Quantized Kinetic Energy of Relativistic Objects

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Discussion Overview

The discussion revolves around the question of whether the kinetic energy of moving objects can be considered quantized, particularly in the context of relativistic physics and quantum theory. Participants explore the relationship between kinetic energy, relativistic effects, and the principles of quantum mechanics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions if the kinetic energy of moving objects is quantized, referencing the relativistic kinetic energy formula KE = (γ - 1) mc².
  • Another participant challenges the notion that all energy is quantized, explaining that in quantum mechanics, some systems exhibit quantized energy while others do not, using the finite potential well as an example.
  • A third participant supports the previous response, mentioning the "particle in a box" scenario, which has quantized momentum and energy, but emphasizes that this depends on boundary conditions and that free particles do not have quantized states.
  • A later reply warns that the "particle in a box" problem often refers to an infinitely high potential well, which presents its own complexities, and suggests that discussions about momentum observables are better suited for the quantum theory forum.

Areas of Agreement / Disagreement

Participants express differing views on the quantization of energy, with some asserting that not all energy is quantized while others provide examples of systems where quantization occurs. The discussion remains unresolved regarding the specific application of these principles to the kinetic energy of relativistic objects.

Contextual Notes

Participants note that the relationship between kinetic energy and quantization may depend on specific conditions and definitions, and that the discussion may extend beyond the scope of relativistic physics into quantum mechanics.

jrvinayak
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Hello,

I want to know if energy added to moving objects is quantized. Kinetic energy of an moving object is given as KE = (γ - 1) mc2 , where γ is 1/√(1-v2/c2).

And quantum theory talks about any energy always being quantized. So can the KE in moving objects be quantized?
 
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Hi jrvinayak, welcome to PF!
jrvinayak said:
And quantum theory talks about any energy always being quantized.
This is a very common misconception. Even in quantum mechanics there are some systems where energy is quantized and other systems where the energy is not quantized. One very interesting and simple system is the so-called finite potential well

https://en.wikipedia.org/wiki/Finite_potential_well

This system includes both bound states which are quantized and free states which are not quantized.
 
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I agree with DaleSpam's response. I'd just add that less formally, the "potential well" problem is known as a "particle in a box". You might google for this term. The particle in a box has quantized momentum and energy, but the details depends on the size of the box. Formally, we'd describe this dependence by saying "it depends on the boundary conditions". The free particle that's not confined to a box doesn't have quantized momentum or energy levels. The best forum to ask for further details would be the quantum mechanics forum, it's not really within the scope of GR.
 
Be, however, warned that "particle in a box" often means the only apparently simpler problem of an infinitely high potential well. However, this is a particularly difficult case, if done mathematically correctly, because for this problem no proper momentum observable exists anymore, but that's a topic belonging more to the quantum-theory forum. The finite-potential well is only a bit more work but has the advantage of having a well-defined realization of the Heisenberg algebra in terms of the wave-mechanics formulation.
 

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