electromagnetism - What is the difference between gravitation and magnetism?

If you compress a large mass, on the order of a star or the Earth, into a very small space, you get a black hole. Even for very large masses, it is possible in principle for it to occupy a very small size, like that of a golf ball.

I started to think, how would matter react around this golf ball sized Earth? If I let go of a coffee mug next to it, it would go tumbling down toward the "golf ball". Isn't that exactly how magnets work, with paperclips for example?

Magnets are cool because they seem to defy the laws of gravity, on a scale that we can casually see. Clearly, the force carrier particles that produce electromagnetic attraction are stronger than gravity on this scale (or are at least on par: gravity plays some role in the paperclips path, but so does electromagnetism).

My question is, why do we try to consider gravity as anything different than magnetism? Perhaps "great mass" equates to a positively (or negatively) charged object. Pull so much matter in close and somewhere you've crossed the line between what we call electromagnetic force and gravity force. They are one in the same, no?

Answer

There are several qualitative and quantitative differences between gravity and magnetism.

1. 
   

   When you attract 'neutral' bits of metal with a magnet, or attach it to something like a plate of metal, what's happening is that individual atoms of the metal react to the magnetic force. In a ferromagnetic metal, one with a similar electronic structure to Iron or Nickel, the individual atoms work like nanoscopic magnets; but they are very weak, and they are not lined up with one another, so that their fields cancel one another out over any macroscopic distance. But if you bring a "large" magnet (such as a fridge magnet) up to them, the field of the large magnet causes them to align with the field, so that they are pulled towards the magnet — and the magnet is pulled towards them. This is why some metal objects are attracted to magnets.

   
   

   Other metals, such as aluminum or silver, also react to magnets, but much more weakly (and in some cases repulsively): the way that they react to magnetic fields is described as paramagnetism (for materials which align very weakly with magnetic fields) and diamagnetism (for materials which align very weakly against magnetic fields).

   
   

   The very fact that different materials react differently to magnetic fields is something that sets magnetism apart from gravity. Gravitation works equally with masses of any sort, and is always attractive (as noted by Nic); magnetism can both attract and repel, and do so with different degrees of force, as between ferromagnetic, paramagnetic, and diamagnetic materials. But of course, quite famously, even a single object can be both attracted and repelled by magnetic forces: the north poles of two magnets repel each other, as do the south poles; only opposite poles attract each other. (This, of course, is the basis on which compasses work.)

   
   
   


2. 
   

   The way that these forces operate over distance also varies. Gravity very famously (but only approximately) obeys an inverse-square law; the field far from a bar magnet, however, decreases like the inverse of the cube of the distance from the magnet.

   
   


3. 
   

   Finally, moving electric charges produce magnetic forces; whereas they don't cause any gravitational forces which could not be accounted for just by the fact that the charged particles have mass (whether moving or at rest).

   
   

So, on both the macroscopic level and on the level of individual atoms, the forces of gravity and magnetism act quite differently.