Why Does C Have a Particular Value, and Can It Change?
Table of Contents
Short answer:
Because c (speed of light) 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 3×108 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 e2/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.
I get an impression that many of the posts in this thread are confusing two different interpretations of the question: "Can the value of c change?"
(2) Is is possible for the speed of light to change over time (perhaps only by a very small amount)?
If (1) is the question, then the answer "The value of c can change if you change the units used," is OK. However it is not an OK answer to (2). I would expect an OK answer to (2) would discuss differences in specific astronomical measurements that would have been detected if the speed of light were to have changed by some specific amount over some specific period of time, and the answer would also state the fact that such changes in astronomical measurements have not been observed.
Thread closed for moderation.
Edit: a whole bunch of off topic posts were deleted and the thread will remain closed.
I really don’t like your condescending tone. I have as much if not more training in physics than you do. I don’t want to get into a shouting match but I still want to defend my position. For example what you said below is flat wrong and seriously goes against over 100 years of physics. Have you heard of the Michelson-Morley Experiment? What about distance measuring interferometry? Read the following two:
[URL]http://action.zygo.com/acton/attachment/4246/f-011c/1/-/-/-/-/file.pdf[/URL]
[URL=’http://www.colorado.edu/physics/phys5430/phys5430_sp01/PDF%20files/Michelson%20Interferometer.pdf’]http://www.colorado.edu/physics/phys5430/phys5430_sp01/PDF files/Michelson Interferometer.pdf[/URL]
Look at your quote below:
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
No, it isn’t. If I have a particular object that is my standard of length, I can lay it alongside any other object and compare their lengths. I don’t need a light beam or a clock to make such a measurement, so I don’t need any definition or standard of time.[B] But if I measure the length of an object with a light beam, I do need a definition and standard of time.[/B] [/QUOTE]
I can easily take a LASER/light source, a few mirrors, and a beam splitter and make a ruler. That’s been done many times before for over 100 years (early on without lasers) in many different ways. I am measuring a distance with light without knowing anything about a time standard for that light by measuring the interference pattern change. I also don’t have to calibrate my interferometer ruler to any other length to use it and I don’t have to know the speed of light is constant. One fringe change as I vary the distance of one arm of the device can = one unit of distance. This experiment is still not independent of time as the light takes time to travel two paths but our equations and the experimental results show that when we set one of these devices up locally we don’t have to involve anything with time. In curving/accelerating space that’s a different story. I don’t need a definition and standard of time to make a ruler with light. I am using the beam of light in a way so it uses its own “clock” without knowing anything about that clock. But like all experiments ever done the results are events which are never truly independent of time and distance even if the experimenter is ignorant/ignores about one or both of them.
A metal ruler is also not independent of time because the electromagnetic forces holding it together are conveyed at the speed of light. There is a constant push and pull between the different atoms in the solid forming an equilibrium. There is a two-way mediation via the fundamental forces creating an equilibrium. However, just like with the interferometer I don’t need to incorporate any time factor UNLESS again I accelerate the object or there is a curvature of space-time across it. That equilibrium distance is MUCH more defined than you seem to keep implying. Sure atoms are a little fuzzy in size BUT they are nowhere near as fuzzy as you keep suggesting.
Atoms are most definitely standing waves: [URL]http://einstein.byu.edu/~masong/HTMstuff/textbookpdf/C17.pdf[/URL]
Look at the following: PSI = psi(x,y,z) e^(-i w t) that’s the wave function with Eigen value E which equals hbar w. PSI is a wave that is keeping its form in x, y, and z but oscillating in time. That’s definitely a standing wave. E = h f deals with more than just photons BTW. The operators for E and p go into the Clien-Gordon Equation and the Dirac Equation. BTW these Eigenstates are assuming delta t goes to infinity so for short intervals of t E and the frequency of the photon are still a little uncertain. ALL clocks and rulers will be a little bit “uncertain” because of quantum mechanics and experimental error. Much less uncertain than you keep claiming as h is quite small. Also a well defined wavelength is NOT the same as a well defined position.
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
I already did that, by quoting the former definition of the meter in terms of the length of a standard metal bar. No notion of time is required for such a definition. And the definition of time in terms of the energy/frequency of light emitted in a particular state transition of a particular atom does not require a notion of distance. Your belief that it does is based on an incorrect understanding of quantum mechanics, as I noted above (and see further comments below).[/QUOTE]
Answered above. I don’t think I have an “incorrect understanding.” Again there is a huge difference between an experiment with proportional factors dependent on time that cancel out because of the way it was designed and an experiment “without” time.
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
Expectation values don’t mean what you appear to think they mean. The electron’s position is not measured during the experiment, so its expectation value is irrelevant. The electron certainly does not move a distance of x2 – x1 during the transition. [/QUOTE]
The orbital changes shape and that is a certain change. We CAN do experiments to show that atoms change shape with different orbitals. So yes the electron represented by the probability distribution changes the set of all possible positions and momentums. I could get into the “Many Histories Interpretations” of QM or other interpretations to explain possible ways of understanding what I meant but this is getting way off topic. Also BTW what I said still matches experiment. Atomic clocks ARE mediated by the fundamental forces and those forces go through a distance and time through the process. Same for a light clock or any other clock.
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
Which is not a distance between identifiable points, so it doesn’t mean what you are thinking it means.[/QUOTE]
Never said that. And yes it does.
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
You didn’t say that explicitly, but whether you realize it or not, that’s what you’re saying. For example, this:
This is not a correct description of what is happening (see what I said above about the expectation value of position); but it can seem like one if your implicit model is the electron as a little billiard ball bouncing back and forth. You might be thinking of it as a “fuzzy” billiard ball, with an “expectation value” for position instead of a definite position, but you’re still thinking of it as bouncing back and forth, moving through space, and that means you’re thinking of it wrong. [/QUOTE]
Never said it was a little billiard ball. Where did I say that? Is it possible you just didn’t understand what I meant? Light propagates from point to point did I EVER say that was a bouncing billiard ball?
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
Sure, it’s certainly [I]possible[/I] to have a clock based on the time it takes light to cover a specific distance. But you are making a much stronger claim: that [I]any[/I] clock must be based on such a principle. That claim is false. [/QUOTE]
Really? I disagree with that. You clearly didn’t know how an atomic clock worked while I did but I did not want to get into a lengthy discussion about it. I am not going to discuss this one any further. You have been too condescending.
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
Once again, this is irrelevant to the discussion in this thread. We’re talking about ##c##, the value of the speed of light measured locally in an inertial frame. It is true that measurements at a distance can show a changed value of ##c## even if local measurements do not. But these effects are well understood parts of GR and are different from speculations that ##c## can change as measured locally in an inertial frame. [/QUOTE]
The general understanding of c is superior to the special understanding of c. I do not see any reason why I cannot discuss it and its very relevant. I am discussing something I think is important to the question that was given. If you don’t think it’s important that’s your personal opinion and I don’t care.
[QUOTE=”PeterDonis, post: 5228504, member: 197831″]
The energy E = hf, where f is the frequency of the absorbed photon, is not the energy of the electron in a given energy eigenstate. It’s the [I]difference[/I] in the electron energy between two different energy eigenstates (the ground state and the particular excited state used in the atomic clock).[/QUOTE]
Oh no you got me I forgot to put in a word. With the Eigenenergy [B]difference [/B]always equal to E = h f.
Did I kill your puppy BTW? Why are you so condescending? You have not convinced me of anything other than I should never discuss anything with you again.