What are the fundamental incompatibilities between quantum mechanics and general relativity?
The best I can tell is that QM requires discontinuity while GR assumes a continuum.
Here is a grotesque over-simplification (my specialty, as a HS teacher) I hope that someone corrects me if this is off:
Quantum proposes that the gravitational force is carried by a particle, while GR supposes that gravity is more like an inertial effect causes by a condition of the space (curved spacetime) surrounding objects.
When trying to determine what happens inside a black hole, using both GR and quantum theory, the results are mathematically nonsensical.
Another take on the answer (from a layperson):
Relativity requires that spacetime be a continuum (smooth, no disconnect from one point to the adjacent point). Quantum mechanics insists that, as the scale decreases, spacetime actually gets *more* rough - i.e. the smaller the scale, the *more* bumps you get (or at least the more potential for larger bumps, you even can get loops and bridges).
When you had relativistic photons making contact with electrons and transferring their energy, they do so over a theoretically zero distance and zero time. But quantum mechanics shows that, if you get actions happening over zero distance or zero time, you get energy potentials that are arbitrarily or infinitely large. It is the physcial world's equivalent of dividing by zero.
These are the infinities that confounded Einstein, which he eventually "normalized", meaning he basically subtracted them from both sides of the equation.
BTW, string theory reconciles the two theories and satisfies both theory's demands. Strings spread the energy out over an (admittedly very small, but nevertheless not insignificant) distance in time and space. This is why the theory is looking so promising.
A simple and non helpful answer is that no-one knows and is the subject of modern physiscs such as string theory. The problem with this is that string theory proposes elements which are so small that they are currently unobservable and exist in 11 dimensions -- which means that they may never may be directly observable by ordinary means. Remember that these conditions are relevant only to the earliest epoch of the universe with almost unimaginable energies which cannot be replicated in the lab -- if we could we'd probably blast ourselves to hell -- Human Curiosity -- Pandoras box !!!!
For a list of the incompatibilities between the General Theory of Relativity and Quantum Mechanics see Dr. Mendel Sach's website http://www.compukol.com/mendel/ or his book "Einstein vs. Bohr".
List on website:
A) Principle of complementarity, implying 'pluralism', versus principle of relativity, implying 'monism'.
B) Atomism, elementarity and seperability of particles of matter and a model in terms of an 'open system', versus the continuous field concept and a model in terms of a 'closed system' at the outset, i.e. the basic inseparability of material components from a system of matter.
C) In our approach to what it is that we truly 'know', we have the conflict of logical positivism versus realism--the former asserting that all we can possibly know is what we can verify directly in measurements; the latter asserting that there is a real world, independent of whatever we do to find out about it, and that indeed we may learn things about the world that are not directly verifiable in measurements, though they are inferable from the logical structure of our theories, if they also predict correct empirical facts.
D) Irreducible subjectivity in the role of measuring apparatus as a fundamental ingredient in our understanding of matter versus full objectivity, in which the 'subject' and the 'object' of an interacting system are truly interchangeable without losing the objective truth of the entire closed system.
E) Indeterminism (all variables of matter are not 'predetermined') versus determinism (all variables of matter are predetermined).
F) Linear mathematics versus nonlinear mathematics.
G) A fundamental role in the laws of nature of probabilities and their calculus, versus the role of probabilities only as a tool for the observer, but playing no fundamental role in the laws of nature.
H) Special reference frame of the measuring apparatus versus no special frame of reference for any component of a closed system, whether or not one of these components is a large macroobserver and another a small bit of micromatter.
Way cool list. This is more what I was looking for.
The side discussion on tflemming's research has been moved to the following thread.
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