Potentiometer Updated 2025-08-08
Electrical resistance Updated 2025-07-27
Irreducible representation Updated 2025-07-16
Schur's lemma Updated 2025-07-16
Special relativity Updated 2025-07-16
Explains how it is possible that everyone observes the same speed of light, even if they are moving towards or opposite to the light!!!
This was first best observed by the Michelson-Morley experiment, which uses the movement of the Earth at different times of the year to try and detect differences in the speed of light.
This leads leads to the following conclusions:
- to length contraction and time dilation
- the speed of light is the maximum speed anything can reach
The "special" in the name refers to the fact that it is a superset of general relativity, which also explains gravity in a single framework.
Since time and space get all messed up together, you have to be very careful to understand what it means to say "I observed this to happen over there at that time", otherwise you will go crazy. A good way to think about is this:
- use Einstein synchronization to setup a bunch of clocks for every position in your frame of reference
- on every point of space, you put a little detector which records events and the time of the event
- each detector can only detect events locally, i.e. events that happen very close to the detector
- then, after the event, the detectors can send a signal to you, who is sitting at the origin, telling you what they detected
General relativity Updated 2025-07-16
Unifies both special relativity and gravity.
Not compatible with the Standard Model, and the 2020 unification attempts are called theory of everything.
One of the main motivations for it was likely having forces not be instantaneous, but rather mediated by field to maintain the principle of locality, just like electromagnetism did earlier.
Regular convex polygon Updated 2025-07-16
Tesseract Updated 2025-07-16
First principle Updated 2025-07-16
Emergence Updated 2025-07-16
Basically the opposite of reductionism.
Figure "xkcd 435: Fields arranged by purity" must again be cited.
Synthetic geometry of the real projective plane Updated 2025-07-16
It good to think about how Euclid's postulates look like in the real projective plane:
- Since there is one point of infinity for each direction, there is one such point for every direction the two parallel lines might be at. The parallel postulate does not hold, and is replaced with a simpler more elegant version: every two lines meet at exactly one point.One thing to note however is that ther real projective plane does not have angles defined on it by definition. Those can be defined, forming elliptic geometry through the projective model of elliptic geometry, but we can interpret the "parallel lines" as "two lines that meet at a point at infinity"
- points in the real projective plane are lines in
- lines in the real projective plane are planes in .For every two projective points there is a single projective line that passes through them.Note however that not all lines in the real plane correspond to a projective line: only lines tangent to a circle at zero do.
Unlike the real projective line which is homotopic to the circle, the real projective plane is not homotopic to the sphere.
The topological difference bewteen the sphere and the real projective space is that for the sphere all those points in the x-y circle are identified to a single point.
One more generalized argument of this is the classification of closed surfaces, in which the real projective plane is a sphere with a hole cut and one Möbius strip glued in.
Model of the real projective plane Updated 2025-07-16
The real projective plane is not simply connected Updated 2025-07-16
To see that the real projective plane is not simply connected space, considering the lines through origin model of the real projective plane, take a loop that starts at and moves along the great circle ends at .
Now try to shrink it to a point.
There's just no way!
Point at infinity Updated 2025-07-16
Homogenous coordinates Updated 2025-07-16
Visualizing 4D Updated 2025-07-16
Activation energy Updated 2025-07-16
Catalysis Updated 2025-07-16
Vehicular Combat video game Updated 2025-07-16
Subquotient Updated 2025-07-16
As an overkill example, the happy family are subquotients of the monster group, but the monster group is simple.
There are unlisted articles, also show them or only show them.