| … | … | @@ -1848,7 +1848,7 @@ what other solns does this nasty horrible diffeq solve? |
| 1848 | 1848 | \begin_inset Quotes eld |
| 1849 | 1849 | \end_inset |
| 1850 | 1850 | |
| 1851 | | what is the topology for the space of these kinds of difffeqs that are constructed in this insane kind of way? |
| 1851 | what is the topology for the space of these kinds of diffeqs that are constructed in this insane kind of way? |
| 1852 | 1852 | \begin_inset Quotes erd |
| 1853 | 1853 | \end_inset |
| 1854 | 1854 | |
| … | … | @@ -1881,6 +1881,641 @@ measure space |
| 1881 | 1881 | and I did not write them down and now I cannot remember them. |
| 1882 | 1882 | \end_layout |
| 1883 | 1883 | |
| 1884 | \begin_layout Subsection* |
| 1885 | 15 January 2026 |
| 1886 | \end_layout |
| 1887 | |
| 1888 | \begin_layout Standard |
| 1889 | Today I will write very little because I have nothing new. |
| 1890 | I'm just reviewing things I've pondered earlier, |
| 1891 | in the fall, |
| 1892 | and to recap, |
| 1893 | it went like this. |
| 1894 | Once I realized that |
| 1895 | \begin_inset Formula $\left|\psi\right\rangle $ |
| 1896 | \end_inset |
| 1897 | |
| 1898 | is non–local; |
| 1899 | took it to heart, |
| 1900 | that is; |
| 1901 | (previously, |
| 1902 | I'd known this |
| 1903 | \begin_inset Quotes eld |
| 1904 | \end_inset |
| 1905 | |
| 1906 | subconsciously |
| 1907 | \begin_inset Quotes erd |
| 1908 | \end_inset |
| 1909 | |
| 1910 | , |
| 1911 | knowing it without the being fully formed and the object of attention.) once I realized this, |
| 1912 | it was |
| 1913 | \begin_inset Quotes eld |
| 1914 | \end_inset |
| 1915 | |
| 1916 | oh |
| 1917 | \begin_inset Quotes erd |
| 1918 | \end_inset |
| 1919 | |
| 1920 | , |
| 1921 | and |
| 1922 | \begin_inset Quotes eld |
| 1923 | \end_inset |
| 1924 | |
| 1925 | what is the mechanism of collapse? |
| 1926 | \begin_inset Quotes erd |
| 1927 | \end_inset |
| 1928 | |
| 1929 | so in my diary entry from October? |
| 1930 | September? |
| 1931 | I envision one |
| 1932 | \begin_inset Formula $\left|\psi\right\rangle $ |
| 1933 | \end_inset |
| 1934 | |
| 1935 | interacting with two tanks, |
| 1936 | loosely connected, |
| 1937 | and the mental model I had there was a thermodynamic phase space one: |
| 1938 | once the w.f. |
| 1939 | started interacting one of the tanks, |
| 1940 | it would |
| 1941 | \begin_inset Quotes eld |
| 1942 | \end_inset |
| 1943 | |
| 1944 | get lost in there |
| 1945 | \begin_inset Quotes erd |
| 1946 | \end_inset |
| 1947 | |
| 1948 | because the phase space was so big, |
| 1949 | it was unlikely it would get out. |
| 1950 | As I recall, |
| 1951 | I even wrote down a (two–particle) interaction Hamiltonian, |
| 1952 | and then hit a brick wall: |
| 1953 | any such interaction state can always be re–orthogonalized into free, |
| 1954 | non–interacting states (a two–particle state, |
| 1955 | at first) and adding three, |
| 1956 | four–particle interactions just means one can diagonalize into three, |
| 1957 | four–particle states that are free. |
| 1958 | And are NOT localized. |
| 1959 | No matter the Hamiltonian, |
| 1960 | this is a property of linear algebra: |
| 1961 | you can always diagonalize. |
| 1962 | So, |
