Re: An Analysis of the Resolution of the Michelson-Morley Experiment

From: Tom Roberts (tjroberts_at_lucent.com)
Date: 01/24/05 

Date: Mon, 24 Jan 2005 11:25:21 -0600

Error...

Tom Roberts wrote:
> [...]
> 2. Use the original author's statements to infer their resolution
> -----------------------------------------------------------------
> Michelson and Morley[4] state "The width of the fringes varied between
> 40 to 60 divisions, the mean value being near 50[...]". In keeping with
> the assumption that the measurement errors are normally distributed,
> I'll assume that this means that 95% of measurements of fringe widths
> were contained in the interval from 40 to 60 divisions of their
> micrometer. That means their resolution for measuring fringe width is 5
> divisions, or 0.1 fringe. As the measurement of a fringe width requires
> two measurements of the location of a fringe, their base resolution is
> sqrt(2) time this.
>
> So this approach yields an estimate of resolution of 0.14 fringe widths.

This value is a difference of two measurements, not an average, so to
get their base resolution one must divide by sqrt(2), not multiply.

So this approach yields an estimate of resolution of 0.07 fringe widths.

Note, however, that such measurements were surely carried out over a
period much shorter than 36 minutes, or even 6 minutes, so the
contribution of their systematic error is significantly less than for
their real measurements.

If I were forced to pick a single value for their resolution, I would
pick 0.11 fringe widths, the average of estimates 2 and 3 (the two
quantitative methods). But I would not quarrel with values between 0.10
and 0.15.

Carrying this lower value into the rest of the article will change the
numerical details, but not the basic conclusions:
  a. their resolution is still far larger than the variations in their
     data
  b. their data are insufficient to determine any value for "velocity
     relative to the ether" other than an upper bound (which depends
     on the theory, as discussed in the article)
  c. a zero-parameter flat line will still fit their data as well as
     that 10-parameter Fourier decomposition

Tom Roberts tjroberts@lucent.com

Relevant Pages

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