Why Do We Use Arbitrary Units for the Speed of Light?

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SUMMARY

The speed of light in a vacuum, denoted as c, is universally accepted as approximately 300,000 km/s (more precisely, 299,792.458 km/s). This value is not arbitrary in its significance but is a constant that remains unchanged regardless of the measurement units used. Discussions highlight that while different units can yield different numerical representations of c, the underlying physics remains consistent. The use of various units, such as light-years or c=1 in certain calculations, simplifies mathematical expressions without altering the fundamental principles of physics.

PREREQUISITES
  • Understanding of fundamental physics concepts, particularly the theory of relativity.
  • Familiarity with measurement units and their conversions, such as kilometers and miles.
  • Knowledge of energy equations, specifically E=mc^2.
  • Basic grasp of dimensional analysis in physics.
NEXT STEPS
  • Explore the implications of using different units in physics calculations, focusing on dimensional analysis.
  • Study the theory of relativity and its impact on the understanding of light speed.
  • Investigate the concept of natural units, particularly the use of c=1 in theoretical physics.
  • Learn about the historical context and evolution of measurement units in scientific discourse.
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Students of physics, educators, and anyone interested in the foundational principles of measurement and constants in science will benefit from this discussion.

stimulus101
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Why is it that the constant c (speed of light in a vacuum) is measured in ARBITRARY units that the human race practically MADE UP and why is this arbitray number (300,000) used universally as a proportion by which to multiply in many equations such as e=mc^2? If an alien race created their own units they could theoretically come up with the number 2 which would really screw things up. Am I the only person on Earth who thinks this is odd?
 
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Keep in mind that energy also includes units of distance and time (1 joule is equal to 1 kilogram * meters^2 / second^2, for example), so if you change your units so that the value of c changes, then the value of energy you assign to a given system will change too, and the equation E=mc^2 will still work. In fact physicists routinely use units of distance and time where c=1 (like light-years for distance and years for time).
 
stimulus101 said:
Why is it that the constant c (speed of light in a vacuum) is measured in ARBITRARY units that the human race practically MADE UP and why is this arbitray number (300,000) used universally as a proportion by which to multiply in many equations such as e=mc^2? If an alien race created their own units they could theoretically come up with the number 2 which would really screw things up. Am I the only person on Earth who thinks this is odd?
It's not the number 300,000 that is used universally as a proportion, it's the speed which, in our arbitrary units, happens to be 300,000 km/s (actually, 299792.458 km/s). An alien race could certainly create different units in which the speed of light would be 2 length-units per time-unit, but it wouldn't screw things up at all. As JesseM explained, the aliens would also use different units for energy (and probably mass as well) and everything would work out consistently.
 
Why is it that the constant c (speed of light in a vacuum) is measured in ARBITRARY units that the human race practically MADE UP

ALL such units are arbitrary such as foot, meter, second,Planck constant, etc...and so is "c"...BUT it's very convenient to do so because if we agree on some units and also that "1" means 1 unit in any scheme of units, 2 means doubel,etc voila, we can communicate unambiguously in mathematics...
 
stimulus101 said:
Why is it that the constant c (speed of light in a vacuum) is measured in ARBITRARY units that the human race practically MADE UP and why is this arbitray number (300,000) used universally as a proportion by which to multiply in many equations such as e=mc^2? If an alien race created their own units they could theoretically come up with the number 2 which would really screw things up. Am I the only person on Earth who thinks this is odd?

You may be the only person on Earth who doesn't understand what it means! (No, I take that back!:wink:)
You dont' have to conjure up an alien race to argue that way. People use both km and miles on earth. (Not to mention "yards", "meters", "furlongs", and "Li".)

How fast something is going does not depend upon what units you use to measure it. A car is going the same speed whether I say it is going at 80 km per hour or 48 miles per hour. Light has the same speed whether it is 300000 km per second or 185000 km per hour.

What "the speed of light is constant" means is completely different from that.

If two people, on the bed of a flat bed truck going past me at 50 km per hour (30 miles per hour) throw a ball back and forth, and can throw that ball at 60 km per hour (36 miles per hour) then the person catching the ball, forward of the person throwing it, will say it is moving (relative to him) at 60 km per hour while I would say it moving (relative to me) at either 110 km per hour.

Light doesn't do that. If a person passing me at 1/2 the speed of light, c/2, were to turn on a flashlight as he passed, we would both say that the speed of light is c.
 
HallsofIvy said:
Light has the same speed whether it is 300000 km per second or 185000 km per hour.
Or 1.803 terafurlongs per fortnight in the FFF (Furlong/Firkin/Fortnight) system. :biggrin:

http://en.wikipedia.org/wiki/FFF_System
 
Hehe, that was actually a question on an exam in one of my classes: calculate the speed of light in furlongs/fortnight. I thought it was a pretty silly question, but given this thread maybe the prof had a point.
 
stimulus101 said:
If an alien race created their own units they could theoretically come up with the number 2 which would really screw things up.

It would not screw anything at all. There are some branches of physics, and specially for some problems, that the units are changed to have c=1 unit. It makes the calculation much easier if you have to multiply by one, or if one is squared.

Therefore, from the units that we normally used, with a kilogram weighing a big bunch of butter, and a meter being yeh long, and a second being one tick, the speed of light is close to 300'000 km/s. Remember that the real value for c is not exactly 300'000km/s, but close to it. It is much more convenient to use 300'000km/s, than 299'792.458km/s.

Cheers
 
  • #10
HallsofIvy said:
Light has the same speed whether it is 300000 km per second or 185000 km per hour.

:eek: And by "km per hour" you meant "miles per second", right?
 
  • #11
Have we left out the hidden wavelength and the frequency associated with "C" in finding a solution to this problem?
 

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