Negative Length: Implications & Meaning

Spin is also a vector, and can have negative values, but negative spin is not a well-defined concept.In summary, the concept of negative length is meaningless because the inner product requires a magnitude to be positive. Negative mass has been discussed, but there is no clear consensus on its existence. Negative temperature is possible, as seen in lasers, but negative momentum and spin are not well-defined concepts.
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Meatbot
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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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  • #2
I don't see how that would work because formally, length is a magnitude and always positive as a result.
 
  • #3
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.
 
  • #4
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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  • #5
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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FAQ: Negative Length: Implications & Meaning

What is negative length?

Negative length is a concept that describes a measurement or quantity that has a value less than zero. In other words, it is a value that represents a deficit or a decrease in magnitude.

What are the implications of negative length?

The implications of negative length depend on the context in which it is being used. In mathematics and physics, negative length can represent a direction or vector that is opposite to a positive length. In other fields, such as economics or finance, negative length may indicate a loss or debt.

Is negative length physically possible?

No, negative length is not physically possible in the physical world. It is a mathematical concept that is used to solve equations and describe certain phenomena, but it does not have a physical representation.

What is the meaning of negative length in the real world?

In the real world, negative length may have different meanings depending on the context. For example, in construction, a negative length may indicate a decrease in the size of a structure due to shrinkage or damage. In financial markets, negative length can represent a loss in investment value.

How is negative length used in scientific research?

Negative length is used in scientific research in various fields, such as mathematics, physics, and engineering, to model and solve complex problems. It is also used in data analysis and statistical modeling to represent relationships and trends that involve a decrease or deficit. Scientists may also use negative length to describe and investigate phenomena that involve negative quantities, such as negative energy or negative mass.

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