[Bored chemist]

There are no black holes involved in this proecess...

Nobody said there were.

Simple questions; you say that you can only get a fixed number of photons in there.
How many?
What actually stops you adding another?

"Perfectly reflective mirror" means, that 100% of incident photons is being reflected from it - there's no physically possible way, to prevent the transfer of momentum.

Yes...
So what?
It's not as if that's new.

So at last you do actually admit, that size of cavity and the wavelenght of traped radiation DO define the intensity and the number of photons inside cavity?

You seem to have hallucinated that.
I never said anything like it.
I said you can't change the intensity and the number of photons independent because they are essentially the same thing.
On the other hand you suffered from the misunderstanding that one can.

you can only increase the intensity of photons - not their number

the importance of cavity size in respect to the wavelenght of trapped radiation - it was you, who insisted, that it has nothing to do with resonance

That's another instance of you saying things that aren't true, isn't it?

What I said was the number of photons that you can put in a cavity is unlimited.

You seem to think they can't fit into the cavity unless they fit "exactly" and, as I pointed out, that's simply not true.

Resonance does depend on wavelength and the size of the box.
But not everything is resonant.
As I have pointed out, if it was then, in order to light my room I would need to start by measuring it to the nearest nanometre or so and buying light sources that produced the "right" wavelength.
That's just silly.

appearing

Yes, but not "actually darker..." which is what matters in science.

And you are still missing the point that you can stack as many bosons in an eigenstate as you wish.

[puppypower]

Don't worry, I've finished high school and I know about the main differences between bosons and fermions - like the rest mass or Pauli exclusion. And it's because of I consider the idea of pernamently turning bosons into fermions as physically impossible. It IS however possible to make photons behave JUST LIKE particles of matter using optical cavities (what a cocincidence) - what was done couple years ago by scientists from my home country

https://scienceinpoland.pap.pl/en/news/news%2C79418%2Cgroundbreaking-research-shows-photons-can-behave-electrons.html

I have been saying for years, photons, although moving at the speed of light also display inertial properties, which are usually considered something done by matter moving less that the speed of light, such as electrons. This was inferred from plugging in the speed of light into the special relativity equations. Photons, if they were exclusively in a c-reference, should all appear the same in our earth reference. Instead they show inertial affects such as a variety of wavelengths that can be tweaked at inertial velocities; Doppler Shift.  It is nice when science catches up.

Photons are not exclusively in just the speed of light reference. They are a bridge state that exists in both inertial and speed of light references at the same time. The hollow mirror experiments are a way to  isolate the inertial aspects.

[Bored chemist]

Your're doing it again...

in a c-reference

our earth reference

speed of light reference

speed of light reference

and it's not helping.

[puppypower]

Say we had a single spherical source of photons deep in open space. Next, gather a fleet of space ships and have them create a wide range of moving references, coming and going in different directions, from the photon source.

What will happen is we will see a wide variety of Doppler shifts, all with the same photon source. Some will see a red shift and some will see a blue shift. Depending on their velocity this can be high or low. Where is the photon energy going or coming from, since a red and blue shift will create photons with less or more energy, from the original source electrons?

We know this affect; Doppler Shift, is connected to velocity, but the change in energy cannot be  connected to this kinetic energy, since the references do not slow down or speed up simply by looking at photons. The enormous number of red shifted photons, from billions of galaxies, each with billions of stars, seen by the earth, does not alter the speed of the earth. So where is the added or subtracted energy going to or coming from?

The simplest answer is connected to the inertial side of the photon and to entropy changes.  Entropy is a state variable, meaning for any given state of matter there is a fixed entropy value. If we approach the photon source, the blue shift is due to the observational state of reference and photon, lowering entropy and releasing energy into the photon. If we move away from the source the observational state reference and photon is increasing entropy, so the photon releases energy into the entropy increase; red shift.

In this thought experiment, source photons change differently as they become part of different observational state. Each instrument, on each moving reference, will gather different source photons. Two instruments separated by time and space cannot capture the same photon. Each photon forms a unique states with one observer who captures it.

Entropy is usually associated with matter, however, the inertial leg of the photon can game the system to create this extra entropic affect. The second law implies a net universal red shift since an increase in universal entropy will absorb energy, even from the photons.

What is interesting is if we assume dark energy is causing the expansion, then the addition of dark energy is also causing the red shift. So why is dark energy giving energy for an expansion that results in the photons losing energy? The inertial leg of photons should also be impacted by dark energy if it is real.

[CrazyScientist (OP)]

Also you seem to ignore the fact, that "nearly massless" mirror will be probably also nearly completely transparent for photons or (and?) will suffer extreme fluctuations of mass/energy due to it's changing kinetic energy....

Are you deliberately missing the point?
It is precisely because the mirror gets bounced about that it can doppler shift the photons up and down to give a BBR like distribution.

Actually the more the mirror is being "bounced around" by incident photons, the smaller Doppler effect will be observed in a 3rd stationary frame.

I didn't "add" radiation pressure- it happens.

It happens only if there's some radiation affecting the cavity beond it's boundaries - and it is an additional variable

When it does work against a mirror (or vice versa) , it changes the energy of the photons.

Yes. Bravo good sir! And there's no physical way of preventing this process...

I mean, mirrors used in experimental cavity QED can reach "only" 99,9% of perfect reflectivity at best,

That might be as good as the physicists get, but the chemists do better.
https://en.wikipedia.org/wiki/Cavity_ring-down_spectroscopy
Where they use mirrors like this
https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=14069

with "R > 99.9969%".

Do you know, that you're digging your own grave here?

