Built on Facts

A reader writes in with a question about the speed of light. Since the meter and second are defined in terms of that speed, how would we be able to tell if the speed of light is changing or has changed throughout history?

It’s a good question. According to the official standard, a meter is defined to be “the length of the path travelled by light in vacuum during a time interval of 1⁄299 792 458 of a second”. If the speed of light gets faster, by definition the meter gets longer. It’s additionally complicated by the fact that the second is also defined in terms of the speed of light. The second is “the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.” If you actually calculate that transition from first principles, you’ll encounter equations involving the speed of light. Therefore a changing speed of light would actually change the definitions of both the meter and the second in a complicated way.

So would scientists notice a changing speed of light, given that the units for distance and time are defined in terms of that speed? The answer, as you might guess, is yes. There’s two classes of constantly ongoing observations that come to mind. We’ll call them the practical and the theoretical.

The Practical: In practice physicists don’t directly use the formal definition of the meter and second. We use measuring devices whose connection to those standards is indirect. If the speed of light changed, those devices wouldn’t automatically resize themselves to fit the new definition. Because we routinely make measurements of length with light to ludicrous precision, we’d notice immediately if the speed of light changed. But even if our measuring devices did instantly update themselves to a new speed of light, we’d still notice just as quickly because all the actual distances being measured (our height, the distance to satellites, the length of interferometers, etc) are still the same, just enumerated with different units. You’d notice the difference too – GPS would quit working, because it functions by measuring the light travel time to you given the distances between the satellites. Those distances wouldn’t change just because our measuring unit changed. A new speed of light, even if the change were just a few parts per billion, would seriously throw off the accuracy of GPS.

The Theoretical: It may not even be meaningful to talk about a change in the speed of light in and of itself. If the other constants of nature changed in compensating ways, the change might be no different from watching a movie in slow motion; nothing in the film happens differently. What we’re really interested in is the speed of light changing with respect to other constants of nature. As such we can look at the ratio of the speed of light with other constants , with the constants arranged in a way that cancels out all the units, leaving just a pure number. The most obvious of these dimensionless constants is the fine structure constant:

It’s equal to about 1/137.035999679. As a dimensionless constant, its value is not in the slightest dependent on how we define our units. If we redefined the meter to be twice its current value, we’d have to re-write the speed of light and the gravitational constant and whatnot to fit the new system, but all of that cancels out for the dimensionless constants. The fine structure constant and the other dimensionless constants would stay exactly the same.

This particular constant is extremely important in the quantum theory of atoms and light. If you want to calculate just about anything in AMO physics, you’ll be using it directly or indirectly. It permeates the laws describing all kinds of processes, including the way atoms emit light. If we look at the spectra of distant stars, we can determine the fine structure constant at the time and place that light was emitted. To the greatest precision we can manage (and it’s pretty great – about one part in a million), the fine structure constant seems to be the same at all times and places we’ve looked in the wider universe. On earth over our short history of measuring the constant in the lab, it’s been rock-solid to a much greater precision. It can’t have changed too much a priori anyway, since stars are only possible for a limited range of values of that constant.

We still can’t absolutely exclude the possibility that the speed of light may not be constant, or may have varied very slightly in he past. But we can be assured that if it changes even slightly, we’ll notice immediately even with our units defined the way they are.

Comments

#1 dWj
February 24, 2010

There was an article in Discover maybe 7 or 8 years ago about a new physical theory with a nonconstant speed of light, and when I read the article, to the extent I could piece together what it was talking about, it seemed much more natural to talk of it as a theory in which the coupling constants were changing. If all of your coupling constants are changing in the proportions that you can instead model it as “everything except the speed of light is constant, but the speed of light changes,” I suppose it’s more economical to label it that way, but it may be easier to understand in other terms, and, if those other terms are mathematically identical, calling one right and the other wrong is more a matter of theology than physics.
#2 ppnl
February 24, 2010

This reminds me of the old philosophical realism question. If over night everything doubled in size would we notice? After all our rulers would be twice as large also.

Short answer is yes. Double the size and you multiply the volume and weight by eight.

You could imagine changing other things like mass and density to compensate. But does size have a real existence independent of these other things?
#3 BOB SYKES
February 24, 2010

From NIST: “The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.”

Time does not depend on the speed of light, so a change ought to be detectable using some sort of distance measure.
#4 Gary Mell
February 24, 2010

Bob
The NIST definition incorporates the speed of light because the interval of time for the specified number of waves to pass a given point is determined by two things, the wavelength and the speed the wave is moving, which is the speed of light because it is an electromagnetic wave.
#5 G.D.
February 24, 2010

ppnl:
The realism question is actually a little more subtle – it is: Take the claim ‘everything doubled in size overnight, and everything else was adjusted so that we would never, in principle, notice’.

The question isn’t whether this claim is falsifiable – it isn’t. The question is whether the claim makes sense at all. And it becomes pressing if you subscribe to, say, the plausible view that to know the meaning of a sentence is to know its truth-conditions – since, the argument would go, you wouldn’t even in principle be able to recognize these states of affairs if they obtained, what sense does it make to say that we can know the truth conditions of the sentence expressing the claim? And if we don’t, then – given such a theory of meaning – the claim does not make sense.

