
Feynman: Simulating Physics with Computers (1981) [pdf] - merrier
https://www.cs.berkeley.edu/~christos/classics/Feynman.pdf
======
michael_nielsen
For those who don't realize, this is (arguably) the first extended discussion
of quantum computers.

The other founding paper of the field is David Deutsch's superb "Quantum
theory, the Church-Turing principle and the universal quantum computer":
[http://folk.uio.no/ovrum/articles/deutsch85.pdf](http://folk.uio.no/ovrum/articles/deutsch85.pdf)

Both papers are excellent reading, and surprisingly accessible.

~~~
sdouglas
By coincidence I just finished reading John Preskill's introductory chapter on
Quantum Computing, which mentioned Feynman & Deutsch, and is also surprisingly
accessible
[http://www.theory.caltech.edu/people/preskill/ph229/notes/ch...](http://www.theory.caltech.edu/people/preskill/ph229/notes/chap1.pdf)

------
tumba
If you enjoyed this, may I also recommend Feynman's Lectures on Computation.
[1] It consists of transactions of a lecture series that begins with computer
architecture and theory of computation and considers interesting subjects like
the physical limits to computational capability--all through the unique lens
of Feynmans' mind.

Feynman worked on this subject working on the Connection Machine supecomputer.
[2][3]

[1] [http://www.amazon.com/Feynman-Lectures-Computation-
Richard-P...](http://www.amazon.com/Feynman-Lectures-Computation-
Richard-P/dp/0738202967)

[2]
[https://en.wikipedia.org/wiki/Connection_Machine](https://en.wikipedia.org/wiki/Connection_Machine)

[3] [http://longnow.org/essays/richard-feynman-connection-
machine...](http://longnow.org/essays/richard-feynman-connection-machine/)

------
alex_hirner
Simulating and thus predicting performance of new technologies with computers
will be the ultimate afterburner towards singularity. Be they quantum or not.
Recent progress has been shown in:

    
    
      - Protein folding [1]
      - Neuroscience [2]
      - Battery technology [3]
    

All of these project have in common that they do (or potentially will) scale
to contributors around the globe in near-realtime. It will simply save us from
expensive real-world experiments. The frontier of computational crowd-science
heralds truly exciting times.

PS: Berkeley has been a major force in that and from where many similar
projects originated (c.f. BOINC project [4]).

[1] [https://fold.it](https://fold.it)

[2] [http://www.openworm.org](http://www.openworm.org)

[3] [http://newscenter.lbl.gov/2015/04/15/electrolyte-genome-
coul...](http://newscenter.lbl.gov/2015/04/15/electrolyte-genome-could-be-
battery-game-changer/)

[4]
[https://en.wikipedia.org/wiki/List_of_distributed_computing_...](https://en.wikipedia.org/wiki/List_of_distributed_computing_projects)

------
javajosh
It would seem to be useful to start with the question of representing the
position of a particle with other particles. For any situation, you will need
some dynamic range of measurement to describe the properties of a particle.
Classical position might want 10 bits, interpreted as meters. With 6 numbers
(position and momentum in 3 directions) that's 60 bits per particle. Even at 1
particular per bit, that's still a ratio of 60:1. And 10 bits is certainly not
enough for some phenomena! The bottom line is that if you converted the
universe to computronium, the _absolute best_ you could do is simulate a
universe 1/60th the complexity. In real life we do many orders of magnitude
worse, memory cells require millions of atoms. This also doesn't deal at all
with the computation required to advance the state of the system. Perhaps by
focusing on the experience of life you can make the ratio make sense again.
E.g. don't simulate particles, simulate minds (for which a _particle_ is only
an abstraction anyway), and you recover that ratio, and more.

------
kordless
> You put a counter out there and you find "clunk," and nothing happens for a
> while, "clunk," and nothing happens for a while. It's riot discretized at
> all, you never can measure such a tiny field, you don't find a tiny field,
> you don't have to imitate such a tiny field, because the world that you're
> trying to imitate, the physical world, is not the classical world, and it
> behaves differently. So the particular example of discretizing the electric
> field, is a problem which I would not see, as a physicist, as fundamentally
> difficult, because it will just mean that your field has gotten so small
> that I had better be using quantum mechanics anyway, and so you've got the
> wrong equations, and so you did the wrong problem!

Things that far away are tiny, in a way. :)

------
amelius
Any good books with a more modern take on this? I.e., discussing discrete
differential forms, multigrid, etcetera?

~~~
sillysaurus3
Feynman wrote one: "Lectures on Computation." It's excellent.

[https://www.scribd.com/doc/52657907/Feynman-Lectures-on-
Comp...](https://www.scribd.com/doc/52657907/Feynman-Lectures-on-Computation)

~~~
amelius
Interesting link, thanks. But I don't think it totally covers the machinery
that people use nowadays for numerically solving complicated physics problems.
E.g., the topics that I mentioned, multigrid and discrete differential forms,
seem to be missing here.

~~~
sillysaurus3
You might like "Fundamentals of Scientific Computing," "Mathematical
Experiments on the Computer," and "Discrete Mathematics for Computing." The
first one in particular may have what you're looking for.

------
brianberns
> Quantum mechanics can't seem to be imitable by a local classical computer.

