Tell me what is wrong for this scheme for a perpetual motion machine:
You put in very close orbit around the Moon an asteroid so that for much of its orbit it is in the shadow of the Moon.
You cover a small area of the Moon plus the asteroid's surface with solar panels that are extremely close to being 100% energy efficient at converting wavelengths around a specific wavelength of light, lets say in the yellow spectrum of light, into electrical energy. Next to each of these two groups of solar panels and powered by any electricity generated by these solar panels, you place a laser that is extremely close to being 100% energy efficient at converting electrical energy into yellow light around that specific wavelength. Each time either group of solar panels are in direct sunlight, they are deactivated so they generate no energy from sunlight (else that would be cheating).
Also, the group of solar panels on the Moon is connected to a battery that is extremely close to being 100% energy efficient.
Now, as the asteroid goes into the shadow of the Moon so its solar panels receive no solar energy, and only for each period of time as that asteroid approaches the solar panels on the Moon and while those panels on the Moon are in the lunar night so they to receive no solar energy, the battery on the Moon initially powers the laser on the Moon which points at the asteroid so the asteroid's solar panels convert that energy to electrical energy which is then powers the asteroid's laser which points back at the panels on the Moon which then converts that energy back into electric energy that then powers its laser ... and so on.
BUT, because of the Doppler effect because this is only done each time when the asteroid approaches the panels on the Moon, each yellow photon of light admitted by each laser is going to be slightly shifted towards the blue spectrum of light and that would therefore slightly increase the energy of each photon and therefore slightly increase the total energy going from each laser to each set of solar panels. Thus, providing all the equipment is extremely close to 100% energy efficient, there is a net gain in energy in this cycle of energy conversions. Some of the resulting excess energy can be used to recharge the battery and the rest be used to power a toaster.
But, surely, that would violate the laws of physics because you are creating more energy out of less!?
So why wouldn't that work?
Just keep it simple. You are asking whether or not the doppler effect results in gain or loss of energy and if so is the law of energy conservation violated.
It would appear the law of energy conservation doesn't hold in general relativity ie it is coordinate system dependent.
http://physics.stackexchange.com/questions/15279/conservation-of-energy-and-doppler-effect
https://www.physicsforums.com/threads/does-doppler-effect-change-the-energy-of-emitted-light.341174/
My guess is that in your scenario, the emission and absorption of photons imparts some velocity on the asteroid and moon which counteracts any energy gained in your system.
Originally posted by twhitehead
Just keep it simple. You are asking whether or not the doppler effect results in gain or loss of energy and if so is the law of energy conservation violated.
It would appear the law of energy conservation doesn't hold in general relativity ie it is coordinate system dependent.
http://physics.stackexchange.com/questions/15279/conservation-of-energy-an ...[text shortened]... parts some velocity on the asteroid and moon which counteracts any energy gained in your system.
It would appear the law of energy conservation doesn't hold in general relativity ie it is coordinate system dependent.
Misedit? I think you meant special relativity here, not general relativity?
http://physics.stackexchange.com/questions/15279/conservation-of-energy-and-doppler-effect
So, if I understand this correctly, as you said, it would appear the law of energy conservation doesn't hold in relativity thus my OP perpetual motion machine setup could in theory actually work and sustainable regularly create more energy out of less energy for an unlimited time! (although, in practice, that OP setup may be considered rather impractical ) .
My guess is that in your scenario, the emission and absorption of photons imparts some velocity on the asteroid and moon which counteracts any energy gained in your system. [/quote]
I had already thought of that but I would guess the reduction of relative velocity would generally be so minute that it wouldn't necessarily be enough to conserve the total energy in the system although I admit I don't know how to do the maths to confirm that.
Anyone?
Originally posted by humyNo, relativity has a way of sorting things out. For a start in any given coordinate system energy is actually conserved. From your perspective standing on the moon, the energy of the photon that left the asteroid was exactly the energy you received. No net gain. From the asteroids perspective it has a different energy, but again, remains fixed throughout. As far as the asteroid is concerned (when transmitting photons) it is not that the wavelength decreases but that the moon encounters it at speed gathering the energy faster.
So, if I understand this correctly, as you said, it would appear the law of energy conservation doesn't hold in relativity thus my OP perpetual motion machine setup could in theory actually work and sustainable regularly create more energy out of less energy for an unlimited time! (although, in practice, that OP setup may be considered rather impractical ) .
Hard to all work out and I don't claim to be able to do it, but I am fairly certain that no perpetual motion machine will result.
I had already thought of that but I would guess the reduction of relative velocity would generally be so minute that it wouldn't necessarily be enough to conserve the total energy in the system although I admit I don't know how to do the maths to confirm that.
Velocity imparted by photons is more significant than you might think. Solar sails have been seriously considered for spaceflight.
In contrast, the energy gain due to relative velocity and frequency shift will also be minuscule.
https://en.wikipedia.org/wiki/Solar_sail#Solar_radiation_pressure
Can you work out for a given photon what its imparted momentum is an what its energy gain is for a given relative velocity? See if they are comparable or different orders of magnitude.
Originally posted by humyWhat about getting free energy from the expansion of the universe? Suppose you have a rope a million light years long and you have one end on a spool hooked to a generator and it unreels because the other end is tied to a planet in a distant galaxy. They would recede apart pulling the rope, unwinding the spool and generating free energy.
