# Invariant fine structure

1. Jan 18, 2004

### wolram

http://arxiv.org/PS_cache/astro-ph/pdf/0401/0401094.pdf [Broken]

a 24 page paper on the "FINE STRUCTURE", concludes
that it is invariant over cosmological time scales.

Last edited by a moderator: May 1, 2017
2. Jan 18, 2004

### marcus

delighted by this paper
thanks for posting the link and calling it to our attention

they inspected MagnesiumII and IronII absorption lines
(in the UV, around 2300 angstrom for Iron and 2700 angstrom for Magnesium) in light from distant quasars

and got narrow bounds on the annual fractional variation in
alpha

the drift in alpha is not more than 2E-16 per year either way
roughly speaking not more than 0.2E-15----a fifth of a part per quadrillion, per year

so in a billion years, the fractional change is no more than
a fifth of one part per million

it could be no change at all, it is just that their data narrows it down to that much or less, of change.
-----------------------

to the extent that we like living in a simple clear understandable universe this is reassuring news
alpha is a key constant known out to 10 digit accuracy or so
and it is much nicer to have it steady than to have it drift

(we humans may never understand the U, may destroy ourselves and planet first, but we have a better CHANCE to understand it if
central proportions like alpha are steady rather than drifting)

-----------

thanks again for noticing this reassuring and encouraging article, I would like to reciprocate by saying quickly what alpha is (I have to go out to an appt. shortly so must be brief)

One mile is within half a percent of being E38 planck lengths
that is 1038 natural length units

Suppose you have a pair of electron a mile apart in otherwise empty space. the force of repulsion between them is
1/137.036.... natural force units divided by the square of the distance

the force falls off with the sq. of the separtation so you have to divide by the sq. which is E76 or 1076,
the square, you see, of 1038.

So the force between the two is 1/137.036... divided by 1076 natural force units.

------footnote---
There is a natural force unit called planck force which if you want to calculate it is c4/G and which they were discussing a month or two ago on SPR whether it was the largest force that you could have in the universe or not. It goes with the rest of the set of units (analogous to how newton force goes with kilogram and meter and second)
------------------

Anyway 1/137.036....is an indicator of how strong or weak the
electrical attraction/repulsion between natural units of charge is.

Plenty of other ways to describe it, "coupling constant"...etc. etc., more abstract descriptions. this more concrete simply a statement of how strong the force is (expressed in natures units)

damn good thing they found it was steady

Last edited by a moderator: May 1, 2017
3. Jan 19, 2004

### wolram

i may be dim but im not sure i understand how the
fine structure is constant in an expanding
universe, can someone explain ?

thanks for alpha marcus.

Last edited: Jan 19, 2004
4. Jan 19, 2004

### Nereid

Staff Emeritus
This is SUCH good news!

Bahcall et al did some work on variation of $$\alpha$$ over cosmological time, based on the forbidden O III lines (IIRC). Their conclusion was in contrast with a wide-ranging set of papers, based on the many-multiplet method (which found a small signal for a time-variant $$\alpha$$).

Now a much more powerful many-multiplet study has been done, showing agreement with Bahcall et al.

Hooray!

BTW, am not sure why this thread is in "Special & General Relativity"; it's got deep significance for General Physics, and for Cosmology.

5. Jan 20, 2004

Staff Emeritus
I suppose it's here because a varying $$\alpha$$ would possibly result in a varying c, and that's key to relativity (over cosmological time).

6. Jan 20, 2004

### Nereid

Staff Emeritus
Good point; it should be in both!

7. Jan 20, 2004

### wolram

fine structure constant
http://whatis.techtarget.com/definition/0,,sid9_gci866284,00.html

The fine structure constant measures the strength of the electromagnetic force that controls how charged elementary particles (such as electrons and photons) interact. Because the constant is nearly equal to 1/137, and because it is a dimensionless constant, some scientists have been led to wonder whether it has mathematical significance of its own, such as pi, the ratio of a circle's circumference to its diameter.
The fine structure constant can be derived from other constants as follows:

Eo = e2 (2ohc)-1

where e is the elementary charge Eo is the permittivity of free space, h is Planck's constant, and c is the speed of light. The constant is also equal to the ratio of the velocity v1 of the electron in the hydrogen atom to c, the speed of light.
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so if alpha is constant, Eo,c,and h, must be constant, c and h
can be assumed to be constants but, space is expanding so how
can Eo be constant?

Last edited: Jan 20, 2004
8. Jan 21, 2004

### marcus

$$\alpha = e^2 (2 \epsilon_0 hc)^{-1}$$

I think that is probably what they wrote, or meant to write, at the "what is" site. But I couldnt get the "what is" symbols to all appear on my screen so I went on to NIST.

