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Is increasing mass part of what governs c, or is it just a side effect?

Seeking Science

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While the speed of light is governed by c = 1/(μo εo)½--a derivation of Maxwell's equations where μo is the magnetic permittivity in free space and εo is electrical permittivity in free space--does increasing mass help govern c as well? As shown by Einstein, when the Lorentz factor (y = 1/(1 - v2/c2)-1/2)is included in E = mc2 as E = ymc2, as a thing approaches the speed of light, its relativistic mass approaches infinity. So does this too help to govern c, or is increasing mass just a side effect? And if it's just a side effect, how does infinite mass when v = c not play a role in restricting this speed?

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In the modern formulation of Special Relativity, mass does not increase with velocity. The only mass which is defined is sometimes called "rest mass" or "invariant mass." Mostly, we just call it "mass." It is an invariant quantity, meaning it is the same in all reference frames. It is defined as:




where [math]E[/math] is the total energy of a particle and [math]p[/math] is the magnitude of its momentum. Back when Relativity was a relatively new subject (no pun intended), physicists invented a quantity called "relativistic mass." Relativistic mass does increase with velocity. It is defined as:




This gives us the relationship [math]m_{rel}=\gamma m[/math], where [math]\gamma = (1-v^2/c^2)^{-1/2}[/math] is the Lorentz factor. It turns out that relativistic mass has very little useful application, and hence is no longer used by the vast majority of the physics community. Unfortunately, physics popularizers like Michio Kaku, Brian Greene, etc., tend to write about how "mass increases with velocity" in their books and interviews. I assume this is because they think it makes the concept that "you can't travel faster than light" more intuitive. Even more unfortunately, this tends to confuse the living hell out of people who go on to actually study Relativity. It sure confused the hell out of me when I started learning Relativity, and I see a couple threads a week on various physics sites like this where people are asking about mass increase.



So, on to your question: mass doesn't increase. A good way to demonstrate that massive objects obtaining a velocity of [math]c[/math] is impossible is to calculate what its kinetic energy would be. The formula for kinetic energy in SR is:


[math]K.E.=(\gamma -1)mc^2[/math]


By the work-energy theorem (which still holds in SR), this is equal to the work required to bring a particle at rest to the given velocity. As you can see, as [math]v \rightarrow c[/math], then [math]K.E. \rightarrow \infty[/math]. So you'd need an infinite energy supply to bring a massive particle to [math]c[/math], which is clearly impossible.

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