Tell me what is wrong for this scheme for a perpetual motion machine:
You put in very close orbit around the Moon an asteroid so that for much of its orbit it is in the shadow of the Moon.
You cover a small area of the Moon plus the asteroid's surface with solar panels that are extremely close to being 100% energy efficient at converting wavelengths around ...[text shortened]... e laws of physics because you are creating more energy out of less!?
So why wouldn't that work?
Originally posted by twhiteheadjust noticed an implied error;
No, relativity has a way of sorting things out. For a start in any given coordinate system energy is actually conserved. From your perspective standing on the moon, the energy of the photon that left the asteroid was exactly the energy you received. No net gain. From the asteroids perspective it has a different energy, but again, remains fixed throughout. ...[text shortened]... n is for a given relative velocity? See if they are comparable or different orders of magnitude.
From your perspective standing on the moon, the energy of the photon that left the asteroid was exactly the energy you received. No net gain.
transmitted just from and just to the asteroid yes; and the same goes from the perspective of the asteroid transmitted just from and just to the moon. However, from the perspective of the moon of the net energy moved both from the moon to the asteroid and then back to the moon again, i.e. the movement of the energy for the whole of the two-way round trip cycle, has increased.
Originally posted by sonhousenote that supply of energy wouldn't last forever because eventually you would use up all the usable mass in the galaxies to make more and more rope to stretch between them and then you would run out of rope.
What about getting free energy from the expansion of the universe? Suppose you have a rope a million light years long and you have one end on a spool hooked to a generator and it unreels because the other end is tied to a planet in a distant galaxy. They would recede apart pulling the rope, unwinding the spool and generating free energy.
Energy is conserved in both Special and General Relativity. Frame dependence is not the same as non-conservation. Any observer sees energy being conserved, but, in general, any two observers will disagree about what the energy is. This depends on the homogeneity in time of the Hamiltonian and so doesn't apply at the start of the universe. I realize twhitehead said that in his above post, but I think it's worth underlining that point.
Imagine a cylinder and piston with a perfectly reflective interior, no friction, and a single photon bouncing around inside it. In the rest frame of the cylinder, each time the photon hits the piston it does some work, so the wavelength of the photon increases with each collision with the piston. To make the set up more like humy's set up we can replace the reflective interior with a material that absorbs light at any frequency but only emits it at one frequency. When a single photon is emitted it will be shifted away from the emission energy so when it is absorbed there isn't enough energy to re-emit it and the perpetual motion machine will stop. You don't even need to invoke the doppler effect to see this. The photon has energy E = hf, it does work W on the piston, so the energy available for re-emission is hf - W < hf.
Originally posted by DeepThoughtOK. I have got a new question;
Energy is conserved in both Special and General Relativity. Frame dependence is not the same as non-conservation. Any observer sees energy being conserved, but, in general, any two observers will disagree about what the energy is. ....
you fire a single photon with a specific wavelength at a mirror moving towards you and it bounces off the mirror and back towards you and then you detect it and measure its wavelength; from your perspective, by the photon bouncing off the mirror that was moving towards you, would the photon have shifted its wavelength to become shorter in wavelength (and thus contain more energy) ?
Because, as I see it, to the mirror, the wavelength was already shorter than what you say you emitted as and thus it is just as if the mirror emitted that shorter photon towards you so surely you would detect a shorter photon than the one you emitted! right? or am I somehow getting confused here?
Originally posted by humyI believe so. And I believe you will find it is close to, if not identical to, the amount of momentum lost by the moving mirror.
....would the photon have shifted its wavelength to become shorter in wavelength (and thus contain more energy) ?
I believe you will find that even a stationary mirror changes the wavelength of a photon by an energy amount equal to twice its momentum.
Originally posted by twhiteheadBoth of those things is now exactly what I strongly suspect. I now plan to later dig up all the relevant equations (from my university courses and I have forgotten these relevant equations ) and see if I can do all the calculations and check that that is all exactly right.
I believe so. And I believe you will find it is close to, if not identical to, the amount of momentum lost by the moving mirror.
I believe you will find that even a stationary mirror changes the wavelength of a photon by an energy amount equal to twice its momentum.
If that is exactly right, then you were right in suggesting the velocity imparted by the photons may be greater than what I would think.
Originally posted by DeepThoughtIt isn't perpet if the wavelength gets longer after each reflection, since the energy of a photon is DEFINED by its wavelength. At some point the wavelength would get larger than the container and the work function would cease.
Energy is conserved in both Special and General Relativity. Frame dependence is not the same as non-conservation. Any observer sees energy being conserved, but, in general, any two observers will disagree about what the energy is. This depends on the homogeneity in time of the Hamiltonian and so doesn't apply at the start of the universe. I realize t ...[text shortened]... gy E = hf, it does work W on the piston, so the energy available for re-emission is hf - W < hf.
Originally posted by sonhouseI was not claiming it was perpetual, the work done on the piston cannot exceed the energy that the photon has to start with, which eliminates the possibility of a perpetual motion machine from the start. However, within my idealization, the photon is contained inside the cylinder which is perfectly reflective. I'm assuming the piston can be pushed out by an infinite distance, so the space between the cylinder base and the piston can increase to arbitrary size. My idealization is not physical since there is no material which is perfectly reflective across all possible wavelengths and infinitely large cylinders can't be built.
It isn't perpet if the wavelength gets longer after each reflection, since the energy of a photon is DEFINED by its wavelength. At some point the wavelength would get larger than the container and the work function would cease.