I was eating dinner and sharing a couple bottles of wine with my friend Mike Fitzmorris last night, and he posed me this two-part question to which neither of us are quite sure about the answer:
Part one: Imagine an iron bar in free-space (no gravity, perfect vacuum, perfect darkness). If you impart a force such that it spins about the short axis, does it ever stop spinning?
It seems that with nothing around to apply a counter-force to the bar, it should spin forever, cosmological and bizarre quantum effects aside.
Part two: Imagine the same iron bar under the same conditions, but magnetized. If you impart a force such that it spins about the short axis, does it ever stop spinning?
The answer to this part seems to be that it should stop spinning eventually, but I can’t explain exactly why. The spinning magnetized iron bar would generate a fluctuating magnetic field, which means that it would be emitting some kind of remotely detectable signal, which, by definition, means that energy is being lost and therefore the bar should eventually stop spinning…
But exactly what is applying the counter-force to cause the bar to stop spinning? The bar is in a perfect free-space, so the electromagnetic waves will never interact with anything…The best explanation I could come up with is that the bar’s self-magnetic field is “catching up” with its emitted magnetic signature, and this interaction induces a counter-current in the metal which would cause an opposing magnetic field that would result in a net braking effect. I’m not very happy with this explanation, however.
Anybody know the correct answer to this question, or have a good explanation for why it might be so? There must be a simple answer and I’m just not seeing it.
[some edits and an addendum here to clarify this post]
A lot of interesting views in the comment area, thanks everyone for the thoughts!
Let me rephrase the thought experiment, because I think my poor phrasing has lead to many people to point toward flaws in the problem statement rather than the problem itself.
Suppose we think now of the spinning magnet in free space as a flywheel, and I couple energy out of the flywheel via a large coil. The changing magnetic field of this flywheel would cause electrons to move in the coil, and clearly since I am coupling power out of the flywheel via the coil’s capture of the changing magnetic field, the flywheel must slow down, otherwise energy is not conserved. In other words, the flywheel’s kinetic energy is converted into electrical energy by this mechanism.
If I remove this coupling coil, no energy is being directly removed from the system, so you might think, okay, the magnetic flywheel should not spin down ever since there are no mechanical frictional effects.
However, now imagine that I create an enormous superconducting coil that spans a diameter of 10 light seconds away from the flywheel. As I start spinning the flywheel, the changing magnetic field flows away at the speed of light. If the argument is that no energy is lost into this magnetic field, then the flywheel will not slow down at all. However, 10 seconds later, this magnetic field hits the coil, and all this energy is captured in the coil…but where did this energy come from?
Clearly, at time = 10 seconds, the flywheel can’t possibly begin instantaneously spinning down; the information about the presence of the coil would have to propagate its way back to the flywheel first, otherwise we have created a mechanism for transferring information at a rate faster than the speed of light. So for the “flywheel does not slow down” hypothesis to be valid, for a net 10 seconds, the system mysteriously has “extra” energy–I took energy out via the coil, yet the flywheel maintained its original rate of spinning and all its kinetic energy for the 10 seconds that it took for the information about the existence of the coil to make it back to the magnetic flywheel.
Therefore, in the absence of any device to couple energy out of the system (other than radiation to free space), the flywheel must slow down with time, otherwise I can spontaneously create energy. Therefore, there must be a completely local mechanism within the flywheel that causes the energy to be debited at the instant that it radiates from the flywheel. This is true whether the bar spins near the speed of light, or if it spins very slowly as any changing magnetic field can compel an electron to move and therefore transfer energy to another part of the system.
It is this local energy-debiting mechanism that I am trying to grasp. Any explanation also has to work if I replace the iron bar with a non-conductive magnet, like a ceramic or organic magnet. That’s a flaw in my counter-eddy current explanation that I proposed above.
Here is a quick sketch that helps illustrate the question.
How can the bar “catch up” to the em field it is generating? Doesn’t that imply that some part of the bar is exceeding c? I think you have to expand on the thought experiment here. If the bar is truly in an empty dark universe then there is nothing to interact with the field and it keeps spinning. However, if there is another charged particle sharing that universe with it, the time-varying field from the bar will cause the particle to move. Then the moving charge generates its own magnetic field which is felt by the bar. If you don’t have another charged particle somewhere in the “bar universe” I’m not sure how you can tell there is a magnetic field.
