Incomsistent results of MMX and the Earth's Totational Sagnac

[vuquta]

MMX And The Earth's Rotational Sagnac

 

MMX experiments are the cornerstone for proving the validity of special relativity. Tom Roberts specifies "The speed of light is said to be isotropic if it has the same value when measured in any/every direction." He then lists a large collection of MMX or round trip speed of light comparisons to prove the speed of light is isotropic or measured c in all directions. This is an alternative way of stating the light postulate of special relativity.

 

However, the earth's rotational sagnac does not show up in MMX experiments. GPS on the other hand validates this rotational sagnac, in particular, Robert A. Nelson and Todd A. Ely, in RELATIVISTIC TRANSFORMATIONS FOR TIME SYNCHRONIZATION AND DISSEMINATION IN THE SOLAR SYSTEM noted:

In the case of a receiver at rest on the Earth, an observer in the ECEF frame regards the receiver as stationary and applies the Sagnac correction. However, an observer in the ECI frame sees that the receiver has moved due to the Earths rotation during the signal time of flight and instead applies a propagation time correction due to the additional path length. The term Sagnac effect is part of the vocabulary of only the observer in the rotating reference frame. The corresponding correction applied by the inertial observer might be called a velocity correction. While the interpretation of the correction is different in the two frames, the numerical value is the same in either frame.

http://tycho.usno.navy.mil/ptti/ptti2006/paper28.pdf

 

This sagnac correction is also noted by Neil Ashby in

http://relativity.livingreviews.org/Articles/lrr-2003-1/

 

Since MMX proves light is measured c in all directions on the earth and the earth's rotational sagnac at that same location uses a velocity correction to the speed of light, then the two results are inconsistent with each other. Curiously, even though both results are inconsistent with each other, both are used to claim SR is experimentally validated .

 

Therefore, we should expect to find this velocity sagnac correction in MMX since the experiment is performed in the ECEF frame. The question is why not. Well, simple math explains this.

 

The timing of roundtrip light travel using the sagnac correction is at most t = d /(c+v) + d/(c-v) = 2dc/( c² - v²) if you happen to be lucky and measuring in or against the direction of rotation. Otherwise it is less. So for one arm of MMX, the round trip timing for light travel is 2dc/( c² - v²) for the arm in the direction of rotation and at the 90 degree arm the round trip light travel is timed at 2d/c.

 

For MMX to detect the difference between the two, the calculation is

2dc/( c² - v²) - 2d/c = 2d[ c/( c² - v²) - 1/c ].

 

So, in the lab we might have

d = 1 meter = 0.001km

c ≈ 300,000km/sec

v ≈ 1669.8 km/hr ≈ 0.46383 km/sec for the speed of the earth's rotation.

 

Then the timing differential is calculated.

∆t = 2d[ c/( c² - v²) - 1/c ] ∆t = 0.002 * [ 300000/(300000² - 0.46383²) - 1 / 300000 ] = 1.5936*10^-20 seconds.

 

No wonder MMX can't find the earth's rotational sagnac correction. This sensitivity requirements is well beyond anything available.

 

Therefore, even though MMX has been used for years to experimentally validate SR, the sagnac correction picked up and proven by GPS is missing in MMX. But as shown by the math above, the two way light travel differential in MMX is invisible to modern experimental devices.

 

Hence, the null results of MMX are not actually null but too small to detect. As such, MMX has been a false positive for SR.

 

 

 

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Edited September 22, 2010 by vuquta

[swansont]

c being constant in all frames refers to inertial frames while the Sagnac effect is due to an accelerating frame, so consistency isn't expected. No competent physicist expects to measure rotational Sagnac using a MM interferometer; the null result from that experiment was not an attempt to measure rotation.

[vuquta]

c being constant in all frames refers to inertial frames while the Sagnac effect is due to an accelerating frame, so consistency isn't expected. No competent physicist expects to measure rotational Sagnac using a MM interferometer; the null result from that experiment was not an attempt to measure rotation.

 

The MMX experiment is used to measure whether light is measured c in two different directions at one place on the earth.

If this is false, please specify.

 

If a handheld unit is at that same location, it does not measure c in all locations.

If this is false, please specify.