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College Physics (Urone)
Found in: Page 1237

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Short Answer

Quantum gravity, if developed, would be an improvement on both general relativity and quantum mechanics, but more mathematically difficult. Under what circumstances would it be necessary to use quantum gravity? Similarly, under what circumstances could general relativity be used? When could special relativity, quantum mechanics, or classical physics be used?

We have provided a brief explanation, keeping in mind that the relevance of these theories varies depending on the energy scales at which they are applied.

See the step by step solution

Step by Step Solution

Step 1: Circumstances that made use of quantum gravity and general relativity necessary.

The effects of quantum gravity are appreciable at very large energy scales (of the order of \({\rm{1}}{{\rm{0}}^{{\rm{19}}}}{\rm{GeV}}\) ), or it can view in size scales, (of the order of\({\rm{1}}{{\rm{0}}^{{\rm{ - 35}}}}{\rm{\;m}}\)). These energy scales are used for extreme phenomena such as the case of the beginnings of the universe (big bang), or black holes. So, to understand these effects, we need a quantum theory of gravity. On the other hand, general relativity is a theory that describes the evolution of systems at very large scales of the universe and at intermediate scales in terms of size. For example, the movement of planets, stars, galaxies, gravitational waves, etc.

Step 2: When could special relativity, quantum mechanics, or classical physics be used?

Special relativity is relevant when the speeds at which objects move in an inertial-systems (in the absence of acceleration), are appreciably compared to the speed of light in a vacuum. Quantum mechanics explains very well the phenomena that occur at atomic scales and at everything related to the wave-corpuscle duality, which are exhibited by particles on these scales. Even the light can be seen as a particle (the photon). Classical mechanics is a special limit where, under certain conditions the previous theories converge. For example, for speeds in the order\((v \ll c)\), special relativity reduces to classical mechanics or Newtonian mechanics. Similarly, quantum mechanics reduced to classical mechanic when Planck's constant becomes zero. Classical mechanics explains very well almost all the phenomena of everyday life, such as the movement of cars, the orbits of satellites and rockets around the earth, the propagation of sound in the air, etc.

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