"epsilon-sub-naught" the "permittivity of free space".

It doesnt affect it. All these constants like h and c and "epsilon-sub-naught" are defined in terms of metric units like meter kilogram and second and they go on the same regardless of the distances increasing between galaxies.

the distances increasing between galaxies does not change the length of the meter or the duration of the second. so it does not affect those constants as far as anyone knows.

For example, when two galaxies get further apart, so there is more meters between them, this does not change the speed of light!
Why should it?
It only means that it takes more time (more seconds) for light to travel between the two galaxies.
Nor does it change h, nor does it change the force between two electrons placed one meter apart (which is basically what epsilon-naught is about)

Last edited: Jan 21, 2004
9. Jan 21, 2004

### marcus

Wolram you should try using the [ tex] and [ /tex]
symbols

If you write A_B
and put the "tex" and "/tex"
around it it will come out A-sub-B

this, with the unnecessary spaces removed
[ tex]A_B[ /tex]

gives this
$$A_B$$

and if you write \alpha
with those symbols around it
it will come out looking like a real alpha

10. Jan 21, 2004

### wolram

thankyou MARCUS

It doesnt affect it. All these constants like h and c and "epsilon-sub-naught" are defined in terms of metric units like meter kilogram and second and they go on the same regardless of the distances increasing between galaxies.
-------------------------------------------------------------------
i guess my problem is understanding the expantion of space,
if i use the rubber sheet analogy "a poor one i know", then
any properties it has must be dilluted as it stretches,
somthing akin to enlarging the physical dimensions of a
capacitor as the capacitor "grows" the electrical properties
change.
on the other hand if its not true that space is "stretching",
then maybe it could be said to be "unfolding", but that would
be akin to slowly unwrapping the layers of the capacitor
with a resultant change in electrical properties.
or is it that as space expands something gives the "new",
space ,"fills vacuum", with its electrical properties
at the expence of some other body.
thanks for the tips MARCUS, but as you may have guessed
i have a slight difficulty, its taken me 30mins to right this.

11. Jan 21, 2004

### marcus

there is a shakespearean echo here.
in As You Like It, the clown Touchstone referred to
his lady-friend as "a poor thing, but mine own"

the echos in our common culture, sometimes conscious sometimes not,
are....well they surprise me sometimes. this clown is actually extremely sharp and funny

12. Jan 21, 2004

### marcus

Holy Moses! I have never once thought you were overcoming any obstacles or handicaps at the keyboard, in all the time that I have been reading your posts.

this may mean that I am very insensitive or inattentive or something.

you come across as fully capable and all there

it is horrible to think of you having some difficulty that
makes it take 30 minutes to write a post!

13. Jan 21, 2004

### marcus

in spite of the name,
the "permittivity of free space" is not diluted as space expands

people have objected to the name for years, because they find it
misleading, but the international bodies in charge of naming the constants have never gotten to the point of reforming the terminology.

in some older CGS systems of units there is no constant of that sort

I think the way to approach this is to think of Coulomb's constant k which tells the force between two charges Q and Q' at a given separation R.

k is an alias for
$$\frac{1}{4\pi\epsilon_0}$$

So the force between two charges can be calculated either as

$$k \frac{Q Q'}{R^2}$$

or as
$$\frac{1}{4\pi\epsilon_0}* \frac{Q Q'}{R^2}$$

It is actually less work to calculate it simply using k, the Coulomb constant.

If k doesnt change then epsilon-naught cant change, because one is just equal to the other in some fool algegraic disguise.

And k is just the force between two unit charges which are placed one unit apart. Expanding space doesnt change the units.

You put two charges a meter apart and you come back a billion years later and see they have crept slightly farther apart. So you say "hmmm this is not longer a unit distance apart"
So you reposition them exactly a meter apart and then, presto, the force is the same as before.
So k has not changed and epsilon-naught hasnt either.

You could say epsilon-naught is just an alias for
$$\frac{1}{4\pi k}$$
(same thing algebraically)

Coulomb constant k is cut-and-dried statement about force at unit distance. Not a distributed property of space that would be diluted or concentrated or anything. It tells about the strength of electric interaction.

"permittivity" tends to mystify people
it is not a substance that can thin out
it is just an algebraic flip of the Coulomb constant
measuring the strength of electric interaction

14. Jan 22, 2004

### wolram

now i understand, i guess in nature theres no blemish but
the mind, and i would give my kingdom for a keyboard
with keys that would stay put.
oh and by the by i have discovered that having a low
brow does not limit inteligence it just effects
facial features
best to you.