What is the contradiction between the theory of relativity and quantum mechanics?

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One of the main tasks of modern science is the so-called

The task of developing the theory is just true in order to reconnect the quantum mechanics and the theory of relativity. Create such a theory that will work equally well both on micro and on the macro level.

Actually contradiction right here in this formula:

In essence, this equation is the whole general theory of relativity. The left side of this equality represents the geometry of space-time, and the right side of energy, impulse.

Speaking very simplistic significance of this equation is that space-time says the matter how to move, and the matter says space-time as being curved.

However, take a look

When Einstein, about 100 years ago, for the first time, wrote this formula no hats over t. But this is simply because the quantum mechanic as a direction in science at that time was in the infancy. Now, we know much more, so t became a quantum operator.

And here is no hope — in the left part of the formula there are no values with a hat. And therefore, strictly speaking the equation does not make sense. This is how to compare apples and oranges. The expression on the right side where the numbers cannot be equated to the left, where quantum operators are located.

With the use of some assumptions, we can still do if you replace the quantum operators in this formula, their expected (medium) values.

And the formula in this form works. Works well. I would even say too well. Gravity is so weak interaction, and quantum effects are so insignificant that in 99% of cases this formula works perfectly.

However, we still do not like it. Because the replacement of the quantum operator’s expected value is a rather cheap trick having a little common with science, although giving good practical results.

Really? Yes, we would be happy, but the trouble is that they would put it there, we need to understand how the quantum (and quantum if) space-time. If we manage to do this, then we can describe gravity using the operators of quantum mechanics.

Under the space-time quantization is understood to find the smallest particles of the components of the space-time. Quantum space-time will be minimally possible in practice segment of space and the lowest possible time interval.

However, while we do not know how the space is quantized. Theoretical physicists have developed many theories of quantum gravity (

Thus, it can be said that at the moment we, a kind of dead end and do not yet know how to advance further semi-chassic gravity. However, I am sure that in a relatively close future, this problem will be overcome and finally will appear