Relativity of simultaneity vs Simultaneity

Relativity of simultaneity vs Simultaneity: Electrodynamics in privileged frames and Special Relativity by Stefano Quattrini ANCONA, July 2018 The two way speed of light can be considered as c in vacuum in any IRF since it has been experimentally measured in several experiments. Special relativity is based on c constant always. What can be affirmed is that Light goes at the same speed c irrespective of its emitter, although it can be interpreted in two totally different ways: a) Light is measured from any IRF and its value is c also in a single path, (no exp. evidence) b) light it does not care of the IRF where it departed from, it goes at c speed in its own “privileged frame” (the two way speed of light is c, in any case, as it is demonstrated from the experiments) The gedanken experiment: A wagon is endowed with a pair of emitters in opposite directions, placed in its middle with the same abscissa of a clock A. The Lab is represented by the IRF0, endowed with the same pair of emitters with the same abscissa of the clock B. The distance in between the two pair of emitters is virtually zero along y direction. Two pairs of light waves (instead of one) in opposite direction are emitted as soon as A and B face each other. Let’s call it Emission event.

A

IRF1 v0

X0

X0

TAIL

HEAD

IRF0

B A

The Tail event, is the event of absorption of the light at the Tail of the wagon, the Tail event is the one relevant to the tail. Since light proceeds irrespective of the motion of the source, the “Head event” will be only one event, both light beams will arrive at the once at the Tail. The light waves departed from the same point and were reaching the same surface, the surface has to see them arriving at once in agreement with the observer in the lab. Same for Head event. MIDDLE SCENARIO

A

y

IRF1

vS0

HEAD

TAIL

IRF0 B A

From IRF0 the Head event is in delay as experienced in B frame tB=x0/(c+v), it is x0/c [1/(1+v/c)], the Doppler effect, and the TAIL event tA=x0/(c-v) is anticipated, seen, from B as x0/c [1/(1-v/c)]. The clock B should count the delay x0/c [1/(1+v/c)] and the anticipation of x0/c [1/(1-v/c)], in comparison to conditions at rest. 2 2 The total difference of the time of the events is x0/c ([1/(1-v/c)] - [1/(1+v/c)]) = x0/c [(1+v/c)-(1-v/c)] /(1-v /c ) = 2 2 2 2(x0/c)(v/c) γ hence 2 x0v/c γ is the actual difference of the event of absorption HEAD-TAIL. -1 2 In a relativistic Doppler, being x0/c ([1/(1-v/c)] - [1/(1+v/c)]) γ = 2 x0v/c γ 2

By considering just the head event, seen from the train and the embankment, the time γ x0v/c would actually be the offset of the clocks A and B in regards to the duration between the Emission event

and the Head event. The interpretation of the experiment according to SR, is based on assumption of being c the speed (of the one-way) of light in every reference frame, and what the observer In the train is supposed to see is that the beams shoot synchronously to HEAD and TAIL. ------------------------------------------------We now can remove the bottom of the wagon to notice that the IRF is just an artefact, descending from a “comfortable concept”. We have already seen that a pair of light waves reach the TAIL of the WAGON, at the same time, defining the Tail EVENT. The length of the moving wagon, measured from within the wagon with EM waves is x0, if this measurement is done with a radar it would take T=2 x0/c. IRF1

A

FINAL

v0 TAIL HEAD

IRF0

B A

Having opened the box, it is more evident that the speed of light, in a single path, measured from within IRF0, the privileged frame, is very likely to be different than the one measured from within the moving frame IRF1. The TAIL and HEAD events are not synchronous in either frames, in disagreement with SR. By emitting, normally to the direction of motion, two beams from same type of atoms (not in a gravitational field), the radiation will be seen blue-shifted from the top of the wagon, due to the transversal motion.In the platform the beam from the wagon is detected Redshifted according to the transversal Doppler effect. Detect Blueshift

IRF1

A

FINAL WITH TRANSVERSE EMISSION

v0

HEAD

TAIL B A

Detect Redshfit

IRF0

Same as found in the Yves and Stillwell experiment. This is enough to discriminate the asymmetrical behaviour of the two IRFs, differentiating clearly who is at rest and who is not. Basically a physical equivalence of the two system cannot be possible, the photons discriminate. While the Doppler Shift of the first order can counterbalance the gravitational redshift only at the first order like in the experiment of Pound and Rebka: 2

Where the frequency shift ratio of the gamma radiation is (1+gh/c ), also the first order approximation of a ratio of transversal doppler shift The transversal Doppler Shift can compensate the gravitational redshift at the first order but also at any 2 2 2 2 2 order: TB(t’’)/TA(t’) = √(1-vA /c )/√(1-vB /c ) with Φ = -v /2

takes the same form as √(1+2Φa/c2)/√(1+2Φb/c2),

so that it is possible to choose a certain speed of A, to cancel out the gravitational redshift. This cancellation of the effects on frequencies of gravitation, has been performed already in the Vessot and Levine experiment, where the kinetic time dilation cancelled the gravitational one. Let’s see the behaviour of SR in symmetrical motion such that the two parts see each other going at speed v, by measuring their reciprocal motion, but they are sliding one on the other, in a LAB. No frequency shift

IRF1

A

HEAD

TAIL B A

IRF0

No frequency shift

IRF2

In such case the systems IRF0, IRF1 are symmetric and the prediction of SR is the same as the nonsymmetric solution seen before. Such that the tail event and head event will occur at the same time in IRF1, but not in IRF0. The times of the clocks instead will not be in agreement if a radar connection is considered. The wave from the embankment produced by the fixed emitter (the lower one) will be frequency shifted -1 -1 according to the Doppler effect. HEAD: redshifted [1/(1+v/c)] γ , TAIL blueshifted [1/(1-v/c)] γ . The upper wave inside the WAGON will maintain the frequency of the emitter (as predicted by SR). Alice in the wagon will see the light striking at the same time into the walls with a radar measurement, and will not see it frequency shifted (as predicted by SR) 2

Electrodynamics in nature does not use the LT in the same way as SR does t’= γ (t-vx/c ), x’= γ (x-vt) same for both to pass from the static to the moving frame The tail event will be seen anticipated by T= x0/c [1/(1-v/c)], in the primary frame. In the moving frame (ALICE) will have c’=c/(1-v/c). In Alice’s T= x0/c’= x0/c [1/(1-v/c)], hence Alice sees the tail event at the same time, at the first order approximation. Hence Lorentz Transformations with a variable speed of light have to be applied, SR is its simplification in case of symmetrical behaviour or if used in a radar path. a) they are the same as the classical ones in a radar path. -1 b) The speed of light is referred to a privileged frame where it is c, c’=c/(1-v/c) γ 2

t= γ (t’-vx/c’ ), x= γ (x’-vt) where c’=c/(1-v/c) γ

-1

Extended Lorentz Transformations which maintain the simultaneity invariant.

.

z ώ

C d D

V v’ O x y

CONCLUSIONS: Experimental Electrodynamics and SR in radar measurements are the same. SR is the same as EE if we consider to see everything from the ARF (Mansuri and Sexl). SR is only a particular case of EE, when the symmetries are complied. There is no relativity of simultaneity in Electrodynamics but the simultaneity is absolute. A frequency shift of the radiation is present in the main IRF, not in within the moving IRF as in SR The prediction of AE in regards to simultaneity are aligned with the experience and a correct application of LT in a single path. SR fails to give a picture of a Physical reality under the assumption of the one-way speed of light as being a universal constant in any IRF