Bunnie, even though I have no useful insight to help you with your quandary, I still enjoy seeing what other geeks like to talk about over dinner and drinks. :)
The oscillating magnetic field generated by the spinning magnet can be viewed in the particle model as giving off photons, which contain some mass equivalent, and thus you have a Newton’s third law rebound which serves to damp the motion of the magnet.
I’m not physicist, but I suspect the problem is the actually more philosophical.
There is no such thing as ‘free space’, or rather there is but it exists only in the mind. If the bar can be observed, it’s not in ‘free space’, otherwise it’s Schrodinger’s cat.
This kind of problem happens all the time when you try and do an objective thought experiment because there’s no such thing as objective thought.
You end up with “If something happens, but you don’t know if it happened, did it happen?” or in this case “Something you can’t know about exists, what do you know about it?” You know it exists, the question makes no sense.
If you assume that the magnetic field is not interacting with anything outside the “system” then you cannot say the bar slows due to that.
If the bar is interacting with its own generated magnetic field then it’s the interaction of the BAR and the magnetic field, not the magnetic field and itself. So at most the magnetic field would be generated eddy currents in the bar, heating it up, which is where the spinning energy would go – the bar would be “warmer” and so the energy would never leave the system.
I doubt that’s the case, though, as the bar would have to be spinning at or nearly C to interact with a field it itself is generating. At that point you have to bring in relativity. Let’s keep it simple for the time being…
I believe that if the spin is well under C, then the bar would not slow down or stop. Imagine yourself on the spinning bar – the field would appear to be normal. It’s only when you place your viewpoint off the bar (and spin the bar relative to you) that the fields start to “bend”. But that only occurs at terrific speeds – this would be like a sonic boom – once you pushed past a certain speed you would re-enter your own magnetic field.
But that in and of itself wouldn’t slow you down because it’s a static field as far as the par itself is concerned. We only notice it from the outside – but riding on the bar you simply see your own field twisting back towards you, and it is still a static field – as long as you aren’t accelerating or decelerating. Thus no other forces (eddy or otherwise) are active since it’s a static system from the viewpoint of the bar.
I am certainly wrong at one or more points, though. But my instinct says even a magnetized bar is no different.
-Adam
My instinct is in a perfect free space i.e. nothing else exists anywhere the magnetic bar would behave the same as a non magnetic bar. What the the magnetism interact with? if moving near C I dont think anyone can predict what will happen with certainty.
I’ll throw in another idea. Not done any physics since 16 but I am under the impression rotation creates gravity. Energy (rotation) can not be created or destroyed. Then again what is gravity, is it energy?
In real life, it would eventually cease to spin.
In an idealistic environment, with nothing to interact whatsoever, regardless of it’s speed, magnetic field would not slow it down, as it would be pushing or pulling against itself.
If the bar were spinning at the speed of light (C), then the mass would increase (relativity), and thus energy would be lost (due to conversion to mass), and therefore it would slow down. At this point mass would convert back to energy, so it would balance at a speed somewhere under C.
If the speed were a more realistic one, still in an idealistic environment, conservation of mass and energy would dictate it would spin forever. No mass or energy would be lost or gained.
Magnetism, similarly to proton/electron charges, don’t lose charge simply because they are charged, only when they interact with something. As the free space is idealistic, there is nothing for which to interact. Therefore, the magnetic field would be of no consequence. It is not until you return to the real environment, where there is at least one particle or field to interact with, that the bar will ever stop spinning.
Of course, all of this assumes time continues forever, which is another question of valid concern, as if time were to end tomorrow, in 10,000 years, or in another trillion years, then the bar could spin for no longer than that amount of time. So on that note, time would also play into the equation, stopping it altogether, due to the change in the laws of physics (or rather sudden absence).
