MMX > Expectations

Imagine a swimmer that swims to one point and back at a constant speed. In the chart below and even visualizing the numbers yourself using the above drawing you can see how the effect occurs. Additionally you can see how the effect decreases as the difference between the swimmer speed and the river flow grows. Finally you can see that length does not affect the relationship. The total time travelling (and path length by the swimmer's estimation) grows by a certain percentage based on the prior mentioned relationship.

One Direction path length	100669.06 (x2 = 201,338.12)
Light Speed (swimmer)	10,066.906
Ether wind (Flow)	1
Norm (no flow)	20
Actual travel time (Swimmer's Est.)	20.000000197350382813136543039538
Relation to Norm	1.0000000098675191406568271519769

 

trip1 -1 = 10.000993452551613337140243511116

trip2 +1 = 9.9990067447987694759962995284223

 

What does this all mean?

 

You can use the "relation to norm" to determine how much longer the path length and/or travel time should be in any MMX-like experiment if there was no such thing as entrainment. The above examples show how distance can scale so long as the relation between the swimmer and flow remain the same. 

 

First we need to examine the device used in the the original MMX  to determine what is meant by path length. If you read the dimensions of the device it is a 1.5m square. By looking at the drawing you can tell that it, at least partially, traverses corner to corner 16 times. If it was exactly corner to corner this would be almost 34 meters. We'll assume that Dr. Michelson has some ability with measurements and only meant that the one-way path was 11 meters but that the total optical path is actually 22 meters. This gives us 217.08 nm extra path length along the direction of the Aether wind. ("Relation to Norm" x Path Length)

 

 

Repeatedly through the publication of the MMX he mentions that they are using yellow light. (577-597 nm)However you'll also find it mentioned in the original publication that a single turn of a 100 thread per inch screw moved "nearly 1000 wavelengths" of what he called white light at that point in the paper.  This screw moved the mirror at the halfway point of the optical path so 1 turn would actually shorten the total path length .02 inch instead of the immediate thought of .01. This would indicate the light to be 508nm at 1000, or as much as 564nm at 900 wavelengths(which I think he would have said directly) So this is slightly vague. Thankfully he goes on to clarify further: 

"Considering the motion of the earth in its orbit only, this displacement should be 2Dx1.0e-8" (220 nm)Next he goes on to say that "The distance D was about 11 meters, or 2e+7 wavelengths of yellow light; hence the displacement to be expected was 0.4 fringe" This tells us with certainty that he believes his light to be 550nm which is actually green. However, the most important consideration that can tell us for certain what the real wavelength of the light being examined in his white light interferometer experiment was the fact that he used sodium light to line up the fringe system! Since the sodium doublet (special double fringes from sodium interferometry)resides at 589.0nm and 589.6nm and he calibrated his interferometer with sodium light, the darkest fringe was set for 589nm and this differs from his belief about the wavelength. (it's also yellow instead of green) This means that his expectation of .4, while close, is not quite right.

 

For those of you following Michelson's mathematical path that would mean that D is 11 meters / 589nm. (18675721.562 waves) resulting in an expectation of a 0.368566 fringe shift without aberration. (29.78^2 / 299,792.458^2) * 37351443.124 = 0.368566.

A Null Result

To actually qualify as a null reading it would have to be below 5% of the expected wind speed, so let's examine that now:

Earth's Orbital speed: 1.489 km/s

Light Speed: 299,792.458 km/s

201,338,118.2 to 1

 

One Direction path length	2,013,381,182.0 (x2 = 4,026,762,364)
Light Speed (swimmer)	201,338,118.2
Ether wind (Flow)	1
Norm (no flow)	20
Actual travel time (Swimmer's Est.)	20.000000000000000493375960986189
Relation to Norm	1.0000000000000000246687980493095

 

trip1 -1 = 10.00000004966769402172595661881

trip2 +1 = 9.9999999503323064716500043673796

 

In this case you have a grand total of 0.00000054271nm extra path length or a 9.214e-10 of a fringe shift. Only readings smaller than this can be considered truly null by typical standards.

 

 

 

 

The Variation of the Readings

 

Another expectation that is not discussed in the relativistic community is the way the readings would change as the interferometer was turned in a full circle if there was an ether wind. This is a very outstanding behavior because it is a half period effect. This means that a full iteration of some cyclical event happens in only one half turn of the device. The wind was expected to cause the readings to both instead peak and trough twice during one full rotation.

As you can see above, as both arms of the interferometer are at some variation of 45 degrees to the wind, both paths are affected equally, bringing the fringes back to the center. The expectation of this behavior is likely the single most important fact to understand when considering the implications of Michelson's and Miller's results. Both of them had this very distinct pattern even after averaging many many readings together. This cannot be mistaken for random error in readings or errors in the device. (But I suppose I've found that faith can always find a way to twist simple fact)