Negative Length: Implications & Meaning

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Discussion Overview

The discussion revolves around the concept of negative length, exploring its implications and meaning within the context of physics. Participants examine whether negative length can be a valid concept, comparing it to other physical quantities like negative mass, temperature, momentum, and spin.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question the validity of negative length, arguing that length is a magnitude that is always positive.
  • One participant cites the mathematical definition of vector length, noting that the inner product requires non-negative values, suggesting that negative length is meaningless.
  • Another participant raises the comparison between negative mass and negative length, questioning how negative mass can be discussed if length cannot.
  • Negative temperature is mentioned as a valid concept, with a reference to lasers as an example.
  • Concerns are raised about the meaningfulness of negative values in vector quantities, such as momentum.

Areas of Agreement / Disagreement

Participants express differing views on the concept of negative length, with no consensus reached. Some argue against its validity, while others draw parallels with other physical concepts that involve negative values.

Contextual Notes

Participants highlight the dependence on definitions and the mathematical framework used to discuss length and other quantities. The discussion remains unresolved regarding the implications of negative length.

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Does such a concept mean anything? I've heard negative mass discussed but not negative size. What are the implications of negative length?
 
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I don't see how that would work because formally, length is a magnitude and always positive as a result.
 
In general, the length of a vector is defined as <v,v> ^(1/2) (where <> is the inner product), and one of the requirements of the inner product is <v,v> >= 0. Therefore the concept of negative length is meaningless.
 
dst said:
I don't see how that would work because formally, length is a magnitude and always positive as a result.

Isn't mass also a magnitude? How are they able to discuss that being negative if so?

What about negative temperature, negative momentum, negative spin? Do those concepts have any value?
 
Last edited:
I have never heard of negative mass being discussed, but a quick google search yields that there are some who say there are no such thing, and some that say there is (could be). So not sure on that one.

Negative temperature is certainly possible. Lasers are an example.
http://en.wikipedia.org/wiki/Negative_temperature

Momentum is a vector, and 'negative' is not a meaningful concept when talking about vectors.
 
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