Quantization is the replacement of classical quantities (in the Hamiltonian) like momentum by their respective quantum operators. Thus quantization transforms a classical system into a quantum system equivalently a classical Hamiltonian is transformed into a quantum Hamiltonian. Quantum...
Picture this gravitons are waves of space time curvature. Propagation of the waves through objects in between the atoms doesn't deter them, it just bends the objects. The graviton waves will reach the other atom. For an example picture wave particle duality as in the earlier days of quantum...
A simple counter example is
F(x)= x ^2
G(x)= 1,000,000,000,000,000,000 x
DF = 2x
D^2F = 2
For x > 500,000,000,000,000,000
is not correct. For anything below those bounds it is right. The inequality you stated is only true under certain bounds because...
Well there are several reasons why a photon is considered is considered massless .
1. Yes through experimentation.
2. Special Relativity implies it as shown below.
- E = m(c^2)/ ( sqrt ( 1-(v^2/c^2))
Multiplying both sides by sqrt(1-(v^2/c^2))
E(1-(v^2/c^2))= m( c^2)
Okay when v= c the E side...
Thank you, and ya for the longest time having not researched quaternions in depth, I always thought they were a 3-d version of the real numbers with three components. After reading the Wikipedia article on quaternion I understand Hamilton's motivation behind the four parts now.