Yes - the idea, that scenario presented in the 1st post of this thread might somehow lead to creation of a black hole of light, is experimentally disproven.

So, you are saying that one experiment didn't make a BH.
Well... good. As far as I know, no human intervention has ever created one.

I'm saying, that the experiment never supposed to result in creation of a BH - even in hypothetical perfect conditions.

Did you feel that failure in one particular set of experimental circumstances precludes the success of a modified experiment?

Only this experiment wasn't in any way a failure - actually it was a complete success. It never supposed to lead to creation of a BH and it didn't...

And, I'd still like to see the experimental details.

You have them given in the paper. But if you don't trust in the published results, then maybe speak with authors of that paper. I'm sure you'll find the missing black hole somewhere between the numbers 

I absolutely might be wrong or uninformed, when I make my statements

And in this case, you absolutely are wrong.
The experiment has not been done because it's' impossible.
It's a thought experiment.
Nobody actually made, for example, a perfectly reflecting cavity or a one-way valve for light.

Still you can calculate the most possible results for a perfectly reflecting cavity and compare them with results obtained from the practical experiment - just as it was done in that paper.

And why should you? Since when science suppose to be based on faith?

Then why did you point out that you said something- without any supporting evidence- such as the tosh about radio.

Saying "I said that..." doesn't influence its truth; providing evidence does.
And you provided none.

Which part of it? The one about the interference between antennas? I did... But here's more if you insist:
https://www.seamagazine.com/importance-antenna-placement/
http://www.til.ca/content/pdfs/12RE466-Technisonic-FM-Radio-Guide.pdf

4. DO NOT mount antennas closer together than the required radius, if you MUST do this,
be certain they are NOT in adjacent or harmonically related bands. Radio performance will
almost certainly suffer in some way for mounting in this manner, and it should not be done
unless all other possible avenues have been completely exhausted

On the other hand it is in fact quite obvious - if you take 3 walkie-talkies and try to communicate using 2 of them,  transmission will get much worse if you place a 3rd receiver on the way between them. By receiving a radio signal, you "destroy" the photons carrying the transmission - so they can't reach a receiver further behind you...

You keep asserting that you can only get a finite set of photons into a cavity; but you don't say why.

Wait - didn't you admit it here?

For a given cavity and wavelength, the intensity is proportional to the number of photons. You can't change them independently.

So the size of cavity and the wavelenght of trapped radiation are the factors, which define the intensity/number of photons inside the cavity...

And how it's possible? It's obviously due to resonance and constructive/destructive interference of EM waves

I , on the other hand, say you can get an arbitrarily large number; and I provide both practical (they do it in laser cavities) and theoretical (photons are bosons)  justification for my view.

You, on the other hand didn't provide a single source, which would prove the idea of infinite number of photons inside a cavity with a fixed volume and for radiation with a specific wavelenght...

Sure, I never denied the possibility of matter creation from photons (like in p-p scattering). But the thing is, that those are not "natural" states of a photon, which require sophisticated manipulation in order to sustain the effect for couple nano seconds. Normally photons don't have energies, that would exceed hard gamma radiation.

You still don't get the bit about the relativistic snail, do you?

Relativistically speaking, velocity of snail doesn't matter for photons nor for the snail - it only matters for a 3rd observer, who is looking in his own rest frame at photons reflected from a moving snail...

[CrazyScientist (OP)]

One paradoxical observation about photons, is that according to Special Relativity, at the speed of light time and space will appear contracted to a singularity state. Photons travel at the speed of light and have both distance and time parameters that we call wavelength and frequency, yet their outward expression in space and time is not homogeneous as predicted by SR. The large variety of wavelengths from radio waves to gamma defines a wide range of visual references, as though all photons are going less than the speed of light.

And this is one of the reasons, why I consider SR as probably the greatest mistake of theoretical physics. According to Einstein, photons don't experience the flow of time - yet it is possible to track down the timeline of each single photon since the moment of it's emission.

The mirror experiment tell us that photons have momentum, however, that momentum is not connected to its velocity at the speed of light, but is due to its finite parameters in time and space. It is creating an inertial velocity based affect while traveling at the speed of light.

This animation shows nicely the relation between momentum of a photon and the wavelenght of EM radiation. Transverse (up/down) velocity of a photon is higher for a shorter wavelenght - so in shortcut higher frequency = greater momentum of a photon

The Doppler shift, due to relative velocity between references, can cause the photon wavelength and frequency to change, without altering the speed of the light

True...

The relative velocity in inertial references does not add or subtract from its speed of light, but only impacts its space and time parameters. Photons appear to exist in both the speed of light reference and inertial reference at the same time, with each independent of the other. Photons appear to be bridge between a pure speed of light reference and all inertial references.

If inertial frame of photons would be independent from each other, it would make the interfernce of EM waves impossible.  Yet we all know, that EM interference DOES occur - espppecially for EM waves with similar wavelenghts.

I think, that there's much more easy solution for that problem - all what has to be done, is to describe the Universe as a HUGE caity with an unified EM field, trapped inside it and then treat photons as finite (but VERY LARGE) number of stationary "pixels" on the "screen" of physical space.

What science does, is to treat potential and kinetic aspects of a single EM field, as 2 separate and independent quantum fields with diffrent sets particles (photons and virtual photons). However what in fact makes the entire difference between a "normal" photon and a "virtual" one, is it's probability of detection at a given frequency band - it's still one and the same photon, which exists as a superposition of all it's possible states... That's all...

When a photon is Doppler Shifted; red shift, the measured energy of the photon goes down. Where does the lost energy go, since energy conservation does not allow one to create or destroy energy? The kinetic energy associated with the constant velocity between references does not increase. Does it go into an entropy increase; state of higher complexity?

