Talk:Arrow of time

An "arrow of time" existed under Newtonian physics
One of the things that Eddington got wrong in his 1928 monograph (and which many subsequent writers on the subject seemed to take on trust and repeat in their own works), was the idea that Newtonian and Einsteinian physics were both 100% symmetrical with respect to time.

Actually, they're not.

While the 1905 Doppler equations of special relativity ("Electrodynamics" paper, chapter 7) are 100% identical under time-reversal, the previous C19th Newtonian Doppler equations aren't – time-reversal changes their energetics. If Newtonian relativity says that a body receding at v m/s has a Doppler shift of E'/E = (c-v)/c, then under time-reversal this prediction changes to a different, higher-energy Doppler shift relationship, of E'/E = c/(c+v). So in a C19th Newtonian universe, you can measure whether time is running forwards or backwards by measuring the Doppler shift on a body that has a known velocity.

Further explanation:
 * The "arrow of time" under Newtonian physics / DOI: 10.13140/RG.2.2.25914.24009

Also, under special relativity, strict traditional energy conservation is adhered to scrupulously. Under C19th Newtonian theory, the redder Doppler equations mean that energy is continually disappearing from the system, creating a bias in equilibrium reactions towards exothermicity, giving a thermodynamic arrow of time. Under time-reversal this bias reverses and you get energy-gains and endothermicity.

So Eddington is wrong when he says:
 * "Objection has sometimes been felt to the relativity theory because its four-dimensional picture of the world seems to overlook the directional character of time. The objection is scarcely logical, for the theory is in this respect no better and no worse than its predecessors. "

From a 1920s viewpoint, special relativity was better in some respects and worse in others: better because SR finally obeyed strict traditional energy-conservation (which Newtonian theory had failed to do), and worse because by strictly conserving energy, and making the Doppler relationships symmetrical w.r.t. time rather than "lossy", it also erased the explicit energetic/thermodynamic "arrow of time" that had existed in the previous system. ErkDemon (talk) 01:11, 10 December 2018 (UTC)

Minkowski stress
Displacement due to Minkowski stress is crucial. It is the answer to why there is an arrow of time. In quantum field theory particles do not have an innate tendency to move towards a specific direction. It is a systemic phenomenon to be calculated; not an innate property. Particles in Minkowski space are never ideal and point-like. Also moments in time - also known as different states of the evolution of a system - overlap and aren't strictly speparate. Each particle's probabilistic horizon of causality, is squished and pushed afar from some direction, and sucked towards a different direction.

Newton was wrong at the Planck level. Fundamental particles don't have an innate tendency towards some direction. Simply their wave functions are causally squished and pushed.

It's all about probabilities. The stresses of Minkowski space causality exerted on wave functions - define the directivity of displacement of the different states of the evolution of a system, and we call that "arrow of time".

Radiative arrow
This section doesn't make sense, since the a point source ALWAYS radiates out by definition of r>0. An extended source (for example a ring) radiates both inward and outward, although the inward wave reflects outward from the origin.

Perhaps it is referring to the retarded Green's function, but that's also a tautology: we specify initial, not final conditions BECAUSE of the arrow of time. But the noncausal Feynman_propagator is often used instead in QFT. In summary, I think this section should be removed. Chris2crawford (talk) 01:16, 2 November 2020 (UTC)
 * A search of Google scholar (here) shows the phrase "radiative arrow of time" is used in physics. Some of the uses predate Wikipedia. So "radiative arrow of time" is a thing. If you think the section doesn't describe it well, then it should be re-written, but not removed. Richard-of-Earth (talk) 00:22, 8 November 2020 (UTC)