- #1
Nusc
- 760
- 2
E = mc^2
Please explain to me why the speed of light is squared.
Please explain to me why the speed of light is squared.
James Jackson said:Firstly, in your counter-argument for the dimensional analysis, you're ignoring the fact that the 'full' equation really reads
[tex]E^2=m^2c^4+p^2c^2[/tex]
So in the case where the particle is at rest, this simplifies to [itex]E=mc^2[/itex]. Anywho, ignoring all that, the equation is pretty simply derived by applying the relativistic Lorentz transforms to energy and momentum. The transforms themselves are derived from the postulates of special relativity (Physical laws hold in all inertial reference frames and the speed of light is constant in all intertial reference frames).
James Jackson said:In that 'derivation' you're assuming that [itex]E=mc^2[/itex] to begin with. Einstein derived it by looking at momentum carrying photons being emitted and adsorbed.
James Jackson said:In that 'derivation' you're assuming that [itex]E=mc^2[/itex] to begin with. Einstein derived it by looking at momentum carrying photons being emitted and adsorbed.
Anyway, I can't see how your final equation can possibly become [itex]E^2=m^2c^4+p^2c^2[/itex] (note this is Lorentz invarient - it holds in any frame).
James Jackson said:In that 'derivation' you're assuming that [itex]E=mc^2[/itex] to begin with.
Einstein derived it by looking at momentum carrying photons being emitted and adsorbed.
Anyway, I can't see how your final equation can possibly become [itex]E^2=m^2c^4+p^2c^2[/itex] (note this is Lorentz invarient - it holds in any frame).
James Jackson said:"the assumption that i started with was the relativistic expression of kinetic energy"
You said it yourself.
This isn't a derivation of [itex]E=mc^2[/itex] as you started with that!
The speed of light is squared because of its relationship with energy. According to Albert Einstein's famous formula, E=mc^2, the speed of light (c) is squared to show that even small amounts of mass (m) can produce large amounts of energy (E) when multiplied by the square of the speed of light.
The speed of light is a fundamental constant that plays a crucial role in the relationship between mass and energy. It shows that mass and energy are interchangeable and can be transformed from one form to another through the speed of light squared.
The speed of light being squared means that it is multiplied by itself. This is a mathematical representation of the relationship between mass and energy, showing that the speed of light is a fundamental factor in this relationship.
The speed of light is considered the limit because it is the fastest speed at which all known forces and particles in the universe can travel. As an object approaches the speed of light, its mass increases, making it more and more difficult to accelerate further.
The speed of light squared is used in many areas of modern science, including nuclear energy, particle physics, and space exploration. It is the basis for understanding the relationship between mass and energy and is crucial in many calculations and formulas in these fields.