Doppler's shift is a purely relativistic effect - it doesn't happen in the rest frame of a moving object and can't lead to any definitive change in the energy level of a moving system...

If we use a relative velocity that causes a blue shift, the measured energy of the photons will increase. Where does this extra energy come from, if the velocity is constant and kinetic energy does not change? Does it come from a lowering of entropy, which will release energy? Is the Doppler shift of photons connected to the second law? Or is there another source to account for the photon energy balance?

It comes from the relativistic energy of relative velocity. Energy level doesn't change in the rest frame of a moving object - it changes for all the frames, that are movinge in relation to that object (depending on direction and relative velocity). None of this is a definitive change in the energy of a moving system...

[Bored chemist]

Only this experiment wasn't in any way a failure - actually it was a complete success. It never supposed to lead to creation of a BH and it didn't...

I see; you really were posting about something irrelevant.

Wait - didn't you admit it here?
Quote from: Bored chemist on 11/07/2021 11:13:28
For a given cavity and wavelength, the intensity is proportional to the number of photons. You can't change them independently.

So the size of cavity and the wavelenght of trapped radiation are the factors, which define the intensity/number of photons inside the cavity...

No.
I already explained that you had hallucinated that I agreed with you.

I never said anything like it.
I said you can't change the intensity and the number of photons independent because they are essentially the same thing.

Perhaps you might try having a go at answering the points I raised.

Simple questions; you say that you can only get a fixed number of photons in there.
How many?
What actually stops you adding another?

And you are still missing the point that you can stack as many bosons in an eigenstate as you wish.

You say silly things like

You, on the other hand didn't provide a single source, which would prove the idea of infinite number of photons inside a cavity with a fixed volume and for radiation with a specific wavelenght...

Well, I have made it clear that, well before you got to"infinity" the photons would collapse into a BH.
So I'm not sating that there are an infinite number of photons, juts that the number you can get is arbitrarily large.
But you seem to think you can only get one photon.

And you think that's because of resonance, even though there's no requirement for resonance to happen.

So, why not address those points?

[Bored chemist]

Relativistically speaking, velocity of snail doesn't matter for photons nor for the snail - it only matters for a 3rd observer, who is looking in his own rest frame at photons reflected from a moving snail...

OK, so , since you don't understand the idea, I will spell it out for you.

If it was possible to make a mirror shell that had amass comparable with a photon, then the shell would obviously  be "light enough" for the context I described.
But, even if the shell weighs many tons, the effect is still there- it is much smaller.
The wavelengths still get scrambled to form an approximation to BBR- which you agreed about.
(Though you tried to pretend that I hadn't said it- a particularly stupid pretence in a discussion thread where everything is written down and date-stamped).

The higher mass just means the effect takes longer.
Since nobody put a time limit on the experiment, that does not matter.
So, given time, an indefinitely heavy mirror is still "light enough".

[CrazyScientist (OP)]

Simple questions; you say that you can only get a fixed number of photons in there.
How many?
What actually stops you adding another?

It's the physical volume of EM waves.

In a cavity with 1m of diameter you can fit only one EM wave with 1m of wavelenght, which makes one photon in this type of radiation. If that EM wave is then reflected back and create a standing wave with 2x greater amplitude, it will still make just one photon with higher density of probability. To increase the number of photons, you would have to increase the diameter of cavity to 2m - so you could "fit" inside it 2 EM waves with 1m of wavelenght...

You seem to think, that the reflected photons will keep "stacking" on top of each other into infinity (or creation of a black hole), but you keep to ignore the fact, that energy of a photon is defined by it's frequency and not it's amplitude. You CAN'T burn a human skin with FM waves - no matter how intense the FM field will get.

Another thing which you seem to ignore, is the fact that intensity of radiation is defined by probability of detecting photons at a given frequency. Probability is NOT infinite, as it can't reach values below 0% and above 100%. If your claims would be true, then in standing waves probability of detecting a photon would have to reach values higher than 100% - and it just doesn't make sense....

"Perfectly reflective mirror" means, that 100% of incident photons is being reflected from it - there's no physically possible way, to prevent the transfer of momentum.

Yes...
So what?
It's not as if that's new.

True - it isn't... Then why do you try using your own definition of a "perfect mirror", where transfer of momentum doesn't occur during reflection of photons?

So at last you do actually admit, that size of cavity and the wavelenght of traped radiation DO define the intensity and the number of photons inside cavity?

You seem to have hallucinated that.
I never said anything like it.
I said you can't change the intensity and the number of photons independent because they are essentially the same thing.
On the other hand you suffered from the misunderstanding that one can.

you can only increase the intensity of photons - not their number

This is what you said:

the importance of cavity size in respect to the wavelenght of trapped radiation - it was you, who insisted, that it has nothing to do with resonance

That's another instance of you saying things that aren't true, isn't it?

What I said was the number of photons that you can put in a cavity is unlimited.

This is exactly, what you said:

For a given cavity and wavelength, the intensity is proportional to the number of photons. You can't change them independently.

"For a given cavity and wavelength", means that all those variables depend on each other - at least this is, how I anderstand it...

Anyway, if the number of photons for each wavelenght of an EM radiation trapped inside a cavity can be infinite, explain me such things, like cut-off frequency in photoelectric effect. Electrons won't respond to photons, until EM radiation won't reach a certain frequency, independently of the intensity. Do you suggest, that at some critical point of radiation intensity, electrons and photons will start to interact gravitationally? And if so, do you have even a SINGLE experimentally validated proof of such possibility?

You seem to think they can't fit into the cavity unless they fit "exactly" and, as I pointed out, that's simply not true.