| 1963 | from linear algebra, |
| 1964 | from non–locality, |
| 1965 | you will never get locality or w.f. |
| 1966 | collapse. |
| 1967 | And this is why, |
| 1968 | duh, |
| 1969 | theories of w.f. |
| 1970 | collapse conventionally include non–linear terms of some sort; |
| 1971 | gravitation being the obvious one. |
| 1972 | \end_layout |
| 1973 | |
| 1974 | \begin_layout Standard |
| 1975 | This morning I'm sitting here, |
| 1976 | thinking, |
| 1977 | |
| 1978 | \begin_inset Quotes eld |
| 1979 | \end_inset |
| 1980 | |
| 1981 | I need to write some more |
| 1982 | \begin_inset Quotes erd |
| 1983 | \end_inset |
| 1984 | |
| 1985 | |
| 1986 | \begin_inset Quotes erd |
| 1987 | \end_inset |
| 1988 | |
| 1989 | , |
| 1990 | because the conclusion yesterday, |
| 1991 | above, |
| 1992 | seemed so stupid, |
| 1993 | idiotic and crazy, |
| 1994 | I did not want to leave the diary for weeks with a sore thumb sticking out like that. |
| 1995 | So I started think a bit about entanglement. |
| 1996 | In the past, |
| 1997 | I thought about two–particle entanglement |
| 1998 | \begin_inset Quotes eld |
| 1999 | \end_inset |
| 2000 | |
| 2001 | interfermoetrically |
| 2002 | \begin_inset Quotes erd |
| 2003 | \end_inset |
| 2004 | |
| 2005 | , |
| 2006 | which, |
| 2007 | I hate to admit it, |
| 2008 | was a code–word for |
| 2009 | \begin_inset Quotes eld |
| 2010 | \end_inset |
| 2011 | |
| 2012 | locally |
| 2013 | \begin_inset Quotes erd |
| 2014 | \end_inset |
| 2015 | |
| 2016 | . |
| 2017 | This is the old idea (not mine, |
| 2018 | someone else's) that in many–worlds, |
| 2019 | plus this sub–conscious assumption of locality, |
| 2020 | the universes split at both measurement sites, |
| 2021 | and stay in superposition until the measurement results are brought back to one location. |
| 2022 | This is the interferometric viewpoint. |
| 2023 | I'm now realizing that it's wrong, |
| 2024 | and the reason its wrong is the usually–hidden deeply–embedded assumptions of locality. |
| 2025 | My brain is just so overwhelmingly use to thinking of spatial relationships, |
| 2026 | a |
| 2027 | \begin_inset Quotes eld |
| 2028 | \end_inset |
| 2029 | |
| 2030 | here |
| 2031 | \begin_inset Quotes erd |
| 2032 | \end_inset |
| 2033 | |
| 2034 | and a |
| 2035 | \begin_inset Quotes eld |
| 2036 | \end_inset |
| 2037 | |
| 2038 | there |
| 2039 | \begin_inset Quotes erd |
| 2040 | \end_inset |
| 2041 | |
| 2042 | , |
| 2043 | that even when admitting non–locality |
| 2044 | \begin_inset Quotes eld |
| 2045 | \end_inset |
| 2046 | |
| 2047 | into my soul |
| 2048 | \begin_inset Quotes erd |
| 2049 | \end_inset |
| 2050 | |
| 2051 | , |
| 2052 | I still habitually fall back into thinking about |
| 2053 | \begin_inset Quotes eld |
| 2054 | \end_inset |
| 2055 | |
| 2056 | what happened here, |
| 2057 | what happened there |
| 2058 | \begin_inset Quotes erd |
| 2059 | \end_inset |
| 2060 | |
| 2061 | , |
| 2062 | even as I know this is the source of confusion. |
| 2063 | Perhaps this is why it took so long for complex numbers to be discovered: |
| 2064 | if you are solving the cubic, |
| 2065 | and it has two complex roots, |
| 2066 | where are those roots located? |
| 2067 | There's a mental block if you keep trying to visualize them as being on the x–axis. |