I will also point out that at the speed of light (or close to), the energy being converted to mass would also result in heat (as noted by Adam Davis), which would remove the magnetic field. As I mentioned, the bar would slow down in this case, and the heat (as it has nowhere to go) would also be turned back into energy, thus continued conservation of mass and energy.
Now I have not checked with any electrodynamics books, so take this attempt of explaining why the bar will stop spinning with a grain of salt:
If I think about the field emitted by a coil antenna (for the reverse process look at the radio controlled alarm-clock near your bed…) the direction of transmit is not along the axis but perpendicular to it. (if you point the rod of your alarm-clocks receiving rod-antenna to the transmitter, the field strengh should go to zero, theoretically).
So if I replace the rotating bar by a rotating coil, and substitute a alternating current for the rotation, it makes sense to me that the radio transmission from your rotating bar will be strongest in the direction of the rotating axis.
Here comes my gut-feeling: somehow it just *has* to be that while the radiation emitted from a fixed and ac-excited coil is linearly polarized the radiation emitted from your rotating bar along its axis is circularly polarized.
If that is true, the circularly polarized photons (switching from fields to particles…) will have their spin aligned either towards or away from the totating bar. Due to them carrying spin they will also carry away the same amount of angular momentum, thereby slowing down the rotation of the bar.
How’s that for some serious handwaving? ;-)
That’s…. hand-waving…. A magnetic isn’t an emission or radiation though.
I think the person who mentioned the frame of reference was on the mark.
The bar only appears to have motion because you are observing it from a frame of reference. If the bar isn’t interacting with anything (you… yes you with the flashlight… shut your eyes), then the notion of “motion” is irrelevent.
A lot of interesting views, thanks everyone.
Let me rephrase the thought experiment that has me puzzled. Suppose I think now of the spinning magnet in free space as a flywheel, and I couple energy out of the flywheel via a large coil. The changing magnetic field of this flywheel would cause electrons to move in the coil, and clearly since I am coupling power out of the flywheel via the coil’s capture of the changing magnetic field, the flywheel must slow down, otherwise energy is not conserved.
If I remove this coupling coil, no energy is being directly removed from the system, so you might think, okay, the magnetic flywheel should not spin down.
However, now imagine that I create an enormous superconducting coil that spans a diameter of 10 light seconds away from the flywheel. As I start spinning the flywheel, the changing magnetic field flows away at the speed of light. If the argument is that no energy is lost into this magnetic field, then the flywheel will not slow down at all. However, 10 seconds later, this magnetic field hits the coil, and all this energy is captured in the coil…but where did this energy come from?
Clearly, at time = 10 seconds, the flywheel can’t possibly stop instantaneously spinning down; the information about the presence of the coil would have to propagate its way back to the flywheel, so for a net 10 seconds, the system mysteriously has “extra” energy–I took energy out via the coil, yet the flywheel maintained its original rate of spinning for the 10 seconds that it took for the information about the existence of the coil to make it back to the magnetic flywheel.
Therefore, in the absence of any device to couple energy out of the system (other than radiation to free space), the flywheel must slow down with time, otherwise I can spontaneously create energy. Therefore, there must be a completely local mechanism within the flywheel that causes the energy to be debited at the instant that it radiates from the flywheel. This is true whether the bar spins near the speed of light, or if it spins very slowly.
It is this local energy-debiting mechanism that I am trying to grasp.
The comment about the speed of light was just to convince myself that a magnet can interact with its own propagating field. If the magnetic flywheel spins very slowly, the interaction is still there, just very minute. So let’s not consider the relativistic effects of the bar spinning near the speed of light, that was more of an error on my part to introduce that into the experiment, because at non-relativistic speeds I can still couple energy out of the flywheel via a coil.
As gravity is mass warping space time, the bars very presence implies gravity which would cause it to slow down … eventually.
This all presumes that General Relativity is correct.
Wait a second… The field just doesn’t suddenly appear in your coil, rather doesn’t it ramp up over a distinct (albeit short) period of time? And that inducted field is going to then affect the flywheel an increasing amount as the inducted field grows. So there doesn’t appear to be any “created energy”.
