Can this be proven incorrect: Particles and waves are separate entities. Waves are the energy mechanism that transports the particle but not part of the particle itself. If a photon gets created the electron that created it drops to a lower energy level, providing the energy wave around the photon to travel in a certain direction. Does this not explain why a particle acts as a particle and as a wave - as it rides the wave energy to a destination. A surfer rides a wave but behaves like a "particle" and as (part of) a wave - moving up an down and along the wave he is riding. But the surfer is not a body/particle and a wave although he acts like a particle and a wave. Therefor with the double slit experiment the wave travels through both slits, but the particle only through one and is affected by the interference pattern on the other side of the slits. The current "crude" particle detectors destroy the wave energy and therefore there is no interference pattern - this should mean the particle should reach the screen with less energy (if the waves are removed) which should be measurable on the electron it interacts with on the screen, if it has sufficient energy/momentum left to reach the screen.
closed as off-topic by Aaron Stevens, Jon Custer, John Rennie, Kyle Kanos, WillO Nov 1 '18 at 16:27
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You have a basic misunderstanding of the particle/wave duality. The wave nature of elementary particles and quantum mechanical complexes is not in their energy distribution or mass. It is in the quantum mechanical probability of detection at (x,y,z,t).
This is clearly seen in the experiment "electron of given energy scattering through two slits of given distance apart and given width" , single electron at a time:
Electron buildup over time
The particle nature is displayed in the dots on the screen, the footprint similar to a classical particle. In the top part where very few electrons accumulate, the hits look random. It is in the lowest one that the probability distribution shows wave interference patterns. Probability distributions are the predictions of the quantum mechanical wave equations that elementary particles have to obey.
So your model contradicts the data.
The answer to the title "Are particles and waves separate entities?" is that there exist quantum mechanical entities which have attributes of classical particles when interacting, as momentum and angular momentum conservation, and localization in space time, but are described by a probability distribution for their manifestation, which obeys a quantum mechanical wave equation. It is this probability that "waves", not the energy or mass of the particle, and in this mathematical sense they are separate, as probability requires many particle interactions, not one.
You absolutely need a something to carry a wave: so water molecules carry the water wave, steel molecules carry the sound wave in a guitar string, air molecules carry sound, a pendulum goes back and forth, etc etc. So a wave is nothing without particles. But for light waves which can travel in a vacuum physicists must theorize an electromagnetic field, EM field. We don't quite understand if its made of anything but we know a lot about its properties. All photons are quantized, that means they have certain energies as they were created by electrons jumping defined energy level in atoms, they show properties of wavelength (color), they refract and diffract, they have a velocity, they travel in integer multiplies of their wavelength (begin and end).
In the double slit experiment we do not see 2 separate items (wave and particle) but you can talk about it with either expression. A good interpretation is that the photon is looking for an efficient path thru the slits to the screen, the photon will interact with the EM field of the slit molecules and finally collapse in an interaction with the EM field (electrons) of the screen. The pattern we see is termed "interference" (from a hundred years ago) but is really a probability pattern based on the photon wave function (its preference to travel n multiples of wavelength) and QM (quantum mechanical meaning probabilistic) interaction with the slits and screen. (The dark bands are where no photons land.)
There is no difference. Imagine a mouse moving under the carpet. The mouse looks like a particle but its bump as it moves under the carpet looks like a wave.
The particle wave distinction is to make certain equations easier and has no fundamental relevance. Anything can be considered an oscillation or an object over some timescale.