Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Joe L. Ogan on 01/06/2013 22:40:42
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In the Equation E=MC2 was the speed of light selected because it is a large constant and really has nothing to do with the energy in a given mass? Thanks for comments. Joe L. Ogan
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The constant c2 was not just a random large number- it was used because it drops out of the equations for the energy of a particle.
This can be seen in cases such as:
- where two particles like an electron and a positron annihilate each other, they release the energy of their matter in the form of two gamma rays, whose energy can be measured.
- In the Large Hadron Collider, the energy in a proton collision consists of kinetic energy due to it's velocity (traveling at almost the speed of light, it carries considerable momentum) plus the energy of its mass (which is the same as when it is stationary).
This article shows how the energy due to mass and the energy due to velocity add up to the total energy of the particle. The familiar equation E=mc2 is derived near Figure 3:
http://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/mass-and-energy/
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If you give c its most natural value, 1, you end up with E=m.
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This one is nice Joe.
Relativity. (http://abyss.uoregon.edu/~js/ast122/lectures/lec20.html)
"Momentum, as defined by Newtonian, can not be conserved from frame to frame under special relativity. A new parameter had to be defined, called relativistic momentum, which is conserved, but only if the mass of the object is added to the momentum equation.
This has a big impact on classical physics because it means there is an equivalence between mass and energy, summarized by the famous Einstein equation:"
So Pete's insistence on the importance of 'relativistic mass' is shared by that equation.
As well as this The only known photo of Einstein's Mass-Energy Equivalence formula. (http://io9.com/the-only-known-photo-of-einsteins-mass-energy-equivale-488731904) You can download a pdf there, telling about the time he first presented it to the public.
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There is one thing though that I don't agree to in Relativity. (http://abyss.uoregon.edu/~js/ast122/lectures/lec20.html) "The energy has to go somewhere, so it is added to the mass of the object, as observed from the rest frame." If you would be at rest with a rocket at .99 'c', in a uniform motion, you would not find any extra energy, measuring inside it locally, to be situated in its 'rest frame'.
Maybe it should be read as the 'rest frame' (rocket) measuring incoming light from stars, but that is a comparison between frames of reference. Although described 'globally' (as over a whole universe, rocket included) it will tell you that there is a 'new energy', related to your uniform motion, you would still not be able to prove it 'stored' locally. It's a relation to me.
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In the Equation E=MC2 was the speed of light selected because it is a large constant and really has nothing to do with the energy in a given mass? Thanks for comments. Joe L. Ogan
It wasn't selected. It came into use because it's invariant, i.e. has the same value in all coordinate systems. With that postulate one constructs the Lorentz transformation and from that one derives the mass-energy relation.
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Well, it does vary in several respects. In one case light was stopped completely. Thanks for comments. Joe L. Ogan
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There is one more way to read "The energy has to go somewhere, so it is added to the mass of the object, as observed from the rest frame." And that is from the point of view of the rocket expending energy. Using that as a lever for 'energy stored as relativistic mass' in the 'rest frame' of our rocket ship it is correct. But it is also so that there is no added resistance from a 'space' around that rocket ship. And if you can't define the energy locally, and you can't define it to a space somehow creating a friction/resistance, then you need the stress energy tensor, which do describes it but as far as I know don't define where that 'relativistic mass' is situated.
Sometimes I wonder if it isn't so that to get this stress energy tensor you must have frames of reference interacting. You should be able to set the rockets 'rest frame' as one macroscopic 'frame of reference', and treat the space and time defined from that rest frame as another, which then, to me, makes it a relation.
As for light 'stopping', that's another thing Joe, and you have to explain how you think there first to make me see how you mean. 'Energy' as such is something physics use to describe a 'quantity' or 'magnitude' of a 'origin', when everything else, as matter, has been transformed into oblivion (disappeared). It's a sort of smallest common nominator for everything, possibly?
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Well, I remember reading that light had been stopped in frozen sodium, I believe. I tried to show the URL but was unsuccessful. Thanks for comments. Joe L. Ogan
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The speed of light is invariant in vacuum. Sodium isn't a vacuum, so there's no problem with light being stopped in sodium. It's extremely common to experience light traveling through matter slower than "c", the speed of light in vacuum. Light is slowed to about 75% of its vacuum speed in water, for example.