Einsteins derivation

[shamrock5585]

so einstein is a genius of all genius. In his derivation of E=mc^2 he used the analogy of a box being in space not moving... he proved that light has matter like qualities in that when you shoot a laser from one side of the box to the other the box would move back from recoil of the laser being shot and when the laser hit the other side of the box it would balance out momentum stopping the box.

this part kind of confuses me... the recoil force on the box would be due to something accelerating forward, but does light actually accelerate... i thought it was proven that light just moves at constant speed all the time and there is no acceleration so how does it recoil on the box theoretically?

 

[cmos]

Well Einstein wasn't around for the laser (although he did theorize it, i.e. the Einstein coefficients). Anyway...

Light carries momentum $$\hbar$$k. So what you are describing is simply an instance of conservation of momentum. The difference here is that for a massive particle, the moemntum is dependent on its velocity. For light however, momentum is velocity independent.

Equivalently, we know that light carries energy. It's therefor simple to show that light impinging on a surface exerts a radiation pressure equal the the Poynting vector divided by the speed of light. This pressure (force per unit area) thus may cause your box to move as per Newton's first and second laws.

 

[shamrock5585]

so your saying this pressure would be exerted when the light was emitted and also when it hits the other side of the box?

 

[maverick_starstrider]

I don't think Einstein derived E=mc^2 that way I think he did it considering two pulses of light heading in opposite directions from a mass. Correct me if I'm wrong but did you read your derivation on the scientific american's 'ask an expert' panel? Because his 'easy' derivation seemed really flawed and was not the one used by Einstein.

 

[shamrock5585]

im not sure if that's exactly how he derived it but i remember reading an analogy that described it in that manner.

 

[cmos]

so your saying this pressure would be exerted when the light was emitted and also when it hits the other side of the box?

When light impinges onto any massive object, there will be pressure exerted onto that object. So when you say that there is also pressure then the light is emitted, there would have to be an object where it were emitted.

If you want to consider the lens as that object, then yes, there will be pressure exerted at the lens. Note though that, in general, the pressure on the lens will not be the same as the pressure on the box because the effect of the lens is to change the collimation of the light beam.

 

[maverick_starstrider]

Well if the derivation was anything like this: http://www.sciam.com/article.cfm?id=significance-e-mc-2-means

there are some significant flaws in it.

 

[shamrock5585]

it was like that example to an extent but more in depth...


basically forget the laser... if somehow one side of the box emitted light and the light was directed at the other side of the box... the recoil from the light being emitted forced the box to move in the opposite direction and when the light hits the other side it stops the box from moving... conservation of momenum... my question was basically asking how the box had recoil backwards from the light being emitted when there is no acceleration of light... there is nothing and then there is a photon moving at light speed instantly.

 

[Littlepig]

it was like that example to an extent but more in depth...


basically forget the laser... if somehow one side of the box emitted light and the light was directed at the other side of the box... the recoil from the light being emitted forced the box to move in the opposite direction and when the light hits the other side it stops the box from moving... conservation of momenum... my question was basically asking how the box had recoil backwards from the light being emitted when there is no acceleration of light... there is nothing and then there is a photon moving at light speed instantly.

Feynman in the book about QED for everyone explains that...the photon that hits the surface isn't the same that goes back. First, isn't 100% true that a photon will go back..but assuming that a photon goes back: what hapens is: the photon hit the surface and one electron absorve the photon and gets exited. Then when he backs to its original ground state, a photon is emited backwards.(not always backwards..., but assuming your initial idea, backwards...) So, does a photon get acelerated? no. a photon is emited by an electron going back to the ground state(and losing potencial energy)

 

[cmos]

The idea of radiation pressure is that a beam of light will induce pressure onto an object when it impinges onto that object. There shouldn't be a recoil by sending out light.

Clarifying Littlepig's post, let us consider an isolated atom. All that exists is the nucleus and several electrons. Should one of those electrons start out in an excited state, the spontaneous relaxation of that electron will produce a photon. That photon now propagates at the speed of light. It did not accelerate to this speed, it was released at this speed.

 

[shamrock5585]

cool.. thanks cmos...

littlepig... try and limit the spelling errors and type clearly... i had a hard time trying to decypher what you were saying.

...sidenote... when you said about the electron relaxation creating a photon... doesn't that apply to LED's to an extent?

 

[cmos]

...sidenote... when you said about the electron relaxation creating a photon... doesn't that apply to LED's to an extent?

That applies exactly. In an LED, light emission is due to the (spontaneous) relaxation of an electron from the conduction band to the valence band. Similarly, in a laser, the light emission is due to the (stimulated) relaxation of an electron from some higher energy level to a lower one. In an antenna, it is the acceleration of charge up and down the device that emits light - acceleration implies force, force implies changing energy.

To paraphrase Newton: to similar effects we must attribute similar causes. Genius.