Understanding Classical Physics: The Role of Planck Constant

In summary, classical physics can be understood as the limit of quantum mechanics when the Planck constant tends to zero. This means that at larger scales, where the Planck constant is negligible, we can ignore quantum effects and use classical physics. However, at smaller scales where the Planck constant becomes more relevant, we need to consider quantum mechanics. This is similar to how special relativity becomes important at high speeds, while at low speeds we can use classical mechanics.
  • #1
scarecrow
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Classical physics can essentially be defined as the limit of quantum mechanics as the Planck constant tends to zero.
If the Planck constant tends to zero, it's obviously just getting smaller, so how would this describe classical physics?

Is this a way of explaining it?:

If energy spacing E = hv, and h --> 0, then E --> 0, which is essentially a continuous energy spectrum and quantization and discreteness goes away. Hence classical physics.


Thanks.
 
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  • #2
It's about Planck's constant relative to the scale you're dealing with. If your scale is meters, Planck's constant is negligible and you get classical physics. If your scale is angstroms or smaller, Planck's constant is quite relevant and you get QM.

It's not unlike the relationship between SR and the speed of light. At low speeds, the speed of light is practically infinite, so you needn't worry about relativistic calculations. At speeds of, say, .8c, the speed of light becomes important.

If energy spacing E = hv, and h --> 0, then E --> 0, which is essentially a continuous energy spectrum and quantization and discreteness goes away. Hence classical physics.
That's definitely one way of looking at it. More accurately, you would say delta_E = hv, and so as h->0, delta_E = dE, and you get a continuous energy spectrum that would require us to consider things like intensity of the wave which we've since largely discarded.
 
  • #3
Yeah, I really meant to say dE. :smile:
 

1. What is Planck Constant?

The Planck Constant, denoted as h, is a fundamental physical constant that relates the energy of a single quantum of light (photon) to its frequency. It is an essential part of quantum mechanics and is used to calculate the energy of particles at the atomic scale.

2. Why does the Planck Constant tend to zero?

The Planck Constant tends to zero as the frequency of the light (photon) decreases. This is because the energy of a photon is directly proportional to its frequency and as the frequency decreases, the energy of the photon also decreases. This phenomenon can be observed in the wave-particle duality of light, where light behaves as both a wave and a particle.

3. What are the implications of Planck Constant tending to zero?

The implications of Planck Constant tending to zero are significant in the field of quantum mechanics. It means that at lower frequencies, the energy of particles also decreases, making it more challenging to observe and measure their behavior accurately. It also leads to the breakdown of classical mechanics and the need for a new theory to explain the behavior of particles at the atomic scale.

4. How does Planck Constant relate to the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to simultaneously know the exact position and momentum of a particle. This principle is directly related to the Planck Constant, as the smaller the value of h, the larger the uncertainty in the position and momentum of a particle. This is because the Planck Constant sets a limit on the precision with which certain physical quantities can be measured.

5. Is the Planck Constant always a constant?

Yes, the Planck Constant is a universal constant and is considered to be one of the most accurately determined physical constants. It does not change under normal conditions and is the same everywhere in the universe. However, there are some theories that suggest that the Planck Constant might not be constant in certain extreme conditions, such as in the early universe or near a black hole.

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