This question always puzzles me. If I put a box on a table, that box can stay there till Judgment Day. It doesn’t have to “use up” any energy to keep from falling through the table; it just sits there. And nobody has any problem with that. Why would it be any different for the force between two magnets? And yet, people think for some reason that a couple of magnets exerting a force on each other must for some reason be using up energy to do so.
Because the separation distance between the magnets is large enough to be seen by the visible eye, whereas the separation distance between physical objects “in contact” is so small that the visible wavelengths of light cannot channel through. That the same forces are involved is not obvious to the layman, or even (disappointingly) to someone educated in general science but not specifically atomic physics or physical chemistry. If you made a survey of the “man on the street” most would even argue that no forces are being exerted on the box, and virtually all (including, in my experience, many first year physics students) will argue that it isn’t even under acceleration.
Electromagnetism (and the other forces) defies what we learn about how the world works though childhood observation; it seems, to borrow a phrase, indistinguishable from magic. Then you take a physics class and learn that in fact we can describe it by a set of equations ginned together by some Scotsman 150 years ago and it all seems rational. Then you take a modern physics class and realize that the equations are just a crude model that actually describes the exchange of particles which may spontaneously appear and then be annihilated (in many cases, by meeting themselves coming backward in time) and the whole thing is explained by breaking the problem into little bits and canceling out almost all the vectors by a mathematics tricks that is apropos to nothing in the real world, and you wish you could just go back to the time when you thought it was all just magic. Especially around exam time.
Stranger
But it’s arguably disingenuous to define acceleration as something other than the second derivative of position with respect to time. Unless you’re talking about rotation of the earth (though where the table is was never specified).
So you’re saying that there are no photons, that they just behave as if there are, but in fact there are not.
So, in fact, I’m still baffled. The magnets act as if there are photons, but there aren’t any. But we pretend there are, just because they act as if there are.
Is nobody trying to figure this out?
The short answer is that that depends on what the definition of “is” is. The world makes a lot more sense if we assume that the virtual photons exist than it does if we don’t assume that, but we can never observe them directly (by definition, because the ones we can observe aren’t virtual). And these things which we can’t observe but which make the world make more sense behave in almost every way just like some other things that we can observe.
On second thought, perhaps you were talking about more 20th Century ideas of position and time. I wouldn’t know how far first-year students get into that.
The object on the table may not appear to be accelerating to an observer, but it is in fact in an acceleration (i.e. force, in this case, gravitational) field and all effects are identical to an object that is being accelerated by a visibly applied force. This isn’t disingenuous; this is the foundation of General Relativity. However, this behavior isn’t obvious to anyone who hasn’t studied modern physics; the “common sense” of the average smart person, a lower division physics student, and practically all other science and engineering students will argue to the object not being under acceleration, even as they apply “Force = mass x gravity” to find the reaction force. (Mathematicians, on the other hand, accept the concept implicitly, but only because they deal with abstracted concepts that are completely divorced from reality and thus are not bothered by the apparent discontinuity between what they see and how the math works out.)
In fact, we can’t even observe “real” photons directly; all we can do is observe the result of an interaction in which the photon is absorbed (or destroyed, depending on your interpretation). So the business of distinguishing between “real” and “virtual” photons is itself an abstraction; what we really have is photons whose interactions we observe directly (light absorbed on the retina, heat absorbed by the body, the photoelectric effect) and interactions we can only offer from the responses between electromagnetically influenced bodies (magnets in repulsion, the Coulomb force, spontaneous emission, vacuum polarization, the Lamb shift). Virtual photons work just as well as real photons, just as a tree falling in the woods does, in fact, make noise even if someone is not around, at least for anyone who holds causality and ontological realism to be a fundamental natural truth.
Stranger
As in y = Ae[sup]kx[/sup], where k can be negative. But most people would prefer to see an explicit negative exponent for exponential decay.
