Massless Photons

[blike]

Faf and I had this discussion quite some time ago, just want you guys input.

 

e=mc^2

 

photons have energy, and energy = mc^2. So if the mass is 0, wouldn't the energy be 0?

[Radical Edward]

cos E = mc^2 is a simplification. the proper derived formula is:

 

E = (p^2)(c^2) + (m^2)(c^4)

 

(p is momentum)

 

so in the limit of zero rest mass, all energy has to be in the momentum of the object, in this case, the photon.

 

an object at rest, simplifies to the more conventional

 

E = mc^2

[aman]

One argument for E to be >0 in a photon is in how it is created and how it is uncreated. An excited electron drops from a high shell to a low shell and the energy released creates a photon. It has an energy and a velocity C released from the electrons drop.

A photon hits a chloroplast in a leaf. It provides energy to transform ADP to ATP which later will be used to make carbohydrates.

The photon starts from energy and vanishes having delivered that energy.

Just aman

[fafalone]

For a long time everyone was convinced neutrinos were massless, but it turned out they actually did have mass. If a photon is massless, why can its path be altered by gravity, and how does a medium slow it down?

[Radical Edward]

1) It is taking the shortest path it can through curved space

2) interacting with the matter. oscillating dipoles and such things.

[fafalone]

Then why are black holes predicted to emit certain waves? How could one pure wave escape, but light cannot?

[Radical Edward]

waves? waves of what? if it is the blackbody spectrum you are talking about, the emission is actually from near the surface of the event horison, rather than from within the black hole itself. granted there are still issues when considering the quantum mechanics of the situation though, as we all know that Quantum mechanics and relativity don't really like one another.

[fafalone]

Pair production... black hole evaporation. Interest theory put forth by Stephen Hawking, where if a pair is created outside the event horizon, one will escape, causing it to appear that the black hole loses mass. Another theory suggest quantum tunneling could very slowly allow particles to escape.

[Radical Edward]

yep. indeed. however we lack the theoretical knowhow to say for sure. As I say, QM and GR do not mix. My bet is on M-Theory - though I don't know enough about it to say for sure.

[aman]

Einstein said there must be a force in our universe that keeps existance stable and called it lambda although he never knew exactly what it was. It must be what keeps an event horizon stable and possibly passes on either side of the horizon without change. It's only known by its effects and mathamatical necessity but seems to be the only force not acknowledged in the field theories. Forces don't have mass but are dependant on it.

Photons don't seem to act like forces but seems to act more like masses dependant on forces.

Just aman

[Radical Edward]

Einstein's lambda was a fudge factor, because he thought that the universe was steady state, and his theory predicted an expanding universe. He stuck lambda in to stop the universe from expanding. Of course when it was discovered that the universe was actually expanding, he regretted adding this spurious constant in, telling a friend it was the "biggest blunder of my life".

 

Since then though, there has been a bit of a turnaround in the books, and lambda has reared it's ugly head again, although now it is the other way round - actually accelerating the universe, and potentially splitting everything up into DeSitter space. Where lambda comes from and how big it is, is still not known, as QM can't even figure it out. The only predictions of it's magnitude (and I've not a clue as to what the calculations are, unless it is the same thing as casmir forces) are about 10^120x too big.

 

no doubt we will figure it out eventually, and it will probably be in a theory of everything.

[quantumdream]

Radical Edward,

 

That should be E^2=...

(Otherwise, you have the crux of the solution.)

 

and light, because of the negative time term, takes the longest path in spacetime.

...........

 

One way to think of photons having energy is their different curvature for different gravitational potentials.

[Radical Edward]

Originally posted by quantumdream

Radical Edward,

 

That should be E^2=...

(Otherwise, you have the crux of the solution.)

 

and light, because of the negative time term, takes the longest path in spacetime.

...........

 

One way to think of photons having energy is their different curvature for different gravitational potentials.

 

missed the E^2 .. thanks for noticing it. and err. what negative time term? I'm, inclined to look at light from the point of view of Fermat's Principle.

[quantumdream]

Four dimensional Pythagorean theorem, with a negative time term (here for simultaneous (s^2=0), lightlike events):

 

s^2=0=x^2+y^2+z^2-(ct)^2

 

(ct)^2=x^2+y^2+z^2

 

(think of this representing a light ray with v=c).