James R said:
Here is a worked example of the relativity of simultaneity, using the postulates of Special Relativity, for those who wish to understand how that comes about.
The relativity of simultaneity means simply that observers in relative motion do not, in general, agree on whether events occur simultaneously or at different times.
The only assumption in the example given here is that the speed of light is measured to be constant for both observers - namely, the speed of light is c, the same value for each. This is one of the two postulates of Einstein's theory of special relativity.
You are leaving out another postulate of light:
Light motion is isotropic and moves indeopendently to the motion of the source of the light. This postulate is is conveneiently omitted by yourself in the tutorial
JamesR said:
The example is as follows:
L--------------M---------------R -> +x
Light detectors are located at the left and right ends (L and R) of a rigid rod. A light emitter is located at the middle of the rod (M). The rod moves in the positive x direction at a constant speed v, relative to the Earth.
We make no assumption that an observer on the rod and an observer on Earth will measure the rod to have the same length, or that clocks held by either of these observers will tick at the same rate.
Data are as follows:
Observer on the ground:
The half-length of the rod is measured to be d.
At time t=0, a flash of light is emitted at M, designated as x=0, and two photons head off towards L and R, initially located at x=-d and x=d, respectively.
The positions of the photons as a function of the time t, measured on the ground observer's clock, are:
PL(t) = -ct
PR(t) = ct
The positions of the detectors as a function of time are:
L(t) = -d + vt
R(t) = d +vt
At what times are the two photons detected? The photon is detected by the left detector when:
PL(t) = L(t)
-ct = -d + vt
Solving, we find t=d/(c+v).
The right-hand photon is detected when
PR(t) = R(t).
Solving, we find t=d/(c-v).
Notice that these two values of the time are different, so the photons are NOT detected simultaneously.
Let us look at the problem slightly different using only the distances traveled by the emitted light.
In a time t the L and R photons (left and right photons) each move a distance ct. L strikes the oncoming LC (left clock/mirror) after moving ct, ergo the LC has moved a distance vt (v is unknown at this time). R has also moved a distance ct and is a distance 2vt from RC.
Here both photons have moved a distance ct from the emission point P. L is detected and reflects a distance ct back to the emission point P after moving another distance ct.
R must cross the distance 2vt plus a distance the frame moves in the time t' that R catches RC or, ct' = 2vt + vt', where t' = t(2v)/(c - v). t' is the time that R is detected by RC after L was detected by LC. In terms of velocity, v = ct'/(2t + t')
After L has traveled a total of ct (outbound and inbound) L is located at P, which verifies the invariance of the point P defined by the equal motion of the L and R photons.
L is located at The emission point p, which has not moved, and L is located 2vt from the physical midpoint of the LC and RC which is moving away from L. At this instant, R is located a distance 2vt + 2vt' from the oncoming physical midpoint of LC and RC.
The frame moves a distance vt' as L and R photon converge simultaneously at M, now located a distance 2vt + vt' from the initial emission point of the L and R photons.
Light moves isotropically and independent (straight-line trajectory at constant velocity c wrt the point of emission of the light) of the motion of the source of the light until acted on by external forces.
James R said:
Observer on the rod:
The half-length of the rod is measured to be d' (which might be different to d).
At time t'=0, a flash of light is emitted at M, designated as x'=0, and two photons head off towards L and R, initially located at x'=-d' and x'=d', respectively.
The positions of the photons as a function of the time t', measured on the rod observer's clock (hence t' instead of t, since these might be different), are:
PL(t') = -ct'
PR(t') = ct'
These positions must be referenced to the point if emission of the photons not from the physical emission point on the frame, which is be moving. The observer on the frame has no physical data to assume his frame is at a state of rest. The observer knows only that he is at rest with respect to the frame.
Why do those pushing special relativity theory want to grant super observational powers to on observer in an enclosed environment, who is completely ignorant of the laws of physics?
James R said:
The positions of the detectors as a function of time are:
L(t') = -d'
R(t') = d'
The statement here is correct only if measured wrt the point of emission of the photons and if the frame is not moving wrt P, the emission point of the light.
