User:Maschen

Undergraduate in physics, 3rd year.

I didn't name this account after the place Maschen in Germany, Harburg: it was sheer coincidence to combine "Machine" into a "name-like" term.

The date is Sunday, July 21, 2024. The time is 21:42 (UTC/GMT).

Content contributed by this user is released into the public domain.

This user has been on Wikipedia for 14 years and 6 days.

σ γ Z Ψ S q p t I S L

Random thoughts on fundamental physics

Currently without expertise...

New theories

Theories like causal dynamical triangulation (CDT) and spin networks look like the right direction to quantum gravity.

CDT takes logical approaches:

spacetime is quantized at small scales and appears as smooth, curved spacetime at large scales,
that timelines must agree and casualty is preserved - not just describing, but possibly explaining, the very nature of space and time itself,
interesting is it's automatic fractal nature.
perfectly simple (minimum number of essential assumptions) and extremely appealing.

Not string theory or the like - which make ludicrous assumptions that particles "are" strings or membranes or whatever and then require extremely complex modifications to spacetime just for consistency (Calabi–Yau manifolds? Really?).

The worst part of string theory is right from the very beginning, is the assertion particles "are" strings etc. How can we ever know that experimentally? We can sit down speculating/guessing/modelling what particles "really are" (only to change again and again anyway in the future) a much as we like:

"let's pretend everything, even the "fabric" of space and time, is vibrating strings or springs or trampolines or twirling tops or spinning wheels or pendulums or twiddling knots/links or... then there are a number of fundamental normal modes/rotational frequencies/tensions of these ... and everything in the universe is derived from these fundamental things..."

It's weak - just making stuff up just for the sake of explaining physical phenomena, and yet the maths is ludicrously excessively complicated just so it works... CDT is not, at all, like that.

Should the unification of forces really be related by the number (10, 11, 26...) of spacetime dimensions??...
Yes, it may combine GR and QFT and has passed internal consistency, but proponents seem too confident that it "is" the only approach, that "only all of the good ideas" come from string theory...
What happens when new forces are found - shall we hope they still fit into the theory, or insert more dimensions, or what?
Without question - the SHO, classical or quantum, or any form of linear normal mode oscillations, are the most inanely dull physical systems to ever solve for.. Yes - SHOs are important systems for perturbation theory methods, and oscillatory systems are ubiquitous and can be modeled by linear oscillations... but even the idea of something oscillating linearly is extraordinarily boring and tiresome. This idea is used in string theory. (Non-linear chaotic oscillations are much more interesting).

Formulations and spaces

Quantum theory: Has the path integral formulation using Lagrangians had its day? Phase space formulation in QM and replacement of wavefunctions by Wigner functions offers new insight - no need to take sides with position/momentum representations as they're on equal footing.

Relativity: Space and time are always deeply mysterious, in classical mechanics and general relativity. GR itself apparently has a number of flaws (but then which physical theory is truly perfect?), one of them is that "events" are points in spacetime. Do points really exist in nature? How can we even physically define a point in spacetime? In superspace (and other spaces I haven't encountered) points themselves are replaced by spaces, no points actually exist. According to the ADM formulation of GR, space itself is 3d and curved, and time-dependent (dynamic).

Fractals, chaos, non-linearity, everywhere

Rather than changing the integer number of spacetime dimensions, and postulating wave or field or evolution equations of integer order, newer methods of

(stochastic) fractal/multifractal geometry filling continua of dimensions between 0 and 3 or 4, and
using geometric algebra and fractional calculus (or even fractional differential forms or fractional geometric calculus?), for example fractional quantum mechanics,

look like the right way forward. "Particles/waves/fields" may be replaced by fractal structures which propagate self-similarly through spacetime.

Given how ubiquitous fractals are everywhere (literally everywhere, one way or another), a better notion of space and time may be dynamic and curved fractal spaces. Replacing the description of "particles/strings (etc)" described by wave-like or field-like probability amplitudes, by a fractal-geometric probability amplitude propagating through curved dynamical space, seems very appealing. Interpreting the constituents of matter always transforms, first "particles" (classical mechanics), then wave-particle duality (quantum mechanics), then fields (quantum field theory).

A non-linear, but simple, theory based on fractal geometry... should connect GR and QFT with SUSY?... Not yet sure how exactly to do that mathematically and make everything work though...

A classic photo

Thanks to user:JdH for uploading this!

