I thought that, when you try to apply general relativity to a world described by quantum mechanics, you end up trying to measure curvature of surfaces that do not have a well-defined curvature, much like how the curvature (derivative) of y = |x| is undefined at x=0?
I’ve heard several different descriptions of the “contradictions” between quantum mechanics and general relativity. One is that the mathematical functions used to define general relativity are undefined on the type of spacetime described by quantum mechanics; naively trying to apply one to the other requires you to find limits that do not exist (or something like that). Another explanation said that yes, you can create a quantum theory of gravity using a “naive” approach, but such a theory requires an infinite number of arbitrary physical constants and is therefore completely useless because 1) you can’t actually measure an infinite number of physical constants and 2) if you don’t measure them, the proper “choice” of constants can give you any result whatsoever, so it can’t make any predictions about the actual universe.
By the way, has anyone else here had the thought that the reason quantum mechanics and general relativity are contradictory yet seem to predict reality perfectly is that “there’s a bug in the code”?
The mathematical inconsistency between quantum mechanics and general relativity illustrates a key point. Most of the time the hypothesis set for new solutions, rather than being infnite, is null. It is often quite easy to illustrate that every available theory is wrong. Even if we know that our theory is clearly inconsistent with reality, we still keep using it until we come up with something better. Even if General Relativity were contradicted by some experimental discovery in 1963, Einstein would still have been lauded as a scientist for finding a theory that fit more data points that the previous one.
In science, and in a lot of other contexts, simply showing that a theory could be right, is much more important the establishing to any degree of statistical significance that it is right.
I thought that, when you try to apply general relativity to a world described by quantum mechanics, you end up trying to measure curvature of surfaces that do not have a well-defined curvature, much like how the curvature (derivative) of y = |x| is undefined at x=0?
I’ve heard several different descriptions of the “contradictions” between quantum mechanics and general relativity. One is that the mathematical functions used to define general relativity are undefined on the type of spacetime described by quantum mechanics; naively trying to apply one to the other requires you to find limits that do not exist (or something like that). Another explanation said that yes, you can create a quantum theory of gravity using a “naive” approach, but such a theory requires an infinite number of arbitrary physical constants and is therefore completely useless because 1) you can’t actually measure an infinite number of physical constants and 2) if you don’t measure them, the proper “choice” of constants can give you any result whatsoever, so it can’t make any predictions about the actual universe.
By the way, has anyone else here had the thought that the reason quantum mechanics and general relativity are contradictory yet seem to predict reality perfectly is that “there’s a bug in the code”?
The mathematical inconsistency between quantum mechanics and general relativity illustrates a key point. Most of the time the hypothesis set for new solutions, rather than being infnite, is null. It is often quite easy to illustrate that every available theory is wrong. Even if we know that our theory is clearly inconsistent with reality, we still keep using it until we come up with something better. Even if General Relativity were contradicted by some experimental discovery in 1963, Einstein would still have been lauded as a scientist for finding a theory that fit more data points that the previous one.
In science, and in a lot of other contexts, simply showing that a theory could be right, is much more important the establishing to any degree of statistical significance that it is right.