Actually, I think that in this case, we’d be a lot better off if we did let common sense hold sway. If you give someone an accelerometer, common sense tells them that the number that the accelerometer reads is the acceleration. It’s not sense at all to think that you have to subtract 9.8 m/s[sup]2[/sup] from the reading, or maybe add it, or apply the law of cosines, depending on whether you happen to be upside-down at the moment, which the accelerometer itself can’t possibly tell you. That’s something that people learn against their common sense, and teaching relativity would be a lot easier if they hadn’t. The central tenet of General Relativity is that the reading on the accelerometer is correct, just as your common sense would tell you.
The question applies to the box as well but, as Stranger pointed out, it’s easier to visualize with magnets.
The same question can be asked with electrons: two electrons will push apart using virtual photons which means, I presume, that the electrons are emitting photons. My understanding is that when an object emits a particle then that object loses a small amount of energy and/or mass equivalent to the energy of the particle.
Even in that picture, though, there wouldn’t be any contradiction because each electron would ‘get’ as many photons as it ‘emits’ from the other electron, keeping the balance nice and tidy.
It’s probably easier to think about if you realize that in order to push each other apart, the electrons must have been brought closer together at first, which means putting energy into the system.
About virtual photons and other virtual things:
There’s a big difference between something that may well really be there but be hidden, versus something that we think couldn’t be there but whose behaviors also fit what we see.
A rope can hold up a weight.
If we pass the rope through a pipe, the portion inside the pipe isn’t visible, but it’s easy to believe it’s holding up the weight that hangs below the pipe.
However, if a weight floats in the middle of the room and we don’t see a rope above it, how reasonable is it to think there’s a rope holding it up, just because a rope there would have explained its behavior? If there are other tests that should have detected a rope, like waving our arms above the weight and hitting nothing, and they don’t, does that make the rope hypothesis unreasonable?
Is a “virtual photon” conceived as real but untestable, or as a mathematical convenience because it predicts experimental results, or as a mystery between those two, or what?
All of the above. The fact is that the formalism of the exchange of virtual photons works mathematically to extremely high precision; it has, in fact, been tested to greater precision than any other theory in natural science. It may be that something entirely different is going on with something other than photons producing the same exact results, but for any practical purpose to date it doesn’t really matter; treating the interaction as an exchange of unseen and unseeable photons works, and that is just about all the current state of quantum physics can say on the topic. Or, as Nobel Prize in Physics laureate, founder of the Institute of Theoretical Physics, father of quantum mechanics, and leader of the Copenhagen Gang Neils Bohr is quoted as saying, “There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.”
Stranger
I can still imagine situations where the number of photons emitted is (probably) more than the number absorbed. For instance, say you move a magnet near a pile of iron filings. The filings move which requires that energy be expended.
Back to the electron example, say they are moving towards each other. When they get close enough they repel each other, changing their direction/velocity in some way. Doesn’t that require an expenditure of energy? In this example I can imagine that the energy would be subtracted from their velocities but that can’t always be the case.
No. Why would it?
I think you’re possibly confusing work with energy (more here). To change their directions/velocities, work must be done, but no net work is done and no energy is required. What happens to the kinetic energy of the electrons as they slow down, you ask? That’s where field theory provides the simplest answer. It’s stored in the field, and then converted back to kinetic energy as they repel each other.
Fields that work this way, in which no net work is done, are called conservative (it has a broader, but more precise, mathematical definition, though that is what it implies). A gravity field is another conservative field - the work done in moving something to particular height will equal the work that could be accomplished by dropping it (if you ignore friction, air resistance, etc.)
OK, I think I see what you’re saying. Let’s go back to the iron filings example for a moment. Where’s the energy coming from that moves the filings? From the movement of the magnet itself?
That’s right. It’s just the same in a generator, which produces electrical energy by moving a magnetic field through a coil of wire (or vice versa, in fact) but the energy doesn’t come from the magnetic field; it comes from the fuel which produces the heat which boils the water which creates steam which drives the turbine which turns the generator shaft which moves the magnets around. Magnets don’t supply energy, they store and release it.