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 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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55 views

Alternate theories of space and time [on hold]

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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71 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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56 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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56 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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91 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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36 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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32 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
81 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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28 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
38 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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48 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
181 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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54 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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24 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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311 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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2answers
849 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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34 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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260 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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70 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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122 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
76 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
104 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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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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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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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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148 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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40 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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82 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
106 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
181 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?
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75 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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107 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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51 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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62 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 ...
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888 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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33 views

Review and mentions about time discretization

I would like to get basic knowledge in this topic of time discretization, at least basics. Because of I'm new in this field I don't know what is better way to start. Could anybody suggest any reviews ...
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118 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 $1.4×10^{32}$ ...
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1answer
116 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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34 views

Quantized spacetime structure? [duplicate]

Is quantized spacetime more like a chessboard or a matrix of lights? I have heard two analogies, the light bulb one appears to allow for movement whilst the chess piece one seems to violate zenos ...
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34 views

Is spectrum of Discrete-Time Fourier Transform (DTFT) periodic or not

I can't think of any better title. Here is the content that I got question http://cnx.org/content/m10247/2.31/ As it state the nature of DTFT's spectrum is periodic as it show in figure 1 However, ...
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390 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 ...
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42 views

How to get discretization coefficients of matrix $A$ in Finite Volume Method (FVM)? [closed]

First we have Discretization of the Transport Equation $$ \frac{\partial \rho \phi}{\partial t} + \nabla(\rho U \phi) - \nabla (\rho \Gamma_\phi \nabla \phi) = S_\phi (\phi) $$ In Finite Volume ...
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2answers
109 views

Infinitely many points of space-time?

Please can someone provided me with academic literature (Journals/Books, titles & links) which discuss the current view on space time i.e. that there is not Infinitely many points of space-time?
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122 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?
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35 views

Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”? [duplicate]

A copy of my question on Mathematics: Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the ...
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2answers
184 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 ...
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1answer
161 views

What arguments are in favour of an atomic structure to space-time?

The atomic theory as first theorised by Democritus has been successfully applied to matter and to energy (quanta). Space-time is still generally seen as a continuum. What arguments are there (if any) ...
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162 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. ...
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42 views

Charge or Charges on the oil droplets?

Due to my poor understanding of various paper and other material provided by google on Millikan's oil drop experiment I ask the following question here. As the drops were charged by either friction ...