(And as a software guy this is way out of my area of knowledge…)
The energy ‘lost’ from the spinning bar/flywheel via magnetic field would cause the coil or super-magnet to begin spinning based upon the amount of transferred energy. So the bar/flywheel would slow down until the two were balanced in energy per unit mass. So it might spin as a rate of 1 revolution per year, but it would still maintain that spin. The energy isn’t lost, it is just moved into a different part of that system.
As Roastbeef points out, the slowdown would be increasing exponentially, as magnetic field, similarly to gravitational and electronegative are exponentially decreasing the further you get, but it is still there.
Oh, and for the record so I don’t unintentionally mislead, I’m not studied in this field, I just find it quite interesting on a personal note.
This assumes that the electrons begin to spin immediately. The electrons start to spin after the information comes back to the flywheel and then back to the coil (T=30s).
I don’t have a confident answer to the thought experiment, but here goes: Maxwell’s laws suggest that there will also be an electric field in the system (due to dB/dt). EM waves carry energy, so the outgoing fields carry energy with them. This line of thought implies that a rotating magnet always radiates.
When the field gets to the superconducting coil, it starts to induce a current, which sets up a B field (Lenz’s law). It takes additional time for the field’s influence to extend back to the rotating magnet. So no speed-of-light violations occur.
I think Mako just said was I was trying to, only in an understandable way!
Hmmmmm…
Trying to take it all in. I believe the electrons will start moving in the coil as soon as they see a changing B field. An electron in a coil has no knowledge of what caused the changing field; it just knows it must move when a changing field arrives. Therefore, by making the coil far enough away from the magnet, one can decouple the motion of the electrons from the origin of the changing magnetic field.
So I agree 100% with mako, but the problem I’m trying to figure out is how does a physically rotating magnet generate EM waves. There must be a process local to the magnet by which this works. There is also a paradox about how the energy is ultimately absorbed. If I were to jacket a magnetic flywheel in a perfect superconductor, it should almost instantaneously stop because the superconductor will create perfect mirror currents to the magnetic field and cause the flywheel to stop. As I expand that jacket outward–say, to the scale of this experiment–why would this fact no longer hold??
Also, what is the process by which a photon–as mouser mentioned above–spontaneously erupt from a macroscale object. Does this mean that if I spin an object fast enough, it could spontaneously start generating light (assuming it could hold itself together, which may be a bad assumption)? Or rather maybe not light, but a lower-frequency EM wave such as an AM radio carrier (certainly could believe a couple kilohertz is achievable).
Here is a diagram to help illustrate what I see the problem as (click on the image to get a version that’s not messed up by the automatic resizer of the browser):
Hm drawing that diagram helped a lot.
I think I have a much better explanation now.
The magnetic field can’t propagate. For example, I can’t build a magnet-laser that shoots a magnetic field (alone) to a remote spot. The only propagating field is an electromagnetic field. Thank you, magnetic monopoles.
Therefore, the paradox of the superconducting jacket catching all the energy has been resolved. There must be two processes happening here. One is the magnetic field. The changing magnetic field on its own doesn’t propagate and diminishes with distance, full stop. This means that at great distances you just can’t couple energy out of that field. I’m not 100% satisfied by this explanation but maybe it’s close enough.
However, a secondary process which we routinely neglect, because the magnetic field at short distances is so dominant, might be taking effect, which is as mouser suggests the spontaneous generation of photons by a rotating magnet siphoning off energy from the magnet. I am still very uneasy with the spontaneous generation of photons by a macroscopic object. Why is it that not all rotating objects create an emission signature? If you imagine the difference between a magnetized and a demagnetized ceramic magnet rotating in free space, there must be some process that depends solely upon the magnetic field acting upon a non-conductive substrate that causes EM emissions. As I understand, you need some kind of a moving electron (either an electron moving in a wire, or an electron jumping energy levels as it orbits an atom) to create an EM wave; where are these moving electrons in this non-conductive ceramic? I suppose if I read a book about the theory of NMR I might find the answer there; I have to admit I’m very weak when it comes to understanding the quantum processes behind magnetism. Magnetism, in general, is a trip.
