# Why is the fine structure constant what it is?

1. Jun 11, 2013

### wotanub

This question occurred to me while working through some textbooks. Since it is dimensionless, its value can't be explained away saying it's because of the way we chose the units.

Well it turns out I'm a 100 years late to this game. I found it's even more serious than I had realized. (And it isn't really a constant?)

Obviously, no one knows that answer to this question, but since it is such an outstanding question, what serious attempts are being made to answer it?

Is there even a way to test it? All Google gives me is these "pop-sciency" quotes and anecdotes about how "amazing" and "mysterious" it is, often ending with an account of a scientist to [incorrectly] predict it's value based on dubious theoretical reasoning.

Who works on this question and how? Do you think we'll know the answer one day? It seems to me that it might be insurmountable, but I'm sure there was a time when someone asked "Why is the sky blue?" and the best answer was "Because it is, and if it weren't then it wouldn't be."

2. Jun 11, 2013

### DennisN

Hi wotanub, have a look at

The fine-structure constant is related to other constants (e.g elementary charge, Planck's constant and the speed of light in vacuum). So asking why it is what it is, is almost like asking why e.g. the elementary charge is what it is. The only answer I can provide is that measurements tells us the value of it. But I know that answer is not quite satisfactory, of course .

Furthermore, it's not the only "mystical" dimensionless constant; there's also the proton-to-electron mass ratio. Here's a recent study of it (from Max-Planck-Institut, Bonn):

* Quite fun title, btw.

3. Jun 11, 2013

### wotanub

Hey thanks for the reply. I had already read the Wikipedia articles and noticed it didn't really "explain" this value of ≈1/137. Those other articles raise similar questions I think. Very interesting.

I think asking why the fine structure constant is 1/137 is different than asking why the speed of light of Planck's constants have the values they do, simply because it's unit-ess. The subtlety is revealed by this line of thinking:

The speed of light is ≈3.0E8 m/s because we defined a meter a certain way and the second a certain way. We can easily change what the "value" is by choosing different units (186000 mi/h). So an alien that has never heard of us could say Planck's constant is 6.45E27 wilgglesworths*pishpops instead of 6.626E-34 J-s because they don't define units like we do. If they're really smart, they could be using "god units" and say c = 1 (velocity units) and every other speed is just some fraction of the fundamental speed.

But this is not so for a dimensionless constant. There is no way to scale it. If we got some alien physics paper and translated it, we should see that their fine structure constant is the same as ours (Maybe they don't use base 10, but it'd be the same number if we convert the base.) because its value is independent of the how you define units.

So it seems the fine structure and other dimensionless constants are the most fundamental entities. Why are they these "weird" numbers? Or maybe they are not actually weird at all and its just some underlying principle that we're missing?

Upon reflection I suppose this question might be the same as "why is pi equal to what it is" (alien pi should be the same as earth pi) or "why does 2 = 2?"

Last edited: Jun 11, 2013
4. Jun 11, 2013

### DennisN

I agree.

Good questions. Furthermore, I just remembered this text, which might interest you:

How Many Fundamental Constants Are There? (John Baez), quote:

Note: the text is from 2011, so it does not reflect the new Higgs detections at CERN.

Yes, I think they are sort of similar questions. But the fine-structure constant question is a better physics question, IMO , since there's a difference between physical constants and mathematical constants.

5. Jun 11, 2013

### cgk

I don't agree that the fine structure constant is more fundamental other constants just because it does not have a unit. Note that while the /numerical value/ we assign to the dimensional constants is arbitrary (and can be chosen to be 1), the actual /constants/ are not affected by that. There most certainly is a speed of light, it is a speed, it is universal. And no matter how you chose your system of measurement, the speed of light is something different than the elementary charge or the electron mass, even if you decide to work in a system of units in which all three of those are chosen as 1.

6. Jun 12, 2013

### Avodyne

The fine structure constant is one of 19 dimensionless parameters in the Standard Model of elementary particles. The Standard Model does not fix the values of any of its parameters. Certain "beyond the Standard Model" theories, such as "grand unified" theories, give relations among some of the parameters of the Standard Model (but also introduce others).

7. Jun 12, 2013

### DennisN

That is a good point, indeed.

8. Jun 12, 2013

### wotanub

Yes this is my thinking, only expanded by more knowledge.

I haven't given thought as to what I mean by "more fundamental." We all agree that there is something different about the dimensionless quantities compared to the ones with dimension. Yes, the speed of light is has a definite value regardless of how we choose to represent it, but what does this freedom of representation imply? Since there is no choice in the representation of the dimensionless quantities, this to me means they are "more rigid" and possibly have a deeper physical meaning. Since they can't be set to one and ignored by anyone no matter how they define their units, they are "more fundamental" just as the Planck length, time and mass are "more fundamental" than the SI units. The Baez link Dennis provided seems to use similar reasoning.

Maybe I have hand-waved the concept of being "more" fundamental, but I only wanted to emphasize there is obviously something fundamentally different about those dimensionless quantities. I guess the questions underlying my original question are things like "Why are they fundamentally different? Why are some scalable and others aren't? Can all the scalable ones be reduced to combinations of some other non-scalable ones? If so, does that mean the scalable ones are the "real" god units and they really are more fundamental?"

EDIT: By "real" god units I mean something like (again, this is a priori):
1. Throw out all notions of length, time, ect
2. Assign a unique dimension to each "dimensionless" constant
3. Express all other constants (hbar, c, e, etc) in terms of these new dimensions
4. Recover length, time, mass, etc from these definitions.

Last edited: Jun 12, 2013
9. Jun 12, 2013

### wotanub

It seems I'm in over my head with these questions, I'm barely in grad school! Those are the exact details I want to know about. Maybe I should switch from AMO experiment to HEP theory haha.

10. Jun 12, 2013

### Ravi Mohan

Maybe the question is not right

Last edited by a moderator: Sep 25, 2014
11. Jun 12, 2013

### turbo

It is often not instructive to ask why, when we are still trying to sort out the relationships between certain values. It seems quite tough to demand "why" answers when we are still sorting out the relationships between standards that we can measure, and try to figure out the rules. Just sayin'