If a photon keeps bouncing between two mirrors that are 100 % reflective would both mirrors keep accelerating away from each other in space (assuming this force can overcome gravity between the mirrors)?
And if we consider a mirror that doesn't always reflect the photon, it would turn into heat, right? But that heat would eventually be radiated away as a photon, right? From which side of the mirror would that photon appear?
>If a photon keeps bouncing between two mirrors that are 100 % reflective would both mirrors keep accelerating away from each other in space (assuming this force can overcome gravity between the mirrors)?
Energy of the photon is proportional to its momentum. If the photon imparts momentum to the mirrors then the total momentum gain is equal to the momentum of the photon. This is disregarding things like virtual photon pressure, redshift, gravity between the mirrors and other light sources
>And if we consider a mirror that doesn't always reflect the photon, it would turn into heat, right? But that heat would eventually be radiated away as a photon, right? From which side of the mirror would that photon appear?
Depends on how long it takes to be radiated again and how fast it moves in the medium
Each impact gives a mirror a "kick". The KE picked up the by the mirror comes at the expense of the photon. So it's reflected back slightly red-shifted and able to exert less force on the next collision. In the limit the photon will waste away into nothing and the mirrors will mutually recede at constant velocity.
It's analogous to bouncing a rubber ball between two movable walls. (Not precisely the same because the ball slows while the photon doesn't, but they both lose energy and momentum.)
In the non-perfectly reflecting case, "which side" depends on the structure of the mirrors. If they were perfectly conducting and had the same surface properties on both faces, it's 50-50. If the "far side" of each plate had an emissivity of 0 (totally white or a perfect mirror) that side couldn't radiate at all and the heat losses would go back on the hemisphere facing the other mirror. Whether the "waste" photon would actually hit the other mirror is a matter of geometry, the spacing and size of the mirrors.
t. heat transfer engineer
OP here. Thanks for the answers. Not sure why I wasn't expecting the photon to lose momentum so this was enlightening.
This does make me wonder what happens if you keep shooting photons from the mirrors at each other just enough to keep gravity from pulling the mirrors together (and not too many that they would escape each other's influence). In this case it would seem that energy is lost somewhere. The mirrors would stay put relative to each other (no increase in potential energy) while photons would keep disappearing over time.
The power source for the photons would of course deplete over time (making the mirrors slightly lighter, not sure if this affects anything) and the mirrors would eventually hit each other.
What am I missing?
Invent a mirror that is >100% reflective then do the same thing or put some light in a sphere of it etc and then see what happens.
You could end up with a photon drive then, a star maker, or simply (relatively) free light.
>red-shifted
how a single wave can change frequency if there is no frequency by defining
If gravity exactly counters the photon pressure then the mirrors don't move.
So there's no red-shift and no energy lost.
The photons just keep accumulating between the mirrors. As there are more and more photons gravity is overcome and the mirrors begin to separate. If you don't want that to happen, you tie them together with string.
Alternately coat the inside of a sphere with your perfect mirror coating. Periodically, open a tiny trap door and throw another photon in. (A very very small trap door, which opens and shuts quickly.) Light will accumulate inside (almost) indefinitely.
The "almost" is because there will eventually be so many photons inside that one or more will "leak" out during the instant you have the trap open.
There is never a violation of energy conservation. The photons never vanish tracelessly and they never build up so there's more energy inside than you supplied one photon-at-a-time. So you don't get
>a photon drive then, a star maker, or simply (relatively) free light.
It's just a storage container for light. A battery, if you will.
Your sentence seems to have been cut off so I'm not entirely sure what you're asking.
You know Doppler effect? Frequency of light, and therefore wavelength, vary (though the speed of light does not) if the source moves towards or away from you.
You've seen Doppler Weather Radar on the newscasts? Radio waves are bounced off raindrops. The frequency shift of the return indicates the motion of the raindrop and the speed of the wind carrying them along.
Lest you think there's a loophole in my sphere-with-trapdoor model, you NEED an opening to add photons. A perfect mirror will not absorb photons -- but neither can it emit them.
"OK (you may say) I put a flashlight inside the sphere. They I don't need to open the mirror."
