A law of physics is Galilean invariant if the same formula works both when you are standing still on land, or when you are on a boat moving at constant velocity.
For example, if we were describing the movement of a point particle, the exact same formulas that predict the evolution of must also predict , even though of course both of those will have different values.
It would be extremely unsatisfactory if the formulas of the laws of physics did not obey Galilean invariance. Especially if you remember that Earth is travelling extremelly fast relative to the Sun. If there was no such invariance, that would mean for example that the laws of physics would be different in other planets that are moving at different speeds. That would be a strong sign that our laws of physics are not complete.
Lorentz invariance generalizes Galilean invariance to also account for special relativity, in which a more complicated invariant that also takes into account different times observed in different inertial frames of reference is also taken into account. But the fundamental desire for the Lorentz invariance of the laws of physics remains the same.
Complexity: NP-intermediate as of 2020:
- expected not to be NP-complete because it would imply NP != Co-NP: cstheory.stackexchange.com/questions/167/what-are-the-consequences-of-factoring-being-np-complete#comment104849_169
- expected not to be in P because "could we be that dumb that we haven't found a solution after having tried for that long?
Open source software that is not-FOSS by
Ciro Santilli 37 Updated 2025-06-17 +Created 1970-01-01
Can't get you out of my head by Adam Curtis (2021) by
Ciro Santilli 37 Updated 2025-06-17 +Created 1970-01-01
Ciro Santilli was touched by this, and then watched several other documentaries by Curtis.
Notably the part of the governments have lost all power to companies, and can't do anything meaningful anymore to actually represent the people, because globalization reduces the power of governments.
Overdetermination of Maxwell's equations by
Ciro Santilli 37 Updated 2025-06-17 +Created 1970-01-01
As seen from explicit scalar form of the Maxwell's equations, this expands to 8 equations, so the question arises if the system is over-determined because it only has 6 functions to be determined.
As explained on the Wikipedia page however, this is not the case, because if the first two equations hold for the initial condition, then the othe six equations imply that they also hold for all time, so they can be essentially omitted.
It is also worth noting that the first two equations don't involve time derivatives. Therefore, they can be seen as spacial constraints.
TODO: the electric field and magnetic field can be expressed in terms of the electric potential and magnetic vector potential. So then we only need 4 variables?
en.wikipedia.org/w/index.php?title=Nutrient&oldid=1075972831#Essential gives somewhat of an overview:
Deterministic, but non-local.
Plausible deniability of email password handover by
Ciro Santilli 37 Updated 2025-06-17 +Created 1970-01-01
You need a secondary password that when used leads to an empty inbox with a setting set where message are deleted after 2 days.
This way, if the attacker sends a test email, it will still show up, but being empty is also plausible.
There are unlisted articles, also show them or only show them.