Conservation of energy of a perfectly decoherent laser

[K1nem4t1cs]

The energy and momentum of a closed system is always conserved.

If a laser can emit perfectly parallel and perfectly superimposed light waves (occupy the exact same space) that are perfectly 180° out of phase and of the same frequency, what can be said about the energy and momentum of the emited light waves? If they will never ever diverge, are they not forever beyond the possibility of observation and indistinguishable from undisturbed space?

If this correct, is energy and momentum still conserved but technically unobservable?

Would they still contribute to the stress-energy tensor of their position in space according to general relativity?

 

[Ibix]

If a laser can emit perfectly parallel and perfectly superimposed light waves (occupy the exact same space) that are perfectly 180° out of phase and of the same frequency,

I would ask how you intend to make a laser do this, other than turning it off.

 

[Dale]

If a laser can emit perfectly parallel and perfectly superimposed light waves (occupy the exact same space) that are perfectly 180° out of phase and of the same frequency, what can be said about the energy and momentum of the emited light waves?

There is no emitted light. As @Ibix says, all you have done is turn off the laser.

 

[Andy Resnick]

That's 'word salad'. This is not:

https://www.osapublishing.org/Direc...4-25-28383.pdf?da=1&id=355641&seq=0&mobile=no

 

[K1nem4t1cs]

I would ask how you intend to make a laser do this, other than turning it off.

There is no emitted light. As @Ibix says, all you have done is turn off the laser.

This is just a thought experiment so I am only considering what happens when you apply the principles of classical physics (or perhaps it will take more than just classical physics) to this scenario. The practical details should be irrelevant because only the principles are being tested here.

If the light is not reabsorbed into the medium inside the laser then is the laser not still producing electromagnetic waves and is energy not still being fed into it?

Equally, one can change the practical details of this thought experiment by using apparatus to collimate said light waves to achieve the same perfect and never diverging decoherence.

 

[K1nem4t1cs]

That's 'word salad'. This is not:

https://www.osapublishing.org/Direc...4-25-28383.pdf?da=1&id=355641&seq=0&mobile=no

Andy, I cannot access this link. The page isn't responding.

Edit: Nevermind, I see it.

 

[Ibix]

The practical details should be irrelevant because only the principles are being tested here.

If you can't - even in principle - do something then considering the implications of doing it is inherently contradictory. I don't believe that you can build a laser to do what you want. If you specify a mechanism it'll be obvious where the energy goes - for example a beam splitter will let you combine two beams to get a zero "straight through" beam, but all the energy will go into the reflected beams.

 

[Nugatory]

If the light is not reabsorbed into the medium inside the laser then is the laser not still producing electromagnetic waves and is energy not still being fed into it?

Because this is a thought experiment we can simplify away many of the practical details and consider a very simple emitter of light: an oscillating charge emits coherent electromagnetic radiation. Now, suppose I wanted to also emit radiation that is 180 degrees out of phase everywhere. I need the electric field everywhere to be exactly the same, except with a different sign - and the way to do that is to do exactly the same oscillation in exactly the same place, but with a charge of the opposite sign. And if I have to charges of equal and opposite sign in the same place, what is the net charge? And how much electromagnetic raidiation do I get by oscillating that amount of charge?

 

[K1nem4t1cs]

I need the electric field everywhere to be exactly the same, except with a different sign - and the way to do that is to do exactly the same oscillation in exactly the same place, but with a charge of the opposite sign.

Could you not have two oscillators one in front of the other?

 

[Ibix]

Could you not have two oscillators one in front of the other?

Then you will get emission to the sides.

 

[K1nem4t1cs]

Then you will get emission to the sides.

One laser in front of another. The light from the rear laser is of a frequency that can pass through the laser at the front.
I swear I will keep going until there is a practical method that theoretically works.

If you specify a mechanism it'll be obvious where the energy goes - for example a beam splitter will let you combine two beams to get a zero "straight through" beam, but all the energy will go into the reflected beams.

I don't understand why combining two beams will force all beams to be reflected just because they are of opposite phase. Which must be what you meant.

 

[Ibix]

I don't understand why combining two beams will force all beams to be reflected just because they are of opposite phase.

It comes from requiring continuity of the electric field at the beam splitter (edit: i.e., from assuming that Maxwell's equations apply).

I swear I will keep going until there is a practical method that theoretically works.

You're trying to find a way to make classical physics (which respects energy and momentum conservation) not respect energy and momentum conservation. I recommend not wasting too much time, and shall take my own advice and duck out now.

 

[Dale]

This is just a thought experiment

Thought experiments require careful description of a physically possible scenario (engineering or economic considerations may be neglected) and a careful application of the relevant physical laws to the possible scenario. So no, your question is not nearly sufficiently well specified or analyzed to qualify as a thought experiment.

To make it actually be a thought experiment you would need to propose a specific mechanism for generating such a wave and then use the relevant physical laws to analyze the scenario

I swear I will keep going until there is a practical method that theoretically works.

Good luck with that. Once you have that then we can discuss that method.