It would be nice if you would also point out to somekind of scientific data, to support your rather exotic claims about black holes creation by increasing the intensity of radiation...

Here's for example my data:
https://www.physik.hu-berlin.de/de/nano/lehre/copy_of_quantenoptik09/Chapter12
Page 170:
Figure 93: Observed intensities, linewidths, and frequency shifts as a function of the cavity detuning
(from bottom to top). The cavity length decreases from left to rigth

Resonance does depend on wavelength and the size of the box.

Woow! We can at last go somewhere from here

But not everything is resonant.
As I have pointed out, if it was then, in order to light my room I would need to start by measuring it to the nearest nanometre or so and buying light sources that produced the "right" wavelength.
That's just silly.

I didn't say, that in everyday life each EM wave is in a resonance. I'm saying, that if you want to amplify waves, you should make it through their resonance and that for each given wavelenght and volume of cavity, there's a specific limit of amplitude that can be reached for a constant source of sound/radiation.

appearing

Yes, but not "actually darker..." which is what matters in science.

What matters, in science is simple logic - if an external beam of light appears to be darker than light trapped in cavity, then it's rather obvious, that it's amplitude is smaller. If the amplitudes would add together, beam would appear brighter than light inside cavity - but to achieve such effect, you need to introduce light at higher intensity compared to light in cavity. It's simple...

You won't increase intensity of radiation due to interference of EM waves at the same wavelenghts. but different amplitudes - in a given volume of space density of probability is being shared by EM waves at similar wavelenghts

And you are still missing the point that you can stack as many bosons in an eigenstate as you wish.

And you are still missing the point that probability of detection can't go beyond 100%

[CrazyScientist (OP)]

Well, I have made it clear that, well before you got to"infinity" the photons would collapse into a BH

And I guess, that i just have to take your word for it, because science is for now unable to test any of this in practice?

So I'm not sating that there are an infinite number of photons, juts that the number you can get is arbitrarily large.
But you seem to think you can only get one photon

No. I think, that in order to get the total number of photons in cavity (according to the current definition of a photon), you need to add all the photons, which are given for each avaliable eigenstate (1 for n=1 or 3 for n=3). What matters is the relation between the wavelenght and volume of cavity.

And you think that's because of resonance, even though there's no requirement for resonance to happen.

So, why not address those points?

What is required, is amplification of EM waves and you can achieve one through resonance.

But maybe instead of resonance you should think about concentrating radiation in one point using a lense or concave mirror...

What if we take a HUUUGEEEE magnifying glass and concentrate 50% radiation of the Sun in one point of space - maybe this is how you should approach your unverified claims about gravitational interactions between photons.due to high intensity of radiation. Only don't forget that such mechanism suppose to work for all avaliable wavelenghts of EM radiation

OK, so , since you don't understand the idea, I will spell it out for you.

If it was possible to make a mirror shell that had amass comparable with a photon, then the shell would obviously  be "light enough" for the context I described.
But, even if the shell weighs many tons, the effect is still there- it is much smaller.
The wavelengths still get scrambled to form an approximation to BBR- which you agreed about.
(Though you tried to pretend that I hadn't said it- a particularly stupid pretence in a discussion thread where everything is written down and date-stamped).

The higher mass just means the effect takes longer.
Since nobody put a time limit on the experiment, that does not matter.
So, given time, an indefinitely heavy mirror is still "light enough".

Let's then imagine a simple scenario, where a stationary mirror has almost the same mass/energy, as an incident photon. What do you think will be observed in the lab frame?

My answer is:
- incident photon will accelerate the mirror almost to c, while being reflected back in opposite direction at c with just a tiny fraction of it's previous frequency/momentum

[Bored chemist]

What if we take a HUUUGEEEE magnifying glass and concentrate 50% radiation of the Sun in one point of space -

You can't; it's one of the laws of optics.

In a cavity with 1m of diameter you can fit only one EM wave with 1m of wavelenght, which makes one photon in this type of radiation.

OK, so, by that "argument" you can only fit 1 photon of wavelength1 mm into a 1 mm space and so on.
So, if I have an object the size of a small bacterium for example- about 0.5 micron then you can get just 1 photon of visible light into it.

And yet, if I suitably stain one, and look at it via a good confocal microscope, I can see structures within it.

Let's go back to the bigger - 1 metre- box.
And, just for a bit of variety, let's imagine it's a mirrored cube.
I open the top  and bottom of the box, and let the sunlight shine through it.
On earth that would mean that about 1KW of various wavelengths of radiation are passing through it.
But, mainly to make the arithmetic easy, lets imagine that the box is next to the Sun.
We can treat the sun as a black body at about 5700K

Well, our black body emits rather a lot of radiation
If this  page is right
https://www.omnicalculator.com/physics/stefan-boltzmann-law
there's about 600 million watts of power travelling through our box.

And now imagine that I suddenly put the top + bottom back on the box and trap the light (Yes, I know it's impractical but that's not the point).

How many photons of about 1 metre wavelength do I trap?

Well, if this
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html
is right  then about 0.6E-9 Watts has a wavelength within 1 micron of 1 metre.

And that's carried by photons with an energy of 2E-25 J
So that's 3E15 of them each second.
And they traverse the box in  1/C  seconds.
So, there are, on average, about ten million of them in the box at any time.
And if I snap the lid shut, that's how many get caught in the box.

Of course, the Sun is a great source of light, but it's not very efficient as a 1 metre radio wave source.
It only emits nanowatts per square meter  of radiation at 1 metre.

