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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2answers
130 views

Are there any true discontinuities in physics?

When we first learn physics, it's often presented very 'discontinuously'. For example, pop quantum likes to talk about objects being "either" particles or waves, leading to a lot of confused questions ...
1
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2answers
61 views

Energy Quantization

Why a free particle gives rise to Continuous Spectrum energy eigenvalues where particle in the Bound States provide the quantization?
0
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1answer
52 views

Representing Hamiltonian in discrete position basis

I am trying to numerically find eigenstates of an Hamiltonian. Let $V(x)$ be some potential. Suppose my space is between $-L,L$ and that the allowed positions are every $\Delta x$, such that $\frac{1}{...
1
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0answers
46 views

What is the cause of discrete or quantized energy levels in an atom? [duplicate]

I understand how it is that electrons move from one energy state to another, however I've not been able to find anywhere that describes why an atom has any particular states. Why should an atom of ...
0
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1answer
62 views

Issues of normalization & differential final state momenta in analysis of normalized differential quantum-field-theoretic probability of scattering

The normalized differential quantum-field-theoretic probability $dP$ of scattering is given by $$dP=\frac{|\langle f |S|i\rangle|^{2}}{\langle f|f\rangle\langle i|i\rangle}d\Pi,$$ where $|i\rangle$ ...
0
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0answers
29 views

How much time a ball stays at rest when throw up?

You throw a ball straight up in the air. The ball attains its maximum height when it is momentarily at rest,(v=0). How mutch time is this moment? If we take time has continuous it is an infinitesimal ...
0
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2answers
50 views

Particle in a box, quantization of energy

I'm learning about how the energy of matter is quantized like how the energy of light is. My textbook illustrates the concept of quantization with the particle in a box: "A particle of mass $m$ ...
1
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0answers
47 views

I want to know about the quantization of mass [duplicate]

Is mass quantized? If yes, then why do we see all amounts of mass? Well , can it be said quantized just for smaller masses?
0
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0answers
43 views

Scale invariance

Physically why should scale invariance break down at the Planck limit? If not what are the other possibilities to save the quantum granularity of spacetime? I would really appreciate professional ...
0
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1answer
41 views

What are all charge-like quantum numbers?

What are all charge-like quantum numbers? In particle physics there are often things (like charge conjugation) that apply to all charge like quantum numbers. Everytime I read something about charge-...
-2
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1answer
43 views

Doesn't modelling using Lie Groups assume spacetime is continuous?

Lie groups are used to some behaviors of quantum mechanics, as well as forming a basis for Kaluza-Klein, Yang-Mills, and String theory. But Lie groups are defined as involving a differentiable ...
1
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1answer
105 views

Symbolic dynamics of a multidimensional system

Let $x_t = F(x_{t-1})$ be a discrete-time dynamical system in the chaotic regime. Starting from an initial condition $x_0$, we can generate a time series $(x_t)$ where $t =1,2,...,T$ indicates the ...
1
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1answer
43 views

Why magnitudes can be quantized? [closed]

If charges and any other magnitude must be or well quantized by multiples of an integer, or simply discrete values. How could we us assign values to the quantized quantities?, beacuse If I measure ...
0
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1answer
93 views

What came before quantum theory?

My professor explained today that the idea behind quantum theory is that particles have quantized energy states. To an undergrad like me, this is kind of strange. Wouldn't it always make sense that a ...
2
votes
0answers
50 views

Lenses that pixeliate incoming light [closed]

Is it possible to make a lens that 'pixelates' the light passing through it? I imagine a pair of glasses, that when put on, turn the world into a grid of discrete pixels, each having, or appearing to ...
1
vote
1answer
22 views

Formation of Line Spectra in light of Bohr's Theory [closed]

I am reading about the electronic structure. It is written that when hydrogen's electron comes back to ground state from excited state, it releases energy in a specific amount according to Bohr. But ...
0
votes
1answer
51 views

How is the range of $x\cdot s$ in Simon's algorithm restricted to $\{0,1\}$?

