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Re: GR prediction for precession of perihelion of Mercury is not
quite right
Posted:
Jun 26, 2010 12:25 PM
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Koobee Wublee wrote:
> On Jun 25, 8:58 pm, Tom Roberts wrote:
>> Before one knows whether or not this is significant, one must compare the
>> discrepancy to the errorbars. The above-referenced article does not do that, and
>> does not include the errorbars.
>>
>> So you must look up the errorbars in the literature before you can determine
>> whether this is important or not.
>
> Not the errorbars again.
Yes, OF COURSE "the errorbars again [sic]". Comparison between theory and
experiment (measurement) ALWAYS requires errorbars.
> What is the errorbar of the one due to other
> solar bodies? They seem to be very big, no?
I do not know, and neither does the author of the post to which I responded, or
the author of the referenced article. THAT IS THE PROBLEM. Yes, I suspect there
are contributions to the errorbars on the measurement that are comparable to the
discrepancy. If, for instance, the errorbar turns out to be 3 arcsec/century,
then the claim "the discrepancy is larger than the observational error" is
correct, yet the discrepancy is not SIGNIFICANT, and thus is not important.
For those of you who don't understand errorbars, let me explain. When making a
measurement, there is ALWAYS some experimental error [#]. So we model the
measurement process as yielding a distribution of values, with the actual value
as the mean of the distribution, and the sigma of the distribution being the
errorbar. It is observed that most measurement processes yield values that are
approximately Gaussian distributed, so this is usually a good model. The best
way to determine the errorbar is to measure it by taking multiple measurements
and determining mean and sigma from the different measurements. With that in
mind, only ~68% of the measurements will yield a value within one errorbar
(sigma) of the actual value, and ~5% of the time the value will exceed twice the
errorbar from the actual value. Assuming one has confidence in the value of the
errorbar, physicists generally consider a discrepancy of 2 sigma or less to be
not significant, a discrepancy between 3 and 4 sigma as inconclusive but
provocative, and a discrepancy of 5 sigma or more as pretty definitive.
[#] Error in the sense of discrepancy from the actual value,
not in the sense of "mistake". This is standard usage.
That said, I would not consider this discrepancy of 3.54 arcsec/century to be a
problem unless the errorbar on the measurement is smaller than about 0.7
arcsec/century. If it's less than about 1.2 arcsec/century then it's probably
worth revisiting.
[Astronomers know this, and the fact that they are not revisiting
this makes me infer that it is not a problem. But new techniques
can often reduce the errorbar, and that can make it worth re-doing.]
Tom Roberts
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