What is the mechanism behind the weight of a box of photons?

[Austin0]

Since none of the above seem convincing I am thinking I must be missing some obvious fundamental factor ?. Any insights welcome

Consider a single molecule, initially moving downwards. It hits the bottom of the box and rebounds upwards - the scale is forced down and registers an increase in weight. But once the molecule starts upwards again, the scale also rebounds, accelerating the box upwards. Thus, at the position where the weight of the box and the upwards force of the scale would be exactly balanced at equilibrium, the box is moving upwards and the scale reads a bit low. And eventually the upwards-moving rebounding molecule hits the top of the box and rebounds again downwards, nudging the box up a bit more, further reducing the reading the scale reading. But now the molecule is heading back down, and gravity is pulling the box back down, so the cycle repeats.

Compute the average over time of the upwards fluctuations and the downwards fluctuations, and it will come out to mg, where m is the mass of the single molecule.

Consider a large number of molecules, all going through this cycle at their own rate with a random statistical distribution of when they're going up and when they're going down, and you'll get an average of Mg where M is the total mass of all the molecules.

As you can see in my OP I had it right.
Somehow I became focused on the instantaneous state of the system and like Zeno's arrow I got stuck and could not see the obvious.
Your qualitative view set me straight where looking at it over time it is glaringly obvious.
It was just such a view of fundamental process I was looking for but escaped me
Thanks

 

[Austin0]

Please work out the math on this as I have suggested previously. Your conclusion is incorrect.

For a single molecule the measured weight fluctuates between three values depending on the acceleration of the COM. One value is higher than the total weight (molecule hitting bottom) and two are lower (molecule hitting top, molecule in free fall).

Since the COM is not moving when averaged over time the measured weight averaged over time is equal to the total weight, including the gas molecule. Similarly when averaging over many molecules.

Hi thanks for your input . Of course everything you said was perfectly correct except for the shut up and calculate advice.

It was not really a quantitative question. All the final values were given. As far as I can see the gas maths themselves produce statistical net results. Instantaneous state conditions. They do not directly entail the dynamic processes behind those net results.
But that was the source of my question and my problem, looking at the instantaneous state rather than the processes over time.
A conceptual question requiring a conceptual resolution.
But thanks for your help.

 

[Dale]

Hi thanks for your input . Of course everything you said was perfectly correct except for the shut up and calculate advice.

It was not really a quantitative question.

I disagree. You knew the correct answer from the OP, but simply did not believe that the magnitude of the effect could correctly account for the necessary answer. That makes it a quantitative question.

Besides, the process of calculating the result is an important learning experience that all of the experts on the forum have gone through in order to become experts. I don't understand why so many non-experts seem annoyed when experts recommend using the most effective method for gaining expertise.

I am sad that you deprived yourself of the opportunity and seem oblivious to the enormous value in it.