I can do rather better than that.
I'd need to tweak the frequency down a bit but the "key fob" transmitters  used for opening garage doors
https://en.wikipedia.org/wiki/LPD433
And that would let me transmit 10 milliwatts. which is about a billion times more power than a square foot of the sun (at 1 metre)

So I can arrange, quite easily , for there to be about 10E12 photons in the box.

By my reckoning, that is more than 1.

Let's then imagine a simple scenario, where a stationary mirror has almost the same mass/energy, as an incident photon. What do you think will be observed in the lab frame?

My answer is:
- incident photon will accelerate the mirror almost to c, while being reflected back in opposite direction at c with just a tiny fraction of it's previous frequency/momentum

And very shortly afterwards, it will hit the other side of the spherical shell, and be kicked back to very nearly the same energy that it had in the first place.
That's fine if we have just one photon.
In reality, we have many
So,  in the mean time (between the two collisions of that one photoon), any other photons which hit the mirror hit a moving mirror. So their wavelengths will also get altered in a way that's chaotic.
This is the mechanism by which the light is scrambled into a black body spectrum.

And that's the  mechanism by which high energy photons are made.

[Bored chemist]

OK that was the case for a mirror of very small mass- comparable with a photon.
For visible light that's something like a millionth of the mass of an electron.
So a les insane guess at the mass for our reflector might be 1 gram.
And that's about 33 orders of magnitude higher.
So the change in photon energy , when it transfer's some to the mirror is about 10^33 times smaller.


But it isn't zero.
Ad, if the mirror weighs a tone, then that's 10^36 times smaller, but it still isn't zero.

So, like the relativistic snail, there is still an effect, it's just rate small.

So the scrambling of wavelengths to give a BBR distribution is slower. at least 10^36 times slower and, I suspect 10^72, times slower.


But it still happens.
And, since nobody set a time limit on the experiment, the timescale is not important.
(Of course, with a large number of photons to start with the process is faster and the plan for the experiment is to keep on adding photons)
The outcome happens eventually.

So, there's a mechanism for getting arbitrarily short wavelengths.
So you can get an arbitrarily large number of photons in the box. (even if we accept your wrong suggestion about only 1 photon per eigenstate and ignore the fact that a sphere has an infinite number of degenerate eigenstates - one for each diameter)
So you can get enough mass of photons  for them to collapse into a black hole.

[Bored chemist]

You CAN'T burn a human skin with FM waves - no matter how intense the FM field will get.

Talking about "FM" is a bit meaningless. I presume you mean the wavelengths typically used to transmit FM radio- about 100 MHz.
You should have learned not to get your fingers burned by being wrong about radio waves.

Yes you can use 100 MHz waves to burn skin.
"Diathermy is produced by three techniques: ultrasound (ultrasonic diathermy), short-wave radio frequencies in the range 1–100 MHz (shortwave diathermy) "
From
https://en.wikipedia.org/wiki/Diathermy

You should stop pretending that you know things.

If your model predicts that it's impossible to get RF burns at 100 MHz, and , in reality, people do get RF burns at 100 MHz, it is clear that your model of the universe is wrong.
https://www.researchgate.net/publication/224188647_Radio_Frequency_Burns_in_the_Power_System_Workplace

Why do you keep trying to insist on it?

[Bored chemist]

What is required, is amplification of EM waves and you can achieve one through resonance.

You do not need "amplification" if you just keep adding photons from an external source.

If I want more cattle in my field I can do that by letting them breed- which is sort of analogous to amplification- the number next year is proportional to the number this year- or I can just buy more cattle and put them in the field.
The rate at which increase the population of the field is dependent on my resources.

(and, of course, unlike cattle, photons take up no space- you can (no mater how strongly you shout otherwise) have an arbitrarily large number of them in a given space because they are bosons.)

[Bored chemist]

"For a given cavity and wavelength", means that all those variables depend on each other - at least this is, how I understand it...

I see the problem lies with your reading comprehension.

What I said
"For a given cavity and wavelength, the intensity is proportional to the number of photons. You can't change them independently."
Is true.
It does not imply what you said it did.

"So at last you do actually admit, that size of cavity and the wavelenght of traped radiation DO define the intensity and the number of photons inside cavity?"


That is clearly not true.
Imagine the case where there is not a single photon in the box.
The intensity and the number of photons is zero.
Now add a single photon in the box.
The intensity and the number of photons have changed- but the box is the same size,
Now add a second photon.
Again the size of the cavity is unchanged and the wavelength is unchanged, but the intensity , and the number of photons have changed.

Do you see how the size and the wavelength do not define the intensity or the number of photons in the box?
Do you see how that falsifies your claim that "that size of cavity and the wavelenght of traped radiation DO define the intensity and the number of photons inside cavity"?

OK
If I double the number of photons in the box, I double the intensity.

So, they are proportional to one another . Adding a third photon will produce treble the intensity, and so on.
Which is why I am able to make the claim in the second clause of my statement
"the intensity is proportional to the number of photons. You can't change them independently"


But it is slightly more complicated than that.
If I use photons with half the wavelength then the intensity - measured in watts per square meter is doubled because each photon has twice the energy.
So, in order to make the statement  "So, they are proportional to one another ."
I have to specify that it's true for a given wavelength.

And similarly, if I keep the number and wavelength (and thus the energy) of the photons the same, but change the size (i.e. the area) of the box, the intensity- in watts per metre squared changes in inverse proportion to the area.

So, again, i need to qualify the assertion "So, they are proportional to one another ." by specifying that the size of the box does not change.

Hence, my statement
"For a given cavity and wavelength, the intensity is proportional to the number of photons. You can't change them independently."

Do you now see that
My statement was true.
Your statement was false and  (logically as well as linguistically) my statement does not imply your statement, nor is it compatible with it?