James R said:
Notice, the detector positions don't change with time in this reference frame (the view of an observer standing on the rod).
The positions of the clocks at each end of the rod do not change distances with the physical center of the rod, true,
but one must ignore the physics of the light motion, that moves independently of the moving frame, remember?
James R said:
At what times are the two photons detected? The photon is detected by the left detector when:
PL(t') = L(t')
-ct' = -d'
Putting "'" primes on the time statement does not change anything. Whether the observer is on the frame or not, the light will move the same velocity as seen from the stationary frame and will arrive at the moving LC (left clock), moving
with respect to the invariant position of the point of the emitted light.
The photon moves ct, which is vt short of the length of the midpoint of the physical frame (distance d in the James R world) to the LC, left clock.
James R said:
Solving, we find t'=d'/c.
The left photon will arrive at the Left clock a distance vt short of the physical distance between the frame midpoint and the clocks.
This statement of James R above is totally bogus.
James R is negating the concept of motion here by ignoring the motion of the frame and inducing erroneous motion attributes to light based on the mere presence of a human observer.This is what SRT is, a psychological aberration.
James R said:
The right-hand photon is detected when
PR(t') = R(t').
Solving, we find t'=d'/c.
Again, James R ignores the invariance in the point P and effectively negates the very concept of motion. The light emanating from the midpoint of the moving frame is only measured properly wrt to the emission point not the physical midpoint of the LC and RC clocks, which are erroneously assumed to be in a state of rest.
James R said:
Obviously, these times are the same, so according to the observer on the rod, the detectors both register the photons SIMULTANEOUSLY.
Noway can the observer accumulate data that shows the photons arriving simultaneously at the LC and RC clocks. You can do it in owrds on paper, but you must ignore the isotropic motion and constant velocity of light to do do, in other words you must ignore the postulates you proclaim as governing the motion of light.
James R, light is measured from P, the point of emission of the photons, Your assumption that the observer can measure everything from the physical midpoint is bogus. You negate the concept of moption by doing so. You also violate the postulate of light that says the speed of light is independent of the motion of the souirce of light, yet you blithely continue on measuring light motion as if the speed of light were somehow attached to the moving frame.
Your tutorial on simultaneity is a testment to the massive scientific misconceptions surrounding the history of SRT.
Take any point P in the universe and emit two photons simultaneously. All measurements wrt the point P are done with regard to the motion of light. Each photon moves the same distance from P in the same amount of time. Each photon moves in a straight line trajectory, on the same trajectory line. If one of the photons is reflected 180 degrees after moving a distance ct from the emission point the photon will return to the emission point P after moving an additional distance ct. This is further verification of the invariance of the emission point P.
Your moving frame scenario does not work properly as you assume erroneously that the frame is not moving. This assumption is made withuout any scientific data. After the photons reflect and converge at the moved physical midpoint may the observer make assumptions regarding frame motion. To do so before the data is all in is pure speculation.
Assume the observer has reams of test data where the frame is statioanry wrt the embankment and reams of data where the experiment is conducted withthe frame is moving at a uniform velocity v. The times for the round trip are different and the observer on the moving frame will be able to detemine his absolute velocity with respect to the invariant point P, sitting nicely at an absolute zero velocity.
[thread=46658]Here is an absolute zero velocity frame of reference system[/thread]
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James R said:
We have just shown that events which are simultaneous in one frame of reference (the rod frame) are not simultaneous in another frame of reference (the ground frame), using only the fact that the speed of light is the same regardless of which frame it is measured in.
This is one of the simple results of Einstein's relativity, although it seems counter-intuitive at first.
If you have questions, please post them in this thread.
James R get your references straight. The light is moving with respect to the point of emission of the light, point P, not wrt the physical midpoint of the frame that is moving. It is your ignorant obsevers that that are screwing up measurements. You must have a talk with them.
Intuition has nothing to do with a system that ignores the laws of motion of light.
1) Light moves isotropically and independently to the motion of the source of light and
2) the speed of light is a constant c measured wrt absolute zero velocity.
Geistkiesel