But if the claim does not even make sense, what does that tell us about our understanding of concepts such as ‘size’ or ‘mass’? It suggests that claims about the ‘reality’ of such things would in general not really make sense either, apart from claims that are implicitly understood in terms of how they are related to each other. And that, again, seems to illustrate the anti-realise suspicion that these phenomena aren’t ‘real’ in any realist sense of ‘real’ (i.e. observation independent) – that claims about their very existence independently from our perception of them aren’t just false, but fails to make sense at all. I.e. realist claims about the universe go beyond what we could even in principle have warrant for – the upshot is not that these claims are unjustified, but that, given a plausible theory of meaning, they fail to be even meaningful.

Well, this is a rough, rough-shod indication of what the problem sort of amounts to (although these are tricky and subtle issues). Personally I’d say it just illustrates the problem of adopting a too epistemic theory of meaning. The unpopularity of epistemic theories of meaning is presumably the reason why verificationist or anti-realist views starting from (an epistemically loaded) semantic theory has kind of fallen by the wayside.
#6 OperationCounterstrike
February 25, 2010

The reason the hyperfine constant is dimensionless is it includes both the speed of light AND planck’s constant. If BOTH of them change, it would not show in the hyperfine constant.
#7 Uncle Al
February 25, 2010

There are numerous relationships that are not linear in c. The Hubble can look back 10+ billion years in time. The universe appears to be homogeneous. Lightspeed and everything associated with it look constant within observational error. A varying lightspeed would be no better than economics or climatology making excuses for theory vs. observation.

The “zoom lens” argument that everything could be expanding is no stronger than mirror arguments. The picture may cooperate but the contents do not.
#8 fatima louise
March 8, 2010

thumbs up for this blog! i’ll be looking forward for more of your blogs!
#9 Graeme Bird
April 1, 2010

“According to the official standard, a meter is defined to be “the length of the path travelled by light in vacuum during a time interval of 1⁄299 792 458 of a second”. If the speed of light gets faster, by definition the meter gets longer. It’s additionally complicated by the fact that the second is also defined in terms of the speed of light.”

Sounds like a good reason to define these metrics three ways. Since if the speed of light were to change, this would not alter the second or the metre. One definition is unlikely to do.
#10 Daryll Arekion
April 18, 2011

Measurements on Earth suggest that the speed of light has decreased significantly between the first measurement in 1675 and when checked in 1975. The rate of decrease appears to have diminished from the first observation until it tapered off to a constant after about 1960 (Setterfield, 1983, Norman and Setterfield 1987 pp.11-29, Bowden 1988a). Even if we allow for the lesser accuracy of the earlier measurements, a backward extrapolation of the graph of the speeds between 1975 and 1675 shows that it could have approached infinity in about 4000 BC. (Origins, Accident or Design? – Colin Mitchell, p. 43)

Now my question would be: is this information confirmed or refuted ? What is your personal view on the subject?
#11 Wow
April 19, 2011

Given there are no figures, how can we tell?

According to one method of interpretation, the charge of an electron has decreased(?) significantly since the original Milikan’s experiment.

Not because the electron charge has changed, but the measured result from experiment changed.

Could that be what they’re going on about?

Who knows.
#12 Dr. Anthony Albert Charles
April 20, 2011

Let’s look at the relationship between light and matter as different resonances of energy.Also, taking into account the ‘new’ information that photonic light can bend matter,remember,vibrations ARE ionic charges of wave-particles and as such resonate across Time. Time is an expansion or contraction of vibrational resonance-FREQUENCY- through matter and as such is a key component, I believe, in addressing the variables of light-speed.
#13 Wow
April 20, 2011

I suspect the above is linkspam.
#14 SesliALeyram
April 21, 2011

Yeryüzünde Ölçümler ışık hızı 1675 yılında ilk ölçüm arasında anlamlı azalma olduğunu ve ne zaman 1975 yılında kontrol öneririz. azalma oranı sonra bir sabite azaltılarak kadar ilk gözlem azalmış gibi görünüyor yaklaşık 1960 (Setterfield, 1983, Norman ve Setterfield 1987 pp.11-29, Bowden 1988a). Biz daha önceki ölçümleri, M.Ö. yaklaşık 4000 yılında sonsuza yaklaştı olabileceğini 1975 ve 1675 gösterileri arasında hız grafiği bir geri ekstrapolasyon ve daha az hassasiyet için izin bile. (Origins, Kaza veya Tasarım – Colin Mitchell, s. 43)
#15 tütüne son
April 26, 2011

Let’s look at the relationship between light and matter as different resonances of energy.Also, taking into account the ‘new’ information that photonic light can bend matter,remember,vibrations ARE ionic charges of wave-particles and as such resonate across Time. Time is an expansion or contraction of vibrational resonance-FREQUENCY- through matter and as such is a key component, I believe, in addressing the variables of light-speed.