The casing of the flashlight (everything except the emitting surface) has to be coated in mirror too or it'll absorb light. The flashlight will then warm up until it re-radiates exactly as much energy as it intercepts.
There's a simple proof that failure to do so would allow you to build a perpetual motion machine of the Second Order. It doesn't create energy (breaking the First Law) but it spontaneously increases the temperature difference between two objects initially at the same temp. This difference would allow you to extract useful work as the bodies came back into equilibrium.
t. heat transfer engineer
OP here.
Are you sure you need to move the mirrors to lose energy? Cause the photons do work counter-acting gravity even if the mirrors don't move (that's why they don't move). Just like you would do work (lose energy somewhere) to flap wings to stay in flight while on a planet.
Or think of it this way: What if you let the mirrors get closer due to gravity for a while, then shoot plenty of photons to grow the distance again (mirrors definitely move), repeat. I think this would be exactly the same as keeping the mirrors at constant distance using photons to counter-act gravity exactly.
Wouldn't the wavelength stay the same but the intensity diminish?
Quite sure.
If the mirrors don't move, there's no place for the energy to go.
Each mirror is surrounded by a gravitational potential well. Right? We'll put the mirrors well apart. Makes no difference but it's easier to visualize two separate "dips". Mirrors are stationary.
Photon leaving mirror A red-shifts as it climbs out of A's gravity well -- then gains back exactly the same energy and blue-shifts as it's attracted by B. Then the same thing happens as it goes back to A. Neither does it make a difference if A is much more massive than B. Gravity is a conservative force. Whenever you traverse a closed path and return to your starting point, you're at the same gravitational potential you started at. No gain and no loss.
Suppose the mirrors drift towards each other for awhile. Then each photon will be blue-shifted (gain energy) as it's reflected. The energy comes from slowing the motion of the mirror. This is just the inverse of the drifting-apart problem. If the mirror distance cycles, everything cancels and, as you guessed, it's just like having fixed mirrors.
Let me put it another way. Perfect parallel mirrors, but not gravity. Photons bounce between them but they don't move because I'm holding one in each hand. So long as the mirrors are stationary, no work is being done but I can feel the light-pressure trying to force my hands apart.
I bring my hands together, moving the mirrors against the light-pressure. I'm doing work. The photons become more energetic. I relax and my hands are driven apart as the photons turn back to their original color. It's like playing an according or compressing a spring. (Except an air-bellows and a spring will have losses, whereas your ideal-mirror setup doesn't)
Convinced yet?
When you stare at a lightbulb you're seeing trillions of photons. When you move away, fewer find their way to your eye, so the light is dimmer.
There was a puzzle around 1900. Light striking certain metals caused electrons to be emitted. The brighter the light, the more electrons. But the energy of the individual electrons depended only on the frequency of the light. If the wavelength of the light was too long (frequency too low) there were no electrons at all no matter how intense you made the light.
Einstein solved the problem by realizing that the energy of each photon was proportional to its frequency. If the frequency was too low, it didn't have enough energy to tear an electron loose.
The Photoelectric Effect is what Einstein got the Nobel for, not for Relativity.
When you say "intensity" you must distinguish between "number of photons" and "energy carried by each photon".
so Einstein asspulled a photon and won nobel prize? wow, that's was an easy achievement
But isn't there opposite momentum when the photon is returning? So the reflected photon must have pushed the mirror away to have been able to change direction.
And if the mirrors don't move because photons are pushing them just as much away from each other as their gravity is pulling them together, don't the photons need to spend energy to do this?
-OP
photon is like 1 unit of energy and mirror mass is worth of trillions units of energy. no way a single photon can push a mirror. he can push a single atom, but that's all.
Work is force times distance.
The photon is exerting force on the mirror when it reflects.
But if the mirror doesn't move, distance is zero.
No work is done and the photon loses no energy.
The magnitude doesn't matter. The most trivial violation of the conservation laws would be just as serious as a smashed-in-your-face violation.
The photon may only interact with one atom but the entire mirror moves.
You might call it "asspull" but most of modern technology, including the LED or LCD monitor you're reading this on wouldn't work if he hadn't been right.
