In the real world, there are many and varied ideas we can comprehend, or at least find conceivable. However, there are concepts beyond our comprehension. This does not automatically make them unreal. One such concept is the imaginary number. Physically, the imaginary number is real. To date, however, no one has satisfactorily explained the phenomenon.
Simplest CaseThe simplest imaginary number is the square root of –1. Does that sound like it should be no problem? Well, the square root of 1 has two values: –1 and 1. That can be proven. 1 x 1 = 1, right? And –1 x –1 = 1, right? Well, what number n is there, that multiplied times itself, equals –1? You don’t know, do you? Don’t feel bad. No one knows, at least not at this point. There is one thing that is known. Quantum mechanics expressions are not complete without the inclusion of imaginary numbers as a reality.
Imaginary Space?All imaginary numbers can be written as some “real” multiple of an imaginary number. The square root of –1 can be written as 1 times the square root of –1. Taking all of this into consideration, it should be obvious that it should be possible to create a coordinate system of imaginary space, with three components, one in the x-direction, one in the y-direction and one in the z-direction. These axes are assigned unit values of i, j and k.
Imaginary Time?As if imaginary space wasn’t bad enough, there is also the concept of imaginary time. The concept of imaginary time remains a bit more speculative. If may or may not prove to be a valid and demonstrable concept for the real world, rather than merely for hypothetical calculations. There is one thing to be said about it. One should not accept it merely on the basis of the name of the one who proposes it. Fact stands on its own merit.
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