I imagine this EM field would almost be impossible to detect because of its extremely low frequency and low amplitude, but it is there and that would account for the missing energy. I wonder if there is a lower limit to the energy, magnitude or frequency of a photon.
The electromagnetic force is quantized in photons in the view of QED. This is a case of particle-wave duality. EM waves are photons and vice versa.
We can look to astrophysical phenomena for confirmation that rotating magnets emit waves. A neutron star’s field is anchored to its surface, “Thus as the star turns the field also must turn. This drives magnetic waves outward…”* Rotating neutron stars can be pulsars; there are also high-field objects called magnetars.
*http://solomon.as.utexas.edu/~duncan/magnetar.html
http://en.wikipedia.org/wiki/Magnetar
http://arxiv.org/abs/astro-ph/0606674
I think the photon-based explanation of Mouser’s is the best so far.
If you spun the magnet at 1,000,000 revolutions per second, the resulting EM radiation from it would be at 1 MHz. That represents a particular amount of energy (by the Planck equation, E=hv) that is being removed from the system. Spin it faster, and more energy is lost due to EM radiation.
Even if you spin it at one revolution per year, that’s still going to result in radiative losses.
To answer both the pickup-coil and relativistic paradoxes: sure, you can remove energy from the system with a coil at whatever distance you like. Any energy you don’t remove is still being generated, though… it’s just being radiated into space. If you rotate the pickup coil around the same axis at the same speed, or place it too far away to pick up the signal in a reasonable amount of time, it simply won’t remove energy from the system.
If you were a fixed observer standing on the bar, you wouldn’t get to withdraw any energy from the system, because the magnetic field (like the bar itself) isn’t rotating with respect to your point of view. No real paradox there.
There will always be eddy currents in the bar as it “catches up” to the field it radiated a fraction of a second ago. Even if it’s a ceramic magnet without a lot of free electrons to conduct electricity on a bulk scale, the eddy currents are still present at the molecular level. (I imagine that the change in eddy currents over time is probably how the photons get emitted in the first place, but that’s just a WAG.)
I thought that the fact that it emits (and therefore looses) energy was undisputed. The problem that remains, in my oppinion, was where the angular torque comes from that makes the bar decellerate its rotation.
You have to conserve (and therefore explain the lack of):
– Energy : that’s the pointing vector of the em-wave E*B, the energy of the particle h*f, check. We loose energy so we have to slow our rotation (the kinetic energy of which is our energy source).
– Momentum: radiated energy carries momentum, google for “pioneer anomaly”, those scientiscs calculated how much the rf-transmissions from the antenna contributes to the spacecrafts’ accelleration… As the bar will emit its radiation symmetrically we don’t have to care about that.
– Angular Momentum: if the rotating magnet-bar slows down its rotation the angular momentum has to go somewhere. My attempt at explaining this would be the angular momentum of circularly polarised photons
Thanks guys–very thought provoking. I have a lot to learn still about the nature of magnetism. I went back to the books and started reading up again, it’s been enlightening. It will probably be a while before I feel like I truly have an understanding (as opposed to isolated knowledge) about magnetism. I’m now doubting my understanding of the origin of EM waves–probably something I should clear up, it’s pretty important to know that stuff if I’m to really understand electronics.
Everyone–thanks for the comments and links. A lot to think about!
It’s got to be something about frame of reference. Imagine if you reversed the problem, a perfectly still magnet with a giant superconducting coil rotating around it.
I’m not nearly smart enough to be able to figure out what would happen here but it’s a really interesting question to ponder.
Sorry, I am jumping in late. Work gets in the way.
The magnetic domains do have acceleration. They all have an acceleration vector toward the center of rotation. So the magnet will radiate a photon proportional to the rate or rotation. The photon is not radiated spontaneously.
I think there is another more interesting question here. Light is obviously quantized. Yet, given my classical approach the bar magnet’s rotational energy will be continuously decreasing. Thus, you would expect a long EM wave of increasing wave length. What would the photon stream look like?
If I reapeated anyone else’s idea, I apologize. I couldn’t read everyone’s post.
You’ll definitely be getting shared on my blog for this :p.
I’m still pretty new to some of this stuff, but with the knowledge I’ve collected as of late there are still multiple ways to look at this problem.
Unfortunately it’s hard to say “quantum effects aside” when postulating a universe with nothing in it because, by definition no observation is possible under those circumstances and, as such, the experiment is entirely within quantum domain because nobody knows whether a tree would make a sound in the woulds if it fell when nobody was there to hear it.
That said, I apologize for complicating what’s supposed to be a simple matter :p, but considering some qualities of string theory, the question would be somewhat complex. In a perfect vacuum there should theoretically be a very large amount of ambient energy (so long as the Higgs field winds up being true) in the “empty” space of the vacuum, which could even account for the energy of the bosons leaving the magnetic rod to then be reintegrated into the ambient medium (not really sure what else could happen to them, the energy itself is not lost, that’s for sure) which may, in turn possibly contribute back to the rod (of course this is untestable right now).
With that considered, the magnetic nature of the rod the gauge bosons communicating these forces, would inevitably drain energy from the rod. I am not, however, confident that this would result in the rod ending it’s rotation; possibly slowing it down, but if the idea presented is that eventually the electromagnetic energy present within the rod would be exhausted and that in and of itself would cause the rod to stop spinning i would disagree. I would think that the rod would emit (so long as it is symmetrical) a symmetrical magnetic force around the rod that wouldn’t affect it’s rotation at all; even if that force were to cease instantaneously that would not actually be a force acting against the rotation of the rod. Instead I believe we would have demonstrated an object with *less* energy than it had before, but still not 0.
Perhaps a little too heavy for some, probably a bit far fetched, but it’s postulated with my current understanding of physics. I do like the idea of circularly ionized photons because that would give some semblance of a counter-spin necessary, but a really important question when analyzing the forces in a universe with only a single object and it’s energy would be to question where the rod is located within said universe (centered symmetrically or of center?) and what happens when guage bosons (or any other particle/field for that matter) approach the edge of said universe. If they are reflected back or looped around then the concept of an inverse reflection over time could somehow counteract the spin because it would be a guaranteed equal, opposite force.
Phew… sorry for rambling when I’m undereducated but this was a very interesting brain teaser for me and I’d love to get more of these :)
It’s easy enough to visualize the magnetic gradients accelerating and dragging spacetime with them to create vibrations. The real question is, since the momentum of light is E/c^2 and the energy per momentum of the bar is less than that, how does the bar have enough energy to make itself stop? The only way would be for the pattern of spacetime vibration caused by the acceleration of the magnetic domains to act to actually emit electromagnetic radiation tangent to a circle much larger than the bar.
The rod’s rotation would slow down and approach a standstill, but never reach it.
There’s no need to invoke quantum mechanics, general relativity, or any other modern physics; a classical approach using Maxwell’s equations leads to the above conclusion. Maxwell’s equations tell us that rod will emit radiation at the frequency of rotation. Qualitatively, energy must be conserved, so rod must slow down to account for the radiated energy. Alternatively, if you’re really a glutton for punishment, you can model a self-consistent set of equations describing the rotation of the bar and the radiated field. The equation can be found in many graduate level optics books, but they usually involve an oscillating electric dipole rather than magnetic one.
Even if we assume the rod is initially rotating *very*, *very* fast, the rotation will slow down to the point where the wavelength (lambda) of the radiated wave is greater than the length of the rod. At this point, the efficiency of the rod’s ability to radiate will drop as 1/lambda^2 or worse (this is basic antenna theory). Assuming 1/lambda^2 decay, the rod’s rotation rate will decay inversely proportion to the elapsed time.
Obviously, if we assume there’s a coupling coil, or the rod’s rotating at the speed of light, the above description isn’t correct, but I can’t think of any reason it would behave significantly different.
Also, by *very* fast, I mean rotation rates on the order of 10^12 Hz. From an experimentalist standpoint, it’s generally easier to talk about continuous E/M fields instead of photons when the photon energy is very small. In vacuum, 1 terahertz = 300 micron wavelength = 100 Kelvin thermal energy = 4 meV. These energies and frequencies are 500 times smaller than a typical optical photon. To detect photons at realistic rod rotation rates, we would need a superbly cold detector.
