An analogous situation (where we can perhaps agree) involves selection of zero point on a temperature scale. As long as "temperature" is simply something read by a thermometer, preference for degrees C or F or K is indeed simply a matter of convention. However adopting a more general physical model identifying heat with kinetic energy makes it possible to discriminate between them. Rather than simply viewing the Minkowski metric as an arbitrary function, we can re-interpret it as magnitude in a Clifford algebra incorporating the Pin group --- effectively, enhanced spacetime symmetries. The sign is now no longer arbitrary, but corresponds to selecting one of two distinct algebras: the paper asserts that these ARE experimentally distinguishable! I'd be happy to continue this discussion, but brevity was requested; besides which I'm hijacking a thread ... Fred Lunnon On 7/29/15, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
I looked at the paper, and it is quite overwhelming. I'm saying the choice of metric is merely a convention since different authors use different choices. Any transformation that preserves one metric automatically preserves the other. So Fred, perhaps you can provide a brief explanation of what I fail to see.
-- Gene
From: Fred Lunnon <fred.lunnon@gmail.com> To: Eugene Salamin <gene_salamin@yahoo.com> Sent: Wednesday, July 29, 2015 10:04 AM Subject: Re: [math-fun] nuclide map
<< and not decidable by experimental observation >>
I have to say that such a snap judgement seems rather facile to me.
Just exactly what makes you so confident?
Have you looked at the paper?
WFL
On 7/29/15, Eugene Salamin <gene_salamin@yahoo.com> wrote:
The (-1,+1,+1,+1) vs. (+1,-1,-1,-1) choice is one of convenience, and not decidable by experimental observation. The former is convenient when one prefers a positive metric on spacelike surfaces. The latter is preferred to make E^2 - p^2 = +m^2 rather than -m^2.
-- Gene
From: Fred Lunnon <fred.lunnon@gmail.com> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Wednesday, July 29, 2015 9:10 AM Subject: Re: [math-fun] nuclide map
Somewhat off-topic I know, but observation of neutrinoless double beta decay would apparently decide a question which has long intrigued me: is there any fundamental physical procedure for discriminating between relativistic physicists' x^2 + y^2 + z^2 - t^2 and particle physicists' t^2 - x^2 - y^2 - z^2 ?
A long paper http://arxiv.org/abs/math-ph/0012006 much of which goes over my head --- and is further obscured by a crucial misprint on page 50, where "Pin(1,3)" should read "Pin(3,1)" --- claims that a positive result would support the former convention (much to my personal satisfaction).
Sadly, more recent experimental estimates of the lifetime have grown unfeasibly large --- see eg. http://arxiv.org/pdf/1402.1170.pdf passim ...
Fred Lunnon