In my last year of schooling, I went to a school run by catholic brothers and fathers.
At some point I asked one of the fathers (i.e., a priest) if an angel was subject to
the speed-of-light limitation that limits all forms of matter.
He told me he would think about it, and, the following day, he had this answer:
An angel is not subject to the speed-of-light limitation, because
if the angel moves from A to B,
it does not need to pass through any intermediate points:
it merely disappears at A and appears at B.
The answer, at the time, seemed to me dishonest in the sense that I did not believe
that he had honestly analyzed the question from scratch, but rather, that,
starting from the answer that he wanted, he sought a way to justify his preferred conclusion.
Many years later, I now feel the need to apologize: professional physicists have repeatedly been finding
examples of entities that are real, immaterial, and that move like the angel was posited to move.
In its most basic form —as pondered by physicists— the idea is that,
if A and B are some distance apart, A can in some way affect B,
without having to move to B, and without having to send any kind of messenger
that travels from A to B on some trajectory (some continuum of intermediate points),
or, if such messenger be sent, then it travels infinitely fast.
This idea was considered, and rejected, by
Isaac Newton in 1692;
considered, and rejected, by Albert Einstein in the 1930s;
in 1947, in a letter to Max Born, Einstein famously states:
“physics should represent a reality in time and space, free from spooky actions at a distance.”But nowadays (early 21st century) there is an even more startling variant of this notion,
which entails the existence of extended entities that can change their shape in an instant.
By
extended I mean diffuse, spread out in space, as opposed to point-like:
things that can be considered functions from spacetime to real numbers, in that,
at every point in some stretch of space and time, a single meaningful value is associated,
so these entities have a shape and a density that can be visually rendered like a kind of fog.
Such entities have been found experimentally and critically analyzed
(i.e. they have stirred controversy among experimentalists and theoreticians)
but there seems to be general agreement now, that they are immaterial (carry no energy, no mass)
and yet they are definitely real, we know, because we experimentally observe that they govern matter:
specifically, I’m thinking of quantum mechanical wave functions and pilot waves.
These entities can change their shape in an instant, or, at least,
at a rate that can be experimentally shown to be
at least thousands of times faster than the speed of light.
Allow me to backtrack: before there were cities; before there was agriculture;
at least as far back as our first petroglyphs and cave paintings,
we have held the belief that, in addition to the world that we see around us,
there is a hidden world, populated by beings that, in modern English,
we call spirits, and don’t normally see.
This hidden world is usually conceived as superimposed, or
parallel, to the conspicuous.
If you allow me, I would rather think of Reality as a single reality,
in which there are numerous objects/entities/things,
of which some have energy or mass (i.e.
matter),
and others, are immaterial: for example, mathematical truths.
Can we justifiably claim that immaterial things exist at all?
Mathematics is a
vast subject, full of axioms, definitions, and theorems,
and one might want to distinguish between a statement that is mathematically correct,
in that it can be justified by a process that respects all the rules, and,
a statement that is actually
true!
The distinction arises because not all mathematical axioms are universally agreed upon,
and some mathematicians delight in exploring the consequences of accepting or denying
some arcane axiom, and come up with mutually contradictory theorems,
depending on which path they follow.
There are, however, some mathematical statements that you can verify empirically,
and in such statements I believe, like I believe in the existence of our moon
(because I can plainly see it), or like I believe in the air in front of my face,
which, although I cannot see it, I do breathe it, so, yes: I have complete faith
in the existence of said air.
Example: it is said that e-to-the-i-pi (e
iπ) equals minus one.
That conclusion is reached, academically, by long mathematical reasoning
that I might not entirely understand, or, even if I did,
how can I be certain that there isn’t some omission or mistake somewhere?
Therefore I might say that I
believe, or I have
faith in,
all the smart people that have analyzed the reasoning and have found it to be good.
However!
There is also a theorem that says that e-to-the-x (e
x) can be calculated as
1 + x + x
2/2 + (more and more terms, but following a simple pattern),
and that this expansion is valid for all x.
Now, if that is true, then we can pull out any simple calculator
(you trust your calculator to do simple arithmetic correctly, yes?)
and, with such help (or without it, if you want to be
really fussy),
we can attempt to calculate that e-to-the-i-pi expression,
taking into account that i*i = i
2 = -1, so i
3 = -i, i
4 = 1,
and higher powers of i keep cycling to i, -1, -i, 1, and on and on the same.
So, if we try to do the e
x expansion with x = iπ, namely
1 + iπ - π
2/2 - iπ
3/6 + π
4/24 + iπ
5/120 etc.
then we separate those terms that have a factor of i from those that have not,
and we add them separately. It turns out that, the more terms we take into account,
the more the sum of terms without an i add up to something that gets closer and closer to -1,
whereas the sum of all the factors of i keep getting closer and closer to zero!
