We all know that Einstein's theory apply to the big universe, and quantum mechanism apply to the nanoscopic scale, and both theory work perfectly in it's realm, but how could two theory contradict each other?
I'm not sure your question as stated makes any sense. The point is that they DO "contradict" each other in that they don't work in the realm where the other works. Do you mean "what is an EXAMPLE of the contradiction?" Pretty much any example of trying to use one in the realm of the other gives you an example that they don't work Do you mean "WHY do they contradict each other"? That's because one or the other or both are incomplete theories. Neither is wrong, it's just that neither one fits all cases and as solid theory should do.
A major source of problems is any regime where both have to apply. The most obvious examples are inside black holes and the universe immediately after the big bang. I am not acquainted with the details, but I understand that trying to determine what happens leaves to mathematical nonsense.
By "contradict each other", usually what is meant is that gravity has not so far been made into a quantum theory. All the other forces of nature, the strong force, the weak force, and the electromagnetic force admit a so-called "quantum field theory" (QCD, electroweak theory, and QED respectively). This means that we have been successful in turning the field equations of these forces into a quantum field (the details of which are far too broad to go over here). We have not been able to do so with gravity. The difficulty mainly comes from the fact that gravity is a feature of the underlying space-time itself (although there are field-theoretic theories of gravity, but this is beyond my knowledge area). The procedure to quantize the gravitational field yields non-renormalizable integrals (integrals which diverge, and which we can't make converge with a finite number of adjustment parameters). Moreover, even the phase space of general relativity is very difficult to pin-point in the Hamiltonian formulation (which leads to canonical quantization as we are familiar with). The phase-space of three-metrics and their associated "super-momenta" has far too many degeneracies (since a large number of different three-metrics will describe the same three-geometry, all related to each other by coordinate transformations). And it is difficult to find the correct phase space (saying "the phase space is the space of 3-geometries" is well and good, but to mathematically formulate such a statement is highly non-trivial). But, since these forces act on such different realms, it's not so easy to experimentally see where the contradictions lie. In the quantum regime, the force of gravity on Earth, for example, is so much weaker than all the other forces, that we can't experimentally see where the breakdown happens. To all energy scales that we have been able to test in the laboratory, the standard model of quantum mechanics has performed beautifully. In all astrophysical applications that we can observe, general relativity has performed beautifully (ignore for the moment possible problems with dark matter). We have not been able to experimentally observe a contradiction in either of these theories, but because the math doesn't work out for a quantum version of gravity, we expect a problem somewhere down the line. We could see such examples of contradiction, perhaps, near the event horizons of black holes, and such, but it's not like we have a black hole in some laboratory somewhere that we can study...
Matterwave: ¿Didn't quantum mechanics fully explained inertial mass? With Higgs, and other fields? As I understand, relativity says that it shouldn't be possible to tell the difference between gravity and acceleration, and since mass is just the flow of gravity field out of a closed surface, why gravitational mass cannot be equaled to inertial mass?
different types of mass are -inertial mass measures an object's resistance to changes in velocity m=F/a. (the object's acceleration) -Active gravitational mass measures the gravitational force exerted by an object. -Passive gravitational mass measures the gravitational force experienced by an object in a known gravitational field. -Mass-Energy measures the total amount of energy contained within a body, using E=mc². -rest mass or invariant or proper mass. The Higg's field affects the mass of W^{+},W^{-} and Z weak guage bosons. It only desribes a small % of the mass of the universe roughly 1% the other types of mass are described by the Compton wavelength, the non reduced Compton wavelength describes the E=Mc^{2} relation. [tex]e=hf=\frac{hc}{\lambda}[/tex] where λ=Compton wavelength, when one divides the Compton wavelength by 2[itex]\pi[/itex] you get the reduced Compton wavelength. The reduced Compton wavelength is used in the Klein-Gordon relations which is essentially the relativistic version of the Schrodinger equation. Though don't ask me the exact details on the debate between this and SR and GR. My knowledge of QM is not great so hopefully I have this correct lol. Although these sites touch on some of the issues http://theory.caltech.edu/people/jhs/strings/str115.html http://en.wikipedia.org/wiki/Bohr–Einstein_debates http://www.askamathematician.com/2009/12/q-howwhy-are-quantum-mechanics-and-relativity-incompatible/ http://en.wikipedia.org/wiki/Quantum_gravity there are numerous more articles, simply google quantum vs relativity debate or general relativity and quantum mechanics incompatible
I'm not sure what you are directing your question towards. I don't see how the Higgs mechanism affects any of the statements I made in my post. 1) I am not intimately familiar with the Higgs mechanism, but as far as I know, it's a spontaneous symmetry breaking mechanism which gives mass to the originally massless vector bosons in the non-abelian gauge theory we call electro-weak theory, thereby making the weak force a short-distance force rather than a long-distance forces like the EM forces. I'm not familiar with how it gives fermions mass. You are better off asking someone else this question. 2) The gravitational mass is indeed equal to the inertial mass. This is the equivalence principle. This has been shown to be true by the Eotovos (someone spell this for me...because I can never spell this...) experiments. I hope I didn't give you the impression in my previous post that this was false. I don't see where in my previous post you are directing your questions to, so I don't see why you would think I was implying that this was false.
I do not ask about a conflict with your statements. I read somewhere that inertial mass is fully explained in quantum mechanics, and since inertial mas equals gravitatory mass/energy, I would expect that to lead to a bridge between gravity and quantum mechanics. I just hoped to get more light about that, from people which knows more than I know.
Although it is true that inertial mass = gravitational mass, this single principle is not enough of a bridge between quantum mechanics and general relativity to give us a theory of quantum gravity. We know that the "m" we get and use in quantum mechanics should be the inertial mass, and we know that this should interact with gravity; however, that doesn't help us describe gravity in a quantum mechanical fashion. In practice, the "m" that we study in quantum mechanics is so small that gravity has a negligible effect on it in comparison to the other effects we study in quantum mechanics, so we neglect it.
Surprisingly enough this page has a decent descriptive covering quantum gravity and its associated problems. http://en.wikipedia.org/wiki/Quantum_gravity however this paper has a far better descriptive of the problems quantum gravity has, particularly when it comes to describing curved space-time. No worries there is very little math, its more a FAQ style article Quantum Gravity for Dummies http://arxiv.org/pdf/1402.2757v1.pdf This article however is a bit more technical and covers Loop quantum Cosmology, in case anyone is interested. Loop Quantum Cosmology : A status report http://arxiv.org/abs/1108.0893 edit: there is one particular descriptive of the singularity problem from the last article I always liked. "However, because gravity is geometry in general relativity, when the gravitational field becomes singular, the continuum tears and the space-time itself ends. There is no more an arena for other fields to live in. All of physics, as we know it, comes to an abrupt halt. Physical observables associated with both matter and geometry simply diverge, signalling a fundamental flaw in our description of Nature"