Light can be closed in a mirror's box?

[swansont]

5 hours ago, John Cuthber said:

Interference isn't a loss mechanism.
The dark fringes are dark, but the bright fringes are brighter, to make up for it.

Also, nobody said the box was an integer number of half wavelengths or whatever.

It's not a requirement that the wavelengths "fit"

Yes, it is. The fringes are not observed as in a diffraction experiment unless you are coupling light out. If you are off-resonance for the cavity, the amplitude in the cavity decreases. 

[John Cuthber]

2 hours ago, swansont said:

amplitude in the cavity decreases. 

Where does it go?

[swansont]

3 hours ago, John Cuthber said:

Where does it go?

Absorption or transmission, or reflection at the input.

[John Cuthber]

9 hours ago, swansont said:

Absorption or transmission,

Are ruled out, because they are perfect mirrors.

" reflection at the input."

What "input"

[swansont]

4 hours ago, John Cuthber said:

Are ruled out, because they are perfect mirrors.

Which is yet another reason why said mirrors can't exist.

4 hours ago, John Cuthber said:

" reflection at the input."

What "input"

The way you get light into the cavity in the first place. Through the other surface of the mirror

[John Cuthber]

6 hours ago, swansont said:

The way you get light into the cavity in the first place. Through the other surface of the mirror

Cooking must be interesting in your house. Rather than take the lid off a pan to put stuff in, you try to force it through the lid.

I'm assuming the box is big enough that I  can open it, flash a light in and then close it before the light bounces back out again.

 

And we all know that perfect mirrors don't actually exist.

That's not the point.

So, where does the light go?

 

[swansont]

27 minutes ago, John Cuthber said:

Cooking must be interesting in your house. Rather than take the lid off a pan to put stuff in, you try to force it through the lid.

I'm assuming the box is big enough that I  can open it, flash a light in and then close it before the light bounces back out again.

My lab isn't that big. Also suffers from real-world problems like having to align the mirror after you "shut the door", and not suffer from vibrations that kill the resonance

27 minutes ago, John Cuthber said:

And we all know that perfect mirrors don't actually exist.

That's not the point.

So, where does the light go?

To Narnia. Diagon Alley. Nambia. 

If you postulate something that violates physical law, it's kind of silly to try and reconcile it with physical law. Perfect mirrors violate conservation of energy. One has invoked magic. At that point "where does the energy go?" is a meaningless question. 

[John Cuthber]

13 minutes ago, swansont said:

and not suffer from vibrations that kill the resonance

I'm still not convinced you need a resonance.

In particular, the vibrations will never go away- there will always be zero point vibrations.

Those will "doppler shift" the photons a bit as they bounce back and to.
I wonder if, in the end, you get a distribution of photon energies that looks like black body radiation.

 

Also, since the initial pulse was finite, the energy, and hence wavelength, of the light is uncertain so the box can't be a "perfect" match to it.

 

If it makes you feel better please assume that the mirrors are sufficiently massive that the effect of photon impact is "small" on a particular timescale- say 3 score years and ten.

Then increase the mass and see what happens to the outcome.

[swansont]

1 hour ago, John Cuthber said:

I'm still not convinced you need a resonance.

The other physicists I asked at group meeting today are convinced.

1 hour ago, John Cuthber said:

In particular, the vibrations will never go away- there will always be zero point vibrations.

How big are they, in comparison to the width of the resonance?

And this sounds like another real-world limitation, which we are ignoring, infringing on the ideal system.

 

What this boils down to is that there are gedanken systems that are beyond engineering capabilities but do not seem to break any physical law, and there are systems that are impossible because they do break physical law. Over-unity systems would be an obvious example of the latter. Perfect mirrors seem to be, too.

[John Cuthber]

If I remember correctly, the finesse of a Fabry Perot resonator depends on how good the mirrors are. If the mirrors are reflective enough then the theoretical bandwidth will fall below the limits imposed by the vibration of the resonator.

Setting aside the theoretical engineering limits of an infinitely stiff or massive system, and the practical problem of shutting the lid fast enough, I still wonder what happens to the spread of frequencies of photons in the box (now defined as having "arbitrarily good" mirrors) over time.

Does energy get "randomly" coupled from one photon to another, and if so what does the distribution look like in the long run?

 

It seems to me to be analogous to the redistribution of energies between molecules of a gas (not the same- they hit don't each other directly) so I wonder if they end up looking something like a Boltzmann distribution or a black body one.

[swansont]

The Boltzmann distribution is continuous. You aren't going to have photons in the box that are not in allowed modes.

[John Cuthber]

OK I built the box (It's a thought expt) and I built a pulsed laser to put photons in the box.

Because I have a strange sense of humour, I built the laser so it's length is exactly a billionth of the diagonal of the square lid of the box (the box is a cube).

So the light that resonates in the laser can't resonate in the box- they are in the ratio root two to one (give or take a billion-fold).

They are incommensurate.

 

OK so I open the box, and shine light into it from the laser for a short while, then I close the box.

At this point, the photons are still flying to the "bottom" of the box. 

 

When, and how, do they realise that they aren't a resonant fit?

 

 

Also, given that the length of the box isn't fixed (thanks to the uncertainty principle) the resonant frequencies are also not fixed.

How can the light "know" to be the right wavelength for a variable length F P interferometer?

[swansont]

When it hits a wall. You have to look at the boundary conditions of the E and B field.

[John Cuthber]

When it hits one wall, how does it know how far away the other wall is in order to know whether or not to disappear?
(I say disappear- because, with perfect  (or arbitrarily good) mirrors, it can't be absorbed.)

That's especially challenging since the other end of the box keeps moving , both as other photons hit it and as the ZPE moves it about.

Equivalently, how does the "perfect" mirror know to become imperfect when there's another mirror a long way away?

[swansont]

It doesn't have to know where the other wall is. The boundary conditions at the reflection are what matters.