cwb736

The thought experiment consits of 3 clocks. Clock 0 is "stationary" on Earth. Clock 1 is heading toward Earth at close to the speed of light (say a speed of v). Clock 2 is heading toward Earth also at the speed v but it is heading towards Earth from the opposite direction from Clock 1. Further Clock 2 is farther away from Earth than Clock 1 to begin with. Now when clock 1 passes Earth, Clock 1 and Clock 0 synchronize (ie. they both start counting). Now later on clock 1 and Clock 2 pass each other. As they pass each other Clock 2 synchronizes itself with the time on Clock 1 ( ie. Clock 2 starts counting from what was read on clock 1). Next, Clock 2 passes Earth. As Clock 2 passes Earth, all clocks are stopped. What will the clocks read. ie. how will the clocks read relative to each other. There is a problem with the question and that is the relativity of simultaneity. If clock 0 sees the other clocks stop simultaneously with itself then the other clocks will see something different. I just can`t wrap my head around the details of it. Thanks for any insight into this.

Hi Timo, Thanks for the reply. This equation is a portion of the Seismic Wave Equation. The non-trivial solutions to this differential equation describes both the P-waves and S-waves that are commonly referred to in discussions of Earthquakes. As soon as I read your reply I realized my mistake. The Lambda in the equation is a constant for a simple Earth Seismic Model, which is the most common convention in Seismology, and using this model then that one term would indeed be zero. However, in the derivation I was reading, the Earth Model was more complex(and accurate) and in this model Lambda is a function of depth and therefore a gradient of Lambda is non-zero. Thanks again.

Hi everybody, here is something I have seen in a geophysics text. I thought I was proficient using the einstein notation convention but I cannot follow this expansion of the wave equation. Note, I have not included the entire wave equation here, it is just the portion of the expansion which I am having trouble following ∂i[ λδij∂kUk ] = ∂iλ∂kUk + λ∂i∂kUk here i,j,k are indices. δ is the kronacker delta such that δij=1 when i=j and zero otherwise. ∂ is the differential operator. U is displacement. λ is the Lame parameter whic is a constant. I would have thought that ∂i[ λδij∂kUk ] = ∂iλ∂kUk Can someone please explain where the second term comes from! thanks very much