Taps are playing for erstwhile relativity theorists . . .
Doc Al said:
You don't get it at all. Both O and O' are perfectly entitled to their different measurements of when the lights were turned on. They don't contradict each other, since they are in
different frames. What you amusingly call my "contrived perception of reality" is what everyone else just calls "physics".
Not until they wish to determine
when the pulses were sent. If all they care about is: "Did the pulses arrive simultaneously?", then everyone agrees that they did!
As long as all you care about is what happens at that
single event in spacetime--the midpoint at the moment the two pulses arrive--you are correct. But I know you wish to
deduce more than that!
As soon as you want to draw conclusions about about
when the pulses were emitted, you are talking about observations of things happening at
multiple points in time and space! This involves clocks and measuring rods, and understanding how they work. It is no longer a "single point measurement". SR demands that moving frames get different answers.
Well... if you had the courtesy to actually
read the previous posts, you will find this problem fully analyzed according to standard SR. (And Janus has prepared some excellent animations illustrating how light behaves according to both observers.)
But you seem to prefer arguing for your "common sense" convictions. But your arguments are nothing more than repeating "it obviously can't be that way" with a few personal insults tossed in for good measure.
Nice attempt at a reversal.
You obvious
didn't do your homework if you can seriously persist in arguing that this problem has nothing to do with relativity. Give me a break.
Take care then. When you are ready to talk physics, come on back.
Okay, Doc AI, here's your break.
The simplest way to solve the problem is to start with O' moving to M at some velocity v(O'). O' must know he is moving otherwise the problem shifts to O who has the same problem. However, we can verify that O' knows he is moving by a measure of the red/blue shifts in the recorded light pulses at M. If this were all, then we can only say that the surface of the radiated wave fronts, A and B, of any arbitrarily located sources must be equidistant from M at
some time in the past. This is so as the O' clocks are stablized at a rate determined by their velocity wrt time in the O'. The time for the light to reach M is the same for both A and B, even though the sources may be anywhere as long as their wave fronts are equidistant from the eventual meeting point at M. The time for the wave frionts located at t/c from A-M and B-M is the same as the O' frame is the same for both wave fronts.
DocAI is partially correct in insisting that light dfrom B must have been turned on before the light from A. The light from B
can be turned on at any time before the light from A is turned on as long as the wave front from B is located at t/c at the time the light from A was pulsed on. We must only determine the time t' when the wave front (or other physical source at A) was at t'/c.
O' can trigger a delayed pulse time, t = 0 for A as he passes by. A can then send pulses calibrating B as long as the delay time from t = zero allows the calibration signal from A to B plus the time for the pulses to arrive at M is sufficiently long. So O' dutifully waits until the signal from A and B arrive at the same time. In O' time O' can then calculate A and B distances from M. Without a physical source at B the requirment for the wave front is as determined above, yet the measured time from passing A to signal arrival detemines the distance for both A and B.
Or O can measure the O' relative velocity wrt M and share the information with O' for all locations to be calculated when M is reached. Clearly, in the O frame M is the midpoint of the A-B line. Likewise, in the O' frame the distances are equivalent. If we take the zero point in time at A then t'(d') = t(d) and all clocks can be calibrated. Even though the output from the clock on O' says t' =d'/c seconds and that t =d/c seconds we know t' < t in absolute second counts, but once determining that t' = d/.8c the clock differences are easily calibrated. As long as there is sufficient amount of time O can send a steady signal of dots measured in dt = 1 second in the staionary frame. O' receives the dots, calculatess the time difference in th O' frame, hence relative velocities may be determined.
Let us take the time zero point (OO') at A when O' passes by. Then we all have to agree that the zero time in both frames is equivalent. Likewise, the stop times when the pulses (delayed) reach M are equivalent and simultaneous. Therefore the distances A-M and B-M in both frames are equivalent notwithstanding that the clock times measuring the distances need calibrating which can be accompliched as described. The distance in both are the same but the clock differences leaves the illusion the distances are different.
Do they play 'Taps" when a cherished theory asks "for whom the bells toll and discovers that it was answered "for thee"?
"
So this sounds like some relativity legs just got cut off at the knees, doesn't it. Like Richard Nixon said " . . . a million dollars in bribe money could be raised, but that would be wrong", that opting only for a "break", by one anyway, we will realize that the "cutting iff at the knees" 'would be wrong', excessive and beyond the request of an erstwhile relativity theorist.
So we will politely retain a semblance of RT by recognizing that there is a measurable difference in the two systems, that is the old SR/GR system and the new SR/GR system.
We all know that an electron will radiate EM quanta during acceleration and at constant velocity the electron radiation ceases, yet the electron's energy is proportional to 1/2 mv
2 wrt the lab frame. The electron is in a higher energy state than before it was accelerated. All moving mass wrt the lab frame has some increase in relativistic mass and at sufficiently high velocities the mass energy difference can be measured as a measuremnt of the 2(pi)hf of the electron.
So very briefly, why do clocks slow down at elevated velocities? Because the masses constituting the the clocks have all increased in energy to a level that the intake of subsequent accleratinmg phonons cannot be processed with the same efficiency as at lower velocities. Likewise, the masses of the clock do not sit in isolation from each other. Any and all inter-mass energy exchange coupling efficiencies are effectivley lowered.
Linear velocity increases, meaning increase in velocity is linear with the increase in energy intake, are sacrificed for the sheer purpose of increasing the vibration rate of the particle. Velocity is a measure of the current relative energy difference of the acclerated mass and the zero lab frame mass. The increase in vibiration lowers the ability of the particle to store energy as iincreases in velocity relaqtive to lower velocities.
Some wanted a break, so there you got it. Relativity phenomena is measured by the relative acceleration of mass wrt to zero velocity wrt lab frame.
An example:
Mossbauer measurements where gamma radiation input into a stationary mass target can show recoiless gamma radiation from the target when the
velocity of the gamma particle source is a few centimers/second. A dv = 0 (for a properly chosen gamma source) there is no recoil experienced by the target particle, or said another way, there is a complete energy exchange efficiency of gamma and target. The gamma source is slightly high, then the target recoils, or the gamma source is low , the target recoils. In either case the gamma-target source velocity differences are, energetically speaking, incoherent.
The effect is a measure of the relative energy difference of gamma particles accelerated with the added mass source velocity many orders of magnitude less than the natural frequency of the test gamma radiation particles at rest in the lab frame.
(It takes at least 4 biggrins to constitute gloating.)