| 2068 | They are not. |
| 2069 | They are not |
| 2070 | \begin_inset Quotes eld |
| 2071 | \end_inset |
| 2072 | |
| 2073 | anywhere |
| 2074 | \begin_inset Quotes erd |
| 2075 | \end_inset |
| 2076 | |
| 2077 | , |
| 2078 | they are non–local, |
| 2079 | in this way. |
| 2080 | They are |
| 2081 | \begin_inset Quotes eld |
| 2082 | \end_inset |
| 2083 | |
| 2084 | somewhere else |
| 2085 | \begin_inset Quotes erd |
| 2086 | \end_inset |
| 2087 | |
| 2088 | . |
| 2089 | So my wave functions are non–local, |
| 2090 | and I run into mental trouble if I keep asking |
| 2091 | \begin_inset Quotes eld |
| 2092 | \end_inset |
| 2093 | |
| 2094 | where do they intersect with the physical reality that I am accustomed to? |
| 2095 | \begin_inset Quotes erd |
| 2096 | \end_inset |
| 2097 | |
| 2098 | They do not. |
| 2099 | \end_layout |
| 2100 | |
| 2101 | \begin_layout Standard |
| 2102 | Hmm. |
| 2103 | Let me put it more strongly. |
| 2104 | The |
| 2105 | \begin_inset Quotes eld |
| 2106 | \end_inset |
| 2107 | |
| 2108 | physical reality that I am accustomed to |
| 2109 | \begin_inset Quotes erd |
| 2110 | \end_inset |
| 2111 | |
| 2112 | is entirely my memory of the past. |
| 2113 | That's all I've got. |
| 2114 | I |
| 2115 | \begin_inset Quotes eld |
| 2116 | \end_inset |
| 2117 | |
| 2118 | live in the present |
| 2119 | \begin_inset Quotes erd |
| 2120 | \end_inset |
| 2121 | |
| 2122 | , |
| 2123 | but the only information that I have, |
| 2124 | the only classical bits and bytes information, |
| 2125 | is that encoded in my memory of what happened just now, |
| 2126 | what I recall from yesterday, |
| 2127 | or the, |
| 2128 | uh, |
| 2129 | I guess the photons hitting my eyeballs, |
| 2130 | coming from my computer screen, |
| 2131 | showing me what I typed mere seconds ago. |
| 2132 | This is the physical reality that I know: |
| 2133 | the untouchable past, |
| 2134 | and the carving–into–stone that I do |
| 2135 | \begin_inset Quotes eld |
| 2136 | \end_inset |
| 2137 | |
| 2138 | in the present |
| 2139 | \begin_inset Quotes erd |
| 2140 | \end_inset |
| 2141 | |
| 2142 | . |
| 2143 | Thanks to object persistence (fermions, |
| 2144 | apparently) I can carve and mold the present in such a way that I can write, |
| 2145 | and see my writing preserved all the way into the |
| 2146 | \begin_inset Quotes eld |
| 2147 | \end_inset |
| 2148 | |
| 2149 | present |
| 2150 | \begin_inset Quotes erd |
| 2151 | \end_inset |
| 2152 | |
| 2153 | , |
| 2154 | and my neurons can write their chemical reactions into a form that I call |
| 2155 | \begin_inset Quotes eld |
| 2156 | \end_inset |
| 2157 | |
| 2158 | my memory |
| 2159 | \begin_inset Quotes erd |
| 2160 | \end_inset |
| 2161 | |
| 2162 | . |
| 2163 | This is the only physical reality I truly know, |
| 2164 | and the object persistence |
| 2165 | \begin_inset Quotes eld |
| 2166 | \end_inset |
| 2167 | |
| 2168 | right know |
| 2169 | \begin_inset Quotes erd |
| 2170 | \end_inset |
| 2171 | |
| 2172 | , |
| 2173 | and the continuity of history, |
| 2174 | fools my mind into thinking the past is the same thing as |
| 2175 | \begin_inset Quotes eld |
| 2176 | \end_inset |
| 2177 | |
| 2178 | physical reality |
