Time dilation has no effect because the photon already has an infinite Lorentz factor-in other words, no time passes at all in the photon's frame of reference.
42.
:: : : It's not immediately clear ( to me at least ) that you can use the Lorentz factor here because the orbit itself is due to gravity.
43.
Then solving for } } } } } } and substituting into the Lorentz factor obtains its alternative form in terms of 3-momentum and mass, rather than 3-velocity:
44.
The elimination of the Lorentz factor also eliminates implicit velocity dependence of the particle in ( ), as well as any inferences to the " relativistic mass " of a massive particle.
45.
If you want the details you'll have to look over special relativity a bit and perhaps the Lorentz factor ( look at what happens when you make v = c ).
46.
In the unidirectional case this becomes commutative and simplifies to a Lorentz factor product times a coordinate velocity sum, e . g . to, as discussed in the application section below.
47.
The differentials in " t " and " ? " are related by the Lorentz factor " ? ", The line element squared is the Lorentz invariant
48.
By starting with the biradial, the draft immediately derives the Lorentz factor, rapidity, and other values and the unit biradial is the hyperbolic versor of a Lorentz transformation between frames.
49.
Currently I've set the K . E . conservation equations and the momentum conservation equations equal to each other and have assumed an elastic collision, where L is the Lorentz factor:
50.
Where \ gamma _ 0 is the initial Lorentz factor, ? is the angular velocity of rotation, r is the radial coordinate of the particle and c is the speed of light.