Can the bar actually spin if there’s nothing else in this hypothetical universe?
If the bar is the only matter in existence, it really can’t move at all for lack of a different frame of reference.
I’ll let alone the question of how you would apply this force in the first place. But to observe the bar spinning, we have to assume some sort of detector in space that is apart from the bar itself and this breaks the whole argument.
Y’all are missing the point…
Without trying to solve grand-unification in one email… lets cover some basics…
Magnets are made of substances with a deficiency of electrons on one end with respect to the other end. The material that the magnet is made up of has physical properties for how easily electrons flow through them and how easy it is to make electrons stay on one place (like one end of a conductor, as opposed to another…)
When you make a magnet out of a nail, you wrap the nail in a lot of wire and hook up the ends of the wire to a battery. You have just made an electromagnet. There is a specific property to all kinds of things nails can be made out of, that says how long our temporary magnet will stay magnetized (surplus of electrons on one end, deficiency of electrons on the other end) – before a normal distribution of electrons is re-achieved.
That is because we have not changed the structure of our nail… only temporarily polarized the material such that the electrons want to migrate to one end, over the other – This is a temporary predicament.
In the case of a permanent magnet (the assumption for this thought experiment), we have a material that is an electrical conductor and we know (because it is a permanent magnet) that the atoms that make up this magnet are aligned in a peculiar, symmetrical manner…. Because of this alignment… electrons naturally migrate to one end of our magnet.
Each of these magnets has a specific field of influence where magnetic lines of force will be useful to perform Work… and for which outside this field of influence, nothing will happen…
So – Considering that this thought experiment has such a magnet spinning in space.. The physical approach to electromagnetics (and Maxwell agrees with me here) says that unless something interacts with the magnetic lines of force, within the field of influence, no Work is performed. No electrons are lost, traded, conducted or are otherwise fabricated… BTW – Photons are not a good model to use here, specifically because of the mass connundrum… When a magnet is doing it’s thing, in free space, it is not performing Work by itself. It is neither gaining nor losing mass… It is not conducting electricity, nor is it performing motion of some sort. It is simply conducting an electromagnetic field, without any external bias… very much like a charged capacitor, or a new battery… Without anything to hook up the capacitor/battery to, there is nowhere for the electrons to flow.
By this thinking, the magnetized rod will spin indefinitely, as long as no other conductive mass is brought within the field of influence of the magnet…
We are assuming that ionizing radiation, cosmic wind, dust particles and solar flares are not present in this universe, as any of these would contribute to a decrease in rotational motion.
The moment you place a conducting mass near enough to our spinning rod to be within the field of influence, you will slow down the rod, as work will have been performed every time the pole of our magnet passes near the conductor… causing a certian amount of reluctance to motion as work is performed… inducing a current in the conductor and creating a momentary attraction/repulsion of the end of the magnet as it swings by… Because no system is 100% efficient, and energy is always conserved… the magnet will eventually slow down and stop.
As the magnet spins, it will have a fixed, unchanging field of influence that, if seen, would be underwhelming… You have to get pretty close to a magnet to get anything useful out of it. Outside of this field of influence, there is simply no interaction that is the result of the magnetic field.
QED.
The last post by Bruce Boettjer is correct.
In fact, the bar is not even spinning! Yes, you may say it’s spinning, but if we are to assume there are no other objects in this space to interact with, then the notion of spin is meaningless. An object can only move in reference to another object.
Sure, you could say that space itself (or the universe) is another object, but because the “external” movement of space itself is unknowable, this notion won’t get you anywhere.
Ark – I think you may be mistaken. The electrons are being accelerated relative to each other as the bar rotates.
You guys have made the problem way too hard. The key to this puzzle is to forget about fields and any other externalities. Focus just on the electrons, photons and nuclei in the bar.
As the electrons are forced to move by the bar’s spin, they emit and absorb photons. Some photons fail to be absorbed because they don’t encounter any electrons before they emerge from the bar and, hence, they carry away energy. Each photon that is spit out by the bar slows the bar ever so slightly and eventually, the bar comes to a complete stop. There’s no need for an absorber or anything else – just photons escaping the bar’s surface is all that’s required to bring the bar to a stop.
