Ciro Santilli @cirosantilli 37

One is reminded of Nick Leeson.

One things must be said: the root cause of all of this is the replication crisis.

This is why he managed to go on for so long.

People felt it was normal to have to try for one or two years to replicate a paper.

The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.

Bibliography:

Suppose that a rod has is length $L$ measured on a rest frame $S$ (or maybe even better: two identical rulers were manufactured, and one is taken on a spaceship, a bit like the twin paradox).

Question: what is the length $L^{\prime }$ than an observer in frame $S^{\prime }$ moving relative to $S$ as speed $v$ observe the rod to be?

The key idea is that there are two events to consider in each frame, which we call 1 and 2:Note that what you visually observe on a photograph is a different measurement to the more precise/easy to calculate two event measurement. On a photograph, it seems you might not even see the contraction in some cases as mentioned at en.wikipedia.org/wiki/Terrell_rotation

Measuring a length means to measure the $x_2-x_1$ difference for a single point in time in your frame ($t2=t1$).

So what we want to obtain is $x_2^{\prime }-x_1^{\prime }$ for any given time $t^{\prime }2=t^{\prime }1$.

In summary, we have:

By plugging those values into the Lorentz transformation, we can eliminate $t_{2}and{t}_1$, and conclude that for any $t_2^{\prime }=t_1^{\prime }$, the length contraction relation holds:

The key question that needs intuitive clarification then is: but how can this be symmetric? How can both observers see each other's rulers shrink?

And the key answer is: because to the second observer, the measurements made by the first observer are not simultaneous. Notably, the two measurement events are obviously spacelike-separated events by looking at the light cone, and therefore can be measured even in different orders by different observers.

As of 2019, the Standard Model and general relativity are incompatible. Once those are unified, we will have one equation to describe the entirety of physics.

There are also however also unsolved problems in electroweak interaction + strong interaction, which if achieved is referred to as a Grand Unified Theory. Reaching a GUT is considered a sensible intermediate step before TOE.

The current state of Physics has been the result of several previous unifications as shown at: en.wikipedia.org/wiki/Theory_of_everything#Conventional_sequence_of_theories so it is expected that this last missing unification is likely to happen one day, potentially conditional on humanity having enough energy to observe new phenomena.

Now that's sweet:With the visual tileset out of box.

Notable mentions:

Other notable people that are likely also awesome but Ciro has less familiarity with their contributions:

By cranks:

Subtle is the Lord by Abraham Pais (1982) mentions that this has a good summary of the atomic theory evidence that was present at the time, and which had become basically indisputable at or soon after that date.

On Wikimedia Commons since it is now public domain in most countries: commons.wikimedia.org/w/index.php?title=File:Perrin,_Jean_-_Les_Atomes,_F%C3%A9lix_Alcan,_1913.djvu

An English translation from 1916 by English chemist Dalziel Llewellyn Hammick on the Internet Archive, also on the public domain: archive.org/details/atoms00hammgoog