The final critical step of Simon's algorithm (before setting up a simpler system of equations to solve) involves taking advantage of the fact that $$x\cdot s \in\{0,1 \}$$ but for $x,s \in \{0,1\}^...
1
vote
1answer
109 views

Planck's Law. It's $E=hf$ or $E=nhf$?

My textbook provides intuition of Planck's Quantum theory which is copied right next. Max Planck proposed that emission or absorption of energy in a blackbody is discontinuous. It is absorbed or ...
1
vote
1answer
118 views

How does the discrete energies of alpha and gamma rays prove the existence of nuclear energy levels

I was reading up about Nuclear Energy Levels and came up with the aforementioned question. To me, there seems to be no direct connection between the two statements and therefore, I would like to know ...
0
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0answers
61 views

Scale factor of the universe

Do we impose that the scale factor $a(t)$ of the Universe is a continuous function? Or there is a physical meaning? Usually in physics we define functions to be continuous, such as the velocity of a ...
1
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1answer
100 views

Is there a simple way to explain quantised conductance? [closed]

I am biologist and I need to pass a nanotechnology class. I am stuck with this term of quantum resistance. Basically this appears to me as normal Ohm's law, except that takes into account Heisenberg ...
5
votes
1answer
131 views

How do we choose how to discretise spacetime in loop quantum gravity?

In LQG we choose a two-complex (or other) on which to discretise GR before quantising. I'm a little uncertain about the nature of this choice. Is the two-complex an a priori property of the universe (...
0
votes
1answer
45 views

Size of box vs. discrete-ness of state of the system

From Statistical Physics, 2nd Edition by F. Mandl, pg. 36: A sufficiently large box (say 10 light-years across) will clearly not affect the properties of our system, ion plus electron sitting ...
1
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1answer
79 views

What is cause of quantization of charge? [duplicate]

What is cause of quantization of charge? When we rub two objects only an integral number of electrons or charges can be transferred is this the reason? Why electron has the smallest possible charge? ...
3
votes
1answer
62 views

Is all energy quantised?

I'm wondering if all energy is quantized? Can a particle with kinetic energy have any value of kinetic energy or is kinetic energy also quantized? My reason for asking this is that if a particle is ...
0
votes
1answer
60 views

What makes things move in a universe with blocktime? [closed]

In a universe with blocktime the past, present and future all exist at the same time. But what makes it appear that for example my body is going from one movement ...
1
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1answer
62 views

How is Zeno's Dichotomy Paradox resolved according to physics? [duplicate]

I always thought of quantum space and quantum time as a solution, but then i figured out that "quantum space-time" is not actually true(yet). I've also heard of the calculus approach and limits, but i ...
0
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1answer
38 views

Decoupling of double discrete Fourier transform

I have a problem with a double Fourier transform I encountered: $$\sum_{j=1}^L \sum_{l=1}^L e^{-i\pi \frac{n_1}{L} (j+l)}e^{-i\pi \frac{n_2}{L} (j-l)}V(j-l)$$ where $n_1,n_2$ are integer. If the ...
1
vote
3answers
96 views

Energy equation in Quantum Mechanics

We know that total energy of the system is classically continuous, but in quantum mecanics (QM) it is quantised. My question is: How can we use the conservation of energy equation to derive ...
3
votes
0answers
44 views

Snyder's Lorentz invariant discrete space-time

Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous? I'm sure this has been ...
0
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1answer
31 views

Is the hypothesis “at some level, spacetime becomes discrete” falsifiable?

Suppose I conjectured that, at some length scale, spacetime was discretized into "cells", Minecraft-style. For simplicity, I guess let's say they're cubes with side length $n$. Presumably we can put ...
3
votes
1answer
137 views

Is the energy always discrete?