Links

Template:Multicol

Generally useful

Wikipedia pages

WikiProjects:

Information, help and guideline pages:

Special pages, lists and databases:

Template:Multicol-break

Other

Image creations [1]
Sandbox: User: Maschen/sandbox
Articles listed in Physics equations
Defining equation
User:Maschen/Mathematical descriptions of physical laws, once an article, now a redirect to Laws of science
User:Maschen/Defining equation (physics)now a mainspace article Defining equation (physics)
User:Maschen/Equation (physics)
Defining equation (physical chemistry)
User:Maschen/Bargmann-Wigner equations, now a mainspace article Bargmann–Wigner equations
User:Maschen/Hamilton-Jacobi-Einstein equation, now a mainspace article Hamilton–Jacobi–Einstein equation
User:Maschen/Schrödinger equation (exact solutions)
User:Maschen/Gluon field strength tensor, now a mainspace article Gluon field strength tensor
User:Maschen/Angular momentum graphs, User:Maschen/Angular momentum diagrams (a redirect)
User:Maschen/Fractional differential forms,
{{equation box 1}}
{{dimanalysis}}
{{braket}}
{{vec}}
{{intmath}}

Template:Multicol-end

Favourites

Tables

This is, without question, the greatest table I ever created (looks trivial to an expert - not if you're learning this for the first time and find it awkward):

Summary of above
Geometry/Algebra	Covariance	Contravariance
Nomenclature of "vector"	vector, contravariant vector	covector, 1-form, covariant vector, dual vector
Basis is...	tangent ${\mathbf {e}}_{i}=\partial _{i}{\mathbf {r}}={\frac {\partial {\mathbf {r}}}{\partial x^{i}}}$	normal ${\mathbf {e}}^{i}=\nabla x^{i}$
...to coordinate	curves	surfaces
...in which	one coord varies, all others are constant.	one coord is constant, all others vary.
The coordinate vector transformation is...	$a^{\bar {\alpha }}=a^{\beta }L^{\bar {\alpha }}{}_{\beta }$	$\Omega _{\bar {\alpha }}=\Omega _{\gamma }L^{\gamma }{}_{\bar {\alpha }}$
while the basis transformation is...	${\mathbf {e}}_{\bar {\alpha }}=L^{\gamma }{}_{\bar {\alpha }}{\mathbf {e}}_{\gamma }$	${\mathbf {e}}^{\bar {\alpha }}=L^{\bar {\alpha }}{}_{\beta }{\mathbf {e}}^{\beta }$
...which are invariant since:	$a^{\bar {\alpha }}{\mathbf {e}}_{\bar {\alpha }}=a^{\beta }L^{\bar {\alpha }}{}_{\beta }L^{\gamma }{}_{\bar {\alpha }}{\mathbf {e}}_{\gamma }=a^{\beta }\delta ^{\gamma }{}_{\beta }{\mathbf {e}}_{\gamma }=a^{\gamma }{\mathbf {e}}_{\gamma }$	$\Omega _{\bar {\alpha }}{\mathbf {e}}^{\bar {\alpha }}=\Omega _{\gamma }L^{\gamma }{}_{\bar {\alpha }}L^{\bar {\alpha }}{}_{\beta }{\mathbf {e}}^{\beta }=\Omega _{\gamma }\delta ^{\gamma }{}_{\beta }{\mathbf {e}}^{\beta }=\Omega _{\beta }{\mathbf {e}}^{\beta }$
The inner product is:	${\begin{aligned}\langle {\mathbf {a}},{\boldsymbol {\Omega }}\rangle &=\langle a^{i}{\mathbf {e}}_{i},\Omega _{j}{\mathbf {e}}^{j}\rangle \\&=a^{i}\langle {\mathbf {e}}_{i},{\mathbf {e}}^{j}\rangle \Omega _{j}\\&=a^{i}\delta ^{j}{}_{i}\Omega _{j}\\&=a^{i}\Omega _{i}\\\end{aligned}}$

Successful files

Yes - they're so trivial, that's no reason to draw them.

Electric charge and magnetic monopoles.
Electric dipole and magnetic dipole.
Exterior product of vectors.
Exterior product of one-forms.
De broglie Plane wave and Wave packet.

De broglie Plane wave and Wave packet.
Lorentz transformation between inertial frames in Minkowski space.
Lorentz transformation between accelerating frames in Minkowski space.
Gravitomagnetic field.
Magnetic field due to a Magnetic moment.
Magnetic field due to an electric current.
Rotational fluid drag.
Wave particle duality (momentum known position unknown).
Wave particle duality (momentum unknown position known).
Matrix multiplication.
Fields due to colour charges (quarks).
High-frequency sinusiodal beating wave created as a GIF using Maple14.
Lorentz transformation between inertial frames in 3-space.

