Sure, the pattern "electron disregarding position" can be conserved; but you are not fully differentiating the electron if you leave out its position. The propertes are the same except the 'property' of position.
Now: is my take on the following right?
One of the best things I read was in a book called "Light" by Ditchburn. On page 700, para.19.34 one learns that:
A particle must change its energy to be observed. Usually in the lab, this occurs through a change in its velocity.
For a photon, its through changing its mass (its frequency is its mass).
Apparantly very high energy particles near light speed change energy by changing mass (frequency) also, and are like high energy photons (little deflected by electric/ magnetic/ or gravitational fields).
At low energies, it's easy to observe the matter particle as it's mass (frequency) is near a minimum value (it's rest value).
But at low energies a photon is hard to observe because one photon is still moving at speed of light but can hardly affect the measure apparatus when it's energy is so weak.
At high energies the photon's track in a cloud-chamber is clear from where electrons have been accelerated by it. No such observation available at low energies.
At low frequencies, the photon is regarded as not being describable as having a probable position; but just as being a fluctuating field. The theory passes into static field theory as the energy and frequency of the photon drops to zero.
The limiting theory for matter is a particle theory, for radiation it is a wave theory.
An idea I came up with:
'Math waves' are not objects; skier-days require skiers and days to have any meaning for cash flow at a ski resort. A season of days and no skiers means no cash for lift passes. A season's worth of skiers looking in for a few minutes is no days and no lift passes and again no cash flow.
A 'quantum' of skier-days might be say twelve skier-days; with a fixed cash (energy) value. But it can be in many states (e.g. it can be 1 skier for 12 days, or 2 skiers for 6 days each, or 3 skiers on 4 days each, or 4 skiers on 3 days each, or 6 skiers on 2 days each, or 12 skiers on one day)(All these 'states' have the same cash value (quantum number) for the ski resort!
But the 'math waves' that describe patterns within a season of 50,000 skier-days are not objects; they just are representations of a complementary phenomenon (skier-days).
Split a quantum (12) of skier-days. Suppose you find 3 skiers and 2 days is the pattern measured in split A. You will automatically get a complementary pattern at B (say 1 skier and 6 days) consistent with A and B making up a single quantum (of twelve-skier days worth of cash-flow (energy)).
In the example a 'quantum' (twelve skier-days) is a whole; imagine that it consists of constantly changing combinations of skiers and days that always equals 12 skier-days. Imagine that measuring part A of that here instantly freezes part B over there into a complementary pattern that maintains the integrity of the quantum.
The puzzles about non-locality of nature, and action-at-a-distance can I think, be resolved by 'pattern conservation' laws, and the idea of reducing things to "pattern A compared C with pattern B" and an outside-time/space dimension of pattern-matching (match-dimension). The self-referent ABC triangles are like agreements or contracts; numerous additional layers of ABC's can be built out from them.
It has been found by experiment that at the quantum level reality appears to be non-local. A measurement of a particle here can instantly affect its sister particle over there.
Here is a clue to how it might work:
Imagine four trucks with open decks. Suppose that on each deck there are two people and four chairs.
The people keep moving past the chairs as in a game of musical chairs, taking turns at sitting on the chairs.
Suppose that the musical chairs games on the four trucks can be divided into two sets of two games. Suppose that in each set of two games, the game on one truck is a mirror image of that on its sister truck. And suppose that the two pairs of games are mirror images of each other as pairs.
By 'mirror image'; I mean if two people are such that: one is on a chair and one is not-on-a-chair, at opposite diagonals, in one (say the four chairs arranged in a square) game; the corresponding game will have a complementary arrangement of people and chairs at that moment.
(That is, collapse the chairs in the games simultaneously and you'd have four people with a chair each)
Then if the four trucks split apart into two pairs; no matter how far away from each other they go, any measurement of one pair of games will create the illusion of interference with the other (because the other will be complementary, always a mirror match).
The whole four games are your photon quantum pattern; which exists outside-time from a photon point of view (which the physicists recognise).
The act of measuring one pair of trucks' games can only give a quantum result (a specific pattern of people on or off chairs, not intermediate). So you won't find the other pair of games with that same chair-person-match-pattern; as it has a complementary pattern!
Worked out in greater detail; the deepest puzzles vanish; become child's play!
Among problems solvable; a solution now possible to the experiment where a one photon beam is split into two paths and reconverged; and a measurement on path A seems to mysteriously prevent that quality being measured at path B!
One could go into further details of complementary pattern matches in a three-way arrangement, show how a fourth dimension comes from a three-way arrangement, and show a wider type of relativity that involves:
difference/ sameness-with-creation-in-new-dimension (to create difference);
the nature of forces as: attraction to distinction;
self-reference as awareness as consciousness,
complexity as new degrees of freedom, as a creation consequence from new dimensions of self-reference/ awareness
and so forth.
In other words, the answer to physicist David Bohm's prayers.