Re: does the fine structure constant change over time?
From: Thomas Dent (tdent_at_auth.gr)
Date: 07/22/04
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Date: 22 Jul 2004 13:07:46 -0400
serenuszeitblomphd@yahoo.com (Serenus Zeitblom) wrote
> carlip@no-physics-spam.ucdavis.edu wrote in message
> > Maybe a little more...if some set of dimensionless quantities were found
> > to all change in concert, it might be helpful to define conventions in a
> > way that let us describe the changes as a single change of a dimensionful
> > quantity. For example, if we found that alpha ``varied inversely with c''
> > *and* that rest energies of elementary particles all ``varied as c^2''
> > *and* that the dimensionless quantity Gm^2/hc (where m is, say, the electron
> > mass) ``varied inversely with c,'' then the abbreviation ``c is changing''
> > would be genuinely useful, as a mnemonic if nothing else.
>
The likelihood that any fundamental theory would give such a neat set
of exact power laws is probably extremely close to zero. And when you
don't know the fundamental theory, you can't make assumptions about
how it might behave when considering observables. The most general
behaviour cannot be summarized as "varying c". For example, if nuclear
binding energy changes relative to the electron mass. You can write
nuclear energy as E, or as m_N c^2 where N is the nucleus. So how does
it "vary"? If you write the electron mass as m_e c^2, you cannot carry
on if m_N c^2 changes relative to m_e c^2. And suppose the muon mass
changes with respect to the electron mass. "Varying c" is really a
very restrictive formulation, in addition to being ambiguous, since it
cannot accommodate any variation in ratios of two quantities of the
same dimension.
> At present the speed of light is N times the maximum speed of
> my trusty old car.
> One day I get up in the morning and find that this
> dimensionless ratio has halved. I declare that the speed
> of light has halved. According to the real die-hards, who claim that
> it is *meaningless* to speak of a varying speed of light,
> this scenario is *impossible*,
No. The ratio of your car's speed to that of light can meaningfully
vary; you can declare anything you like to declare; nothing in the
scenario is "impossible", according to anyone, die-hard or -soft. If
you want to say things that make no sense, no-one can stop you.
> indeed unthinkable.
It is perfectly thinkable that the ratio of your car's speed to that
of light will change, and also that you will make some curious and
nonsensical statement about it, in a situation where a normal person
would visit the garage.
> I assume that by this they mean
Your argument becomes (more) confused here. Not content with putting
words in other people's mouths, you are not clear about what words you
are talking about. What is "this"?
> that "changing" the speed
> of light will produce changes in the fuel in my car and its
> structure, in just precisely the right way that the two effects
> cancel. That is, halving the speed of light halves
> the speed of my car.
I have no idea what this paragraph means. If the speed of your car
changes relative to c, there is no question of "cancellation", since
there is a real physical effect. (Such an effect may well be easily
explicable by some variation in the structure or fuel of the car, such
as the failure of half of the spark-plugs, but this can always be
expressed in terms of dimensionless variables.)
> This may be true. My question is: how do they
> *know* that it is true? Could it be that we simply *don't know*
> whether a "changing" speed of light makes sense?
By simple application of logic and the well-known freedom to transform
the system of units into one where c is constant.
Now, knowledge is justified true belief, so if you don't believe that
"varying c" is (on its own) a scientifically meaningless formulation,
you don't know it. But I do!
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