Background

Likes

logic, symmetry, duality, and self-similarity underlying fundamental principles of any form of knowledge, although also like randomness, chaos, irregularity and non-linearity also (nature isn't "perfect" and regular),
maths (especially set theory, geometry, all things permutations, chaos theory), physics (especially QFT, GR), chemistry, engineering and technology,
emo/heavy metal/J-rock music
Graffiti IF it IS artistic and NOT offensive and NOT on people's personal property - it makes derelict factories, city buildings, bridges, tunnels, transformer assemblies, trains look awesome! In fact when handwriting calligraphic letters in formulae I adopt graffiti-style text in equations!
chess, card games, juggling, jigsaw puzzles/3d (or multidimensional! [2]) puzzles, Rubik's Cube,
spirograph, epicycloids, hypocycloids, epitrochoids, also coils, spirals...
gyroscopes,
Geomag, Meccano, Fischertechnik,
whiteboards AND blackboards
and in plenty: drawing.
Slightly prefer the city to the country.

Drawing and diagramming everything; so that information and meaning is actually transferred to a reader as directly and simply as possible, happens to be my obsession. Ironically I'm not very good at it, usually due to my sore misunderstanding of the concept to draw/diagram...

Drawing for recreation (for instance mathematical patterns, technical drawings, people in Japanese manga style, building architecture, and when a kid: almost every form of European train, and so on...) is also very fun, although I can do technical graphics I'm not good at artistic at all! (much of these creations end up in the bin or deleted instead of storage for later leisure!!)...

IMO There is nothing like drawing: simply a pencil on paper allows one to literally release imagination pictorially in no other precise (or vague/mysterious) way, and can be viewed later any number of times to think and rethink the concept of the image endlessly. Of course there is immense diversity of drawing tools and materials mechanically and electronically for any purpose required, to amplify the power of the pencil and paper...

Dislikes

"pop" (except for the very unfortunately late legend Micheal Jackson), tacky "romance (genre)", "hip hop", and "(c)rap" music
hippys, religion, jewelry,
junk food (like poisonous McDonald's), meat, illegal drug trade, smoking, alcoholic beverages, nudity/sex-obsessive behavior, death-torture,
the practices/ideology of Nazis, totalitarianism, Saw (film) and its worse sequels... Seven (film), and A Clockwork Orange (film), films of these types are very negative, disturbing, and encourage disastrously wrong behavior and ideas for people to copy... they should be BANNED but Hollywood/whatever enjoy the money which is all it's about...
I'm not an animal person: they not are for our entertainment. Zoos and pets are unfair; animals should be free in the wild although restrained from entering human-populated areas to prevent interference.

Isn't it sad that:

in all years of civilization - science, mathematics, technology, industrialization have developed far slower than they could have because of irrelevant and empty customs, religions, and personal preferences of the "higher-uppers"; "leaders" of a country or a "inflexible generations" blocking the way? (i.e. any case where people are forbidden to think outside of some falsely obscure box, and make new discoveries in the service of civilization with mutual respect to the planet)
how many potentially brilliant minds have been (and still are) WASTED in slavery and/or poverty (which ought to be collaborative team work with mutual respect between so-called "peasants" who build the land and need to be rewarded with wealth from it and "leader/s" who rule), and wars?

Wouldn't it just be awesome that instead of going to war - governments and armies from every country would drop their weapons, disarm, leave the f~#@!%* armies, and transform all expertise, time, energy and resources in creating weapons of mass death and destruction and hellish poverty into:

space technology,
particle physics facilities,
renewable energy sources,

since these

require the very limits of people's minds and talents collaborating to create the finest cutting-edge technology, so people are challenged, work hard, gain tremendous experience and satisfaction and results in the process,
encourage, interest and demand new future generations of professionals in all areas (not just science/technology/engineering but business, finance, econometrics, computing, media, education...), hopefully less crooked yobbos on the streets,
are peaceful, although inevitably stressful times and disagreements/conflicts will arise; that is a million times better than going to war by compromising there and then, and the excitement of probing into outer spacetime and developing new technologies should assist removal of violent/criminal attitudes,
are generally beneficial for our knowledge, planet, and civilization...

Astonishing that this has yet to actually happen globally - maybe never, maybe when we're on the edge of annihilation...