In the von Neumann axioms for quantum mechanics, the first postulate states that a quantum state is a vector in a separable Hilbert space. It means it is assumed the Hilbert space has a basis with at ...
0
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0answers
32 views

Is there a fundamental frequency of time? [duplicate]

Our eyes and brains can only perceive frequencies as individual frames up to some limit, after which we perceive the motion to be "continuous." Is there such a frequency of time? Along the same line,...
5
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0answers
137 views

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 ...
0
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0answers
44 views

Angular momentum $J_z$, how do we get eigenvalue of $m\hbar$?

If we have angular orbital momentum for $z$-direction, we assume that for state $|j,m>$ that eigenvalue is $m\hbar$. Similarly for $J^2$, we assume $j(j+1)\hbar^2$ Can I get reference of ...
2
votes
1answer
86 views

Does limiting to infinity violate laws of physics?

It is noteworthy that one cannot simply divide any length more than the Planck-length. If so, one cannot simply divide any volume more than the $(Planck-length)^3$. So if I want to find the limit of ...
2
votes
1answer
98 views

Why are harmonic oscillators quantized? [closed]

What physical reason is there for a mass on a spring to have discrete energy levels? And why are those energy levels equally spaced, i.e. why is $E \ \alpha \ f$? Personal background and ...
0
votes
1answer
128 views

Proof for quantized angular momentum [duplicate]

In Bohr's model, Bohr stated that the angular momentum of the electron is quantized and stated that $$L=\frac{nh}{2\pi}$$ So what is the proof for that equation or, in other words, how did he derive ...
1
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0answers
22 views

Is the position of matter discrete in universe? [duplicate]

In computer, for example, if we use integer to represent position of objects, position can be (0,0) , (3,5), but not in (1.5,3.5). In real world, there are something that is discrete, such as atomic ...
1
vote
2answers
106 views

How does quantum mechanics and quantum field theory explains discrete energy levels of particles?

Please give me a brief explanation as to how qm and qft describe and explain the energy level that exist in an atom. I understand that in QM energy state is quantized but does not offer an ...
0
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0answers
71 views

Trying to understand why energy must be quantized/discrete

So I'm reading about bound systems right now in my quantum text. It is beginning to explain why energy must be quantized, and is doing so by introducing the reader to the one dimensional "quanton in a ...
1
vote
1answer
197 views

Is there a minimum distance?

I would imagine there is no limit to how small space can get. Is this correct? I am aware of planck's constant, but cannot objects be closer than Planck's constant is short? Perhaps this question is ...
0
votes
2answers
90 views

If the Universe is going to last infinitely long, what is the type of this infinity?

Let's say we've built a machine, that prints a sequence of all natural numbers from 0 to $\infty$. We "could" do this in a Universe with an infinite amount time (if we also make many other assumptions ...
0
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0answers
28 views

Minimum amount of space [duplicate]

I always believed that there were no limits in the world and then I learned that a minimum temperature exists, and maybe a maximum speed. And now I am wondering about the boundaries of the world. Is ...
0
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0answers
19 views

Resources on the discreteness of space and time

Does anyone know any books or other sources of information on the discreteness of space and time? The only ones I've managed to find require graduate level physics knowledge, which sadly I do not ...
13
votes
2answers
533 views

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 ...
3
votes
3answers
227 views

Is Bekenstein entropy limit inconsistent with universal continuity?

It is unknown whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Can universal continuity be experimentally falsified? Is the universe finite ...
1
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4answers
100 views

Where is the fallacy in this issue related to electric charge quantization? [closed]

Suppose there are two identical conducting objects; one with 5 units of positive charge and the other is uncharged. Initially these are separated and later these are brought into contact. I guess net ...
0
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1answer
60 views

Intuitive way to think about discrete energy levels

I'm currently taking an introductory quantum mechanics course and we just finished learning about the infinite square square well scenario. I understand all the maths used for calculating the ...
1
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0answers
52 views

Discrete Fourier transform for periodic signal?

From the Signal and System textbook, by Oppenheim, I learned that the discrete-time Fourier transform can be written as $$ x[n]=\frac{1}{2\pi}\int_{2\pi}X(e^{j\omega})e^{j\omega n}d\omega $$ $$ X(e^{...