
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0answers
173 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) ...
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3answers
583 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?
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3answers
1k 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 ...
13
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3answers
834 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 ...
4
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2answers
378 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
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1answer
392 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 ...
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3answers
571 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 ...
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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 ...