Negative Length: Implications & Meaning

[Meatbot]

Does such a concept mean anything? I've heard negative mass discussed but not negative size. What are the implications of negative length?

 

[dst]

I don't see how that would work because formally, length is a magnitude and always positive as a result.

 

[nicksauce]

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.

 

[Meatbot]

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?

 

[nicksauce]

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.