# Is the speed of light really just a conversion constant, like 2.54 cm/inch?

1. Nov 2, 2012

### pervect

Staff Emeritus
Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

Rather than arguing about the usual, (which we have a spate of at the moment), I'd like to see if this is a fair summary of how physics and physicists view the speed of light - as a units conversion constant.

I rather suspect the answer is "yes", by the way. But there's enough uncertainty about the issue to give me pause before putting it this baldly. Part of it may be the nature of the question, it doesn't seem like something one could give textbook references on. Though I'd say that Taylor and Wheeler at least suggest it strongly in "Space Time Physics", with "The Parable of the Surveyor".

I suppose when I"m cautious I head more for the idea "it's a common view, but it's more philosophy than science so it doesn't get argued much".

2. Nov 2, 2012

### PAllen

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

I haven't seen any answer to the proposed way too look at it that I posted in one of the other threads (it is not original, but I like it):

If you could compare our universe to some some other universe, how would you determine if the the speed of light is different?

I don't see any conceivable way to do this other than to relate c to other constants that determine a fundamental length and time (hydrogen atom radius being a concrete realization of distance, for example). The result is that you are comparing a dimensionless ratio of fundamental constants between the two universes.

Last edited: Nov 2, 2012
3. Nov 2, 2012

### Meir Achuz

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

"Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?"
A better analogy is that it is just like 5,280 feet/mile.
Historically, people didn't know about Minkowski space-time, and used a different unit (second) for one of the four axes.
In America, we still use a different unit for one of the three axes on a topographical map.
I myself,prefer to remember the number 1 ratherthan 2999792458 for c.
(Is there a good mnemonic to memorize 1?)

4. Nov 2, 2012

### pervect

Staff Emeritus
Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

As I think about it, another argument for this view is the SI standard itself, which nowadays defies the speed of light to be a constant.

5. Nov 3, 2012

### Bill_K

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

I can only say that when I do a serious calculation, I keep all the ħ's and c's. Not because I like to torture myself, but for two reasons, (1) it reduces the math errors and (2) it reminds me which terms are big and which are small. The MLT dimensions are highly useful, I think it's significant that they are even possible. For on the other hand, I know of no meaningful way to keep lengths segregated into "cm lengths" and "inch lengths".
The SI system is appropriate for engineering applications, but physicists should not be shouldered with it. What particle physicist in his right mind works in coulombs and meters? How many joules is the energy of the beam at the LHC? And how many meters away is the Andromeda galaxy?

6. Nov 3, 2012

### pervect

Staff Emeritus
Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

I find that it increases the math errors when I keep the c's. Considerably. The other constants aren't such a big deal, (the G's, for example), but I'm way too used to 4-velocities having a norm of -1 (for example) to be proficient at keeping the c's. It's frankly easier and less error prone to put them back in when the calculation is done.

I'll use different units for different purposes, I would guess this is pretty common but your examples made me realize it. A lot of the time I'll think in terms of meters for distances, times, and masses, with 1 meter = 3ns, and 1.5km = 1 solar mass. But if I was thinking about andromeda, or accelerating spaceships, I'd use years / light years. And probably kg.

If you keep all the h'c and c's and whatnot, it must be easy for you to convert back to SI, even if you tend to "think" in other units?

Last but not least, would you have any suggestions for the FAQ https://www.physicsforums.com/showthread.php?t=511385 [Broken] "Why does the speed of light have a particular value, and can it change?"

Last edited by a moderator: May 6, 2017
7. Nov 3, 2012

### harrylin

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

As you put it in the "relativity" forum, I bring up a* view of Einstein:

I share that view, which implies that any speed (incl. that of light) is more than just a conversion constant of the inches-to-mm kind.

Note that that question should not be confounded with the habit to put c=1! It is not uncommon in physics to put a proportionality constant between physically very different concepts equal to 1 for convenience.
[EDIT:] As a matter of fact, that's also what Einstein did in that same chapter.
And of course, a consistent unit system cannot make all proportionality constants equal to 1.

* not necessarily "the" view, as he sometimes changed his mind as all reasonable people do!

Last edited: Nov 3, 2012
8. Nov 3, 2012

### Naty1

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

What are my other choices.....??

My old Halliday and Resnick calls it a 'physical constant' as does Wikipedia, currently:

http://en.wikipedia.org/wiki/Speed_of_light

9. Nov 3, 2012

### harrylin

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

Well yes, according to GR it's a (local) physical constant. That means that if one measures length with a laser, a mirror and a clock, then one should find the same length as with a ruler.

