I am fond of maintaining that, thanks to relativity, a radio signal emitted halfway between two neighboring equatorial villages arrives at the two villages simultaneously, in the actual rotating frame to which those villages belong. But I don't know the math. Maybe you can help, 1100f, considering your know-how... or anyone else too. This much I know: if you use an inertial frame unmoving WRT Earth's center, then there is a sizeable computed disparity between eastbound and westbound EM signal transit times for the scenario cited. Yet if you choose an inertial frame that is moving eastward, at Earth's tangential velocity WRT Earth's center, and that frame is momentarily oriented tangential to Earth at the midpoint of the two villages when the signal emits; then the calculated disparity between eastbound and westbound EM signal transit times pretty much disappears altogether. The only problem is that such an inertial frame is merely a close approximation, and the villages actually belong to no such frame. I don't know how to cipher the actual rotating metric, but based on what I have shown above, it seems only natural that in the actual rotating coordinate system of Earth, there must be null or negligible disparity between eastward and westward transit times of an EM signal, over a suitably small range, landmark to native landmark. Please Register or Log in to view the hidden image! edit: I am perfectly well aware of the Sagnac findings, but I think that when you're dealing with arcs that are far less than one radian in length, relativity still operates as expected, especially for a slowly-rotating orb such as Earth.
Yes the natives belong to the frame, the physical frame., Ve, the planet earth. Here we have a frame as you describe. We call the villages L and R and we will look at the light is three different stages. Code: |_______________<|>_________________|R -> east Abive the photons have just been emitted towards the villages located equidistant between the villages L and R, The left moving photon (lmp) covers a distance ct before colloiding withe reflector at village L. The distance between the midpoint an L is D., Therefore to start ct + vt = D. Now R has moved the same distance to the east and at the time the lmp ihas just arrived at L the rmp has arrived at a point 2vt from the R reflector. and we have the situation shown below. This phase one of the discussion. with the midpont also moved vt to the right. Code: |__|<--_________ |__| ____________-->_____|R -> east I have left the original location with respect to the stationary frame, and with respect to the motion fo the photon as each photon initially travels the same distance in the same amount of time. Now the lmp reflects and in time t it has traveled a distance ct in the opposite direction, the direction of the frame. while the rmp still has to move a distance 2Vt to catch up to R. which it does, and then some. The rmp is looking at the display just as the lmp has reached L. Code: lmp -->. vt | vt >|||R<. the distance between > < is vt' The rmp must move through the disrtabnce 2vt + the distance vt' the distance the frame moves when the photon is moving through the distance 2vt. Therefiore ct' = svt + vt', which boils down to t' = t(2V)/(C - V). At the end of the 2nd phase here both photons have traveled the same distance ct, the only difference being the rmp was reflected after the lmp. This takes us to the positions shown below. Now the lmp has the same diistance to travel to reach the O' observer as the rmp had to travel to catch up to R. The rmp now is looking at the on coming frame and the O' observer still at the original midpoint of the L and r villages. Code: |_____________->|__|__|||________<-________|R -> east As the photons are moving toward each other their mutual midpoint in space is defined at the instant the photons were moving in a collision course. Actually this midpoint was predictable at the time the photons wee emiotted.The lmp arrives at the O' observer after crossing the same distance recently crossed by the rmp when chasing R..The midpoint is not at the present position of O' as the frame is still moving and the photons haven't arrived, which means O' still a slight movement to finish and that the mutual midpoint is t' the right of the moving frame a distance Vt'. The photons arrive simultaneously, the O' observer looks at the computer output of L anmd R and her own and discovers the difference in arrival time of the R and L photons at their respective reflectors and this difference is the exact difference the O' sees on her watch that measured the time from photon emission to absorption when the photons arrived back at her station. As the arrival times of the photons at L and R differ by t' and because the arrival time at L by the lmp is less than the stationary condition, where the photon would travel the distance D, instead of D - Vt there is only one rational conclusion availabe to the O' observer. t' > 0 implies motion to the right, t' = 0 implies a statioanry frame and any consideration of her being at rest wrt Ve would be a physical error in the assumption.. As a footnote the t' is the missing timne that is confused by SR as a perturbation fo simultaneithy due to the motion of the frame, but now that we have found the missing t' we can all go back on absolute time, recover absolute space, and simultaneithy and shit can time dilation and frame contraction. Yes, we can all begin to live! t' = t (2V)/(C - V) and one can substitue for t with t = L/(C + V).
Think again, air head. 'Funny how geistkiesel is continually calling people "stupid incompetent jerk" and telling people to "go fuck yourself " and "go fuck off" -- and yet those posts stand. But I can't use the term "air head". Sounds like a double standard to me! I've suddenly lost interest in this entire forum. Don't expect to see my posts herein any longer, because this forum obviously caters to corruption and lies and favoritism. It's worthless. Good riddance to bad rubbish! Good riddance!
OK I did think again. So your smirking retort is your physics? I believe it. Di you ever say anything that isn't cute? or designed to bullshit someone?
The post you responded to was "fuck" free and you can use "air head" all you like. come back to us Dristam and thicken you skin.
You could use Relativity here but there is no need. The speed of light is so much faster than the rotation of the Earth the difference in transit times is negligible. The biggest problem would be signal lag times on satellites.
