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 energy discrete [duplicate]

It is often stated that because the energy in an em wave is $E=hf$, the energy comes only as multiples of $h$, ie quantized. But we know that $f$ is a real number, and you could have fractions of one ...
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Method of solving functional equation with discrete time [migrated]

I need to solve the following equation for $M(t)$: $$M(t+1)=a+bM(t)+\frac{c}{t}\sum_{t'=0}^tM(t')+df(t)$$ Where $f(t)$ is a kwonw function and $a$, $b$, $c$ and $d$ are known constants. I've never ...
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1answer
42 views

Infinite halving of a distance

If an object is, say, 100 cm. from a wall, and I move the object halfway to the wall and stop, then the distance is reduced to 50 cm. If I continually move the object by one half of the remaining ...
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1answer
31 views

Is there a sensible fully-discretized Hamilton's principle?

In computational physics it is common to formulate Hamilton's principle in a semi-discrete way, where space is continuous but time is discrete: in other words the Lagrangian $$L(q, \dot q, t): ...
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2answers
96 views

Does each photon have a unique wavelength?

Since the frequencies (or inversely, wavelengths) of photons are part of a continuous realm, doesn't this mean that no photon has exactly the same frequency? Two photons might have the same apparent ...
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5answers
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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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1answer
40 views

Quantum physics and constructable numbers [duplicate]

I do not know much about quantum physics. However, I do know it believes the world is discrete ( has quanta). This seems to contradicts the fact that we can create an object of length root 2 since you ...
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53 views

Is the elementary charge really a constant of nature? - Accuracy of QED

There are a couple of natural constants; examples are Planck's constant or the Speed of light in vacuum. The elementary Charge is the coupling factor to all Kind of electromagnetic interactions; this ...
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2answers
48 views

Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
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6answers
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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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2answers
190 views

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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0answers
69 views

In string-net condensation, what does the quantized charge means? [closed]

The electrical charge is quantized strictly for elementary particles. What kind constraints does this fact applied to string-net theory? For the this question, I want to understand why electrical ...
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0answers
19 views

Discrete Laplacian with geodesic distances

Normally, I have a a scalar function f(x,y), sampled on a two dimensional, regularly spaced grid in Cartesian coordinates. Evaluating the Laplacian of this function just requires the standard ...
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0answers
54 views

Trace part of Hamiltonian

Given an electron in one discrete dimension, the Hamiltonian is given by $H_{n,n'}\in Mat_{N\times N}\left(\mathbb{C}\right)$ acting on $l^2\left(\mathbb{C}^N\right)$ where $N$ is some integer ...
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2answers
97 views

Is time infinitely divisible? [duplicate]

Simple question (I think). Is time infinitely divisible? I heard that it was, although not from a particularly explanatory source. If so, are we sure that it is, without a shadow of a doubt?
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4answers
183 views

Is nature quantized?

I was reading Planck's postulate the other day on Wikipedia and couldn't help but noticing the sentence: "...is the postulate that the energy of oscillators in a black body is quantized..." ...
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0answers
64 views

Alternate theories of space and time [closed]

Do mainstream theories in physics make implicit assumptions about the nature of space and time? In particular, are there any theories which implicitly assume that space and time are continuous, or is ...
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1answer
107 views

Is there an error in Susskinds' derivation of Euler-Lagrange equations?

http://imgur.com/kZO5C0V First, I believe there is a trivial error. The second equation should have another $\Delta t$ multiplying everything on the right. It is divided out later when the equation ...
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1answer
159 views

Discrete vs Continuous spectra of operators [duplicate]

Why is it that if an operator $Q$ has a discrete spectra, that the eigenfunctions are all in Hilbert space? Why is it that if the spectrum is continuous we automatically know that the eigenfunctions ...
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1answer
78 views

Are there more reasons why we can not be part of an $n$ dimensional Game Of Life?

After talking with a colleague about the possible nature of the limitation of information propagation to c, and how everything can be seen relative to it, we wondered if the nature to this could be ...
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2answers
104 views

Will Quantum Computation fail if spacetime is discrete?

Will Quantum Computation fail if spacetime is discrete? Basically, would a discrete spacetime impose unexpected limits on how many Qubits could be used in calculations? Conversely, can quantum ...
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1answer
52 views

Convergent series in the real world with equal time for each term

A few months ago someone was explaining a philosophical principle in Aikido (a martial art) which involved a convergent series. The analogy he used was that, say you have a pool, and each day the pool ...
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1answer
43 views

How did Planck use the concept of statistical entropy in trying to understand the meaning of his own law?

