Light & Energy... A question...

[RyanJ]

If light is composed of "packets of energy" (Quanta) then what gives light its energy too move? Does it use up its own energy or is this a combnationof my lack of sleep and flawed logic working again?

 

Any help clearning this up for me would be most appreciated

 

Cheers,

 

Ryan Jones

[Klaynos]

this is what I was told:

 

In a photon the E and B fields are orthoginal to each other. A moving B or E field creates one of the other form, so a moving E field creates a B field and vise versa. So the photons B field creates an E field and it's E frield creates a B field, in this way the photon "bootstraps" itself to propogate.

[timo]

If light is composed of "packets of energy" (Quanta) then what gives light its energy too move? Does it use up its own energy [...']

The energy light has is purely kinetic energy and connected to a momentum p=E/c. However, that´s only half of the answer. Having a state where your photon has a definite momentum will not produce anything you´d consider movement at all.

 

I´ve written a small gnuplot file in which I try to visualize where movement of photons comes from. Copy the following lines to a file and load this file in gnuplot:

f(x,t,k) = cos(k*x-k*t)
g(x,t,k) = sin(k*x-k*t)

r(x,t) = (f(x,t,1)+f(x,t,1.5)+f(x,t,2)+f(x,t,2.5)+f(x,t,3)+f(x,t,3.5)+f(x,t,4)+f(x,t,4.5))/(8**0.5)
i(x,t) = (f(x,t,1)+g(x,t,1.5)+g(x,t,2)+g(x,t,2.5)+g(x,t,3)+g(x,t,3.5)+g(x,t,4)+g(x,t,4.5))/(8**0.5)

w(x,t) = r(x,t)*r(x,t) + i(x,t)*i(x,t)

set xlabel "position"
set xrange [0:8]
set ylabel "relative probability density"
set yrange [0:10]

plot w(x,1) title "time=1"
replot w(x,4) title "time=4"
replot f(x,1,1)*f(x,1,1)+g(x,1,1)*g(x,1,1) title "pure k=1, any time"

 

f and g are the real and the imaginary part of a photon state with definite energy k at time t, respectively (note that when one puts c=1, energy and momentum are equal, which is the reason the same factor k appears before x and t).

 

From these states with definite momentum, I now construct a linear combination of different momenta. The resulting state (whose real and imaginary part are denoted by the variables r and i) will not have any definite momentum -the momenta 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5 all have equal probability of being measured- but as you will see in the plot, it´s position can be determined better.

 

To view the position of the photon, the probability density for its position is calculated in the next step. w(x,t) gives you the relative probability to find the photon at position x at time t (relative, because I was too lazy to normalize the wavefunctions).

 

The next lines are only plotting commands, then. The probability density for the photons position are plotted for two different times and a reference curve for a photon with a definite momentum is plotted.

The first interesting thing is that for the case of a definite momentum, there is no way to tell where the photon is. This is true for all times. This is the reason why I said that you cannot associate a state with definite momentum to motion.

In contrast to that, the linear combination shows a clear peak region in which you´ll most probably find the photon. You can see that the photon moves to the right with velocity 1 (guess which phyiscal constant I set to one in above ...).

 

I don´t know how much this helps you but I think it´s nice seeing some math and seeing it visualized. The output of above script is attached to this post, in case you don´t want to download gnuplot.

 

EDIT: There is a typo the definition of i(x,t). The 1st summand has to be a g, of course. The plot below is made with this flawed version because the features I wanted to show remain the same, anyways.

[swansont]

If light is composed of "packets of energy" (Quanta) then what gives light its energy too move? Does it use up its own energy or is this a combnationof my lack of sleep and flawed logic working again?

 

There's no "friction" involved, so it doesn't have to "use up" any energy to move. Unless it collides with something, it has whatever energy with which it started.

[RyanJ]

Ah, I think I understand now - thanks guys - great job explaining too

 

Cheers,

 

Ryan Jones