Negative Length: Implications & Meaning

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SUMMARY

The discussion centers on the concept of negative length and its implications in physics and mathematics. Participants assert that length, defined as a magnitude, is inherently positive due to the properties of the inner product, where must be greater than or equal to zero. The conversation also touches on related concepts such as negative mass, negative temperature, and negative momentum, concluding that while negative temperature is valid in specific contexts like lasers, negative length remains a meaningless concept.

PREREQUISITES
  • Understanding of vector mathematics and inner product properties
  • Familiarity with the concept of magnitude in physics
  • Basic knowledge of thermodynamics, particularly negative temperature
  • Awareness of momentum as a vector quantity
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  • Research the properties of inner products in vector spaces
  • Explore the implications of negative temperature in thermodynamics
  • Investigate the concept of negative mass and its theoretical applications
  • Study the characteristics of vector quantities, focusing on momentum and direction
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Physicists, mathematicians, and students interested in advanced concepts in vector mathematics and thermodynamics, particularly those exploring theoretical physics and the implications of unconventional physical properties.

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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?
 
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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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