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That has been a topic of much debate since th1900's. There has been no fully successful tying of the two branches of physics yet but, many proposed theories have made great leaps forward to the answer. For example quantum gravity theory and the string theory, the latter being the more current and relevant.

There are two areas in which the transition from quantum mechanics to classical mechanics is rather obvious: Statistical thermodynamics and wave-particle duality.

Answer2:

Classical and Quantum Mechanics merge in Quaternion Mechanics.

Quaternion Mechanics consists of Quaternion quantities like energy

W = -vh/r + cP where -vh/r is the scalar enrgy and cP=cmV is the vector energy.

Classical and Quantum Mechanics need Quaternion quantities. In general the potential energy -vh/r is a scalar aka a Boson and vector energy cP is a vector aka a Fermion. Bosons/Scalars have integer spin and Fermions/Vectors have 1/2 integer spin.

For the most part like Newtonian Physics use only scalars -mGM/r a scalar and no vectors. Likewise, Quantum mechanics use mostly Fermions or Vectors and few scalars. The speed of light is a scalar as is Planck's Constant h.

Quaternion Mechanics merges Classical and Quantum Physics.

The Laws of Quaternion Mechanics are:

0 = XB = [d/dr, DEL] [B,B] = [dB/dr -DEL.B, dB/dr + DEL B ]

0 = X2B = [(d2/dr2 - DEL2), 2d/dr DEL] [-vh/r,cP]

This Quaternion Wave gives the

scalar/Boson wave -(d2/dr2 - DEL2)vh/r - 2d/dr DEL.cP =0

and the

vector/Fermion particle (d2/dr2 - DEL2)cP + 2d/dr DEL -vh/r =0

In Nature, Quaternions rule and Quaternions combine Bosons and Fermions.

A Quaternion can be a Boson or a Fermion or Both as in

X2W =[ -(d2/dr2 - DEL2)vh/r - 2d/dr DEL.cP,

(d2/dr2 - DEL2)cP + 2d/dr( DEL -vh/r + DELxcP) ]

Quaternions consist of Scalars and Vectors , Bosons and Fermions.

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βˆ™ 11y ago
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βˆ™ 6mo ago

Classical mechanics provides a useful framework for understanding quantum mechanics in limit of large systems. Many quantum concepts, like wave-particle duality and Hamiltonian mechanics, can be connected to their classical counterparts. This allows us to make sense of quantum phenomena by relating them to the familiar concepts of classical physics.

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βˆ™ 13y ago

Not sure what you mean by "connected," but a basic principle of quantum mechanics is that its laws must merge with those of classical mechanics if the particle being observed over a certain distance has a momentum significantly larger than the Planck's Constant divided by that distance.

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βˆ™ 14y ago

When the system gets big. This is called the correspondence principle.

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βˆ™ 14y ago

Classical mechanics is not used in quantum mechanics.

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Q: Why you use some classical mechanics in quantum mechanics?
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