20180215

What Black Holes Are Made Of?


https://www.patreon.com/posts/black-holes-must-16994748

Wikipedia says Planck particle "defined as a tiny black hole whose Compton wavelength is equal to its Schwarzschild radius".

Can we really think of Planck particles as tiny Black Holes themselves, as Wikipedia says? I think the answer is yes. Then, could we also really and truly call them Black Hole particles? I think the answer is yes. Would it be logically consistent to say, Black Holes are made of Black Hole particles? I think the answer is yes.

Would that be consistent with General Relativity? I think the answer is yes. Because, would it really make any difference from GR point of view, if we divided a single Black Hole into N smaller Black Holes? Would the total gravitational field around of that Black Hole, would really change then? I think the answer is no. (Actually, the total gravitational field around of that Black Hole would be locally different from the total gravitational field around of a single Black Hole, but it would become more and more similar/indistinguishable, as N increases toward infinity. And, if Black Holes are really made of Planck particles, then N would be an astronomically large number for any real Black Hole, and so the gravitational field around any real Black Hole (made of Planck particles) would be practically indistinguishable from the gravitational field around of a single Black Hole.)

Would that be also consistent with Quantum Mechanics? I think the answer is yes. Because, if we are assuming Black Holes are made of Black Hole (Planck) particles, then we are assuming Planck particle is real and so it is a (new) member of Standard Model. And if we are assuming that, then would it be consistent with Quantum Mechanics, if Black Holes are made of Black Hole (Planck) particles? I think the answer is yes.

And, if any theory of Quantum-Gravity (now/future) is really correct, would it not say that, all objects in the Universe (including Black Holes) must be made of particles? If so then, should not we consider, which theoretical elementary particle(s) we know about, could be really fully consistent with, what we know about Black Holes and GR and QM, altogether?

I think only a particle that is by itself a (tiny) Black Hole would be consistent with General Relativity, for BHs could be made of. Is there any other theoretically possible particle that is a tiny Black Hole itself? I think the answer is no. So if any Quantum-Gravity theory is correct, and so BHs are made of particles, then only valid possible option would be Planck particles.

So, I think the idea that "Black Holes are made of Planck (Black Hole) particles" is actually consistent with both Quantum Mechanics and General Relativity. Can we say the same for the idea that "the center of any Black Hole is a singularity"? It is obviously consistent with General Relativity, but, is it really consistent with Quantum Mechanics, also? I think the answer is no. Because, Quantum Mechanics (Standard Model), does not, also cannot, have any elementary/composite particle that can represent a singularity!

So, it seems to me that, it is physically/realistically more plausible, Black Holes are made of Planck particles, compared to, Black Holes contain a singularity in their centers, which has infinite density and zero size and can have/hold any amount of mass/energy/information.

20180211

Proving Quantum Supremacy

What would be the simplest way to compare the power/capability of classical and quantum computers?

Assume a basic N-bit Classical RISC processor (each processor register is N bits). How its insruction set would need to change for it to become an N-bit Quantum RISC processor?

Actually most of the instructions would not need any change. For example, arithmetic and logic instructions would still be the same, but they would process qubit states (0,1,U) instead of bit states (0,1).

Maybe just load/store instruction(s) need to be modified (from a programmer point of view):
Assume that, if a LOAD instruction for a basic N-bit Classical RISC processor is:
LOAD Ri, 'a literal string of N 0/1'
Then the LOAD instruction for N-bit Quantum RISC processor would be:
LOAD Ri, 'a literal string of N 0/1/U' (U for Unknown/Undetermined states)

Quantum algorithm examples for such a N-bit Quantum RISC processor:

Quantum Integer Factorization Algorithm:
Problem: Assume A*B=C; A and B are known to be prime numbers; the value of C is given. What are the values of A and B?
LOAD R0, 'U'*N     # 'U'*N: a literal string of N 'U's
LOAD R1, 'U'*N     # 'U'*N: a literal string of N 'U's
MULT R0, R1, R2    # R0*R1 -> R2
LOAD R2, C         # => A -> R0 and B -> R1 after this instruction! (C is N-digit binary (as literal string) value.)
Imagine that, when R2 is forced to have the value of C in the end, that causes states of R0 and R1 change from unknown to real values of A and B, thus solving the problem.

Quantum First Degree Polynomial Equation Solving Algorithm:
Problem: Assume A*X+B=0. What is X if A and B are given? (Analytical solution: X=-B/A)
LOAD R0, 'U'*N     # 'U'*N: a literal string of N 'U's
LOAD R1, A         # A is N-digit binary (as literal string) value
LOAD R2, B         # B is N-digit binary (as literal string) value
MULT R0, R1, R3    # R0*R1 -> R3
ADDN R2, R3, R3    # R2+R3 -> R3
LOAD R3, '0'*N     # => X -> R0 after this instruction (which is the solution)!

Quantum Second Degree Polynomial Equation Solving Algorithm:
Problem: Assume A*X*X+B*X+C=0. What is X if A and B and C are given? (Analytical solution: Quadratic formula!)
LOAD R0, 'U'*N     # 'U'*N: a literal string of N 'U's
LOAD R1, A         # A is N-digit binary (as literal string) value
LOAD R2, B         # B is N-digit binary (as literal string) value
LOAD R3, C         # C is N-digit binary (as literal string) value
MULT R0, R0, R4    # R0*R0 -> R4
MULT R1, R4, R4    # R1*R4 -> R4
MULT R0, R2, R5    # R0*R2 -> R5
ADDN R4, R5, R4    # R4+R5 -> R4
ADDN R4, R3, R4    # R4+R3 -> R4
LOAD R4, '0'*N     # => X0 or X1 (with %50 probability for each) -> R0 after this instruction (which is the solution)!

Quantum Second Degree Polynomial Equation Solving Algorithm 2:
Problem: Assume A*X*X+B*X+C=0. X0+X1=-B/A & X0*X1=C/A. What is X if A and B and C are given? (Analytical solution: Quadratic formula!)
LOAD R0, 'U'*N     # 'U'*N: a literal string of N 'U's
LOAD R1, 'U'*N     # 'U'*N: a literal string of N 'U's
ADDN R0, R1, R2    # R0+R1 -> R2
MULT R0, R1, R3    # R0*R1 -> R3
LOAD R2, -B/A      # as N-digit binary (as literal string) value
LOAD R3, C/A       # as N-digit binary (as literal string) value
=> X0 -> R0 and X1 -> R1 after these (which is the solution)!

Realize that such a N-bit Quantum RISC processor could also still work as a N-bit Classical RISC processor (by simply never setting any register qubits to unknown states)! Meaning, a quantum computer has at least the same power as a classical computer for any/all worst problem cases! Meaning, finding even a single problem that a quantum computer can solve faster, would mean a proof of quantum supremacy! And realize that the Quantum Integer Factorization Algorithm above uses only 4 instructions! Could there be any chance that the N-bit Classical RISC processor (which has the same instruction set as the N-bit Quantum RISC processor), could solve the same problem using an equal or less number of instructions? The answer is obviously no, which means we have a proof of quantum supremacy!

What are the advantages of quantum computers against classical computers, in general?
Realize that the Quantum Integer Factorization Algorithm above evaluates (in the end) all possible values of A and B instantly to find the (unique) solution.
(Imagine that whenever a problem has multiple possible solutions then a quantum computer randomly picks one each time.)