What I meant by not moving was that gravity between the mirrors would have pulled the mirrors together that same amount that the photon(s) pushed them apart. That still requires the photons pushing them apart (and thus losing energy).
- OP
When a helicopter is hovering in the air 1 meter from the ground it's doing work, right? Work against the pull of gravity. Work is force times distance even though the helicopter is not moving. How do we calculate work in this case? The same case should apply to the mirror/photon example, right?
- OP
If the plates are close together then pushing them apart against their mutual gravity does require work. The photons lose energy doing so.
No work is being done ON THE HELICOPTER! Someone could drag supports underneath the skids and then you could turn off the engine and the helicopter would remain one meter off the ground.
Work is being done on the air! Still air is being grabbed by the blades and thrown downwards.. Ultimately, the energy (including the noise) degrades into random thermal energy. You're heating the air you move.
How much energy is required? The kinetic energy being added to the moving air. Half the mass of air moved per second times the downdraft velocity squared.
For a given air flow, required energy is proportional to the square of the velocity. Momentum transferred (which is what support the copter) only varies as the first power of the air velocity. Which is why it's cheaper to move a large amount of gas at low speed than it is to move a small amount of gas at high speed. Which is why helicopter blades are so large compared to aircraft propellers.
Scenario A:
We have 2 mirrors at a distance of 1 meter from each other. No photons. We wait until gravity pulls the mirrors together.
Scenario B:
We have 2 mirrors at a distance of 1 meter from each other. Some photons bounce between the mirrors and the distance between the mirrors doesn't decrease due to gravity for a while and the photons lose their energy because of this. Then we wait until gravity pulls the mirrors together.
Where did the energy of the photons in Scenario 2 disappear?
-OP
You're not listening and I'm going to stop answering.
>distance between the mirrors doesn't decrease
>the photons lose their energy
For the Nth time, the photons DON'T lose any energy so long as the mirrors don't move!!!!!!
I have no idea why photons only lose energy due to the movement of the mirrors but not due to working against gravity regardless of net movement. So let's change the scenarios slightly so that there is actual movement.
Scenario A:
Mirrors apart 1 meter. No photons. Gravity pulls them together.
Scenario B:
Mirrors apart 1 meter. Photons push them apart some more so we get 1.01 meter separation. Gravity pulls mirrors a bit closer together and they are at 0.99 meters. Photons push them back to 1.00 meters apart. Gravity pulls them together.
I fail to see the difference but now there's the movement you wanted. Still, we seem to have lost the photons.
One last time.
Photons lose energy when they push them apart.
Photons gain it all back when the mirrors move together again.
>There was a puzzle around 1900. Light striking certain metals caused electrons to be emitted.
I've read this story so many times in so many different contexts that I am almost shocked when people don't know about it.
After some of the posts I've seen on Veeky Forums, very little shocks me. Some people just don't know. Others don't want to know.
There is a cult of ignorance in the United States, and there always has been. The strain of anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that "my ignorance is just as good as your knowledge."
---------- Isaac Asimov
He was very depressed in his last days. After spending most of his life trying to educate people, he could see the new Dark Ages coming.
>You might call it "asspull" but most of modern technology, including the LED or LCD monitor you're reading this on wouldn't work if he hadn't been right.
Le Einstein invented photoelectric effects
>The photon may only interact with one atom but the entire mirror moves.
Does your body moves if I throw at you a grain of sand? That impulse will probably wont even reach your back and be conserved as a tiny amount of heat.
You know zero physics. Momentum and heat aren't the same.
Bother some other board.
you can throw a car at me and it won't do shit since you are a dyel cuck with shit analogies
>But that heat would eventually be radiated away as a photon, right? From which side of the mirror would that photon appear?
It would eventually be radiated away as many photons of lower energy. Infrared(or heat) is a lower energy wavelength, you would get several infrared photons radiating away from the mirror in multiple directions.
photons don't have mass though
I'm sure there's quantum physics stuff going on here
Photons carry energy. E=Mc^2
Therefore, they have mass. Also momentum.
What they don't have is 'rest mass', because they're never at rest. They move at lightspeed. Always.