## An experiment to demonstrate the first order anisotropy of the propagation of electromagnetic (EM) waves in interplanetary space

I propose the following experiment to unambiguously and irrefutably demonstrate the first order anisotropy of the propagation of electromagnetic (EM) waves in interplanetary space to decisively disprove Einstein’s Relativity paradigm.

It will demonstrate that the one-way propagation time of an EM signal between two nearby spacecraft orbiting the Sun is different for a signal sent from spacecraft A to B compared to a signal sent from B to A at the same time.

Two spacecraft (called A and B) containing atomic clocks are launched into an interplanetary orbit of the Sun. They are initially joined. They can send microwave signals to each other with embedded timestamps similar to GPS satellites.

After they’ve achieved Solar orbit, their clocks are synchronized and they are then slowly separated. For example: speed of separation: v = 0.03 km/sec; duration: t = 10000 seconds; final distance apart: D0 = 300 km. (note that all distances here are in km.)

They are each controlled so that their orientation is fixed in space with respect to the International Celestial Reference Frame 2 (ICRF2) and an arrow pointing from B to A, points to a fixed location in space – let’s say the direction of the vernal equinox for 2018 (00 right ascension, 00 declination).

They therefore belong to a common non-rotating inertial reference frame (called K) that also has a fixed orientation with respect to the ICRF2. It is as valid to consider K to be a non-rotating inertial reference frame as the Earth Centered Inertial Reference Frame (the ECI).

Definitions:

Electromagnetic (EM) waves include light.

U is the orbital speed of both spacecraft, ~30 km/sec.

θ is the angle between a line connecting A and B and the tangent to the orbit with the origin at A.

D0 = distance between A and B (in km) = 300 km

D = distance a signal actually travels from the instant of emission to the instant of reception: D = D0 + ΔD

τ = amount of time for an EM wave to propagate a distance D km at c km/s = D/c

τ0= amount of time for an EM wave to propagate D_{0 }km = D0/c

τAB = amount of time for an EM wave to propagate from A to B

τBA = amount of time for an EM wave to propagate from B to A

Each spacecraft is programmed to send signals to the other at, let’s say, once a second. The signal contains the reading of its clock at the instant of emission.(the Signal Emission Time or SET). The receiving spacecraft records the SET and the reading of its own clock at the instant of reception. The difference between the two times is the signal propagation time: τAB or τBA.

To use the Einstein method of clock synchronization see the following quote from “On the Electrodynamics of Moving Bodies” near the end of §4 (note that K is an inertial reference frame):

“*If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at* *B by **tv*^{2}*/2c*^{2} *(up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.*”

**According to Einstein’s Relativity:**

From the above, clock B is out of sync with clock A by ~5(10^{-11}) (50 picoseconds behind).

The round trip two-way signal propagation time is 2τ_{0} = τ_{AB} + τ_{BA} = 2D0 / c ~= 600 / 3(105) = 0.002 sec to second order in 1/c.

The one-way signal propagation time for A sending to B is the same as B sending to A: τ_{AB} = τ_{BA} = τ_{0 }= D0 / c ~= 0.001 seconds. And │τ_{AB} – τ_{BA} │ = 0. This is because both spacecraft are at rest in K.

**According to the classical paradigm for wave propagation in a medium:**

The round-trip two-way signal propagation time is the same as for Einstein’s Relativity = 2D_{0 }/ c to first order in 1/c (but not to second order).

The one-way signal propagation time is different for A sending to B vs B sending to A (contradicting Einstein’s Relativity): │τ_{AB} – τ_{BA} │ = 2UD0 cos θ /c^{2}

For this example the maximum difference is when θ = 0 or 180^{0}^{ }: │τ_{AB}– τ_{BA} │ ~= 2 * 30 * 300 / 9(1010) = 2 (10^{–}^{7}) sec = 200 nanoseconds (to first order in 1/c).

This is based on the following:

Time and space ate Newtonian: time is absolute (no time dilation) and space is Euclidean (no length contraction).

EM waves propagate as other types of waves propagate in a medium such as sound. This implies:

There is a unique inertial reference frame for which the medium is at rest. All locations and motions of sources and receivers for EM wave propagation are with respect to (wrt) the unique inertial reference system. For EM wave propagation in interplanetary space, it is the Sun Centered Inertial frame (SCI) (also known as the Heliocentric inertial reference frame). As an aside: for EM wave propagation in the vicinity of the Earth, it is the Earth Centered Inertial frame (the ECI). And the influence of the ECI extends out to where the SCI becomes dominant – about 10^{6} km.

EM waves propagate in the medium at a speed (wrt the unique inertial reference frame) that is characteristic of the medium.

EM waves obey the classical rules for wave propagation for moving sources and receivers in a medium. Therefore the actual propagation distance of an EM signal is the distance between the location of the source at the instant of signal emission (the SET) and the location of a receiver at the instant of signal reception (both wrt the SCI for interplanetary).

The velocity of the source wrt the SCI has no effect on the propagation (this is the same as the second postulate of SR).

However the velocity and acceleration of the receiver wrt the SCI does matter – in contradiction to Special Relativity (SR). This is because the location of the receiver wrt the SCI can change during the period the EM wave is propagating to what the receiver’s location was at SET. Therefore the actual propagation distance is the distance between source and receiver at SET (D_{0}) plus or minus any change in distance due to the velocity (and to second order, the acceleration) of the receiver up to the instant of reception. = D0 + ΔD. And therefore the actual transmission time is τ = (D0 + ΔD) / c.

ΔD = D0 v cos θ / c to first order 1/c; v is the velocity of the receiver wrt the SCI.

Therefore:

τ = D / c = D0 (1 + v cosθ / c) / c

Note that precise distance between the spacecraft is not needed because the measurement is based on the difference in propagation times.

This is the classical interpretation of the linear one-way Sagnac effect – no rotation or acceleration is involved.

The linear one-way Sagnac effect is a simple intuitive consequence of classical wave propagation in a medium. It is true for sound waves and EM waves.

A positive result would demonstrate the existence of the linear one-way Sagnac effect in interplanetary space and decisively disprove Einstein’s Relativity.

The problem for Special Relativity and the Lorentz transformation is that they were conceived to interpret a second order phenomenon (the Michelson-Morley experiment for example) so that they can’t account for the linear one-way Sagnac effect which is a first order phenomena.

Even if the Lorentz transformation were applied to this experiment, its calculated effect would be negligible compared to the magnitude of the predicted Sagnac effect.

And since this experiment takes place in an unambiguous non-rotating inertial reference frame, arguments about clock synchronization aren’t relevant. Also, arguments that the reference frame formed by the two spacecraft is not inertial because it rotates or accelerates aren’t relevant.

What result would you predict?