Does Greater Energy Equal Greater Mass in Classical Mechanics?

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Discussion Overview

The discussion revolves around the concept of position-dependent mass in classical mechanics, particularly in relation to the Lagrangian equation and harmonic oscillators. Participants explore its implications in both classical and quantum contexts, raising questions about its physical applicability and theoretical foundations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the position-dependent mass concept and seeks clarification on its relevance in classical mechanics.
  • Another participant questions the validity of the term "position-dependent mass," suggesting it lacks practical application in physics and may be a mathematical abstraction.
  • A participant shares a paper related to the topic but admits difficulty in understanding its content.
  • There is a mention of Professor Roger Penrose's work discussing the relationship between gravitational energy and mass, raising the question of whether greater energy implies greater mass.
  • Some participants note that while greater energy may suggest greater mass in certain contexts, it diverges from the original inquiry about position-dependent mass.

Areas of Agreement / Disagreement

Participants generally express uncertainty regarding the concept of position-dependent mass, with multiple competing views on its applicability and relevance in physical systems. The discussion remains unresolved, with no consensus on the topic.

Contextual Notes

Participants highlight limitations in understanding the practical applications of position-dependent mass, indicating a reliance on mathematical frameworks without clear physical interpretations.

Ibrahim Mustafa
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Hello, I have some trouble understanding the position-dependent mass concept in classical mechanics especially with the lagrangian equation and the relation with the harmonic oscillator. Is there a person can provide a brief on the subject?.
 
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I have no clue what you mean by "position-dependent mass concept". It doesn't make any sense to me anyway, but do you have a reference?
 
I upload paper related to this topic and there is more but I couldn't understand them.
 

Attachments

Ok, that's a funny mathematical study. I've no clue, where this is used to describe real physical systems. So what are your specific questions concerning the paper?
 
And this talk about this term in classical and quantum.
 

Attachments

I want to know the meaning of "position-dependent mass", also why and where we use it?
 
As I said, I have no clue, where in physics this idea is applied. It looks to me as if this is a purely mathematical exercise. Perhaps other forum members are more knowledgeable about this subject.
 
vanhees71 said:
As I said, I have no clue, where in physics this idea is applied. It looks to me as if this is a purely mathematical exercise. Perhaps other forum members are more knowledgeable about this subject.
Thank you for paying attention.
 
I read in Professor Roger Penrose's book "The Road To Reality" in section 20 dealing with gravity's role in quantum state reduction that the total gravitational energy of two masses is different when they are separated than when closer together. So would this mean that in this case greater energy means greater mass?
 
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  • #10
wwoollyyhheeaa said:
So would this mean that greater energy means greater mass?
Yes, but that's different from what Ibrahim Mustafa is asking about.
 
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