I am constantly seeing references to phrases like: Sometimes, the thingy-wingy exhibits “wave-like behaviour” and sometimes it exhibits “particle-like behaviour.” Well, it doesn’t make any sense to say what a thing is like if we don’t have good definitions about what each of these things are in the first place.

I’m not sitting here asking idle questions, the answers to which can be found in any undergrad physics text. In fact, the answer to this question lies at the very center of my philosophical system which I am trying to expound on the philosophy forum.

Is this like one of those things where you already know the answer, but you’re going to get all socratic and make us come up with it? If so, I think it might be nicer if you just went ahead and told us what particles and waves are. Or, we could start here…

This is actually a big problem in science man. Particles and waves. Are they seperate? Are they the same? are either real, or are they just the terms by which we try and understand things? How can they both exist when any definition of one, taken far enough seems to cancel out the possibility of the other. It’s good stuff. You could read about it for years.

First of all you need to specify if you mean classical of quantum particles/waves.

classically a (ponit)particle is a thing with a postion, time, mass, energy and momentum.

a classical wave has a frequency, wavelength, energy and momentum but its spread out over space and time(as follows from it haveing a wavelength and a frequency).

now quantum particles have both the properties of waves and particles so to call them either is misleading. Interestingly though depending on how you measure them they may seem to be more like a particle or more like a wave. With these quanta the energy is aways proportional to the frequency and the momentum inversly proprtional to the wavelength. Hence if we know exactly the momentum of the particle it must have a definte wavelength and hence we can’t say ‘where it is’. On the other hand if we know where it is exactly we can’t say exactly what its wavelength is and hence we cannot define it momentum.

A particle and wave are simply different speeds. Like skin changing speeds when it ‘rots’, or becomes electromagnetic waves. A change in speed means a change in geometry, etc. Understand that speed means velocity along with dissipation ‘speed’.

Here is the only difference: continuity vs. discontinuity.

Waves are simply “well-behaved” mathematical functions that are everywhere differentiable. Picture a sine wave. There are no corners, discontinuities, or vertical tangents. This is all it means to be a “wave”.

Particles, on the other hand, are simply an arbitrarily degenerative case of a well-behaved wave function. There might be discontinuities, corners, vertical tangents and other physically meaningless notions.

The ultimate problem with the “particle picture” of physics is that it violates the law of identity. In other words, whenever there is a vertical tangent on a time vs energy graph, for instance, it just means that this is a point in time in which the state of the system is undefined. Or, the system exists in an infinity of different states at the given moment. It truly has no identity.

It is not a coincidence that “Quantum Mechanics,” which is based upon the idea of discontinuity, came upon these exact same difficulties within their formulations.

All particles act as if they were a wave with a wavelength inversely proportional to their mass and velocity. As objects increase in mass, their quantum wavelengths shrink to ranges contained within the boundaries of their physical size, masking any wave-like properties on the macro-scale. If the mass of a “particle” shrinks to a degree that the quantum wavelength exceeds those boundaries of form, then these intrinsic wavelike properties become dominant - producing novel behaviour.

Get small enough and you cannot measure both mass and velocity with any meaningful accuracy. But probability math gets around this, kinda. Identity holds, we just can’t meaningfully examine it.

Tab, you sound well versed in quantum theory. This kind of insane logic is exactly the kind of thing that I’m trying to destroy with my big TOE. I’m not saying that you are insane, I’m saying that everything you just told me is the result of a series of “expedient” formulations that attempted to combine thermodynamics with electromagentism in a rather ad hoc way. I’ve just gotten finished with Thomas Kuhn’s book about the history of quantum theory (Black Body Theory and the Quantum Discontinuity), and the results were highly revealing, to say the least. Your attempts to correlate: 1) Newtonian mechanics of point-masses that have definite positions and linear momentums --with-- 2) standard wave mechanics wherein energies are related to resonance frequencies of various integral proportions – is something that just doesn’t make any real “sense.” But this was precisely Bohr’s “correspondence principle,” and it was no coincidence that this was the very same person who suggested that we all “give up hope” in terms of trying to make logical sense about what all of this was supposed to signify.