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I'm a fairly educated person, but not a scientist by any stretch. I don't understand relativity, but I know that it explains the effect of gravity on light, and that prior theories explain the basic effects of gravity very accurately. After looking around on the Internet today, however, I as amazed to read that no one has any idea how gravity actually operates, or what it is. Is this right? How can this be? I'm kinda blown away that such a ubiquitous concept is actually a complete mystery.

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To be more specific, the current theory of gravity makes as much sense as the classical theory of electromagnetism (Maxwell's equations). The difference is this: we now have a quantum theory of electromagnetism, and it is understood as a gauge theory (like the strong and weak nuclear forces). This shows a "deeper understanding" of the theory, in some sense.

Gravity, it turns out, is difficult to quantize -- nobody has succeeded yet. Also, since other theories (like electromagnetism) are quantized on a given, background spacetime, they are somewhat easier to understand. Gravity, however, is the study of spacetime itsself -- thus there are some immediate interpretational issues. Does it make sense to specify a background spacetime, and then quantize gravity as perturbations about the background? Apparently, it does not -- approaches like this have failed, giving rise to infinities that destroy the theory's predictive power. But if you take away the background -- what are the variables of the theory? "x" and "t" no longer make sense as "locations in spacetime" since you have done away with the background! How, then, do you start without a background, and end up with one at the end of the day? This is a very real problem for people working in the field -- nobody knows how to answer that question...