The difference with for example the conversion from mass to force with a spring (on a scale), is that a spring with g isn't a physical constant; that is less suited for standardisation (nevertheless there used to be kgf).

Last edited: Nov 3, 2012
10. Nov 3, 2012

### pervect

Staff Emeritus
Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

The point I was making is that according to SI, the speed of light is, nowadays, defined to be a constant.

See for example http://physics.nist.gov/cgi-bin/cuu/Value?c

This constant value of 'c' is a consequence of the SI definition of the meter http://www.bipm.org/en/CGPM/db/17/1/

Where does this leave all the people struggling with relativity who want to "measure" the speed of light - when strictly speaking it's defined to be a constant?

Well, I tend to assume that they are using the original 1890'ish definition of the meter, based on the prototype meter bar kept by the BIPM, before the days where 'c' was defined as constant.

11. Nov 4, 2012

### harrylin

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

Right. Naty and I agreed: it is a physical constant, in contrast to the human mm/inches constant. SI bases itself on trusted theory. According to general physics theory measurement standards have no memory. And according to GR one can conveniently measure lengths by relying on the local constancy of the speed of light.
That is a slightly different issue than the one that you started the discussion with (and which is apparently not finished). I think that there have been a number of articles and discussions about that practical decision and its consequences; it boils down to consistency checks.

The reason for the redefinition was that as the measurement of the speed of light became extremely accurate, it became, as the physics FAQ puts it, more practical to fix the value of c in the definition of the metre and use atomic clocks and lasers to measure accurate distances instead.
"nvlpubs.nist.gov/nistpubs/jres/092/jresv92n1p11_A1b.pdf" [Broken]
http://en.wikipedia.org/wiki/History_of_the_metre#Krypton_standard
There it is remarked that an old proposal was to use as length standard the length of a pendulum that beats seconds.

Last edited by a moderator: May 6, 2017
12. Nov 4, 2012

### Murdstone

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

The non-divisibility of the four-dimensional continuum of events does not at all, however, involve the equivalence of the space co-ordinates with the time co-ordinate. On the contrary, we must remember that the time co-ordinate is defined physically wholly differently from the space co-ordinates. The relations [..] which when equated define the Lorentz transformation show, further, a difference in the role of the time co-ordinate from that of the space co-ordinates. - The meaning of relativity, 1921

You can say whatever you like in this discussion. Time is related to space but space is not related to time. If nothing changing, space remains the same, has any time evolved.

The concept of space is still elusive.

The muddling of space with time is anthropomorphic and is impeding progress in the understanding of the truth of things.

13. Nov 4, 2012

### AJ Bentley

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

If time and space were arguably the same with only the matter of a constant between them, you'd have to say that energy and momentum were the same.
Since the one is a scalar and the other is a vector - that might be problematical.

14. Nov 4, 2012

### D H

Staff Emeritus
Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

An even better analogy is the non-unity value of k in F=kma, where k=6096/196133≈1/32.174, which is how Newton's second law is expressed in the English system of units. The International System (SI) expresses Newton's second law as F=ma. The early interpretation of F=ma was that the metric system set the constant k to unity merely for computational convenience. The modern interpretation is that force and mass*acceleration are the same thing, that force is a derived quantity. That force appears to be a distinct unit in the English system is merely a consequence of using an inconsistent set of units.

The other choice is that time and distance are fundamentally the same thing. They only appear to be different because the SI ultimately is an inconsistent set of units, just as is the English system. The interpretation of the Lorentz transformation as a hyperbolic rotation of space-time coordinates has to be viewed as a trick that happens to get the math right if one insists on viewing time and distance as fundamentally different. It's not a trick if one views time and distance as fundamentally the same thing.

15. Nov 4, 2012

### harrylin

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

Perhaps you are thinking about 4-force? That is not the force of Newton not of SI which are measured in the lab; probably it's not a good example for what you want to say. The modern interpretation which followed from SR is incompatible with the idea that force and mass*acceleration are the same thing, as by chance was just explained here:

Last edited: Nov 4, 2012
16. Nov 4, 2012

### pervect

Staff Emeritus
Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

As long as the velocity is zero, it doesn't matter whether you use the three force or four force...

I think DH has made a very good analogy, as a matter of fact.

17. Nov 5, 2012

### harrylin

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

Force is defined as discussed in the link; [EDIT: That was still wrong, it is merely the law of motion for net force. There is nothing more common than large forces at zero speed and zero acceleration!]
thus while I agree with the analogy, it's similar to the ones that I provided earlier to illustrate the motivation behind the contrary opinion.

