Re: does the fine structure constant change over time?
From: Thomas Dent (tdent_at_auth.gr)
Date: 07/14/04
- Next message: Carlos L: "Re: Pioneer 10 acceleration"
- Previous message: p.kinsler_at_imperial.ac.uk: "Re: Interaction of photon with electron"
- In reply to: Oz: "Re: does the fine structure constant change over time?"
- Next in thread: greywolf42: "Re: does the fine structure constant change over time?"
- Messages sorted by: [ date ] [ thread ]
Date: 14 Jul 2004 11:49:57 -0400
Oz <oz@farmeroz.port995.com> wrote
> >> Naively c is determined by u_o and e_o of the vacuum. (...)
> >
> >The numerical values of these constants are a matter of conventional
> >definition and have no physics content.
>
> I wasn't talking about their numerical values, but the value they have
> (in whatever units you might choose).
How can they have values that are not numerical? The numerical values
of u_0 and e_0 are simply a reflection of the choice of units for
length, time, electric charge etc. What other values can one talk
about?
> >They have these values as a result of historical accidents (...)
>
> c = 1/sqrt(e_0 u_0),
>
> so their values are of some interest, whatever units you choose.
Well, if you somehow define units which do not depend on the speed of
light then it is possible to measure (at least some combinations of)
e_0 and u_0 and c, which is indeed what Maxwell pointed out. However,
I can choose units such that c = 1 and e_0 = 1/4 pi and u_0 = 4 pi, or
even e_0 = 1 and u_0 = 1, and I don't think these values are very
interesting.
> >> (...) Now I presume that the current
> >> assumption is that Em doesn't couple at all with dark energy, but what
> >> if it did, just a teeny bit? I would imagine that any coupling would
> >> slow a photon (from infinite speed)
> >
> >Photons don't travel at infinite speed.
>
> Precisely. But why should they travel at c?
Because the local structure of spacetime is (so far as we know)
described by the Lorentz group, for which c is the invariant speed,
and massless particles in such a spacetime automatically travel at c.
You simply impose that particles should be in a representation of the
Lorentz group. Conversely, if they travel at some speed other than c,
their mass^2 is different from zero.
Even if there were no dark energy at all, you could still have a
locally Lorentz invariant spacetime in which massless particles travel
at c (and not at infinite speed, which would require the Galilean
invariance).
> One possibility is that the
> vacuum is behaving as a medium, with some interaction which affects c,
> because it is filled with (quite a lot of) dark energy.
I don't know where the idea comes from that there is "quite a lot of"
dark energy. The energy density of dark matter is of the order of 1
hydrogen atom per cubic metre (the critical density). Plus, I don't
know what is meant by c being "affected". You can if you like think of
spacetime itself as a "medium" in which light propagates. Because of
the local Lorentz symmetry of the "medium", light (being massless)
goes at c.
> >Plus, one can couple
> >electromagnetism to 'dark energy' (in the form of a scalar field) in a
> >Lorentz-invariant way that also respects gauge invariance, so that
> >both c and the speed of photons are unaffected.
>
> Very probably, but is that the only way to couple it?
Well, of course not, you can write down all sorts of nasty-looking
terms which violate any symmetry you like. You will find out that most
of these are ruled out by experiment, I think. Even if some of them
survive, why do something complicated like explicitly breaking Lorentz
symmetry or gauge symmetry when there is no experimental reason for
it?
> > you can *always* define units such that c=1, or
> > c=300,000, or any number you like, at all points in spacetime.
>
> I am well aware of that.
Then take account of it!
> >The horizon problem can be stated in terms of dimensionless numbers,
> >namely, the size of the particle horizon at decoupling relative to the
> >size of the currently observable Universe.
>
> That is surely model-dependent. A model that had c very much larger than
> it is today then the horizon problem would vanish.
Your second sentence is contradicted by your first sentence. "Varying
c" on its own does not solve anything. It *completely* depends on on
what else happens in the model, which you have not specified. What
happens to particle masses, energy density, etc. etc.? You need to say
that c changes *relative to some other speed*. I can redefine units
right now so that the speed of light becomes 10,000 times smaller:
I set c = 0.0001. There! I did it!
Now, have any cosmological problems been solved? Of course not.
So you need to show explicitly that whatever you propose cannot be
absorbed by a redefinition of units. This is what "varying c" people
have not (to my knowledge) done.
- Next message: Carlos L: "Re: Pioneer 10 acceleration"
- Previous message: p.kinsler_at_imperial.ac.uk: "Re: Interaction of photon with electron"
- In reply to: Oz: "Re: does the fine structure constant change over time?"
- Next in thread: greywolf42: "Re: does the fine structure constant change over time?"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
