One single universal wavefunction, and every possible outcomes happens in some alternate universe. Does feel a bit sad and superfluous, but also does give some sense to perceived "wave function collapse".
Harvard's e-learning thing. Weak. Related: The Purpose of Harvard is Not to Educate People by Sean Carroll (2008).
www.zdnet.com/article/googles-quantum-focused-sandbox-division-is-being-spun-off/ Google's quantum-focused Sandbox division is being spun off (2022)
They seem to do some cool stuff.
They have also declined every one of Ciro Santilli's applications for software engineer jobs before any interview. Ciro always wondered what does it take to get an interview with them. Lilely a PhD? Oh well.
In the early days at least lots of gamedev experience was enough though: www.linkedin.com/in/charles-beattie-0695373/.
See also: Ciro Santilli's minor projects.
A random field you add to make something transform locally the way you want. See e.g.: Video "Deriving the qED Lagrangian by Dietterich Labs (2018)".
Does the exact position of vertices matter in Feynman diagrams? by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16The algorithm is completely analogous to Diffie-Hellman key exchange in that you efficiently raise a number to a power times and send the result over while keeping as private key.
The only difference is that a different group is used: instead of using the cyclic group, we use the elliptic curve group of an elliptic curve over a finite field.
Elliptic curves by Computerphile (2018)
Source. youtu.be/NF1pwjL9-DE?t=143 shows the continuous group well, but then fails to explain the discrete part.Variant of Diffie-Hellman key exchange based on elliptic curve cryptography.
Running:gives:
hd hello_world.o00000000 7f 45 4c 46 02 01 01 00 00 00 00 00 00 00 00 00 |.ELF............|
00000010 01 00 3e 00 01 00 00 00 00 00 00 00 00 00 00 00 |..>.............|
00000020 00 00 00 00 00 00 00 00 40 00 00 00 00 00 00 00 |........@.......|
00000030 00 00 00 00 40 00 00 00 00 00 40 00 07 00 03 00 |....@.....@.....|
00000040 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
*
00000080 01 00 00 00 01 00 00 00 03 00 00 00 00 00 00 00 |................|
00000090 00 00 00 00 00 00 00 00 00 02 00 00 00 00 00 00 |................|
000000a0 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000000b0 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000000c0 07 00 00 00 01 00 00 00 06 00 00 00 00 00 00 00 |................|
000000d0 00 00 00 00 00 00 00 00 10 02 00 00 00 00 00 00 |................|
000000e0 27 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |'...............|
000000f0 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000100 0d 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 |................|
00000110 00 00 00 00 00 00 00 00 40 02 00 00 00 00 00 00 |........@.......|
00000120 32 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |2...............|
00000130 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000140 17 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 |................|
00000150 00 00 00 00 00 00 00 00 80 02 00 00 00 00 00 00 |................|
00000160 a8 00 00 00 00 00 00 00 05 00 00 00 06 00 00 00 |................|
00000170 04 00 00 00 00 00 00 00 18 00 00 00 00 00 00 00 |................|
00000180 1f 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 |................|
00000190 00 00 00 00 00 00 00 00 30 03 00 00 00 00 00 00 |........0.......|
000001a0 34 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |4...............|
000001b0 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000001c0 27 00 00 00 04 00 00 00 00 00 00 00 00 00 00 00 |'...............|
000001d0 00 00 00 00 00 00 00 00 70 03 00 00 00 00 00 00 |........p.......|
000001e0 18 00 00 00 00 00 00 00 04 00 00 00 02 00 00 00 |................|
