The discrete tag has no wiki summary.
3
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0answers
53 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 ...
0
votes
1answer
70 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 ...
0
votes
0answers
27 views
Problem with Discrete Parseval's Theorem [migrated]
I think I must be missing something obvious, but I can't for the life of me see what it is. The discrete version of Parseval's theorem can be written like this:
$\sum_{n=0}^{N-1} |x[n]|^2 = ...
1
vote
1answer
52 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 ...
3
votes
1answer
56 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 ...
4
votes
2answers
145 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.
0
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0answers
39 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 ...
0
votes
0answers
16 views
Implementing Explicit formulation of 1D wave equation in Matlab #FiniteElements #FiniteDifferences [migrated]
so the theory is straight forward.
we have:
$\frac{d^2U}{(\Delta t)^2}=c^2 \frac{d^2U}{(\Delta x)^2}$
discretizing it gives:
$\frac{U(i+1,j)- 2U(i,j) + U(i-1,j)}{(\Delta t)^2} = c^2 ...
1
vote
0answers
66 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
votes
1answer
71 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 ...
5
votes
0answers
78 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 ...
2
votes
1answer
119 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 ...
2
votes
2answers
145 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 ...
1
vote
1answer
170 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 ...
3
votes
3answers
195 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 ...
0
votes
1answer
76 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 ...
2
votes
4answers
183 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 ...
1
vote
0answers
79 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, ...
12
votes
4answers
575 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 ...
2
votes
2answers
420 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: ...
11
votes
5answers
970 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
votes
0answers
98 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)
...
4
votes
2answers
271 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
votes
1answer
222 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 ...
7
votes
2answers
1k views
Is reality discrete at the quantum level? (…and what does it imply not only mathematically?)
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 ...
3
votes
3answers
523 views
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. ...
5
votes
3answers
349 views
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 ...
2
votes
3answers
625 views
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 ...
26
votes
7answers
2k views
Is there something similar to Noether's theorem for discrete symmetries?
Noether's theorem states that, for every continuous symmetry of a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
