# Varying Fine Structure Constant and Vacuum Energy Density

1. Apr 16, 2012

### asimov42

Hi all,

I have a bit of a variation of a question I asked some time ago.

Webb et al. continue to publish results which suggest that the fine structure constant may vary over space and time. I realize the results are controversial - what I'm wondering:

If the fine structure constant were shown to vary, would this imply a difference in the vacuum energy density at different points in spacetime? (since, e.g., the value of c could change) I guess I'm wondering if you would use a different Feynman diagram for e.g. an electron moving through the vacuum at one point in spacetime (where alpha has one value) as compared with another point (where alpha has a different value)?

Or does the vacuum energy density have to remain constant across spacetime?

Apologies if this question isn't very clear - still learning :). Thanks all!

2. Apr 17, 2012

### Chronos

Studies of distant quasars suggest the fine structure constant has been remarkably 'constant' for billions of years. The fine structure constant is not 'fundamental'. It is a ratio between the elementary charge constant [e], speed of light [c], and Heisenbergs constant [h]. For it to vary as Webb, etal, suggests demands a temporal / directional variance in one or more of these fundamental constants. Note that no mention is made of vacuum energy density as a variable.

3. Apr 17, 2012

### rbj

Chronos, maybe it's a semantic issue and i defer fully to your expertise about all things astronomical, but i think i have to disagree with you that The fine structure constant is not 'fundamental' and what it seems to imply that $c$, $\hbar$, $e$, or even $G$ or $\epsilon_0$ are the "fundamental" constants.

it is the other way around. it's the dimensionless constants of nature that are fundamental and the dimensionful constants are really a reflection of the units one uses to express them. and Nature doesn't give a rat's @ss what units we choose to use.

more specifically, the 26 constants cited by Baez at http://math.ucr.edu/home/baez/constants.html are the Fundamental constants and $\alpha$ is one of them. it is true that (using a more explicit relation) that the fine-structure constant is

$$\alpha \ = \ \frac{e^2}{4 \pi \epsilon_0 \hbar c}$$

but if $\alpha$ has been shown to change, we really don't know (and it really does not matter) which of the constituent factors have changed. which one has apparently changed only depends on the units used to express the things of nature.

i happen to be partial to Planck units, so then a change in $\alpha$ would imply a change in $e$. but it really doesn't matter. as pointed out by Michael Duff in http://arxiv.org/abs/hep-th/0208093 and in http://xxx.lanl.gov/abs/physics/0110060 , it makes no operational difference. ultimately, the only quantities that we measure in physical experiments or in our perception of reality are dimensionless numbers. we continue to experience reality, we continue to measure the same results in our experiments, independently of the unit system we choose.

4. Apr 17, 2012

### asimov42

Thanks Chronos!

Do changes in any of the fundamental constants have implications for changes in measured energy? For example, if c were found to be changing, what are the implications for E = mc^2? Would, e.g., an electron at position (a) where c = c_1 have a different rest energy (value for E) than at position (b) where c = c_2?

I was wondering specifically about the vacuum energy density as I would think that changing c or h would change the energy density - unless some type of 'correction' were applied? Or would the vacuum energy density be completely independent? I'm not sure how variable-alpha / variable-speed-of-light theories deal with this?

5. Apr 17, 2012

### rbj

6. Apr 17, 2012

### asimov42

Thanks rbj.

Sorry, I'm still not quite clear - if there's a changing alpha value (different in different parts of the universe), and therefore varying strength of electromagnetic interaction, shouldn't this affect how we calculate (potential / kinetic) energy of charged particles in different regions of spacetime?

7. Apr 17, 2012

### rbj

no you're pretty clear.

and i expect that a changing $\alpha$ would show up as an observable and operational change of physical quantity. i.e. we would know the difference.

an increase of $\alpha$ would make charged particles appear to have increased attraction to each other. and it's purely because $\alpha$ has increased, but it could be interpreted as an increase in $e$ which means all charged bodies have increased their charge while their mass and size have not changed. or it could be interpreted as a decrease in $c$ or $\hbar$ (with the other four constants held constant). it could even be viewed as a decrease in $\epsilon_0$ which is the reciprocal of the Coulomb constant.

what i am taking issue with is that a change $\alpha$ must mean a change in $c$ or any other constituent factor. it could be any of them and the operational result (how we perceive reality to have changed) would be no different, independent of which is assumed to have been changed.

8. Apr 17, 2012

### asimov42

Thanks again Chronos.

So are quantities, specifically the vacuum energy density, completely independent of the value of the fine structure constant? I would think that changing the strength of the electromagnetic interaction would have an effect on, e.g., the electron field, etc., but I'm not sure what that effect would be (if any).

Maybe a better, more general question is whether the vacuum energy density must be constant across the universe?

9. Apr 18, 2012

### rbj

everything that i read says it's related directly to the cosmological constant $\Lambda$. i wonder if it would be true that a variance of $\alpha$ means a variance $\Lambda$?

unless the vacuum is different across the universe. i know that, besides a little more density (maybe a stray atom per meter2, there is more EM energy density in the space between stars than there is in the space between galaxies. maybe that affects the vacuum energy density and the apparent comological constant. i dunno.