What are the main differences between these three quantum theories?

  1. Quantum Mechanics (QM),

  2. Quantum Field theory (QFT),

  3. Quantum Gravity (QG).

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    $\begingroup$ This question is way too vague. You would learn more about the answer by just looking these up in Wikipedia or a survey-of-physics textbook. $\endgroup$ – Keenan Pepper Jan 21 '11 at 16:19
  • $\begingroup$ Your question seem much to vague to me, you are mixing things at different levels. Could you be a bit more specific about "what you don't understand" or what you want to know ? $\endgroup$ – Frédéric Grosshans Jan 21 '11 at 16:27
  • $\begingroup$ Dear Amir, I am not sure whether a full-fledged answer is appropriate here. But all "quantum" things are quantum while the classical physics is not. Quantum physics has all the special things. Quantum field theory and quantum gravity are two special cases of quantum mechanics; quantum gravity may also be viewed as a "slightly modified" special case of quantum field theory. Quantum field theory is quantum mechanics with special relativity included while quantum gravity is any quantum mechanical theory with general relativity included - string/M-theory is the only known example. $\endgroup$ – Luboš Motl Jan 21 '11 at 19:28
  • $\begingroup$ @Lubos If you write your text with some more explanation about quantum theories it would be an acceptable answer. $\endgroup$ – Amir Rezaei Jan 24 '11 at 8:24
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    $\begingroup$ I would +1 this post if it had the limited task of asking about the relationship between quantum mechanics and QFT. (i.e. "what domains of application"). $\endgroup$ – Carl Brannen Jan 24 '11 at 8:41

Classical mechanics and quantum mechanics are subfields of the branch of physics called mechanics, that deal with two realms of size, the big and the small, respectively. The border between big and small has not be scientifically defined yet, but almost every object we deal with can be assigned to a respective group (i.e. galaxies, stars, planets, people, ants, and dust particles are all big. Atoms, quarks, photons and electrons are all small). Classical mechanics is a set of physical laws and their corresponding equations that describe/govern the motion and interaction of big bodies within the universe. These equations are Galilean invariant which means they do not apply to non-inertial reference frames. Classical mechanics is sometimes still called Newtonian mechanics because it's basis is on the work of Isaac Newton. Classical mechanics is an approximation of General Relativity in a weak gravitational field. Quantum Mechanics is a set of physical laws and their corresponding equations that describe/govern the motion and interaction of small bodies within the universe. Quantum mechanics as we know it is the Copenhagen Interpretation which has a set of several main principles . There are two widely taught formulations of QM, the wave formulation (Schrodinger), and the matrix formulation (Heisenberg).

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Physics frameworks lead into each other as follows:

Mechanics leads to Statistical Mechanics

Statistical Mechanics leads to Thermodynamics

Then there is the quantum frameworks, which in their limiting case become the corresponding classical ones

Quantum Mechanics, limiting case Mechanics

Quantum Statistical Mechanics, limiting case Statistical Mechanics

Then there is Quantum Field theory, which developed as a way to calculate crossections and is appropriate for particle physics, i.e. small dimensions, high energies.

Mechanics leads to Neuton's Gravity Theory

General Relativity has a limiting case Neuton's Gravity Theory

There is no consistent quantum gravity outside of String Theory, which is the frontier being studied now.

String Theories have as limiting cases General Relativity and Quantum Field Theory.

All capitalized theories are "physics conceptual frameworks used for calculations"

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  • $\begingroup$ Could you explain main differences between The quantum/Mechanics/Field theory/Gravity ? $\endgroup$ – Amir Rezaei Jan 24 '11 at 9:00
  • $\begingroup$ @Amir . Quantum mechanics is the study of the state functions of single particles in potential wells using Schrodinger's or Klein Gordon equations. $\endgroup$ – anna v Jan 24 '11 at 16:59
  • $\begingroup$ @continued: or Dirac equations for relativistic situations.Classical field theory, like arising from Maxwell's equations, describe the motion of particles and waves. Quantum field theory studies the many body problem using the state functions found from the solutions of one particle problems using creations and annihilation operators and Feynman diagrams to calculate measurable quantities. Classical gravitation is a field theory that studies the behavior of bodies under gravity, solar system and rockets etc. Quantum gravity as we learn here is enclosed in string theories. $\endgroup$ – anna v Jan 24 '11 at 17:02
  • $\begingroup$ thank you very good explained. You can add your comment to your answer later. $\endgroup$ – Amir Rezaei Jan 25 '11 at 7:55
  • $\begingroup$ Hmm, I don't think that quantum field theory developed specifically as a way to calculate cross sections. That is particle physics solipsism :) It developed as a way to quantize the electromagnetic field. $\endgroup$ – Gordon Jan 30 '11 at 2:53

in general answer :Quantum mechanics is a general theory and classical mechanics is a sub-theory from quantum mechanics.

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