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CLASE DE RELATIVIDAD CON EJERCICIOS. TRANSFORMACIONES
Tipo: Apuntes
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It was found that there was no displacement of the interference fringes, so that the result of the experiment was negative and would, therefore, show that there is still a difficulty in the theory itself…
For a point P ◼ In system K: P = ( x , y , z , t ) ◼ In system K’: P = ( x ’, y ’, z ’, t ’) x K P K’ x’-axis x-axis
Step 1. Replace with. Step 2. Replace “primed” quantities with “unprimed” and “unprimed” with “primed.”
Results of Maxwell's electrodynamics ◼ Visible light covers only a small range of the total electromagnetic spectrum ◼ All electromagnetic waves travel in a vacuum with a speed c given by: (where μ 0 and ε 0 are the respective permeability and permittivity of “free” space)
As the direction of the ether wind is unknown, the apparatus has to be turned around by 90 degrees to see a shift (starting form many different initial settings)
◼ Another hypothesis proposed independently by both H. A. Lorentz and G. F. FitzGerald suggested that the length ℓ 1 , in the direction of the motion was contracted by a factor of …thus making the path lengths equal to account for the zero phase shift. ❑ This, however, was an ad hoc assumption that could not be experimentally tested. It turned out to be “less than half of the story”
Length contracted for the moving muon, it’s own life time just 2.2 micro seconds Life time of the muon delayed for observer on Earth so that it can travel the whole distance as observed from Earth Great thing about special relativity is that one can always take two viewpoints, moving with the experiment, watching the experiment move past, the observations need to be consistent in both cases They move with about 98 % the speed of light
Mary has a light clock. A suitable clock is just any periodic process, the time it takes for one cycle of the process is the period, its inverse is the frequency. Tom watching Mary go by figures that her time is delayed (dilated) due to her moving in a straight line with a constant high velocity with respect to him.
No simultaneity if not also at the same position, just a consequence of the Lorentz transformations
Relativistic dynamics can be derived by assuming that mass is increasing with velocity. The Lorentz factor gets larger when velocities get larger and so does mass apparently as we can see from the relativistic momentum equation. Einstein derived relativistic dynamics that way. His derivations are sure correct, but the foundations are somewhat shaking as there is no really good definition for mass.
