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Quote from: Bored chemist on 29/06/2021 12:17:51Quote from: Bored chemist on 28/06/2021 21:57:19Just keep reading this"so photons, which are slowing down the mirror are giving up their own energy"until you realise it is nonsense.But they ARE giving up their energy...
But in order to create a "Kugelblitz" you need to have a constant amplification of the emitted light
Sure, there are limitations of our current technology
Strictly, what it does is tell you that a perfect measurement is meaningless.It's not an issue of measuring things.The diameter of the sphere does not exist to a greater precision than that permitted by the uncertainty principle.
Screen will always appear to get darker in the sunlight...
EM fields with similar bandwidth can SHARE the probability distribution in one volume of space. If they would overlap each other, their amplitudes would be added. Thing is, that when 2 (or more) EM waves at similar wavelenghts pass through the same space, probability of detecting a photon at one of those wavelenghts is being shared between interfering waves, according to their intensities of that probability
Quote from: CrazyScientist on 01/07/2021 02:20:30Quote from: Bored chemist on 29/06/2021 12:17:51Quote from: Bored chemist on 28/06/2021 21:57:19Just keep reading this"so photons, which are slowing down the mirror are giving up their own energy"until you realise it is nonsense.But they ARE giving up their energy...OK, so the bat slows down- which means it has less energy.And (according to you) the photons are losing energy- so they have less energy.So there is less energy overall- in total.Which is a breach of the conservation of energy.
, if the mirror is moving fast enough
I have a perfect mirror sphere with an internal diameter of 1 metre.In spite of needing magic to do this, we assume it's exactly 1 metre.I can set up a standing wave with a length of 1 metre.And also 1/2 metres and 1/3 metres and so on.There is, in principle, no reason why I can't keep adding photons with shorter and shorter wavelengths.(as an aside, I can add one going left to right, and one going up and down for each frequency too and, as in a laser cavity, I can have many photons bouncing back and to along any axis).And, as I go to higher and higher energies,the photons get more and more massive.So the sum of the masses of all the photons tends to infinity, but the diameter of the sphere stays the same.So, eventually, there's enough mass inside the 1M sphere to collapse into a BH.
Quote from: CrazyScientist on 01/07/2021 02:20:30But in order to create a "Kugelblitz" you need to have a constant amplification of the emitted lightNot really.The model I'm using says you simply keep adding light to a cavity from outside or you add light to the cavity and then make the cavity smaller.
Only both actions will lead to different results
Quote from: CrazyScientist on 03/07/2021 22:20:07, if the mirror is moving fast enoughAnd, if they are not, where does the energy go?In the experimenter's frame of reference, both bat and ball suddenly slow down, but the energy has no place to go?And, since absorbtion isn't allowed...
But... whatever.I will just move the mirror quickly.
Quote from: CrazyScientist on 03/07/2021 22:27:29Only both actions will lead to different resultsSo you keep saying.But you have yet to explain why the result isn't a BH in both cases.
1. Photons DON'T change their velocity.
If the mirror doesn't move fast enough, then reflected photons will have higher frequency than those reflected from a stationary mirror, but it still will be lower, than before the reflection
Because in the case of EM radiation, intensity ≠ frequency.
If the creation of a Kugelblitz is somehow possible, then it can be achieved ONLY by the increase of frequency of trapped radiation and not it's intensity
Actually you need to apply a constant force to it, to counter the radiation pressure
. This is what you'll observe:
However, there's another way to do it.You can imagine a nearly massless mirror.When a photon hits it, it will move and take some energy from the photon. But that means that, when another photon hits it on the other side, it will add energy to that photon.Overall, the sum of the energies will be conserved The wavelengths of the photons will be "scrambled" and will settle down to a black-body distribution.
Quote from: CrazyScientist on 01/07/2021 02:20:30Screen will always appear to get darker in the sunlight..."appear to".Because the eye / brain system which perceives the brightness is a non linear detector.That's nothing to do with physics.You may have noticed that scientists doing measurements don't typically gauge things "by eye" because it's very unreliable.Were you not aware of that?
