Why is it that everything is so so different between the two worlds ...?
It's not true.
Can You be more specific ?
On the contrary, relativity can absolutely apply in the quantum world. Special relativity that is. Special relativity has already been combined with quantum mechanics to create a relativistic quantum mechanics.
GENERAL relativity and quantum mechanics...Well, they don't play so nicely. Gravity, as a fundamental interaction, must be compatible in QM equations and it is not. To simplify the problem: general relativity necessitates the existence of a space-time continuum: an entity which covers all of the universe and can be bent and warped by energetic objects, causing distortions in the movements of other objects around it--this is what we understand today to be gravity.
General relativity is a classical theory which says that space-time is perfectly smooth and flat on all levels, from the infinitely big to infinitely small. Quantum mechanics tells us that there must be uncertainty in gravitational energy on the smallest of scales, and therefore we must modify the nature of gravity and space-time so as to truly be valid at all scales. This turns out to be trickier than you might think. Quantum mechanics also suggests that, like the other three fundamental forces, gravity should have a carrier particle--the graviton. The graviton is predicted by many theories which attempt to unify gravity and quantum mechanics, but it is extremely difficult to experimentally observe such a particle--almost impossible.
The two main quantum gravity theories: theories which combine general relativity with quantum mechanics are String Theory and Loop Quantum Gravity. There are many others, but these are the two most popular ones currently. String Theory proposes that at the smallest scales of the universe, the planck scale, energy and mass are made up of extremely tiny "strings" of energy. This strings are capable of bridging the uncertain terrain of QM with the smooth predictability of GR just correctly. The downside is that we must radically alter what we know about GR and essentially argue that space-time is flat, not curved, which flies in the face of Einstein's theories, among other predictions. We have not found a way to test this theory. Loop quantum gravity takes a more canonical approach, as it attempts to find the simplest correction we can make to curved spacetime on the quantum level to make it compatible as a quantum theory. It is a complete quantum theory, and requires fewer radical and controversial changes to our current understanding of gravity and physics, but as a downside, we have not recovered Einstein's laws from this theory yet.
The main difference between the general relativistic world and the quantum world is that in the quantum world, everything is governed by statistics, probability and uncertainty. We can't determine the position, energy or momentum of particles absolutely, but only make statements about the averages of those quantities for a particle. General relativity requires we know all quantities at all energy levels. Einstein hated the idea of indeterminism in physics, and worked hard in the later part of his career to show why a probabilistic theory of quantum physics had to be wrong, but was unsuccessful.
Hope that answered your question!
If you're talking about general relativity, it's because most of atoms are empty space, so there's too much area to cover between the nucleus and shells of electrons, so by the time the miniature area of space-time is warped by the nucleus, which is so small that by the time the gravitational waves would have reached the electrons, the space-time has evened out. So the electrons rely on the electromagnetic force to keep them in orbit. So, theoretically, general relativity is still taking effect on the sub-atomic world, but on a scale that isn't large enough to affect it.
quantum mechanics and relativity combines to form what is known as quantum field theory. A very broad field now.
When considering foundational aspects of physics and such problems as the double slit experiment and entanglement, it is only relativity that provides a picture of the universe that resolves these puzzles.
It appears that both GR and QM are approximations, really good ones by the way, for the entire universe, except not so good at the big bang and black hole singularities. So far, GR [gravity] has not been incorporated in the Standard Model of particle physics.
We need a more general theory [and maybe new math] apparently to combine them into a unified theory. They were unified at the moment of the big bang, but that is long gone so we can't observe that either.
Don't quote me on this figure, but I think the electromagnetic force may be on the order of 1030 times as strong as the gravitational force, say between a nucleus and a bound electron. So QM handles subatomic particles pretty well neglecting gravity. I read somewhere that gravity is so weak it would take longer than the age of the universe for an electron to exchange a single graviton with it's nucleus...so detection is REALLY difficult. [Again, that figure is to provide some perspective rather than a precise comparison.]
The EM force is just about 1036 times stronger than Gravity.
I think what you read about graviton exchange is actually that it would take a time scale longer than the age of our universe to DETECT a graviton being exchanged between electron and nucleus. I feel like there are a lot of graviton exchanges that would happen but we wouldn't see. I could be wrong about that, though, who knows.
Only calling on the 4-dimensional world of special relativity can you make any sense out of the results of the QM entanglement experiments.
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