Originally posted by jekeckel But c^2 here is a conversion factor between anthropocentric units. In the natural units, which one generally uses when doing space-time calculations, c disappears. This seems to be the most natural way to do such calculations. c^2 serves the same purpose here as the number 1.61 is in the equation M=(1.61)K, the conversion between miles and kilometers. I would certainly call 1.61 a conversion factor.
It still exists in the equation and is required for its units ( m / s ) for the equation to make sense.
As has been pointed out, this is incorrect. By connecting space and time, you use the same units of measurement for both, and the units disappear entirely.
The speed of light as far as I am aware is a physical constant of the universe and cannot be derived from the Theory of Relativity or any other theory to date.
In a sense it can be derived from classical electromagnetism. Maxwell was able to relate the speed of propagation of electromagnetic waves in a vacuum to the permeability and permittivity of free space. Although these constants are now defined, like the speed of light, they were measured experimentally in Maxwell's time. The observation that the speed of propagation for electromagnetic waves coincides with the speed of light allowed Maxwell to unite the two previously unrelated fields of electromagnetism and optics.
If this is the case then building the speed of light into your units then pretending it doesn't exist is simply wrong.
Meters, and seconds are rather arbitrary, human creations. The way to do physics for space-time calculations is in the natural units. I have yet to come across a general relativity text that does not use the natural units.
The relationship between miles and kilometers tells us absolutely nothing about the universe. The equation E=mc2 does.
Mathematically speaking, both equations use a conversion factor, though.
http://en.wikipedia.org/wiki/Speed_of_light#Fundamental_role_in_physics
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Special relativity has many counter-intuitive implications, which have been verified in many experiments.[24] These include the equivalence of mass and energy (E = mc2), length contraction (moving objects shorten),[Note 4] and time dilation (moving clocks run slower). The factor y by which lengths contract and times dilate, known as the Lorentz factor, is given by y = (1 - v**2/c**2)**(-1/2), where v is the speed of the object; its difference from 1 is negligible for speeds much slower than c, such as most everyday speeds—in which case special relativity is closely approximated by Galilean relativity—but it increases at relativistic speeds and diverges to infinity as v approaches c.
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According to special relativity, the energy of an object with rest mass m and speed v is given by ymc2, where y is the Lorentz factor defined above. When v is zero, y is equal to one, giving rise to the famous E = mc2 formula for mass-energy equivalence. Since the y factor approaches infinity as v approaches c, it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with non-zero rest mass.
Edit: replaced some characters (such as lowercase gamme with y) due to RHP mangling.
Originally posted by zeeblebot http://en.wikipedia.org/wiki/Speed_of_light#Fundamental_role_in_physics
...
Special relativity has many counter-intuitive implications, which have been verified in many experiments.[24] These include the equivalence of mass and energy (E = mc2), length contraction (moving objects shorten),[Note 4] and time dilation (moving clocks run slower). The factor ...[text shortened]... t mass.
Edit: replaced some characters (such as lowercase gamme with y) due to RHP mangling.
It's people like you that give wikipedia a bad name. Take a link and a quote from a reputable academic source:
But in relativity, the symmetric appearance of
the transformation tells us that space and time ought to be treated on the same footing, and measured in the same units.
Originally posted by adam warlock If you are talking about different Universes and varying light speeds you are totally outside the context of the derivation of E=mc^2 and so you have to state precisely what you mean and your assumptions so that this dialog can continue.
I think I am understanding better what you are saying, however, I am still certain that E=mc2 is a more general equation than E=m and it is wrong to simply call c or c2 a conversion factor just as it would be wrong to call 'a' a conversion factor in F=ma when we are talking about gravity at sea level. Just because we know a is constant (about 9.8m/s2 ) in the equation is no reason to forget that it is acceleration.
Similarly, to say E=m is equivalent to saying "in the special case of our universe where the speed of light is thought to be constant".
Originally posted by twhitehead I think I am understanding better what you are saying, however, I am still certain that E=mc2 is a more general equation than E=m and it is wrong to simply call c or c2 a conversion factor just as it would be wrong to call 'a' a conversion factor in F=ma when we are talking about gravity at sea level. Just because we know a is constant (about 9.8m/s2 ) in ...[text shortened]... ng "in the special case of our universe where the speed of light is thought to be constant".
it is wrong to simply call c or c2 a conversion factor just as it would be wrong to call 'a' a conversion factor in F=ma when we are talking about gravity at sea level.
But energy and mass are describing the same thing. The c^2 term converts between arbitrary, man-made units! The miles to kilometers analogy (or vice-versa) fits much better here, in my opinion.
Similarly, to say E=m is equivalent to saying "in the special case of our universe where the speed of light is thought to be constant".
Saying E=mc^2 is equivalent to saying "in the special case of our universe where the speed of light is thought to be constant."
Originally posted by twhitehead I think I am understanding better what you are saying, however, I am still certain that E=mc2 is a more general equation than E=m and it is wrong to simply call c or c2 a conversion factor just as it would be wrong to call 'a' a conversion factor in F=ma when we are talking about gravity at sea level. Just because we know a is constant (about 9.8m/s2 ) in ...[text shortened]... ng "in the special case of our universe where the speed of light is thought to be constant".
Your analogy isn't a good one for two reasons:
1 - c is a universal, cosmological constant in modern day Physics while a (more normally g) is just an accidental value that we get near the surface of planet Earth
2 - While E=mc^2 is a derived equation from a more basic set of postulates f=ma is a postulate in "normal" classical Physics (it can be "derived" in Lagrangian Mechanics though).
If you look at the the Terry Tao link I already provided in this thread you can see a derivation of E=mc^2 and hopefuly you'll understand why c^2 is just a conversion factor.
Also check this out:
But in relativity, the symmetric appearance of
the transformation tells us that space and time ought to be treated on the same footing, and measured in the same units.
Originally posted by adam warlock Your analogy isn't a good one for two reasons:
1 - c is a universal, cosmological constant in modern day Physics while a (more normally g) is just an accidental value that we get near the surface of planet Earth
2 - While E=mc^2 is a derived equation from a more basic set of postulates f=ma is a postulate in "normal" classical Physics (it can be "deri ...[text shortened]... the same units.[/quote]