I guess that the expressed opinion of Einstein appeals most to physicists (in particular experimental physicists), while the expressed opinion of Minkowski appeals most to mathematicians (including mathematical physicists). A poll would be interesting.

PS. I vaguely remember that Einstein once complained about such a thing, something like that he didn't understand his own theory anymore after the mathematicians took over. Does anyone know what it was exactly that he said?

Last edited: Nov 5, 2012
18. Nov 5, 2012

### D H

Staff Emeritus
Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

Perhaps not. You missed the point of the analogy. There is no 4-force in Newtonian mechanics. I was talking about the relation between force, mass, and acceleration in the context Newton's second law. In that context, consider that ratio of one unit force to the product of a unit mass times and a unit acceleration. This obviously has a numeric value. What about its units? Is this quantity dimensionful (units are force·time2·mass-1·length-1) or is it dimensionless?

If this ratio is dimensionful, there's nothing fundamentally wrong with units such as pound mass and pound force, or kilogram mass and kilogram force. Choosing units of force, mass, length, and time such that the ratio has numeric value of one is merely a computational trick that helps keep the math simple and thereby eliminates a lot of sources for human error. On the other hand, if this ratio is dimensionless, choosing units such that the ratio is one is consistent with the fact that the ratio is dimensionless. A set of units of force, mass, length, and time that makes this ratio anything other than unity is in a sense inconsistent with the dimensionless nature of this ratio.

The early view was that this ratio was dimensionful, making F=ma a convenient abuse of notation. Per this point of view, the proper notation for Newton's second law is F=kma, where k is a dimensionful quantity that can conveniently be made to have a numeric value of one. The modern view is that this ratio is dimensionless. This point of view makes F=ma dimensionally correct.

So how does this analogy apply to the topic of this thread? The question at hand is whether velocity is a dimensionful or dimensionless quantity. If velocity is a dimensionful quantity, choosing units of length and time such that the speed of light has a numeric value of one is just a mathematical trick that makes some calculations easier. If velocity is a dimensionless quantity, it's not a trick. There is one universally agreed-upon velocity by all observers of some phenomenon, and that's something moving at the speed of light. This is the natural value that makes a system of units consistent.

More fundamentally, I think the question being raised in this thread is how many fundamental units are there in the universe? Are there
• Seven? (the number of fundamental units in the International System, SI)
• Five? (SI again, but discounting the dimensionless mole and the candella, which is a physiological rather than a physical unit)
• Three? (Lev Okun; see reference below)
• Two? (Gabriele Veneziano; see below)
• Zero? (Michael Duff; see below)

Michael J. Duff et al, Trialogue on the number of fundamental constants, JHEP03(2002)023 doi:10.1088/1126-6708/2002/03/023
Preprint at http://arxiv.org/abs/physics/0110060

Last edited: Nov 5, 2012
19. Nov 5, 2012

### Dickfore

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

The speed of light is really a conversion factor, but unlike your example 2.54 cm/in, which is dimensionless (but has units), the speed of light has dimensions (in SI, at least).

This is precisely the reason why someone would doubt whether it is a conversion factor. Namely, it converts two physical quantities with different dimensions, in this case length and time.

It is really the progress of physics that made the speed of light have this role. The theory of relativity treats space and time symetrically, and the only logical value for the speed of light (which was shown to coincide with the limit speed of propagation mentioned in the 2nd Postulate) is $c = 1$. As the meter had been defined historically through the length of the Earth's meridian, and the second through the length of Earth's period of rotation, we are stuck with this rather inconvenient number.

But, it tells us something about our home planet. Namely, the distance travellled by a point on the Earth's equator in a day (86400 s) is 40000 km, giving it a speed of 0.463 km/s. Compare this to the speed of light (300000 km/s), and you get the ratio $1.54 \times 10^{-6}$, or, as a fraction 1/649351. (turns out this number is very close to $\alpha^e$, where $\alpha$ is the fine structure constant, and e is the base of the natural logarithms).

20. Nov 5, 2012

### harrylin

Re: Is the speed of light "really" just a conversion constant, like 2.54 cm/inch?

OK, now I copy.

And interesting article - thanks!

I think that your clarification clarifies the second part of my last reply: it may well be that experimental physicists (at heart) tend to consider physical analysis ("physical meaning", as Okun puts it) just as much as dimensional analysis, while mathematical physicists (at heart) tend to consider only dimensional analysis. Thus while a mathematician would ask, as you do, "how many fundamental units are there in the universe", a physicist would ask "how many physical dimensions are there".