Hi,
Repeating the last paragraph from above:
He then says let us examine the paths of those entities of interest, each by itself, in the absence of the others. "The differential path length along the trajectory is exactly what is referred to as Einstein's invariant interval along the path of the thing being represented by that path. This fact is commonly used in high energy physics to determine the expected apparent path lengths (in x,y,z space) of particles with short half lives."
COMMENT:
What does "the differential path length along the trajectory" mean?
Not just "path length" but "differential path length"...
If you differentiate something you separte it into its components. So I guess he means "the component path length along the trajectory".
For example: over the whole time-slice of a particular thing juggling x,y,z over its t sample: the component path length could be the x-component of that length, the y component, the z component; the (x + y) net component, and so on (x+z) or (y+z) or (x+y+z) .
What about t component? Well the t-component would be the change in t-value.
A (t+x) component would be change in (t value + net change in x-value) so you've got the way x (influenced by y and z), changed t value PLUS the way t-value (influenced by y and z) influenced x-value: some cancelling out would occur.
You get effectively a meeting of t and x in the "space" y,z influence.
You could have:
a meeting of t and x in the space of y,z influence;
a meeting of t and y in the space of x,z influence;
a meeting of t and z in the space of x,y influence;
a meeting of t and x and y, in the space of z influence;
a meeting of t and x and z, in the space of y influence;
a meeting of t and y and z, in the space of x influence;
a meeting of x and y, in the space of t and z influence;
a meeting of x and z, in the space of t and y influence;
a meeting of y and z, in the space of t and x influence;
a meeting of x and y and z, in the space of t influence (which would be either zero if "t" just defines a period of x,y,z juggling; or "p" if a parameter "p" is constant over this sample of particle trajectory in x,y,z,t space
x in the space of y,z,t influence
y in the space of x,z,t influence
z in the space of x,y,t influence.
In the above three generations of "particles" (if "particle" means "unit meets group" as in "x meets y" as a unit meeting the group that potentially influenced them) can be seen:
1: "cancel" (when item meets item, in a background that influenced both of them; there is a possibility that the respective influences cancelled out (had relatively for this particular comparison event of the items, opposite "charges" or bias say). (Example: the "x meet y" against a background of z,t influence: some of the z,t influence on x might cancel out effect of some of the z,t influence on t such that these two z,t impacts are neutralised giving a neutral zone in the final z,t perspective of "x meet y".
In that circumstance you could call each z,t impact a "downquark" in the neutral result, the "x meet y" cancelling of these downquarks could be called an "upquark" as it reveals an aspect of "x meet y" that neutralises the downquarks in the neutral zone so keeps alive something about "x meets y"; the "neutral zone" built of the two downquarks and the upquark could be called a "neutron" in the final z,t perspective of "x meet y".
I initially wrote "up-quark" for "down-quark" and "down-quark" for up-quark"; but to keep with actual definitions in physics I changed it. Seems like a change in perspective can convert these roles? I was thinking of the neutral result and how to get it. The two initial contributors I thus called "up-quarks" as they were upwardly defining things; but from the perspective of seeing the final neutron as an object IN "x meets y" they would seem to have been trying to split up the neutrality and "bring "x meets y" down to earth" that is to a less complex state?
2. "not cancel" (when background meets internally, say z,t influence space looked at as two halves in meeting of "x meet y"; so the z,t influences (in our sample of z,t space over our path-sample) on "x meets y" do not cancel; allowing some differentiating betwen x and y to occur.
Various sub-atomic particles can be mapped I would suggest.
3. "uncertain" (when item meets item, in a background that influences both of them; AND background meets internally; the cancelling effect and not-cancelling effect may overlap eactly giving an "uncertain" zone.
The above patterns in generations 1, 2, 3 can give rise when looked at in detail to much modelling of sub-atomic particle physics and forces involved, I suggest.
more comments next post...
-dolphin
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