I was reading Introducing Quantum Theory: A graphic guide (by J.P.McEvoy & Oscar Zarate) and came across Planck's predicament of understanding his very own law that accurately explained the ...
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3answers
89 views

Is the world we are living in discretized? [duplicate]

I do not know how to use professional words to ask my question, so I will try to use a layman language. Please bear with me for a moment. A ROUGH GUESS The world our eyes are seeing every moment is ...
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0answers
36 views

Making An Energy Momentum Plot For A Rashba Model (Using Discretization)

I want to make a plot of the Energy versus the Momentum of the Rashba model, using discrete matrices. First Ill show how I did this for the free particle. Subsequently I will show what goes wrong for ...
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1answer
44 views

How to discretize a finite crystal?

I am trying to find a general method to discretize a finite crystal system. How I have been discretizing systems so far (using Wannier functions): When you have an infinite crystal, you may apply ...
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0answers
51 views

What lives in the Hilbert Space? [duplicate]

Consider the eigenvalue equation: $$\hat{Q}\Psi = q\Psi$$ where $q$ and $\Psi$ are eigenvalues and eigenfunctions of the hermitian operator $\hat{Q}$. If the spectrum of the hermitian operator is ...
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3answers
193 views

What is the physical intuition behind the fact that 'energy is not continuous'?

First of all I am a novice regarding my knowledge of quantum mechanics. But curiously I do want to know what is the problem if energy is continuous like spontaneously flowing tap water. In fact I ...
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1answer
61 views

Can time be Quantised? [duplicate]

Can time be quantised? Would it be the smallest distance between two photons moving in the same direction or the shortest wavelength?
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27 views

Is the continuity (discontinuity) one of the intrinsic properties of all physical objects?

Is the continuity (discontinuity) one of the intrinsic properties of all physical objects? How do we define continuity? Which of the definitions of continuity are used (and why) in physics? This ...
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1answer
342 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: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
2
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2answers
855 views

How many atoms exist within a continuum body?

Materials, such as solids, liquids and gases, are composed of molecules separated by "empty" space. On a microscopic scale, materials have cracks and discontinuities. However, certain physical ...
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0answers
40 views

Argument for the Smallest Division of Time? [duplicate]

Okay so a couple of months ago I was watch Vi Hart's video on how .999999... is equal to 1. Some really interesting arguments that I had never heard before. Yesterday, I came across an article on ...
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2answers
294 views

1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...
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1answer
94 views

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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1answer
221 views

Turning a finite difference equation into code (2d Schrodinger equation)

I am trying to convert the following finite difference equations into code (taken from the bottom of page 12 of this thesis by Maike Schulte Numerical Solution of the Schrodinger Equation on Unbounded ...
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1answer
82 views

Interpretation of $\vec{x}$ in QFT

I am still at an early stage of studying Quantum Field Theory (I am reading QFT In A Nutshell by A. Zee). In the book I'm reading, it starts from a discrete lattice of material "lumps" labeled by ...
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1answer
105 views

What measurement of time is so small that it qualifies as quantum?

Quantum mechanics (QM; also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the ...
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0answers
11 views

Is Sorkin's causal growth dynamics a Galois Connection

Sorkin is well known for his causal growth dynamics. I think it is a sensible question to ask if his growth dyanamics, which I think can be seen as a poset map (though his work is much more ...
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1answer
71 views

Are temperature increases discrete? [duplicate]

Are temperature increases ever discrete in nature, or is it a continuous variable? If a discrete case exists, is there any material that exhibits particularly strange behavior?
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4answers
2k views

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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3answers
228 views

Is the energy of a photon continuous/discrete?

I was struggling today with this question: does a free photon have a continuous energy spectra? Free means in no context of any energy system (eg. an atom, em field). Although I'm asking myself if ...
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0answers
49 views

Planck time, time or time interval? [duplicate]

Planck time is really a weird topic, if we try to find out that is it time or time interval. It is the time taken by light to travel a Planck LENGTH so it must be time interval. But we also know that ...
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1answer
98 views

Why is it more convenient to consider space or time as a continuum?

I often find that phisicists and cosmologists make use of Planck's units. I have read propositions that sound like "...at the level of Planck's units many law of physics break down" ...
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1answer
123 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 ...
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4answers
196 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?
3
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1answer
82 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 ...
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3answers
145 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 ...
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1answer
65 views

How is that the life of a virtual particle duo is shorter than Planck Time?

I have always thought that the time is discrete (jumping), not continuous and the shortest time is Planck Time. One reason for that was the information on ...
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1answer
65 views

How is quantization implied by quantum mechanical theories? [closed]

Can anyone please explain(both by mathematical equations and by intuition) how the Schrodinger equation and Heisenberg matrix mechanics imply discrete states of energy, momentum etc and lead to ...