So is this a fatal flaw in Wolfram's "new kind of science" based on cellular
automata?

~~~
nicholast
I'm not sure if this is meant as an update or merely my misinterpretation of a
brief passage, but while NKS book's chapter on principle of computational
equivalence talked about the principle applying to any process of any kind
both natural and artificial, the current definition of the principle on
Wolfram's mathworld only defines as applying to systems found in the natural
world.
[https://twitter.com/_nict_/status/727513301274529792](https://twitter.com/_nict_/status/727513301274529792)

------
raattgift
I found this: [https://magnusopium.wordpress.com/2011/05/12/deleuzes-
bergso...](https://magnusopium.wordpress.com/2011/05/12/deleuzes-bergson-and-
the-einstein-debate/)

I have no idea if it's a fair summary of D&G.

I don't really want to touch on anything having to do with scriptures in the
most general sense (vedas, charkras, nadis, and the works that describe them);
I don't think they are likely to have any utility in understanding
gravitation, acceleration, or uniform linear motion at all, and if there is
anything in there, it is probably easier to re-discover in a modern
theoretical framework than to translate.

Instead, the interesting thing is the Achilles-vs-tortoise argument in a
context in approximately 1920 but before the work by Lemaître, Friedmann,
Robertson and Walker that led to the underpinnings of the standard cosmology,
and most particularly before the late 1920s when the Hubble flow was described
and found to apply to all then-known distant galaxies.

Einstein in 1920 had a personal bias towards a static universe for a variety
of reasons, although in part that is because evidence at the time did not
disfavour one. In such a universe, making some assumptions about the behaviour
of its non-gravitational content, there is probably no "universal clock", and
so a resort to GR in an Achilles-vs-hare argument likely would not prove
illuminating (and would be much harder to do quickly).

However, our universe is so close to being isotropic and homogeneous (as far
as we can tell) that we almost certainly can rely upon the scale factor from
the Friedmann-Lemaître-Robertson-Walker model to be equally valid for all
observers. There are additionally relic fields which manifest the scale factor
(e.g., the average temperature of the CMB radiation).

The resolution to Achilles-vs-hare is that both can agree on the scale factor
at the boundary conditions, namely, when they are together at the start of the
race and when they are together again after the race has ended. What they will
disagree on is only the amount of wristwatch time has elapsed.

The tortoise has simply travelled much further in _spacetime_ than Achilles,
and all observers at both boundary conditions will agree with that, no matter
how they have travelled from the start to the end. Even more strongly, any
observer who can place the pair of them together start of the race at time
a(t_start) and the pair of them together at a(t_end) will agree that the
tortoise has travelled further in spacetime, although their count of the
elapsed time in, say, picoseconds, between a(t_start) and a(t_end) may be
unique.

But even if we drop the examination of the scale factor, and we resort only to
Special Relativity, we can see with a Minkowski diagram (available in 1920!)
that the slopes of the race are different. The tortoise's slope is more
vertical (where the y axis is the vertical axis is the timelike axis). If we
choose convenient units where c=1 and we use seconds as the coordinates (so,
actual seconds on the y axis, light-seconds on the x axis, but with light
travelling at one light second per second by choice of units), and we use a
metric like ds^2 = cdt^2 - dx^2, and Achilles takes 300 seconds to run from
origin to finish (on the x axis) while the tortoise takes 3000 seconds to run
from origin to finish (on the y axis), "s" is much bigger for the tortoise
from start to finish, but approximately the same when you trace from boundary
condition (the pair together at the start) to boundary condition (the pair
together at the end). But, using just SR, the less time Achilles takes to run
the race, the smaller his "s" is compared to the tortoise's. He is travelling
a shorter distance in _spacetime_ , even though the number of ticks along the
x axis are the same for him and for tortoise, and we can calculate the exact
difference in distance using the Lorentz formula.

We are not required to use the flat space metric, or Euclidean coordinates
(heck, what's the difference between between "x" and "r" (from polar
coordinates) in the example above?); general covariance (from General
Relativity) _guarantees_ that no matter what set of smooth coordinates we use,
or what units we use, faster Achilles traverses less spacetime between the
boundary conditions than slower tortoise.

The critical point that I do not see in the debate is that the fixing of the
boundary conditions are important (and we now know this because of work done
since Einstein's death, particularly since the development of 3+1 formalisms).
The critical boundaries are when the pair are together again, not when either
of the pair is at the start gate and the end ribbon.

To us in 2016, this is a simple Cauchy problem. However, in 1920 it would have
been at least novel (IIRC, Hadamard's lectures hadn't happened yet, for
example) and certainly not a first choice tool to resolve a seeming paradox.

edit: I reread the article at the top and realize I should substitute April
1922 for 1920 (and various approximations) above. I don't think the exact date
is terribly important; the key thing is that April 1922 is before the Hubble
flow was understood, and before initial-values-surface/boundary-conditions
approaches and close relatives were in use in a GR context.

------
linxzu
Here I read through this only to stop at this line in the second paragraph on
the first page:

 _Therefore my question is, Can physics be simulated ..._

The C, on the word Can, is capitalized after a comma?

~~~
Jtsummers
Imagine quotes around the question. It's a sentence in a sentence.