| 2179 | \begin_inset Quotes erd |
| 2180 | \end_inset |
| 2181 | |
| 2182 | . |
| 2183 | Again it is not: |
| 2184 | it cannot be: |
| 2185 | there is no instrument I can devise that can |
| 2186 | \begin_inset Quotes eld |
| 2187 | \end_inset |
| 2188 | |
| 2189 | see the past |
| 2190 | \begin_inset Quotes erd |
| 2191 | \end_inset |
| 2192 | |
| 2193 | , |
| 2194 | that can |
| 2195 | \begin_inset Quotes eld |
| 2196 | \end_inset |
| 2197 | |
| 2198 | review the past |
| 2199 | \begin_inset Quotes erd |
| 2200 | \end_inset |
| 2201 | |
| 2202 | , |
| 2203 | if I missed it when it came around the first time. |
| 2204 | The point is, |
| 2205 | I guess, |
| 2206 | I am trying to make an analogy: |
| 2207 | I ask |
| 2208 | \begin_inset Quotes eld |
| 2209 | \end_inset |
| 2210 | |
| 2211 | where does the wave function intersect physical reality? |
| 2212 | \begin_inset Quotes erd |
| 2213 | \end_inset |
| 2214 | |
| 2215 | and the answer is |
| 2216 | \begin_inset Quotes eld |
| 2217 | \end_inset |
| 2218 | |
| 2219 | it mostly doesn't, |
| 2220 | you just have a flawed idea of what physical reality is, |
| 2221 | you were fooled and tricked by the persistence of objects into thinking that the past is |
| 2222 | \begin_inset Quotes eld |
| 2223 | \end_inset |
| 2224 | |
| 2225 | physical reality |
| 2226 | \begin_inset Quotes erd |
| 2227 | \end_inset |
| 2228 | |
| 2229 | when the past is not and cannot be: |
| 2230 | only the present is. |
| 2231 | |
| 2232 | \end_layout |
| 2233 | |
| 2234 | \begin_layout Standard |
| 2235 | So asking about the location of the wave function is misleading, |
| 2236 | as, |
| 2237 | in the past, |
| 2238 | there is no more wave–function. |
| 2239 | W.f.s are in the present, |
| 2240 | only. |
| 2241 | And yes, |
| 2242 | the present is many–world–ish, |
| 2243 | because that is |
| 2244 | \begin_inset Quotes eld |
| 2245 | \end_inset |
| 2246 | |
| 2247 | where the w.f. |
| 2248 | is |
| 2249 | \begin_inset Quotes erd |
| 2250 | \end_inset |
| 2251 | |
| 2252 | ; |
| 2253 | the past is single–world–ish, |
| 2254 | because there is no w.f. |
| 2255 | in the (true) past. |
| 2256 | And as the Renninger negative–measurement result demonstrates, |
| 2257 | the present not only has a |
| 2258 | \begin_inset Quotes eld |
| 2259 | \end_inset |
| 2260 | |
| 2261 | width |
| 2262 | \begin_inset Quotes erd |
| 2263 | \end_inset |
| 2264 | |
| 2265 | , |
| 2266 | but the present can be very fat. |
| 2267 | Although, |
| 2268 | as I'm writing this, |
| 2269 | as I've repeated before, |
| 2270 | I wonder if this idea of fatness is another fount of confusion. |
| 2271 | Just like asking |
| 2272 | \begin_inset Quotes eld |
| 2273 | \end_inset |
| 2274 | |
| 2275 | where do the complex roots of a cubic equation intersect the x–axis? |
| 2276 | \begin_inset Quotes erd |
| 2277 | \end_inset |
| 2278 | |
| 2279 | there is a bit of a flaw when I ask |
| 2280 | \begin_inset Quotes eld |
| 2281 | \end_inset |
| 2282 | |
| 2283 | where does time intersect with space? |
| 2284 | \begin_inset Quotes erd |
| 2285 | \end_inset |
| 2286 | |
| 2287 | as it is some Cartesian product, |
| 2288 | when (obviously) the metric signature + + + – or – – – + means that one or the other is pseudo–uh–Riemannian. |
