I didn't forget. I didn't know, and I didn't assume it to be fact, or fiction.

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 sometimes people forget the dr. isn't for show! this is my field, i can lecture about it for hours.

Wow Dr. A! Yeah magnetism isn't the answer in this case. Sure, you could replicate the hover board, in a controlled environment....I've simplified the matter for myself. I'll stick to a regular skateboard. Gravity is a harsh mother fucker, I have the scars to prove it.

the reason ultimately it because we're dealing a lot of power output that would have to be cooled. small fans and solid state coolers are great for CPU's but this is a lot of heat you'd be dealing with. speaking of which, we have yet to discuss how exactly all of this gets powered!

i donno, man, i'm coming at this from the point of view of a nerd who'd want to see the actual BttF hoverboard replicated. but who knows; tomorrow they might discover anti-gravity and then all of this moot.

Also, hummingbirds.

 And since I can't figure out how to edit posts, I'll reply again: the "shadow" board could read the rider's or hoverboards motion's, either through radio signals or optical lasers, and follow along. You wouldn't have to generate a magnetic field then.

Oh, and this is just me with no advanced training in engineering spitballing here, but would it be so rediculous to have an electric skateboard follow around beneath you with embedded magnets powerful enough to support a "hoverboard" with opposing magnets and someone on top of it? I'm not sure if you could find/make/have magnets that powerful, and it wouldn't be like in the movie, but with the right marketing it could sell. You could call it "the Hoverboard Shadow." (Well not really, I'm pretty sure "hoverboard" is trademarked)

 That explains why heat would be generated, but not why a suitable venting/cooling system couldn't exist in an efficient and small enough form to preclude it's use on a surfboard or skateboard-sized vehicle. And again, there are other options. Rotors or compressed air can make something hover, and just because you cant fit them onto a board right now doesn't mean it can't ever be done. Also, personally I would consider a hoverboard to be invented if someone set up a giant room in Vegas or Epcot or somewhere that had "boards" that you could float around on over a surface, via magnets or compressed air or something else (like the old Flying Saucers ride at Disneyland, but not lame). In this case, size constraints would be much larger.

you need to take the nature of materials into account; yes we can make things smaller but there is a size below which we cannot go - at least not without circumventing the physical principles that make things like CMOS, etc, work. in other words, too small, and you're in the quantum world. yes, this means that there is a fundamental limit to how small circuitry can go before quantum tunneling makes a mess of it. there are ways to get around this issue, but they don't involve minuaturization. now let's go back to magnetic fields generated by currents. P = I ^2  x R; where P is the power lost, I is the applied current and R is the resistance of the wire. this comes to us from ohm's law. whenever current is passed through a wire, some of the energy is lost to heat, which is P in that formula. now, it's possible to tweak R, make it smaller if you will. but like the speed of light's consistency, this formula will never go away. and if you're going to use currents to make magnetic fields, you're going to deal with the limits and constraints imposed by said law. which translates to - we need a cooling system. that right there defeats the whole idea of a hoverboard using magnetism.

now, moving away from magnetism, there was something developed by hiller in the 50's that looks like a personal hovercraft. you're essentially sitting onto of a rotor. mythbusters actually showed some of it. insanely cool. and large and not something you'd put a kid on. shrinking that, possible, but that also shrinks its power output and thrust. again, materials make things dirty. don't get me wrong, the laws of nature do allow hovering, but they also cap the application.

It doesn't have to use magnets. If you don't assume a hoverboard has to be able to go offroad, you could make a comparative small "board" that could float over a magnetic track like a maglev train or over air blasted up through a floor (ie make a giant air hockey table). Maybe you could have a separate magnetic board that rolls around the ground while you hover above it. Obviously getting hover technology onto a skateboard isn't feasible right now; that's why it hasn't been invented yet. And technology gets smaller and more efficient all the time. Just because the Write brothers' plane couldn't carry an engine powerful enough or enough fuel to fly across the Atlantic doesn't mean we can't now. It's like someone in the 60s saying we could never have a handheld computer, because where would we put the vacuum tubes? I'm just saying it's ridiculous think of the impossibility of hovering as a universal constraint like the speed of light.

again, all of this assumes that board is supposed to run on magnetism, which is my recollection -admittedly, i haven't watched the movie in years....

the earth's magnetic field as i stated is abysmally weak; the chances of using it to repel a field of opposite polarity are nil unless your opposing field is equal to or less than the earth's magnetic field. (q. ever seen a magnet just float on its own by repelling against the earth's magnetic field? btw, those images of metal spinning while suspended are actually repelling the magnetic field generated by a superconductor and not the earth). so, if we wanted to use magnetism to make an object hover, we'll need to provide another magnet of more or less equal strength to give us something to repel against. there are ways to do it - generate an opposing magnetic field or through a permanent magnet of suitable strength. now, let's make a toy that enables a kid to hover over any distance untethered using the repulsion of magnetic fields. you could have the ground be an entire slab of magnetic material. doesn't seem practical, as in the movie it was possible, although limited, to use it to hover over water. you could have coils under the board that generate the field - hm, not really. first those coils would have to be separate from the board otherwise you'd have repulsion vertically but no real impulse laterally - well maybe but then unless those coils are able to follow along with the board, no doubt with a parallel system of motion, say, placed on top of a regular skateboard, all that's going to happen is that the repulsed board will move a bit then tumble onto the ground as soon as it's cleared the field of the coils.

sorry, lots of things are possible, practical is another matter.

i've always been under the impression that the board uses magnetism to hover; which begs the question - how? the earth has a magnetic field which is only strong enough (at the surface) to move needles floating on water. further, to generate enough magnetic force to lift anything as large as person requires some heavy duty electronics, and i imagine quite a potent cooling system (the magnetic flux generated by an electromagnet is proportional the the current - stronger current, stronger field - now imagine the joule heating of the apparatus - yeah, you need to cool that sucker before it melts). how are you going to fit all of that into a board, make it safe for the tykes and yet still be able to lift not only said human but also the equipment. ball's onion's in your court.

 Also, helicopters.

You realize hovering isn't some cosmic impossibility, right? Magnets be crazy. Also, have you ever seen an air hockey table?

(Please, no ICP references)