# Why Does C Have a Particular Value, and Can It Change?

**Short answer:**

Because c has units, its value is what it is only because of our choice of units, and there is no meaningful way to test whether it changes. These questions are more meaningful when posed in terms of the unitless fine structure constant. Nobody knows why the fine structure constant has the value it does, and there are controversial claims that its value may have changed.

**Long answer:**

The SI was originally set up so that the meter and the second were defined in terms of properties of our planet. The meter was one forty-millionth of the earth’s circumference, and the second was 1/86,400 of a mean solar day. Thus when we express c as 3×10^{8} m/s, we’re basically specifying the factor by which c exceeds the speed at which a point on the equator goes around the center of the earth (with additional conversion factors of 40,000,000 and 86,400 thrown in). Since the properties of our planet are accidental, there is no physical theory that can tell us why c has this value in the original French-Revolutionary version of the SI.

The base units of the SI were redefined over the centuries. Today, the second is defined in terms of an atomic standard, and the meter is defined as 1/299,792,458 of a light-second. Therefore c has a defined value of exactly 299,792,458 m/s. Again, we find that the numerical value of c has no fundamental significance; it is merely a matter of definition. In fact, physicists often choose to work in a non-SI system of units in which c=1 exactly.

One might object that c *could* have a numerical value that was not merely an accident of natural or human history, if we instead chose to express it in terms of base units of time and distance that were universal. For example, suppose that SETI succeeds, and we initiate two-way radio contact with an alien civilization. We want to know whether the speed of light has the same value in their neighborhood of the galaxy as it does in ours. We agree to use an atomic standard for our base units. As our distance unit, we’ll use the circumference of the electron’s orbit in the ground state of the Bohr model of hydrogen; and as our unit of time, we agree on the corresponding orbital period. In these units, the speed of light equals 137.0359991. But this number is simply the inverse of the fine structure constant, defined as e^{2}/ħc, where e is the fundamental charge and ħ is Planck’s constant over 2π. It now becomes clear that it is not possible for us to find out whether the aliens’ local value of c is or is not the same as ours. If they get 134 instead of 137, it could be because e or ħ is different where they live.

The moral of this story is that it is never meaningful to ask why a universal constant has a particular value, unless that constant is unitless (Duff 2002). Currently, there appear to be about 26 such unitless fundamental constants (Baez 2011). The unitless constant most closely related to c is the fine structure constant. It is meaningful to ask why the fine structure constant has the value it has, but nobody knows the answer.

It has been claimed based on astronomical observations that the fine structure constant actually varies over time, rather than being fixed (Webb 2001). This claim is probably wrong, since later attempts to reproduce the observations failed (Chand 2004). Webb et al. responded with even more extraordinary claims that the fine structure constant varied over the celestial sphere (Webb 2010). Extraordinary claims require extraordinary proof, and Webb et al. have not supplied that; their results are at the margins of statistical significance compared to their random and systematic errors. Even if this claim it is correct, it is not evidence that c varies, as is sometimes stated in the popular press; it is only evidence that the fine structure constant varies.

**Further Reading**

Duff, “Comment on time-variation of fundamental constants,” http://arxiv.org/abs/hep-th/0208093v3

Baez, Baez, http://math.ucr.edu/home/baez/constants.html

J.K. Webb et al., “Further Evidence for Cosmological Evolution of the fine structure Constant,” Phys. Rev. Lett.87 (2001) 091301,http://arxiv.org/abs/astro-ph/0012539v3

J.K. Webb et al., “Evidence for spatial variation of the fine structure constant,” http://arxiv.org/abs/1008.3907

H. Chand et al., Astron. Astrophys. 417: 853

The following forum members have contributed to this FAQ:

bcrowell

pervect

PhD in physics. I teach physics at Fullerton College, a community college in Southern California. I enjoy writing, playing viola, brewing beer, climbing and mountaineering.

What is the difference between a constant which can be "made unitless" like c and h-bar, and units which are "inherently unitless" such as the fine structure constant? It's always bothered me that we can just measure time in units of length due to c. I get that since c is universal we can naturally relate one arbitrary unit of distance to a unit of time, however it doesn't seem immediately obvious to me that this warrants equating the two quantities.

No. C is constant. The variable lies in the conditions in which this standard is influenced. All the constants that we have established to this point are based on our unique (base) perspective. The reality of the physical properties that we observe and postulate are slightly skewed. Accepting the fact that all constants are subject to the effects of the properties and/or restrictions of any environmental variables that may alter that constant. We now understand that the constant is not our own perspective. The constant that exists is with out. The constant is 0. A very cold 0, It has no variables. Our perspective tells us the symbol g has relative standard. The numerical value for the acceleration of gravity, most accurately known as 9.8 m/s/s. This also is subject to the variables of a its surroundings. Now that we have established that all constants are measurable by: wave, speed, density, strength, length, resonance or all of the above. A constant does not mean it cannot change. It simply means it is a scale to measure inconsistencies.

The original poster and all other commenters should read this paper recently published on Academia.edu: Redimensioning of Momentum Space and Quanto-Geometric Derivation of the Speed of Light [c]. Right on the money.

This question has been wrongly understood. It is really about the existence of any speed for light and how the particular value of it comes about regardless of the units. How might we calculate this speed from other constants in physics?

“Extraodinary claims require extraordinary proof” seems to me only a way to favor one hypothesis over another based on popular consensus.

There was a time in the history of science when claims of invariance were the extraordinary claims, and claims of variance were more ordinary.

The turning of the tide of consensus is more a matter of human opinion.

Hypotheses should only be ruled out based on data: hard data. In principle, the claim of a changing fine structure constant is falsifiable to within much smaller uncertainties than the reported changes. I prefer to keep an open mind until technologies catch up to do the experiment and provide the data. I tend to be skeptical when epistemological preferences get used to malign one view and favor another while waiting on the data.

I have no idea

“Extraodinary claims require extraordinary proof” is just Bayesian logic. If I say to you: “jump out the second story window, there is a fire on the first floor” versus “jump out the second story window, there is a 15 foot spider on the first floor”, would you really say there is no difference between your acceptance threshold between these? Rejecting “Extraodinary claims require extraordinary proof” is tantamount to saying there is no such thing as an apriori unlikely claim, and is the basis for crank reasoning.

The process of making c unitless is equivalent to the process of selecting an inherently unitless constant. Both entail the feature that you lose the ability to state whether a change in the unitless value is attributable to a change in a particular constant with dimensions.

Actually, it is the correct way for rational individuals to reason in the face of uncertainty and incomplete evidence. This idea of extraordinary claims requiring extraordinary evidence can be formalized in Bayesian inference which allows you to calculate how strong a given piece of evidence is and how much it should change your belief in a hypothesis.

And the claims of invariance were accepted after being supported by the requisite extraordinary evidence.

Edit: I see that PAllen beat me to it! I should have read before replying.

Even if we accept that “extraordinary claims” require extraordinary evidence, we should recognize that there is extraordinary proof in this case.

In many scientific questions, a 95% confidence level (1.95 Sigma) is accepted as significant supporting evidence worthy of publication.

The variation in the fine structure constant actually fits a spatial dipole at a 4.2 sigma significance level.

Like Occam’s Razor, rigid adherence to Bayesian stats is an epistemological preference, not an inherent or essential feature of the scientific method.

I see no advantage in biasing scientists that one hypothesis is more likely than another to eventually be rejected as future data becomes available. Better to wait for the data.

The scientific method only needs two kinds of hypotheses: falsified and not falsified.