# Re: Constant 'c'?

Moorad Alexanian (*alexanian@UNCWIL.EDU*)

*Thu, 06 Nov 1997 09:27:44 -0500 (EST)*

At 05:21 PM 11/5/97 -0500, David Bowman wrote:

*>Concerning what Moorad Alexanian wrote:*

*>>In the case of length and energy, the numerical constants, 2.54 and 4.184,*

*>>have no physical content and are only a historical curiosity. Note that one*

*>>is dealing only with energy or only with length.*

*>*

*>*Now* we know that heat and work are just different methods of changing the*

*>internal energy of a thermodynamic system. Heat was shown to be equivalent*

*>to macroscopic work by Joule. Before this heat and work were not necessarily*

*>thought of as being so interchangable. Heat had been thought of in terms of*

*>a caloric substance. Before the work of Joule if you told someone that*

*>the calorimetric property of heat was "the same stuff" as a force times a*

*>distance (work) that person would probably have thought you were crazy. Heat*

*>and work were thought to have their own separate (engineering) dimensions.*

*>*

*>> On the other hand, the*

*>>constant c is the speed of light in vacuum, a measurable quantity.*

*>*

*>Not any more. Now c is a *defined* quantity. An experiment done before*

*>1983 that proported to carefully measure c in terms of two independent *

*>definitions for time and length *now* actually would carefully measure*

*>the length of the prior length standard (wavelength of an orange Kr-86 line)*

*>in terms of the modern meter.*

*>*

*>> By*

*>>defining the value of c to have an exact number, 299792458, one is only*

*>>defining the meter in terms of the unit of time, the second. But note that*

*>>we are dealing with two different quantities---space and time, albeit,*

*>>components of a 4-vector---which have different dimensions.*

*>*

*>One of the main lessons of relativity is that time and space are *not**

*>such different things that they deserve their own separate dimensions and*

*>units. Time and space are very intimately tied together by relativity*

*>theory into a *single* geometric manifold called spacetime. This is not so*

*>different from the marriage of work and heat by the first law of *

*>thermodynamics into the single energy change concept.*

*>*

*>Why would you think giving different components of a (4-)vector different*

*>dimensions is a sensible thing to do?*

*>*

*>> If somewhere in*

*>>the universe, the velocity of light is different, then by using our*

*>>definition of the second and the meter, they would get a different length*

*>>for the meter.*

*>*

*>Or for the duration of the second, or both. How could you possibly tell if*

*>the speed limit of causation c was different in one place to another given*

*>that time and space are defined in such a way keep c constant? We attribute*

*>differences in local dilations between locally measured proper lengths of *

*>measuring rods and locally measured proper times of clocks in different*

*>regions of spacetime as being due to inhomogeneous local curvature effects in*

*>the spacetime manifold caused by gravitation. If some region of spacetime*

*>effectively had a different speed limit of causation relative to some other*

*>part of spacetime and this effect was not due to different local*

*>concentrations in the stress-energy-momentum tensor of the matter there then*

*>there would be some prior geometry not determined by Einstein's equations and*

*>General relativity would be incorrect. But even in this case the effect*

*>would be interpreted as a geometric distortion of spacetime and not as an*

*>actual change in the speed limit of causation which is the standard by which*

*>the geometry is measured.*

*>*

*>> The numbers 2.54 and 4.184 are the same anywhere in the *

*>>universe.*

*>*

*>True. But suppose that in some far away place it actually took 6756 J of*

*>work (via a Joule-type paddle wheel device) to raise the temperature of a*

*>kg of water by 1 deg C, while here it takes only 4184 J of work to*

*>raise the temperature of a kg of water by 1 deg. C. Then your 4.184 J/cal*

*>number would not be as universal as you had thought. Of course we could*

*>always define the calorie so that the conversion factor stayed the same. In*

*>this case we would interpret the effect as there being a weird spatially*

*>dependent specific heat for water. This is analogous to discovering local*

*>differences in a prior geometric curvature of spacetime not generated by the*

*>matter/energy/stress/momentum in it.*

*>*

*>Similarly suppose that we had defined the inch via a definition which was*

*>independent of the definition of the centimeter. Say we defined the inch as*

*>1/12 of the length of the average adult human's foot length. Using this*

*>definition we can measure the the length of people's feet in centimeters*

*>and conclude that experimentally there are 2.54 cm/in. Now suppose that in*

*>some other place some local effects take place that stretch or shrink the*

*>foot length of the people who live there. Also assume that travelers who*

*>go there have their foot length similarly modified by the weird effect as*

*>soon as they enter this twilight zone. If we measured the average adult*

*>human foot length in the this twilight zone then we would discover that the*

*>length of the inch (being 1/12 of the average foot length) is different*

*>in this place being something other than 2.54 cm. Your energy and length*

*>examples are not as different from the defined constant c case as you think.*

*>*

*>>Moorad*

*>>*

*>>p.s. Perhaps we do need a referee to settle the issue.*

*>*

*>Do you really think so? Where is Don Page anyhow? :-)*

*>*

*>David Bowman*

*>dbowman@gtc.georgetown.ky.us*

*>*

*>P.S. I discovered that the name of the paper in a reference I gave in an*

*>earlier post about a possible spatial directionality or arrow in the universe*

*>(birefringence of the universe) was in error. The correct citation is: Borge*

*>Nodland & John P. Ralston, "Indication of Anisotropy in Electromagnetic*

*>Propagation over Cosmological Distances", Phys. Rev. Lett., 78, 3043, Apr. 21,*

*>1997.*

I do not want to belabor the point but what I had in mind all the time was

the following: If I take the length of one inch and the length of one

centimeter as defined here and now such that the ratio of lengths is

precisely 2.54, and then either transport them in space and/or time anywhere

in the universe, it seems to me that irrespective of any theory the ratio

would have to remain 2.54 per force. Whatever affects one length would have

the affect the other equally so that the ration would have to remain 2.54. I

believe the same would be true for the 4.184 between doing work and adding

heat in raising the temperature of water. However, if I define the meter and

the second here and now and experimentally determine the speed of light, I

am not assured that the same equipment and measurement when transported

elsewhere in space and/or time would give me precisely the same speed of

light. Of course, one can assume that the speed of light is a universal

constant or else say that such and such a theory implies that the speed

would be a constant, and thus we would have to get the same numerical value

for the speed of light. However, that would be a physical assumption and not

the result of a purely logical conclusion as in the case of length or

energy. Is it clear what I have in mind? I would appreciate your comments on

it. BTW the article I read by F.J. Dyson on the possible time dependency of

the constants of nature when I was involved in the nature of the

fine-structure constant is in "Aspects of Quantum Theory" edited by A. Salam

and E.P. Wigner. Unfortunately, our university does not have a copy of it

for me to look up since that was the issue that started all these discussions.

Take care,

Moorad