After such an experiment I declare that e
iπ = -1 is no longer a matter of
faith,but rather, it is something that I can verify empirically, and therefore I declare,
that I shall believe in it like I believe in the existence of the Moon!
That piece of math, I give as an example of a
mathematical truth.There is, of course, an infinity of mathematical truths
— just think: e
i2π must equal plus one, right?—
and I claim that all of them
exist:
they are real, in the sense that all matter must obey them,
or, rather, that there never has been, and never will be,
any piece of matter that in any way violates a mathematical truth.
Now, you might counter that, even if e
iπ = -1 is
true,an elementary particle doesn’t really care one way or the other; what would I say to that?
What occurs to me is that all matter obeys physical laws, and that currently,
physicists have a pretty good idea of what these laws are, and have formulated them
in mathematical terms, meaning, in practice, that an experimenter can set up
an experiment that culminates in some measurement, and,
even before the experiment starts, a theoretician can calculate what value
said measurement should yield, and will most likely be proven right.
[Contemplate the jaw-dropping feat of probes to the moons of Jupiter and Saturn:
everything moves, so you don’t point your rocket in the direction of Jupiter or Saturn;
you point it toward Venus! The probe gets a gravity-assist from Venus,
swings around toward Earth, gets another gravity-assist and another bend in its trajectory,
but eventually gets to where it was predicted to!]
In order to arrive at the theoretical prediction, the theoretician has, of course,
made abundant use of mathematical truths (including truths involving e-to-the-x),
so, if the theoretical result is experimentally confirmed, I would consider that
a strong indication that those truths are governing matter; wouldn’t you?
All mathematical truths are ubiquitous and eternal, and they are perfectly static.
There exist also, however, parts of Reality that are immaterial, and
dynamic.They demonstrably exist, because they govern matter, dynamically.
As of late 2018 (review
here), there is still controversy over whether such an entity
(specifically, a particle’s
wave function) merely
advises the particle where to go,
by generating a probability density, or whether such a function (then called a
pilot wave)
actually compels the particle to follow a particular path, but, in either case,
the guiding function itself can be probed experimentally by its effects,
even though it does not in itself contain any matter.
Experimentally it is possible to generate two or more particles that share the same wave function.
When that happens, we say that the particles are
entangled, and, any time one of the entangled particles
interacts with anything, the wave function changes, and therefore changes its influence upon the other particles.
That change in influence can be detected, and thus, the
speed at which the wave function deforms
(or rather, the speed at which the deformation propagates over a potentially large distance)
can in principle be measured. For example, in
2012, three entangled particles were generated
at the Observatory of La Palma (Canary Islands), one of which was sent to, and detected, 143km away,
on Tenerife —again and again: over nineteen thousand successful trials—
and the effect of that detection was noticed at La Palma with no measurable delay,
meaning that, if some kind of messenger was sent back by the particle received at Tenerife,
said messenger would have had to travel faster than light by a factor of more than a thousand.
The preferred interpretation is that there was no messenger, but simply,
non-locality on the part of the wave function.
Much like my highschool teacher’s concept regarding angels, right?
Except, it’s not so much that the angel disappears at A and appears at B,
but rather, that it maintains a presence simultaneously at A
and B,
even though they are far apart, and yet, its train of thought is throughout
consistent and without delay. Not baad.
Note 1: I am not trying to insinuate that a wave function has a psychology
resembling that of a human, but I do think it’s clear that such functions
pick up, process, and deliver
information, and that the processing
is highly sophisticated, in addition to fast,
—as witnessed by anyone trying to calculate with computer algorithms!
Note 2: Poetically speaking, mathematical truths constitute a cage and rigid scaffolding,
that constrains and supports all matter inside it. Matter itself is dynamic, and its morphs and motions
are governed by dynamic immaterial extended entities that somehow oblige each particle to follow
precise instructions that, in turn, obey physical laws that are generically fixed, but whose dicta
are highly dependent on the particle’s history (otherwise known as
initial conditions) and environment.
To go, from a thorough analysis of said history and environment, to specific dicta
(thou shalt move exactly as follows: ...) necessarily involves highly sophisticated information processing,
and this raises in me the question:
where is the infrastructure that does the processing?For perspective on processing power, consider e.g. the mass of a proton:
it is well defined, and has been measured (in 2017) to a precision of
32 parts-per-trillion, even though
well over 99% of this mass comes from kinetic energy rather than the
rest mass of its components.
[Remember Einstein’s discovery that all energy bears mass, in the proportion of E = mc² ]
Now, every proton internally quakes on its own; yet they all converge to the same mass value!
Calculating what this mass should be takes so much computing power that it was achieved
(to a much lower precision) only in
2008.
If the wave function (or, the pilot wave) picks up all the necessary environmental information,
one might suggest that the same function also does, somehow, perform the calculations.
Frankly, that does not ring true to me; it seems to me that the computational infrastructure
is truly and permanently hidden from us. I propose that, the one who continually does the calculations,
is God.