Now if this were so then also real particles would be math. — EugeneW
So this is one of your main divergences from the thinking of the current majority of physicists, yes?
What is an excitation? A field is just a mathematical aid which consists of distributions assigned to all points of spacetime, and these distributions have operators as "value". These operators are creation and annihilation operators. These operators create or annihilate one particle states in so-called Fock-space, a direct product of single particle Hilbert spaces. A free particle field is just a particle with a single momentum state or, when localized, a normalized superposition of a spectrum. In a Feynman diagram, there is one line only and begin and end state have the same momentum. The particle is localized if it has a spectrum of momenta. If it has a well defined position though there are infinite associated momenta, due to uncertainty — EugeneW
But in 3D space is a 'field' not a 'volume,' in that it has 'cubic spacial-expansion?'
This is how I have always perceived the term 'field' as used in physics.
For 'excitation' I conceive the cuboid area as containing liquid like water and I see excitation as a disturbance within the water, like shaking a snow globe.
So not a mathematical aid but a real area of space. I see the 'mathematical aid' part as the conceptual breaking up of space into a 3D grid of contiguous cuboids. So all of space is in reality one big field.
What do you mean by "distributions assigned to all points of spacetime"? what specifically do you mean by 'assigned?' What/who performed such assignment? Do you use the term 'distributed,' as random or is the distribution based on a mathematical function? Are these 'operators' you mention variables/parameters/inputs for a mathematical process?
Ok, these matter/antimatter annihilations seem to me to produce a kind of 'all square' outcome.
The conservation of the total energy of the Universe seems to indicate that this creation/annihalation cycle is much less interesting than the fact that something else happened which created an imbalance within this process and that's why the Universe has galaxies, planets and us.
A free particle field is just a particle with a single momentum state or, when localized, a normalized superposition of a spectrum.
How can a particle BE a field?
The particle is localized if it has a spectrum of momenta. If it has a well defined position though there are infinite associated momenta, due to uncertainty
I think you are typing here, that a particle/quanta/disturbance which forms within a field can move in a particular direction but how fast it will move and exactly which direction it will take and the exact shape of the path (straight, curved etc) will take, is very hard to predict. Is this correct?
no creation and destruction of particles (only couplings) — EugeneW
What do you mean by 'coupling' here?
So, what is a particle? A particle is a tiny geometrical Planck-sized structure on which charge can safely reside, without leaking out. The extra space dimensions in which it exists are perpendicular to the 3D bulk and this ensures that the Planck length is Lorenz invariant (for which physics still has no answer...). The smallest measurable distance (the Planck length) follows naturally from the particles small extension in space. Within the bounds of the wavefunction (the temporal cross section of a field) the particle just hops around erratically if you propagate it in time. Which is to say it travels on tiny parts of all paths Feynman talks about, coupling to the timeless virtual field to reach others, and being itself a time extended virtual particle with its antiparticle component somewhere in space. — EugeneW
So you are saying that the structures that you are calling particles, exist 'outside' of the known 3D of space, yes?
Do You mean 'Perpendicular' to 3D space as in 90 degrees to it? So your 4th spatial dimension is not 'wrapped around' every point of 3D space but is 'perpendicular' to every point in 3D space.
Would this be mathematically represented as a 90 degree direction away from a set of three spatial coordinates (so, dimensionless) and one instant/coordinate of time?
So a position in your space would be (x,y,z,t,90)?
the particle just hops around erratically if you propagate it in time. Which is to say it travels on tiny parts of all paths Feynman talks about,
But what makes it 'hop'? and what do you mean by 'hop'? Are you relating this to the proposed motion of an electron in orbit around a nucleus? A jump from an outer orbit to an orbit closer to the nucleus?
Does your particle jump right or left, then move forward for a time and then jump left or right again?