[CrazyScientist (OP)]

What if we take a HUUUGEEEE magnifying glass and concentrate 50% radiation of the Sun in one point of space -

You can't; it's one of the laws of optics.

I didn't hear about any law of physics, according to which it is impossible to concentrate EM radiation with a lense or concave mirror - can you please tell me, what exactly is that law? From my own observations, it appears that a magnifying glass or a satellite dish DOES work pretty well by doing just that - concentrating EM waves, which are scattered in a volume of space in one point, to increase the intensity/amplitude of radiation.

If your claims about creating black holes by increasing the intensity of radiation are true, then you should be able to achieve it by concentrating enough EM radiation in one point of space using star-sized lenses or intergalactic concave mirrors. It's only a matter of scale - the bigger is the radius of a lense/mirror, the more EM waves will be concentrated in one point, resulting in higher intensity... What makes it theoretically impossible?

In a cavity with 1m of diameter you can fit only one EM wave with 1m of wavelenght, which makes one photon in this type of radiation.

OK, so, by that "argument" you can only fit 1 photon of wavelength1 mm into a 1 mm space and so on.
So, if I have an object the size of a small bacterium for example- about 0.5 micron then you can get just 1 photon of visible light into it.

And yet, if I suitably stain one, and look at it via a good confocal microscope, I can see structures within it.

Since you claim to have a proper education in the field of optics,and quantum electrodynamics, you know probably about such thing, like diffraction of waves and how important for that mechanism is the size of obstacles in relation to wavelenghts - but just in case, this is how it works:

Generally speaking, nothing fancy... And you don't need to be a genius, to know how to apply this process in your scenario and guess, what will happen if we'll try to observe an object with the size of around 500nm (0,5 micron) under a microscope.

In shortcut, you will be able to see your bacteria in great details, if the background light will have blue color. However light with a green color will giive you much worse results and internal structures of that bacteria no longer will be visible as clarly as with the blue light. And with the red light, the entire bacteria will become barely visible (or even completely invisible if the wavelenght will get large enough in relation to the size of observed bacteria)... Shortly speaking, the shorter will be the wavelenght (higher frequency) of light used by your microscope, the better results you'll get...

Let's go back to the bigger - 1 metre- box.
And, just for a bit of variety, let's imagine it's a mirrored cube.
I open the top  and bottom of the box, and let the sunlight shine through it.
On earth that would mean that about 1KW of various wavelengths of radiation are passing through it.
But, mainly to make the arithmetic easy, lets imagine that the box is next to the Sun.
We can treat the sun as a black body at about 5700K

Well, our black body emits rather a lot of radiation
If this  page is right
https://www.omnicalculator.com/physics/stefan-boltzmann-law
there's about 600 million watts of power travelling through our box.

And now imagine that I suddenly put the top + bottom back on the box and trap the light (Yes, I know it's impractical but that's not the point).

How many photons of about 1 metre wavelength do I trap?

1.There's a significant difference for radiation emitted by a single point-source and for radiation emitted from some area/volume.  If the EM waves are being emitted by a single point-source at a constant frequency, we'll get a radiation which is coherent and monochromatic. And in such case, it will be possible to know the exact number of photons at 1m wavelenght, which at a given moment are being trapped inside a cavity which is 1m long - and this number won't never be higher than 2...

However things become much more complicated if the radiation is being emitted by a bigger volume/area of space. It wouldn't be a bigger issue, if we could simply make a point-source bigger, but it isn't howit works. In this situation radiation isn't in fact radiated by a single source, but by multiple point-like sources, which are distributed in a given volume of space. it means that here, in every given period of time, multiple EM waves are being emitted simultaneously - and each one of them can have different wavelenght, phase or magnitude. All of this  can lead to (at least) 3 different types of EM radiation:

And since you brought up radiation of the Sun, in this scenario we'll have to deal with a radiation, which is not only non-coherent but consists multiple EM waves at different wavelenghts and amplitudes - in shortcut the worst possible case for the subject discussed in this thread.

So now in order to trap a specific type of radiation (at 1m wavelenght), you need to "filter it out" from the entire spectrum of radiation, which is produced by the Sun. In the end, all what you did here, is to make everything 10 times more complicated without any logical purpose

2. Your box has 3 dimensions and EM waves can be distributed in all 3 of them. If I understand your intentions correctly, then we should probably focus only on the LENGHT of cavity (orientation along the direction of wave propagation), while ignoring it's width and height. Let's simply reduce the volume of cavity to 1 dimension only - so maybe instead of a box (cube), let's use a 1m long tube and make EM waves at 1m of wavelenght enter this tube through a tiny pinhole or a narrow slit in it's "top" lid. This way we will be able to have control over the type of radiation and the number of photons at 1m wavelenght, which will be moving through the cavity in a given period of time.


3. It's possible that In the moment, when you shut the top+bottom (or rather the entry+exit) of the 1m long cavity tube, there might be more EM waves at 1m wavelenght inside it, than just one. However in order to keep (store) the trapped radiation of 1m wavelenght inside a 1m long tube, we have to trap the EM wave right in the moment when it's wavelenght fits precisely into the cavity ("ends" of that wave can't stick out from the tube). Only this way we'll be able to get a standing wave, which can be amplified through constructive interference with itself (own reflection). EM waves at 1m wavelnght, which be "sticking out" beyond the cavity boundaries, will be out-of-phase after their reflection, what will leadi to destructive interference.

