It's really a sort of unique but trivial way of progressing from F=r to defining a new fixed point, b. Bifurcation is usually meant to "split" one fixed point into two fixed points. A kind of "Adam's Rib" sort of thing. — jgill
I can't see a parabole, as you write. — EugeneW
What's philosophical is the idea of a dimensionless point producing an offspring. — jgill
That's so incoherent it's actually funny. — Metaphysician Undercover
In the context of this thread, is a zero-dimension point considered to be Real or Ideal, Physical or non-Physical? As a philosophical or mathematical thought-experiment, the notion of "nothing producing something" might be a valid ideal concept. But as a scientific observation it might be as unrealistic as a vacuum fluctuation popping a particle of matter into existence.What's philosophical is the idea of a dimensionless point producing an offspring. — jgill
In the context of this thread, is a zero-dimension point considered to be Real or Ideal, Physical or non-Physical? As a philosophical or mathematical thought-experiment, the notion of "nothing producing something" might be a valid ideal concept. But as a scientific observation it might be as unrealistic as a vacuum fluctuation popping a particle of matter into existence.
As I understand it, a Virtual Particle is equivalent to a dimensionless point — Gnomon
But as a scientific observation it might be as unrealistic as a vacuum fluctuation popping a particle of matter into existence. — Gnomon
Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways — Gnomon
A vacuum fluctuation can be seen as an eternal presence of a particle in the vacuum. — EugeneW
That's coming close to what I was getting at. The linked quote below indicates that a Virtual Particle is treated as-if it's "Real", but it doesn't add your qualification : "but not physically real". So my question, is "in what sense is a non-physical object Real?. Is that faux reality an equivocation?I would say a zdp is both real and ideal, but not physically real. As for vps, they are excitations of the underlying quantum fields, so perhaps zdps are as well.
It's all Greek to me. I just try to do the math. — jgill
Since Quantum Fields consist of dimensionless-points-in-space, they are "real" only in the sense that they have the Potential to produce physical particles. — Gnomon
What is this concept of "a particle in the vacuum"? Is it a vacuum, which is not really a vacuum because there is something there, which must be a particle, but it's not really a particle because it has no location? So it's not really a vacuum, nor is there a particle, just convenient terms. — Metaphysician Undercover
Is math invented or discovered? :
Mathematics is an intricate fusion of inventions and discoveries. Concepts are generally invented, and even though all the correct relations among them existed before their discovery, humans still chose which ones to study. ___Mario Livio, theoretical astrophysicist — Gnomon
Yes. An immaterial grid-point in empty space is like the symbol "X" (unknown) which serves as a stand-in for a real number, that is un-realized until calculated. I assume that, for a physicist, defining a Virtual Particle as a mathematical point, is essentially an ellipsis, a blank to be filled-in at a later date. So it points toward something imaginary, that could be realized, but not yet physically real.You could say that the point signifies something. — Metaphysician Undercover
If so, why give one of them an un-real name? I'm aware that mathematical theorists treat "Virtual" Particles as-if they are real. But the differentiating name they pinned on them belies their reality from a common sense perspective. This is just one of many paradoxes emanating from the Pandora's Box of quantum science. They make our world seem to be an mirage of many delusions, as contrasted with the mundane Actual Reality of classical science. Biologists & Chemists are still mostly working in the old-fashioned Real world. But Physicists seem to be exploring a sci-fi fantasy realm of parallel Realities.Virtual particles are as real as real particles. — EugeneW
Yes, but energy-without-momentum is what we know as Potential energy, as contrasted with the Kinetic (or Actual) energy of moving matter. For example a typical car battery has 12 volts of Potential, but when no current is flowing there is no Actual physical work being done. That reminds me of the storage box used by the Ghost Hunters to trap poltergeists so they can do no harm. :joke:energy with zero momentum — EugeneW
If so, why give one of them an un-real name? — Gnomon
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