So, if the mirror has a high enough, mass the momentum transfer will be small.And if it's moving fast then ...
Nobody said they were.But a given number of photons where the photon energy is higher (i.e. the wavelength is shorter) will have more massandA larger intensity (strictly, a larger number of photons) at a given wavelength will have more mass.And if I want a BH , all I need is lots of mass in a small space.
That seems to be proof by loud assertion, and your record on that (FM radio etc) isn't good.
It's been proven experimentally, that matter creation due to p-p scattering is possible only with EM radiation at very high frequencies (gamma radiation)
If due to constructive interference of 2 EM waves with the same wavelenght, probability of detecting a photon at the given frequency will get amplified to a specific level, then the total number of photons detected in a given period of time, will be divided between those 2 waves, according to their intensities.
t's quite an interesting question- bright schoolkids usually ask a related one.When you show them interference fringes on a screen, the clever pupils ask where the energy from the dark stripes has gone to.And the answer is that it goes into the bright stripes.
Momentum transfer will be exactly the same, no matter what's the rest mass of the mirror - mirror with less mass will just accelerate faster than one with higher mass due to smaller inertia (resistance of rest mass to acceleration).
And if in the laboratory frame, mirror will move fast enough, then due to Doppler shift, reflected radiation will have higher frequency (shorter wavelenght) than before the reflection...
Quote from: CrazyScientist on 03/07/2021 22:48:38Actually you need to apply a constant force to it, to counter the radiation pressureAs you point out, the intensity (w/m^2) will increase and so the pressure will increase.The area falls.Which effect wins is left as an exercise for the interested reader.
I won't observe anything- I won't be in there.Nor will anything else.
We really need to sort out what a perfect mirror does.There are two things I pointed out ages ago.If the mirror has a large enough mass the transfer of momentum to it is small.
Imagine you have a sphere with some photons- all of the same wavelength, bouncing back and to across the middle of it, horizontally.The photons are in a bunch.So they all hit the left hand side of the sphere and they impart some momentum to it. They bounce off to the right, with slightly reduced energyThe sphere starts to move to the left.The photons carry on to the right.So the photons now hit the right hand side of the sphere, but it's moving towards them.And, as a consequence, they bounce off with a slightly shorter wavelength than they had.The symmetry is such that the photons are back as they were and the sphere is (in the lab frame) stationary again.The sphere bounces back and to, very slightly and the photons bounce around inside it.
Now imagine that there was a photon bouncing up and down, slightly out of phase with the horizontal photon bunches.It now hits the top of the sphere at a point when the sphere is moving slightly to the left or the right (depending on the phase).And so it gets reflected slightly out of line with the vertical.And that , of course means that next time it hits the wall, it is even further from the flat bits of the mirror (the top + bottom) so it gets knocked even further away from vertical.
You can also consider a photon that's bouncing back and to "nearly horizontally".As the photon hits the moving wall s of the mirror it will gain or lose energy.And, of course, the original photons are not perfectly bunched. The early ones hit a mirror that is (initially) stationary and lose momentum to it.The later ones hit a mirror which is moving (very slightly) away from them, so they lose slightly less momentum to it.So, even if they start off bunched, their momenta get scrambled a bit with each reflection.So there's a way by which the energy and momentum of all the photons in the sphere will get shared out.My best guess is that (as I said ages ago) they photons will end up looking like a black body distribution.
It's going to get horribly complicated but, here's the clever bit.Imagine that I add a lot of photons randomly to the sphere.They all get "scrambled" in this way into a BBR distribution.As I keep adding more and more photons, I increase the total energy in the sphere.So I increase the temperature of the distribution.And that raises the (average) energy and thus shortens the average wavelength.So, even if I add monochromatic photons, I do end up with my sequence of increasing energies - with increasing masses and , eventually, I get a black hole.