Ok, maybe I just make a simple image, to show you what I mean... On top is a cavity containing a single standing wave of 1m wavelenght in resonance with a corresponding probability distribution of a single photon (green curve). Image below shows a cavity containing 2 out-of-phase and non-resonating waves with the corresponding probability distribution of photons... Of course I've made this image using Microsoft Paint, so don't expect it to be a precise representation of this scenario - it only represents the general idea...

Well, if this
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html
is right  then about 0.6E-9 Watts has a wavelength within 1 micron of 1 metre.

And that's carried by photons with an energy of 2E-25 J
So that's 3E15 of them each second.
And they traverse the box in  1/C  seconds.
So, there are, on average, about ten million of them in the box at any time.

I don't know, how did you calculate it - here's what I got:

I've set the area to 100cm2 since your box has 1m3 so it can't contain radiation produced by the entire surface of Sun. And then according to this site:
https://www.sensorsone.com/em-waves-vac-wavelength-to-photon-energy-calculator/
A single photon of 1m wavelenght has the energy of: 1.98644586e-25J - so let it be 2e-25J just as you said

But Anyway, what I want to discuss here, is a situation, where 2 or more EM waves at the same wavelenghts occupy the same space and interfere with each other, while in a 3D box/cube multiple EM waves can be distributed in different locations of height and width of that box without causing any interference.

What matters is, how many EM waves at 1m of wavelenght can remain trapped in a cavity, which is 1m LONG

And if I snap the lid shut, that's how many get caught in the box.

Of course, the Sun is a great source of light, but it's not very efficient as a 1 metre radio wave source.
It only emits nanowatts per square meter  of radiation at 1 metre...

I can do rather better than that.
I'd need to tweak the frequency down a bit but the "key fob" transmitters  used for opening garage doors
https://en.wikipedia.org/wiki/LPD433
And that would let me transmit 10 milliwatts. which is about a billion times more power than a square foot of the sun (at 1 metre)

So I can arrange, quite easily , for there to be about 10E12 photons in the box.

By my reckoning, that is more than 1.

Yes - in a 3D box, where they can be located next to each other without causing any interrference.
Anyway, as for your scenario, solution can be found here:
Electromagnetic Waves in a Cubical Cavity http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html#c1

Or here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/phodens.html#c1

And to end the entire discussion about a possibility of infinite intensity gain for radiation trapped in a perfectly reflective cavity - here are the proper equations:

Let's then imagine a simple scenario, where a stationary mirror has almost the same mass/energy, as an incident photon. What do you think will be observed in the lab frame?

My answer is:
- incident photon will accelerate the mirror almost to c, while being reflected back in opposite direction at c with just a tiny fraction of it's previous frequency/momentum

And very shortly afterwards, it will hit the other side of the spherical shell, and be kicked back to very nearly the same energy that it had in the first place.
That's fine if we have just one photon.
In reality, we have many
So,  in the mean time (between the two collisions of that one photoon), any other photons which hit the mirror hit a moving mirror. So their wavelengths will also get altered in a way that's chaotic.
This is the mechanism by which the light is scrambled into a black body spectrum.

And that's the  mechanism by which high energy photons are made.

Thing is, that your scenario can't lead to any definitive gain in the energy level of that system, even if the hypothetical perfect conditions are met - this would violate the law of energy conservation. Without resonance you can only get as much as 100% efficiency for any constant source of sound/radiation. You simply won't be able to increase the frequency of any trapped radiation without adding some 3rd external source of mechanical pressure. You can't get an infinite source of energy from any possible configuration of your scenario - get over it, because it sounds like somekind of scientific heresy

But on the other hand, If you think about it - isn't the law of energy conservation in some part violated by the effect of resonance? I mean you get the gain of amplitude/intensity of any sound/EM wave only by enclosing it in a proper volume of space and have more than 100% efficiency of the source...

And that's the  mechanism by which high energy photons are made.

NOPE. This is a mechanism by which high energy photons are made:
https://www.extremetech.com/extreme/182701-scientists-work-out-how-create-matter-from-light-finally-proving-einsteins-emc2

You NEED to have an additional source of energy, to increase the frequency of any EM radiation. If your claims would be true, you would be famous as someone who discovered the infiinite energy source...

Hmm... Now I really start to wish, for your unproven claims to be true... Maybe you should try doing somekind of practical experiments? I really hope that you're right... I mean, who wouldn't hope - any one would love to have free energy and you will become famous... Sadly in this particular and rare case, I prefer to trust the mainstream science, so I don't think that any hopes in your claims matter here at all...


TBC

[CrazyScientist (OP)]

You CAN'T burn a human skin with FM waves - no matter how intense the FM field will get.

Talking about "FM" is a bit meaningless. I presume you mean the wavelengths typically used to transmit FM radio- about 100 MHz.
You should have learned not to get your fingers burned by being wrong about radio waves.

Yes you can use 100 MHz waves to burn skin.
"Diathermy is produced by three techniques: ultrasound (ultrasonic diathermy), short-wave radio frequencies in the range 1–100 MHz (shortwave diathermy) "
From
https://en.wikipedia.org/wiki/Diathermy

You should stop pretending that you know things.

If your model predicts that it's impossible to get RF burns at 100 MHz, and , in reality, people do get RF burns at 100 MHz, it is clear that your model of the universe is wrong.
https://www.researchgate.net/publication/224188647_Radio_Frequency_Burns_in_the_Power_System_Workplace

Why do you keep trying to insist on it?