| 2289 | Hmm. |
| 2290 | \end_layout |
| 2291 | |
| 2292 | \begin_layout Standard |
| 2293 | Well, |
| 2294 | I guess I have to clarify the difference between |
| 2295 | \begin_inset Quotes eld |
| 2296 | \end_inset |
| 2297 | |
| 2298 | Cartesian |
| 2299 | \begin_inset Quotes erd |
| 2300 | \end_inset |
| 2301 | |
| 2302 | and |
| 2303 | \begin_inset Quotes eld |
| 2304 | \end_inset |
| 2305 | |
| 2306 | metric |
| 2307 | \begin_inset Quotes erd |
| 2308 | \end_inset |
| 2309 | |
| 2310 | . |
| 2311 | As before, |
| 2312 | the notion of 3D space is intimately entangled with the |
| 2313 | \begin_inset Quotes eld |
| 2314 | \end_inset |
| 2315 | |
| 2316 | natural topology |
| 2317 | \begin_inset Quotes erd |
| 2318 | \end_inset |
| 2319 | |
| 2320 | . |
| 2321 | All discussions of manifolds presuppose, |
| 2322 | well, |
| 2323 | not just the atlas, |
| 2324 | but that |
| 2325 | \begin_inset Formula $\mathbb{R}^{n}$ |
| 2326 | \end_inset |
| 2327 | |
| 2328 | is |
| 2329 | \begin_inset Quotes eld |
| 2330 | \end_inset |
| 2331 | |
| 2332 | flat |
| 2333 | \begin_inset Quotes erd |
| 2334 | \end_inset |
| 2335 | |
| 2336 | can can be coordinatized by |
| 2337 | \begin_inset Formula $n$ |
| 2338 | \end_inset |
| 2339 | |
| 2340 | –tuples |
| 2341 | \begin_inset Formula $\left(x,y,z,\cdots\right)$ |
| 2342 | \end_inset |
| 2343 | |
| 2344 | – the so–called Cartesian coordinates, |
| 2345 | and that there's a topology that is Hausdorff, |
| 2346 | and that the space is measurable, |
| 2347 | in that we can attach some sigma–algebra of measurable sets, |
| 2348 | and that there is a set–membership predicate |
| 2349 | \begin_inset Formula $\Delta\left(x,y,z,\cdots\right)$ |
| 2350 | \end_inset |
| 2351 | |
| 2352 | that is true when |
| 2353 | \begin_inset Formula $\left(x,y,z,\cdots\right)$ |
| 2354 | \end_inset |
| 2355 | |
| 2356 | belongs to the set, |
| 2357 | and is false when it does not. |
| 2358 | (The |
| 2359 | \begin_inset Quotes eld |
| 2360 | \end_inset |
| 2361 | |
| 2362 | subobject classifier |
| 2363 | \begin_inset Quotes erd |
| 2364 | \end_inset |
| 2365 | |
| 2366 | for small sets.) The physical notion of |
| 2367 | \begin_inset Quotes eld |
| 2368 | \end_inset |
| 2369 | |
| 2370 | where is it? |
| 2371 | \begin_inset Quotes erd |
| 2372 | \end_inset |
| 2373 | |
| 2374 | is a linguistic apparatus attached to my memory of the past, |
| 2375 | that can be axiomatized a la des Cartes into Cartesian coords |
| 2376 | \begin_inset Formula $\left(x,y,z,\cdots\right)$ |
| 2377 | \end_inset |
| 2378 | |
| 2379 | . |
| 2380 | But that axiomatization is appropriate only in the past. |
| 2381 | That there is some sort of trouble elsewhere is hinted by the pseudo–Riemannian metric signature, |
| 2382 | where, |
| 2383 | of the four spacetime coordinates, |
| 2384 | some have to be |
| 2385 | \begin_inset Quotes eld |
| 2386 | \end_inset |
| 2387 | |
| 2388 | not real |
| 2389 | \begin_inset Quotes erd |
| 2390 | \end_inset |
| 2391 | |
| 2392 | . |
| 2393 | There are values for |
| 2394 | \begin_inset Formula $\left(x,y,z,t\right)$ |
| 2395 | \end_inset |
| 2396 | |
| 2397 | for which the |
| 2398 | \begin_inset Quotes eld |
| 2399 | \end_inset |
| 2400 | |