000001f0 04 00 00 00 00 00 00 00 18 00 00 00 00 00 00 00 |................|
00000200 48 65 6c 6c 6f 20 77 6f 72 6c 64 21 0a 00 00 00 |Hello world!....|
00000210 b8 01 00 00 00 bf 01 00 00 00 48 be 00 00 00 00 |..........H.....|
00000220 00 00 00 00 ba 0d 00 00 00 0f 05 b8 3c 00 00 00 |............<...|
00000230 bf 00 00 00 00 0f 05 00 00 00 00 00 00 00 00 00 |................|
00000240 00 2e 64 61 74 61 00 2e 74 65 78 74 00 2e 73 68 |..data..text..sh|
00000250 73 74 72 74 61 62 00 2e 73 79 6d 74 61 62 00 2e |strtab..symtab..|
00000260 73 74 72 74 61 62 00 2e 72 65 6c 61 2e 74 65 78 |strtab..rela.tex|
00000270 74 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |t...............|
00000280 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000290 00 00 00 00 00 00 00 00 01 00 00 00 04 00 f1 ff |................|
000002a0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000002b0 00 00 00 00 03 00 01 00 00 00 00 00 00 00 00 00 |................|
000002c0 00 00 00 00 00 00 00 00 00 00 00 00 03 00 02 00 |................|
000002d0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000002e0 11 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 |................|
000002f0 00 00 00 00 00 00 00 00 1d 00 00 00 00 00 f1 ff |................|
00000300 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000310 2d 00 00 00 10 00 02 00 00 00 00 00 00 00 00 00 |-...............|
00000320 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000330 00 68 65 6c 6c 6f 5f 77 6f 72 6c 64 2e 61 73 6d |.hello_world.asm|
00000340 00 68 65 6c 6c 6f 5f 77 6f 72 6c 64 00 68 65 6c |.hello_world.hel|
00000350 6c 6f 5f 77 6f 72 6c 64 5f 6c 65 6e 00 5f 73 74 |lo_world_len._st|
00000360 61 72 74 00 00 00 00 00 00 00 00 00 00 00 00 00 |art.............|
00000370 0c 00 00 00 00 00 00 00 01 00 00 00 02 00 00 00 |................|
00000380 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000390Array of
Elf64_Shdr structs.Each entry contains metadata about a given section.
e_shoff of the ELF header gives the starting position, 0x40 here.So the table takes bytes from 0x40 to
0x40 + 7 + 0x40 - 1 = 0x1FF.Some section names are reserved for certain section types: www.sco.com/developers/gabi/2003-12-17/ch4.sheader.html#special_sections e.g.
.text requires a SHT_PROGBITS type and SHF_ALLOC + SHF_EXECINSTRRunning:outputs:
readelf -S hello_world.oThere are 7 section headers, starting at offset 0x40:
Section Headers:
[Nr] Name Type Address Offset
Size EntSize Flags Link Info Align
[ 0] NULL 0000000000000000 00000000
0000000000000000 0000000000000000 0 0 0
[ 1] .data PROGBITS 0000000000000000 00000200
000000000000000d 0000000000000000 WA 0 0 4
[ 2] .text PROGBITS 0000000000000000 00000210
0000000000000027 0000000000000000 AX 0 0 16
[ 3] .shstrtab STRTAB 0000000000000000 00000240
0000000000000032 0000000000000000 0 0 1
[ 4] .symtab SYMTAB 0000000000000000 00000280
00000000000000a8 0000000000000018 5 6 4
[ 5] .strtab STRTAB 0000000000000000 00000330
0000000000000034 0000000000000000 0 0 1
[ 6] .rela.text RELA 0000000000000000 00000370
0000000000000018 0000000000000018 4 2 4
Key to Flags:
W (write), A (alloc), X (execute), M (merge), S (strings), l (large)
I (info), L (link order), G (group), T (TLS), E (exclude), x (unknown)
O (extra OS processing required) o (OS specific), p (processor specific)The
struct represented by each entry is:typedef struct {
Elf64_Word sh_name;
Elf64_Word sh_type;
Elf64_Xword sh_flags;
Elf64_Addr sh_addr;
Elf64_Off sh_offset;
Elf64_Xword sh_size;
Elf64_Word sh_link;
Elf64_Word sh_info;
Elf64_Xword sh_addralign;
Elf64_Xword sh_entsize;
} Elf64_Shdr;Experiments to measure it:
The 2019 redefinition of the SI base units defines it precisely and uses it as a measure of charge: en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units#Ampere
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