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# Two mirrors watch

1. Anyone ever heard of an attractive force created when two mirrors are placed really close together? I remember reading it somewhere but i never understood it... Anyone help?
2. this arises because any radiation in between the mirrors (or metal in general) will have to have a whole number of half-wavelengths between the two mirrors (or metal plates in general); and so only certain frequencies (therefore energies given by E=hf) can exist between the mirrors. outside the mirrors, any possible energies can exist - so there is more energy outside than inside the mirrors - and this causes a pressure pushing the plates together, which can be construed as an attractive force
3. I always wondered how that was caused. I was always wondering why the mirrors wanted to connect I just assumed there was some form of electrostatic attraction.
4. This is known as the casimir effect. It is due to quantum vacuum fluctuations of the electromagnetic field. Basically because only particles of certain wavelengths can fit between the plates the energy density outside the plates is greater than within. So a force is felt between the plates, similar to air pressure really.
5. but what i dont get about this effect is you are getting something for nothing. The virtual particles are being created and then destroyed on each other. But if some are using their energy to push the plates together, surely you end up with the energy gain in this world. You're allowed to borrow energy from nothing as long as you give it all back. So where's the trade off? If someone can just point out the small mistake i'm making, would be greatly appriciated.
6. (Original post by Willla2)
but what i dont get about this effect is you are getting something for nothing. The virtual particles are being created and then destroyed on each other. But if some are using their energy to push the plates together, surely you end up with the energy gain in this world. You're allowed to borrow energy from nothing as long as you give it all back. So where's the trade off? If someone can just point out the small mistake i'm making, would be greatly appriciated.
It's a guess, but I'd say the energy comes from that which was used to put the mirrors together in the first place, as the "energy difference" between the area between them and the surrounding space develops then. It's a bit like if you change the moment of inertia of a spinning object by moving its weight closer to the axis and it speeds up - the energy which appears to have been gained was provided by you.
7. (Original post by Willla2)
but what i dont get about this effect is you are getting something for nothing. The virtual particles are being created and then destroyed on each other. But if some are using their energy to push the plates together, surely you end up with the energy gain in this world. You're allowed to borrow energy from nothing as long as you give it all back. So where's the trade off? If someone can just point out the small mistake i'm making, would be greatly appriciated.
You are not getting energy from nothing, you are getting energy from the electromagnetic field.
8. no i thought the idea is that this happens in a vacuum as well due to virtual particles appearing and disappearing throughout the universe. And that between the plates, you only get certain frequency virtual particles appearing, and so you get an outer pressure.
9. (Original post by Willla2)
but what i dont get about this effect is you are getting something for nothing. The virtual particles are being created and then destroyed on each other. But if some are using their energy to push the plates together, surely you end up with the energy gain in this world. You're allowed to borrow energy from nothing as long as you give it all back. So where's the trade off? If someone can just point out the small mistake i'm making, would be greatly appriciated.
When the mirrors are far apart they have higher potential energy. Just like a stone far away from earth can lose its potential energy and gain kinetic energy as it falls, the mirrors can do the same (only here the force is caused by quantum fluctuations rather than gravity).
10. so when you pull stuff apart you are losing energy into nothingness because those items which started close together must have got that way by using taking a debt from nature?
11. (Original post by Willla2)
no i thought the idea is that this happens in a vacuum as well due to virtual particles appearing and disappearing throughout the universe. And that between the plates, you only get certain frequency virtual particles appearing, and so you get an outer pressure.
Yes. The energy still comes from the electromagnetic field.
12. (Original post by Willla2)
so when you pull stuff apart you are losing energy into nothingness because those items which started close together must have got that way by using taking a debt from nature?
Energy exists in two forms, kinetic and potential. When you stretch a spring you have to use energy to overcome the force pulling the string back, thsi energy is stored as potential energy in the spring. If you release the spring the spring froce contracts the spring and the potential energy is released in form of kinetic energy ( the ends of the spring are now moving and thus they have kinetic energy). In a similar way it takes some energy to lift a stone, but this energy is released again when you drop the stone. The potential energy stored between the stone and the earth is released as the stone falls faster and faster and is converted into kinetic energy. If a large enough stone is dropped from sufficient height you can feel that the ground is warm afterwards because teh energy has been converetd into heat energy.