Of course. it seems, that for some reason, you forgot to mention about this part: https://en.wikipedia.org/wiki/Dielectric_heating

Radio-frequency heating
The use of high-frequency electric fields for heating dielectric materials had been proposed in the 1930s. For example, U.S. Patent 2,147,689 (application by Bell Telephone Laboratories, dated 1937) states "This invention relates to heating systems for dielectric materials and the object of the invention is to heat such materials uniformly and substantially simultaneously throughout their mass. It has been proposed therefore to heat such materials simultaneously throughout their mass by means of the dielectric loss produced in them when they are subjected to a high voltage, high frequency field." This patent proposed radio frequency (RF) heating at 10 to 20 megahertz (wavelength 15 to 30 meters).[4] Such wavelengths were far longer than the cavity used, and thus made use of near-field effects and not electromagnetic waves. (Commercial microwave ovens use wavelengths only 1% as long.)

TBC

[Bored chemist]

I didn't hear about any law of physics

It shows.

[CrazyScientist (OP)]

"For a given cavity and wavelength", means that all those variables depend on each other - at least this is, how I understand it...

I see the problem lies with your reading comprehension.

What I said
"For a given cavity and wavelength, the intensity is proportional to the number of photons. You can't change them independently."
Is true.
It does not imply what you said it did.

"So at last you do actually admit, that size of cavity and the wavelenght of traped radiation DO define the intensity and the number of photons inside cavity?"


That is clearly not true.
Imagine the case where there is not a single photon in the box.
The intensity and the number of photons is zero.
Now add a single photon in the box.
The intensity and the number of photons have changed- but the box is the same size,
Now add a second photon.
Again the size of the cavity is unchanged and the wavelength is unchanged, but the intensity , and the number of photons have changed.

Number of photons in a standing EM wave is constant for each avaliable mode - and the number of modes depends on the wavelenght and/or volume of a cavity. Read this paper: http://physics.ucsc.edu/~drip/5D/photons/photons.pdf

Do you see how the size and the wavelength do not define the intensity or the number of photons in the box?
Do you see how that falsifies your claim that "that size of cavity and the wavelenght of traped radiation DO define the intensity and the number of photons inside cavity"?

No, I don't... This is how I see it: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/phodens.html#c1

In shortcut: you have a specified number of photons in a volume of space for specified frequencies of EM radiation (cavity modes)

OK
If I double the number of photons in the box, I double the intensity.

So, they are proportional to one another . Adding a third photon will produce treble the intensity, and so on.
Which is why I am able to make the claim in the second clause of my statement
"the intensity is proportional to the number of photons. You can't change them independently"


But it is slightly more complicated than that.
If I use photons with half the wavelength then the intensity - measured in watts per square meter is doubled because each photon has twice the energy.
So, in order to make the statement  "So, they are proportional to one another ."
I have to specify that it's true for a given wavelength.

And similarly, if I keep the number and wavelength (and thus the energy) of the photons the same, but change the size (i.e. the area) of the box, the intensity- in watts per metre squared changes in inverse proportion to the area.

So, again, i need to qualify the assertion "So, they are proportional to one another ." by specifying that the size of the box does not change.

Hence, my statement
"For a given cavity and wavelength, the intensity is proportional to the number of photons. You can't change them independently."

Now that's strange - I mostly agree with this part. Maybe there's still a tiny chance as for your scientific reliability...

But then you ended with this:

Do you now see that
My statement was true.
Your statement was false and  (logically as well as linguistically) my statement does not imply your statement, nor is it compatible with it?

Sadly, everything I see, is some guy, who claims to have authority in science, while making claims which are 100% false. I have an advice for you - before you assume, that your claims are always absolutely valid due to your self-proclaimed authority, try makng just a bit of basic research (just a bit)...

Because it just so happens that I'm a guy, who doesn't believe in your supreme authority and always makes just a bit of research, before admitting own wins/loses - and it's because of those traits of me, that I can say with 99,8% of certainty (you still have a bit of chance), that you know s**t about the subject, while trying to sound smart af...

Well, allow me to burst your small virtual bubble:of mental comfort:

https://physics.stackexchange.com/questions/47105/amplitude-of-an-electromagnetic-wave-containing-a-single-photon

https://physics.stackexchange.com/questions/27851/producing-photons-with-same-frequency-different-amplitude-wave

This is EXACLY what I'm telling you from the very beginning - EM radiation, which is trapped in a (hypothetical) perfectly) reflective cavity, will ALWAYS reach a constant thermal equilibrium at a specific energy level, which is characteristic  to each given wavelenght,(mode), For any given wavelenght of trapped rradiation, there is a specific "as much" in the photon number, that is defined by the volume of cavity.

Inside a 1D tube, which is 100cm long, you can succesfully trap as much as 1 photon of 100cm wavelenght and/or 2 photons at 100//2cm wavelenght + 3 photons at 100/3cm wavelenght + 4 photons at 100/4cm wavelenght and so on.
For every avaliable mode, each trapped photon has a specific energy equal E=hƒ and photons at greater than 100cm wavelenghts (with a tiiny degree of error allowed by probablity distribution) won't fit into 100cm cavity...

Thing is, that using resonance in a perfectly reflective cavity, you can fit twice as much photons for each avaliable mode and increase the energy of trapped radiation by 200% without changing the wavelenghts of photons - how is that possible? Well, it's because besides having the 3 spatially defined components (momemtum, electric and magnetic vectors), every EM wave is also defined by an "imaginary" component of probability, which is also localized in space and has a specified amplitude in the range from 0% to 100% without having any spatial orientation.

So now the question is -  is it possible for photons at the same wavelenghts to have different amplitudes of their electric/magnetic components/vectors?

And the answer is: pretty much YES - as proved in this example:
https://en.wikipedia.org/wiki/Dielectric_heating

I didn't hear about any law of physics

It shows.

Then maybe try to enlight me...

TBC

[Bored chemist]

I didn't hear about any law of physics

It shows.