Light... building the standard model

I like Serena

Thanks for the links which provide interesting reading material.
Btw, as you can see I avoided calculation of force or acceleration, restricting myself to impulse, which is the change in momentum (since I was not entirely sure how force or acceleration would turn out ).
Aren't my results correct?

DaleSpam

Oh, I didn't read carefully enough. Let me look again.

For impulse a more useful link would have been:
http://en.wikipedia.org/wiki/Four-momentum

The conservation of four-momentum contains the concepts of conservation of energy, momentum, and mass, all in one nice neat mathematical package.

I like Serena

Yep!
That's why I picked this one to work things out.
It keeps things nicely neat and simple, and shows the relation with classical mechanics, whereas force and acceleration tend to become messy.
And btw, doesn't the relation f = dp/dt hold?
In my example the average force would be the impulse divided by the time to accelerate the box.

DaleSpam

OK, so looking back at your post I have made a more relevant reply. For a massive system the four-momentum is a four-vector with a length given by the rest mass and a direction given by the four-velocity.

So, assuming that you want the four-velocity to be the same for both the empty and the photon-carrying boxes after the impulse then you can just use a basic "similar triangles" argument to show that the norm of the four-impulse is larger for the photon-carrying box by a ratio equal to the ratio of the (invariant) masses:
[tex]\frac{m+2E}{m}[/tex]

If you boost that into any frame then the similar triangles argument still holds, as you would expect from the fact that the norm is frame invariant. So in all frames the ratio of the norms of the impulses depends on the ratio of the masses of the systems.

I like Serena

I'm still puzzling on relativistic masses.
I can see from wiki entries that the concept is avoided, and that there are separate parallel and transversal forms.
As it is I can distinguish 6 types of masses.

Let's say we have 4-momentum P = (E, p), where p is the 3-momentum, v is the velocity to a (distant) inertial observer.
I'm setting c=1 for ease of notation.
Let furthermore f = dp/dt be the 3-force.


The 6 types of masses I see, are:

1. The rest mass m₀, which is also the invariant mass for a single object.

2. The invariant mass, which is the norm of the 4-momentum P. This one is the same for all observers.

3. The energy-mass E, which is the first component of P.

4. The momentum-speed-ratio [itex]\frac {|\boldsymbol p|} {|\boldsymbol v|} = \gamma m_0[/itex].

5. The parallel force-acceleration-ratio [itex]\frac {f_\parallel} {\dot v_\parallel}[/itex].

6. The transversal force-acceleration-ratio [itex]\frac {f_\perp} {\dot v_\perp}[/itex].


Numbers 5 and 6 are messy and probably best avoided.
They can be derived from the time-derivative of the momentum.

Number 3 is ambiguous, since we saw with the box of photons, that it matters to an observer whether we are talking about a box of photons or a box of sand.

The interesting thing is that number 4, the momentum-speed-ratio, appears to match perfectly with the old relativistic mass concept, which appears to be consistent (but not the same) in all frames of reference, and which obeys the rules of classical mechanics as long as it is only being used in combination with momemtum and impulse.


Please correct me if I'm wrong, because I would really like to know.

TheTommy1

Correct me if I'm wrong, but my understanding is that light bends around the sun, not because light has mass but because the mass of the sun is so great it "warps" space/time and that light is following this "warped" space/time.

I like Serena

Yes, this is true and it is what is stated in general relativity theory.

If we try to explain it with classical mechanics, the mass of the sun exerts a force of gravity on the photons (whose mass is still irrelevant).
Apparently, as pengwuino stated, the resulting deviations of the photons are off by a factor of about 2.

I'm afraid the discussion in this thread has spun a bit away from the OP.

cragar

Light also has its owns Gravitational field.

DaleSpam

True, but it is not significant in this case.

elegysix

How do we know light has its own gravitational field? This certainly was never mentioned in my physics classes so far... and I've not seen any mention of it with electromagnetic waves... Where can I find information on this?

cragar

Well relativity says that mass energy or pressure bends space-time and light has energy.
If a positron and an electron collide they produce a photon or 2, im not sure if its 1 or 2, but the electron and positron have mass and im sure you would agree they have a Gravitational field. So if energy is conserved why would the gravitational field go away. It would seem weird. Even tho the Electric and magnetic field go away. But its something think about. Google gravitational field of light.

DaleSpam

It is called a pp-wave spacetime:
http://en.wikipedia.org/wiki/Pp-wave_spacetime

HallsofIvy

Because, in some extreme cases, classical mechanics doesn't work. Specifically, the Michaelson-Morely experiment gives results different from classical mechanics and so do experiments in the photo-electric effect.

elegysix

So light has its own gravitational field... even more reason for me to think it has mass. Lol.
Just out of curiosity, does anyone know what the calculated mass from its gravitational field would be? Is this the same as the mass calculated from radiation pressure?

I know that your immediate response is that this is pointless to do, but humor me please lol

cragar

Are you asking what rest mass a particle would have that had an equal G field to a photon. I think they call it Gravitational effective mass. Im sure you could do it with E=mc^2. If light had mass it seems like it would pulverize other things because it is traveling so fast could you imagine the kinetic energy. When we collide protons together in accelerators after the collision we can have the sum of the rest masses of the particles greater than the 2 protons, we are turning kinetic energy into mass. Thats why we build bigger accelerators to find more massive particles. If you think light having its own G field is weird, you could ask does the G-field itself have its own field or does an E or B field have a Gravitational field. Are gravitational waves affected by gravity.

elegysix

Anyone know the most important experiments done with light? I wanna review them.

I like Serena

Well, a few that spring to mind:

Relativity theory:
Michelson-Morley experiment
Deflection of light by the Sun
Gravitational redshift

Quantum theory:
Young's double-slit experiment
Photoelectric effect
Compton effect