Now, considder the mirrors. The further the mirrors are apart the more energy you can get by letting them atract each other, just as a stone at a great altitude has a large potential energy. Thus the mirrors then have a potential energy. If you let the mirrors move together due to the quantum mechanical force, they lose this potential energy but they gain kinetic energy because they move faster and faster. Therefore no energy has been lost, or borrowed or anything like it, it has merely been converted from one form into another. The energy needed to pull teh mirrors apart is equal to the energy gained when they smash back together.
13. (Original post by AntiMagicMan)
Yes. The energy still comes from the electromagnetic field.
That is kind of misleading. The electromagnetic field itself does not contain energy, but waves traveling in the field carries the energy. Compare this to ocean waves where the energy is moving with the waves whereas the water molecules oncly occilate around their equilibrium position (Yes I know that the electromagentic field is not composed of matter, but it doesnt change the fact that it is the waves that carry the energy and not the field itself)
14. but what i'm still getting at is the potential energy comes from somewhere! When you pull the plates apart, the energy you put in is working against the quantum pressure and this work is stored as potential energy as a loan to nature. When the plates move back together, nature gives that energy back. I was always taught that virtual spontaneous particles loan energy from nothingness, as long as they give it back. But my point here is that this mechanism allows you to leech energy out of nothing, as long as you never give it back. The principle was well described in a book, which i can't remember the title of, of such a device that does this, and describes how it can be built:

take a slinky made out of fine gold leaf, or something incredibly light. Positively charge it with electricity and it will spring apart. Then leave it, and the caismer effect will gradually pull the slinky together, causing a current out of nothing! Obviously it doesn't come out of nothing, it comes from the vacuum, which has an inherent "energy" associated with it. Of course, the energies you could extract are pathetically feeble. But it's the principle!
15. The thing I was considering (and I know little about physics) is that if you have one mirror there is no potential energy/attraction. As soon as another mirror comes into beingthen this energy just "appears" I guess i'm missing something.

MB
16. well yes, that's the idea, it looks like it's come out of nowhere, but it hasnt. In the beginning of the universe, everything was on top of everything else, there was no space. As soon as everything started to pull apart though, it had to use energy against the caiser effect acting like a sort of anti-gravity. This energy was stored as "caiser potential energy" in the aether that exists everywhere (it's just lent to nature, doesn't matter where it goes, it is just stored away), so when you put stuff together, if the caiser effect starts to pull it together, then the "caiser pe" is converted back into KE. You just have to imagine it like a really pathetic version of gravity, but the difference is it exists everywhere, even in a vacuum with apparently no mass.
17. (Original post by Willla2)
but what i'm still getting at is the potential energy comes from somewhere! When you pull the plates apart, the energy you put in is working against the quantum pressure and this work is stored as potential energy as a loan to nature. When the plates move back together, nature gives that energy back. I was always taught that virtual spontaneous particles loan energy from nothingness, as long as they give it back. But my point here is that this mechanism allows you to leech energy out of nothing, as long as you never give it back. The principle was well described in a book, which i can't remember the title of, of such a device that does this, and describes how it can be built:

take a slinky made out of fine gold leaf, or something incredibly light. Positively charge it with electricity and it will spring apart. Then leave it, and the caismer effect will gradually pull the slinky together, causing a current out of nothing! Obviously it doesn't come out of nothing, it comes from the vacuum, which has an inherent "energy" associated with it. Of course, the energies you could extract are pathetically feeble. But it's the principle!
But you would require energy to produce the positive charge in the first place, wouldn't you? Isn't the energy just coming from the positive charge you started with?
18. (Original post by musicboy)
The thing I was considering (and I know little about physics) is that if you have one mirror there is no potential energy/attraction. As soon as another mirror comes into beingthen this energy just "appears" I guess i'm missing something.

MB
Only if the second mirror just "appears" also. In reality it has to be put there by some external force, be it simple mechanical movement, gravity, electrostatic attraction or whatever, but in any case work has to be done to put the mirror there. Some of this is "stored" in the higher state of energy between the mirrors - just like the energy you could "store" between two same-pole magnets by forcing them together, and when you let go, they spring apart, the energy used to do this comes from that you supplied in the first place to put them there.

Of course I could be totally wrong, but it looks like the same principle to me.
19. (Original post by Jonatan)
That is kind of misleading. The electromagnetic field itself does not contain energy, but waves traveling in the field carries the energy. Compare this to ocean waves where the energy is moving with the waves whereas the water molecules oncly occilate around their equilibrium position (Yes I know that the electromagentic field is not composed of matter, but it doesnt change the fact that it is the waves that carry the energy and not the field itself)
Er, it isn't misleading at all. The electromagnetic field has an energy density. Waves are not the only possible way for energy to exist in the electromagnetic field.

Consider a fixed point charge, it creates an electric field, the energy density of the electric field is given by 1/2 (epsilon nought) times the magnitude of the electric field vector squared. And a similar expression exists for the magnetic field. Even waves store their energy in the electric and magnetic fields anyway, so your comment is a bit misleading.
20. (Original post by calumc)
Only if the second mirror just "appears" also. In reality it has to be put there by some external force, be it simple mechanical movement, gravity, electrostatic attraction or whatever, but in any case work has to be done to put the mirror there. Some of this is "stored" in the higher state of energy between the mirrors - just like the energy you could "store" between two same-pole magnets by forcing them together, and when you let go, they spring apart, the energy used to do this comes from that you supplied in the first place to put them there.

Of course I could be totally wrong, but it looks like the same principle to me.

yeah, I was thinking yu could use the magnet analogy again. There is a magnetic field regardless of whether it is shown by affecting anything.

MB

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