Somehow individual measurements are physical but tabulating them makes them incapable of being physical. — fdrake
Nature can "know" about the vector elements but not the vector — fdrake
EG: if the criterion for a theory (as a whole) being physical is successful prediction of experimental results ("manifesting as real"), it's silent on theory elements... — fdrake
Yes. Vectors are a way of dealing with multiple similar quantities which transform in similar ways. Some of those quantities may be related to one another, but there's nothing I can think of that makes the interpretation of the vector as anything more than a notational convenience. — Kenosha Kid
I won't quote the rest, just sum up. A theory is tested empirically, not it's individual elements. If the theory as a whole (or a subset of elements, catering for irrelevancies to a particular experiment) yields otherwise inexplicable or more accurate predictions for experimental outcomes, it's a good theory. — Kenosha Kid
Nature cannot care that much how we represent it. — Kenosha Kid
Which is why I'm pressing the issue; if nature doesn't care how we represent it, why would whether something could be physical or not vary with an isomorphism of structures? Why would a criterion to decide whether a structure is physical decide differently depending upon which representation of a structure you choose? — fdrake
Note that electric impedance is a complex variable. So there exist classic physical variables described by complex numbers. — Olivier5
If complex numbers fit the bill better than real numbers to describe a particular phenomenon, maybe it means something... — Olivier5
Well, if complex numbers are nothing more than a mode of computation, there's no reason to worry about their use in the wave function. — Olivier5
it's a wave after all so Fourier's methods must apply? — Olivier5
As intriguing as complex representations in physics, for me, is how linear operators are so effective. One would think nature to be complicated and non-linear; linearity is a very stringent condition, while simplifying the math. — jgill
As intriguing as complex representations in physics, for me, is how linear operators are so effective. One would think nature to be complicated and non-linear; linearity is a very stringent condition, while simplifying the math. However, it is a seasoned trick in the profession to approximate the non-linear by linear constructs, and, of course, ordinary differentiation and integration are linear operators. — jgill
the square and the circle, are fundamentally incompatible. — Metaphysician Undercover
Straight lines can never be reconciled with curved lines — Metaphysician Undercover
I have done quite a few investigations into linear fractional transformations, and one feature that makes them important is they transform Circles into Circles, where the capital C is in recognition of the fact that a straight line is simply a circle with infinite radius. This has to do with the Riemann sphere. — jgill
It appears the rest of your post goes into the hyperreals, where others on TPF have greater competence. — jgill
Maybe that's the reason they are used in the wave function as well: it's a wave after all so Fourier's methods must apply? — Olivier5
A circle with an infinite radius is an incoherency. This is exactly the problem I am talking about, the faulty attempts by mathematicians to make circles compatible with straight lines. It necessarily results in incoherency. The logical thing to do when faced with this glaring incompatibility is to address the nature of reality, and attempt to determine the reason for that incompatibility, rather than to attempt to veil it, or cover it up with such incoherent principles. — Metaphysician Undercover
Hey, just to let you know, I want to think on this some more, don't want to reply just for the sake of saying something. — SophistiCat
Like the flock of sparrows sitting on your fence, the peanut gallery has no interest in the true nature of space and time. — Metaphysician Undercover
The truth about reality is just too far removed . . . — Metaphysician Undercover
I will never reveal such a thing, because it is not understood by anyone. — Metaphysician Undercover
I already showed you how your thesis, which is a turning away from the vast array of evidence that energy is transmitted as waves, towards a theory which treats this transmission as a movement of particles, is a turn in the wrong direction. — Metaphysician Undercover
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