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Imagine I use one static magnet to levitate another magnet indefinitely. This levitating magnet is in a narrow tube that wont allow it to rotate and get attracted. So it will keep levitating forever, right?

Since gravity uses energy to push us down to earth, and this magnet is counteracting gravity, where is this energy to counteract gravity come from?

Qmechanic
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PedroD
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    A tabletop also counteracts gravity by holding my coffee mug. Where is the energy for that coming from? – safesphere Jul 12 '18 at 20:19
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    "Gravity uses energy to push us down to earth" may be a misunderstanding of energy. Gravity is a force that points in the direction of earth, and if an object's height is lowered, the force of gravity turns one form of energy (gravitational potential energy) into another form (possibly kinetic energy). But if the height of an object is not changed, then no energy is exchanged. So no energy is being "used" to keep an object in the air (unless there are dissipative forces that turn some energy from a usable form into an unusable form, but those don't apply in this case). – probably_someone Jul 12 '18 at 20:21
  • Note that when one magnet lifts another work is done. i.e. as the magnet rises. – JMLCarter Jul 12 '18 at 20:48
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    The correct question would be: From where does the magnet get energy to lift the other magnet from the ground. No energy is required to hold the object in place. https://physics.stackexchange.com/questions/67826 – Nitin Shaji Jul 14 '18 at 05:21

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Since gravity uses energy to push us down to earth

This is incorrect. Gravity does not use energy to pull in us.

If we started falling, then yes, gravity used energy do make us move. But that is only in the special case where gravity makes us move. In general, gravity spends no energy pulling in us.

In general, a force spends no energy. An apple lying on a table is both pulled down by gravity and held up by the table's normal force. Gravity spends no energy here. The normal force doesn't spend any energy either. This situation of apple-lying-still-on-table will stay like that forever. It will never change, since no energy can "run out" when no energy is spent.

The levitating magnet is the same case. No energy spent. Thus, this will theoretically remain forever. (Unless there are other forces acting as well, that do spend energy.)

Steeven
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  • So why do we get tired when holding a heavy object still? – PedroD Jul 12 '18 at 23:14
  • I believe your answer is essentially incorrect here, as magnets can lose their magnetism over time. There's a related Q&A here. Why they can lose their magnetism seems to be disputed by the answers, but not that they do. So in this case a pair if repelling magnets will presumably not go on forever and ever. – StephenG - Help Ukraine Jul 13 '18 at 00:05
  • I also think you're "guilty of dogma" (for want of a better expression) by saying "force expends no energy" without explaining in some way why that is the case. Why, in this case, does a pair of repelling magnets not use energy (power) ? I think the why is the OP's main interest. – StephenG - Help Ukraine Jul 13 '18 at 00:07
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    @StephenG This is due to a sort of "decay" of the material - in the same way you could say that the table that holds up the apple looses it's strength when it rusts. This is a different mechanism and doesn't change the specific point about a force not necessarily spending energy. – Steeven Jul 13 '18 at 05:11
  • @PedroD You get tired when holding an object for a long time, not because your force spends energy on the object, but because it your boy spends energy on producing your force. Similar to a rocket exerting its force until all fuel has been spent - in certain situations, the object spends energy to produce a force, but the force itself spends no energy on the objects it is acting on. – Steeven Jul 13 '18 at 05:13
  • So, no energy is used to create a force, but energy is used to counteract it? Another example, I have a vacum cleaner, and I cover the tube with an object and the object gets stuck by the vacum. The vacum cleaner is spending energy to keep the object stuck there, and I have to spend energy if I want to take the object out. So this shows that you need to spend energy to create a force, no matter if work is done (kinetic) or not (potential). So why is gravity different? – PedroD Jul 13 '18 at 12:24
  • @ PedroD gravity is different, because there is no quantum gravity yet. We do not know how it works on the QM level. We do know how magnets work on the QM level, and we use math, and virtual photons to describe the magnetic fields' force. And the magnet's megnetic dipole moment is caused by the electrons' magnetic dipole moment in the magnet. The electron's does not need extra energy to orbit the nucleus, because it is moving in free space around the nucleus, and keeps its momentum. – Árpád Szendrei Jul 13 '18 at 14:45
  • The Heisenberg uncertainty principle does not let the electron go closer to the nucleus, and the EM force attracts it, the two forces equal out. – Árpád Szendrei Jul 13 '18 at 14:46
  • @PedroD I think you misunderstood, sorry for not being clear. No, energy is not necessarily spent by a force, or to counteract a force or to create a force. There are some special situations where energy is spent to create a force, but that is not a general rule. – Steeven Jul 13 '18 at 15:20
  • @PedroD Regarding your vacuum cleaner example, it is not correct that energy must be spent when trying to take the paper off. When you pull, then yes, your body spends energy to create the force you pull with. But if you instead hang a heavy object in the paper, which pulls downwards due to its weight, then no energy is spent by this object on the paper if it doesn't make it move. In one case energy is spent to produce the force, in another case no energy is spent. It is not a general rule that energy must be spent - it is only in certain cases. – Steeven Jul 13 '18 at 15:21
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    @PedroD So, all in all, it is not gravity which is special - it is rather your body with is special. There are so many examples of forces that do not require any energy to be exerted. And then there are some other examples of forces that do, such as the vacuum cleaner or a rocket (in general electric or fuel-spending engines) or your body. – Steeven Jul 13 '18 at 15:23
  • @PedroD Because humans are inefficient. In the case of holding a stationary object, 0% efficient. – user253751 Dec 27 '18 at 12:02
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A way to look at is, is like the force is constant but no energy is exchanged until it katalyses.

So putting something on a table is not exchanging energy as the table molecules are to big of a counterforce and this holds it in check. Remove the table and potential energy is converted in heat and momentum.

So the force of the magnet is too high to overcome and no energy exchange is started.

The object will move a bit due to air being pushed on it, but the magnet will return this kinetic energy by returning potential energy, so no energy is lost.

In the case of your arm holding it, you are generating the counter force with muscle tension instead of just putting molecules between it and the pulling force. So you are spending energy.

The degrading is not because of gravity, but due to material properties degrading in time.

Like holding a heavy rock with a stick. The counter force is there, but on microscopic level there is stuff going on like molecules loosing bonds because their counter force is lower than the force of gravity, and energy starts exchanging.

Rutger van de Putte
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The magnet's energy comes from magnetic dipole moment.

The real cause of magnetic dipole moment is the magnetic dipole moment of electrons in the magnet, and that is a multiple of spin because spin has deep reasons to do with the structure of angular momentum.

Gravity does not pull the magnet down. Stress-energy bends spacetime, and the magnet is following a geodesic towards the center of mass.

So the top magnet is in freefall on a geodesic towards the center of mass, and the other bottom magnet on the ground is repelling it and the top magnet levitates.

The two magnet's are exchanging virtual photons and those are excitations of the magnetic field. The EM force is what keeps the top magnet levitating.

So the top magnet is following a geodesic in freefall through bent spacetime and the magnetic fields of the bottom and top magnet repel each other.

So the two forces are the two magnetic fields' forces that repel.

The net of these two forces would in free space be the same levitation.

In this case both magnets are in free fall on a geodesic towards the center of mass.

The bottom magnet is levitated by the surface of Earth (because the atomic and molecular structure and the repulsive EM force of the EM fields between atoms of the surface and the bottom magnet).

The top magnet is levitated by the repulsive force between the two magnet's magnetic fields' force.

The EM repulsion between the bottom magnet and the Earth's surface is so that the distance between them becomes hardly visible.

The EM repulsion between the top and bottom magnet is so that the distance between them is visible.

So where does the energy come from that levitates the bottom magnet on the surface of Earth? It is the Pauli exclusion principle, Heisenberg uncertainty principle, and the EM repulsion between the atoms in the bottom magnet and the surface of Earth.

It comes from the electron's energy, where does that come from? Electrons around the nuclei are in vacuum, and are in certain energy levels around the nuclei as per QM. They are on the certain energy levels because those levels are stable, and the electron is moving in vacuum and does not need extra energy to do so. In vacuum, the electron keeps its momentum. It does not need extra energy. Just like any object in vacuum would keep its momentum.

The top and bottom magnet's fields' forces energy comes from the electron's energy too. The electron's in the magnets keep exchanging virtual photons. The electron's do not need extra energy to do so because the net energy of both magnets together is the same.

Árpád Szendrei
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