On 25.10.2016 01:43, Peter Riedt wrote:
> On Monday, October 24, 2016 at 8:45:43 PM UTC+8, Paul B. Andersen wrote:
>>
>> What I initially did find puzzling, though, was
>> why Huygens principle didn't give the same result
>> as aberration in the non-relativistic case.
>> I understand it now, though.
>> It is simply because:
>> In a frame which is moving in the ether to:
>> observe a beam from a mirror which is
>> stationary in the ether,
>> is different from:
>> In the ether frame to:
>> observe the beam from a mirror that
>> is moving in ether.
>>
>> The former is aberration, while Huygens principle
>> is the right approach for the latter.
>> So Michelson's calculation was indeed slightly off.
>> The difference is however much smaller than
>> the other approximations done in his calculations.
>>
>
> I note that you accept the existence of the aether
> but please enlighten us where 'stationary' mirrors
> or frames can be found in the universe.
Don't be ridiculous.
We are discussing the MMX which was designed to test
the rigid ether theory which Michelson and most
scientists of the 19. century thought had to be valid.
Now we all know that the MMX falsified this ether theory.
(In the following: "Michelson's Ether Theory")
Understand this:
When performing an experiment to test a theory,
one must:
1) Calculate what the theory predicts will be
measured when the experiment is performed.
2) Perform the experiment.
3) Compare the results of the experiment
with the predictions of the theory.
If the results of the experiment are in
accordance with the predictions of the theory
within the precision of the measurements,
then the theory is confirmed. (NOT proven!)
If the results of the experiment are different
from the predictions of the theory by more than
the precision of the measurements, then the theory
is falsified (proven wrong, not valid)
The discussion here was:
Did Michelson correctly calculate the predictions
of "Michelson's Ether Theory" in his 1887 paper?
https://paulba.no/paper/Michelson_1887.pdf
Specifically has the discussion been about
the pathlength of the beam along the transverse arm.
(Michelson had got this wrong in the paper for his
1881 experiment, where he simply assumed the pathlength
to be 2D where D is the length of the arm.)
In his 1887 paper he corrected this pathlength to be
2D sqrt(1+v^2/c^2) which means that the angle of
the beam from the beam splitter is arctan(c/v).
Since this is the same as non-relativistic aberration,
I have always considered this to be correct.
However, Prokaryotic Caspase Homolog made me aware
of the fact that the correct angle, calculated
according to Huygens principle is: 2 arctan(1-v/c)
The reason for this difference is:
> Paul: It is simply because:
> In a frame which is moving in the ether to:
> observe a beam from a mirror which is
> stationary in the ether,
> is different from:
> In the ether frame to:
> observe the beam from a mirror that
> is moving in ether.
So Michelson's calculation was slightly off.
The difference is however smaller than
the other approximations done in his calculations.
For v/c = 0.0001c, the orbital speed of the Earth we have:
arctan(c/v) = 89,99427014 degrees
2 arctan(1-v/c) = 89,99427042 degrees
The relative difference is less than 10^-8,
which is of the same order of magnitude as the other
approximations in his equations, where v^2/c^2 = 10^-8
is ignored compared to 1.
So the bottom line is:
Michelson's calculations of the prediction of his theory
are correct. (The error in the approximations are orders
of magnitude less than the error bars in the measurements.)
The MMX falsified "Michelson's Ether Theory".
--
Paul
https://paulba.no/