| 2401 | distance |
| 2402 | \begin_inset Quotes erd |
| 2403 | \end_inset |
| 2404 | |
| 2405 | |
| 2406 | \begin_inset Formula $\sqrt{x^{2}+y^{2}+z^{2}-t^{2}}$ |
| 2407 | \end_inset |
| 2408 | |
| 2409 | cannot be |
| 2410 | \begin_inset Quotes eld |
| 2411 | \end_inset |
| 2412 | |
| 2413 | real |
| 2414 | \begin_inset Quotes erd |
| 2415 | \end_inset |
| 2416 | |
| 2417 | , |
| 2418 | and so of course, |
| 2419 | I cannot point my finger in the direction in which |
| 2420 | \begin_inset Quotes eld |
| 2421 | \end_inset |
| 2422 | |
| 2423 | time flows |
| 2424 | \begin_inset Quotes erd |
| 2425 | \end_inset |
| 2426 | |
| 2427 | , |
| 2428 | because that is not a |
| 2429 | \begin_inset Quotes eld |
| 2430 | \end_inset |
| 2431 | |
| 2432 | direction |
| 2433 | \begin_inset Quotes erd |
| 2434 | \end_inset |
| 2435 | |
| 2436 | accessible from 3D space. |
| 2437 | And to go in circles, |
| 2438 | and to repeat myself over and over, |
| 2439 | the Cartesian axiomatization only works for |
| 2440 | \begin_inset Quotes eld |
| 2441 | \end_inset |
| 2442 | |
| 2443 | things in the past |
| 2444 | \begin_inset Quotes erd |
| 2445 | \end_inset |
| 2446 | |
| 2447 | . |
| 2448 | I almost wrote |
| 2449 | \begin_inset Quotes eld |
| 2450 | \end_inset |
| 2451 | |
| 2452 | past light–cone |
| 2453 | \begin_inset Quotes erd |
| 2454 | \end_inset |
| 2455 | |
| 2456 | , |
| 2457 | which would have been technically true, |
| 2458 | but would have obscured that the past exists only in a platonic form, |
| 2459 | remembered only by memory (object persistence) in the (many–worlds) present. |
| 2460 | Calling it the |
| 2461 | \begin_inset Quotes eld |
| 2462 | \end_inset |
| 2463 | |
| 2464 | past light–cone |
| 2465 | \begin_inset Quotes erd |
| 2466 | \end_inset |
| 2467 | |
| 2468 | tricks my brain into giving it some kind of |
| 2469 | \begin_inset Quotes eld |
| 2470 | \end_inset |
| 2471 | |
| 2472 | existential reality |
| 2473 | \begin_inset Quotes erd |
| 2474 | \end_inset |
| 2475 | |
| 2476 | when that |
| 2477 | \begin_inset Quotes eld |
| 2478 | \end_inset |
| 2479 | |
| 2480 | existentialness |
| 2481 | \begin_inset Quotes erd |
| 2482 | \end_inset |
| 2483 | |
| 2484 | exists only in the platonic realm, |
| 2485 | in the noosphere, |
| 2486 | in the past. |
| 2487 | Hmm. |
| 2488 | I'm going in circles, |
| 2489 | stating the obvious. |
| 2490 | Am I getting any closer? |
| 2491 | Well, |
| 2492 | the first steps of converting perception into understanding is to take a damn good look at your object of attention, |
| 2493 | without being judgmental. |
| 2494 | So I am taking a hard look at |
| 2495 | \begin_inset Quotes eld |
| 2496 | \end_inset |
| 2497 | |
| 2498 | reality |
| 2499 | \begin_inset Quotes erd |
| 2500 | \end_inset |
| 2501 | |
| 2502 | . |
| 2503 | Without yet offering any |
| 2504 | \begin_inset Quotes eld |
| 2505 | \end_inset |
| 2506 | |
| 2507 | explanation |
| 2508 | \begin_inset Quotes erd |
| 2509 | \end_inset |
| 2510 | |
| 2511 | of what it is, |
| 2512 | because, |
| 2513 | well, |
| 2514 | so far, |
| 2515 | I can't offer one. |
| 2516 | |
| 2517 | \end_layout |
| 2518 | |
| 1884 | 2519 | \begin_layout Section* |
| 1885 | 2520 | The End |
| 1886 | 2521 | \end_layout |