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Newton's Second Law, Revisited
eldavojohn writes "Dust off your fundamental physics books, an aspiring astrophysicist by the name of Alex Ignatiev has published a paper that proposes testing special cases of Newton's Second Law on earth's surface. His goal is sort of ambitious. The time he has to test his theory is only 1/1000th of a second, twice each year, in either Greenland or Antarctica. What would he look for? Spontaneous motion. From his interview with PhysOrg: 'If these experiments were to take place, Ignatiev says that scientists would look for what he calls the SHLEM effect. This acronym stands for static high latitude equinox modified inertia and would be noticed in a condition where the forces of the earth's rotation on its axis, and of the orbital force of the earth as it moves around the sun, would be canceled out ... In the end, if Newton's Second Law could be violated, he would be forcing physicists to reevaluate much of what we understand derived from that law — which is quite a bit.'"
Or is it?
Reminds me of what Patrick Moore did:
Stolen from
http://en.wikipedia.org/wiki/Patrick_Moore
Eccentric personality
Due to his long-running television and xylophone playing career, eccentric manner, distinctively rapid speech delivery and in later years his ever-present monocle, Moore is widely-recognised and well-respected in the United Kingdom, even by those with no interest in astronomy. This was used to great advantage for a 1976 April Fool's joke on BBC Radio 2, when Moore announced that at 9.47 am a once-in-a-lifetime astronomical event was going to occur: Pluto would pass behind Jupiter, temporarily causing a gravitational alignment that would reduce the Earth's own gravity. Moore informed listeners that if they could jump at the exact moment that this event occurred, they would experience a temporary floating sensation. The BBC later received hundreds of phone calls from listeners claiming to have felt the sensation.
Moore joined the Flat Earth Society as an ironic joke though many have taken this seriously.
It could be worse, it could be Monday.
"Fall heavy towards the moon, and the moon falls also towards you." -- Nietzsche
Hammer and feather are dropped simultaneously from equal heights (as measured by distance from the center of the moon), separated laterally by a distance substantially less than the moon's diameter. Both hammer and feather experience force from the moon's gravity proportional to their mass, and hence both accelerate at the same rate. Meanwhile, the moon is also accelerating towards the other two objects, but unevenly so: the hammer exerts a greater gravitational pull due to its greater mass. The moon is therefore subject to a torque, causing it to accelerate more rapidly towards the hammer.
The hammer is first to hit the ground.
Anyone who denies this truth is a spatially absolutist lunocentric whose refusal to recognize the validity of hammer/feather mechanics places him wholly beyond the help of Galilean metaphysics. Such hammer/feather rejectionists ought to be banished from planetary space, for their own good and for the good of not only hammers and feathers but all subjugated smaller objects, everywhere, who find themselves victims of this scientifically perpetrated emassculation.
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a756f345ec354225c08ff1a10a43162a
You're right that you can still use an equation that looks like F = dp/dt in GR, but I still think the original second law is wrong with all the quantities defined as they were. Writing it your way, it is then the definition of momentum which is wrong (or going on, the definition of velocity as dx/dt not dx/dTau). (Also in GR F= dp/dTau, not dp/dt if t is the time coordinate). The symbols in GR just happen to look and act quite like the newtonian symbols, but are interpreted differently.
Anyway, it is the error in predicted motion that is interesting here, where 'F=ma' gives the newtonian motion,
but this becomes like 'F = ma + m Gamma Vi Vj' in GR. You can't clearly see the different motions each theory gives in F = dp/dt.