So, let me get this straight… If I take a metal bar that is magnetized, spin it in free space, it’ll emit photons!!! Wow!! my own personal sun!!! Grand unification revealed!!! the answer to all the universes energy problems solved in one fell swoop!
The bar will never ’emit’ photons… It may reflect photons and it may even absorb energy… but it will never spontaneously emit a photon.
Bruce
Everything you see is emitting photons – otherwise you wouldn’t be able to see it. Even in a perfectly dark room, the electrons in the bar are still emitting and swapping photons – if they didn’t there wouldn’t be anything to hold the atoms together. Whether an emitted photon is absorbed by an electron in the bar or escapes the bar is a matter of which way the photon was headed when the source electron emitted it.
When the problem at hand befuddles, it’s often useful to look at systems with analogous properties. Why does an antenna have “radiation resistance” – an equivalent electrical resistance across its terminals? Because of the magnetic field around the conductors, which induces another component of current in them. Conservation of energy says the real component of the resulting driving-point impedance sucks real energy from the transmission line at the same rate that energy is radiated. Suppose instead of a dipole antenna, we had an idealized ferrite-rod antenna. Idealized means no hysteresis loss etc. We could induce an alternating magnetic dipole in the rod by passing AC through a coil wound on it, or we could cut a gap in the center and put a spinning magnet in the gap. Let’s try the latter. In the absence of anything external to interact with the field, if not for the “displacement current” in free space (more on that later) there would be no net loss of energy from the spinning magnet. There would be a “cogging” effect which accelerates the magnet half the time and decelerates it half the time, but no net loss of energy. Now, there is a circular electric field induced around the rod proportional to the rate of change of flux. Even a vacuum has electrical permittivity and therefore any contour line (surface, really) of the electric field has a capacitance. There is effectively an electric current flowing in this capacitance – that’s the “displacement current”. Because it’s capacitive, it leads the electric field by 90 degrees. Remember, the electric field is proportional to the rate of change of the magnetic field in the rod, so it already leads the magnetic field by 90 degrees. So the displacement current, which surrounds the rod, leads the magnetic field in the rod by 180 degrees. As Maxwell predicted, this displacement current induces a magnetic field just like the current in a conductor. The resulting magnetic field opposes the field in the rod. Here’s where my understanding is limited. I suspect that because of energy being radiated the phase relationships are altered, so the magnetic field from the displacement current is not exactly 180 degrees out of phase with the original field in the rod. This makes the cogging forces mentioned above assymetric so that the acceleration and deceleration do not quite cancel. If we take the idealized ferrite rod out of the system, we’re left with a circularly symmetric system that behaves essentially the same way due to the permeability of free space. Instead of assymetric cogging, we simply have a constant drag. BTW, the concept of rotation *does* make sense in a refrerenceless system. If you had two masses connected by a spring and spinning about their combined center of mass, you could determine the angular velocity by measuring the tension in the spring.
Shorter explanation than my last post:
The spinning bar magnet (in free space, no ferrite rod) is creating an electromagnetic wave. To do this, it must induce that “displacement current” in space. Free space really does have a characteristic impedance, equal to sqrt(u/e), where (since my keyboard doesn’t have Greek) u is the permeability of free space in Henrys per meter, and e is the permittivity of free space in Farads per meter. This works out to around 377 Ohms (see ). You can’t measure this with an ohmmeter, but anything that launches an EM wave sees it. It’s as though the magnet were spinning in an electrically lossy medium, except that instead of being converted to heat the work is converted to EM waves.
Correction to my comment about determining angular velocity from the tension in a spring: I should have said angular speed (a scalar). The only way I can think of to determine the direction of rotation is to cut a piece of mass loose and see which way it flies off. You could still observe that even if you were tied to one of the masses, but you’d have to illuminate the piece.
In total vacuum and no gravity it will probably not be possible to exist.
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related, newton’s bucket: http://en.wikipedia.org/wiki/Bucket_argument