Question

A physical quantity which can not be negative is *

Answer 1

Answer:

Any notion of distance can never be negative: for example, any mathematical definition of a metric space requires that the metric be non-negative. A metric space is a mathematical set that has structure imposed on the members including that there is a notion of a “metric” or “distance” between member objects. This is defined quite generally. There are all kinds of metric spaces that people have thought about as well. Euclidian space is a type of metric space, and physical space is generally described as Euclidian space. Even if in some theories, physical space is non-Euclidian, if it has a notion of distance defined on it, the notion of distance is still non-negative.

Another example of a metric space is the space of physical operations or transformations that take some N-dimensional classical or quantum system from one state to another state. There is a distance that can be defined between such operations, and it corresponds to how you might intuitively think of distance in this context: if two different operations/transformations take similar initial states to similar final states of the system, then we expect these operations to be close to each other in whatever distance metric has been defined, but if they take similar initial states to very different final states, then their distance would probably be larger …

In the two examples, the quantities in question are non-negative as imposed by mathematics (i.e. by logic), rather than by physics. Physical systems lend themselves to a notion of distance, which logically is required to be non-negative.

Explanation: