Let us look at the fundamental
particles of nature, and consider the question: how many, if any
coincidences can we find there? At this time I will not be
considering what are sometimes called anthropic coincidences,
meaning an agreement between some value of nature and the value that
is required for beings like us to exist (those interested in that
topic can see this post). Here I will merely be considering numerical
coincidences, meaning a case of one fundamental number in nature
matching another in nature without any obvious explanation, or one
number being the exact opposite (or a simple integer multiple) of
another number in nature, without any obvious explanation.
The Stable Particles in Nature
To start out looking for possible
coincidences, we can create a table listing all of the massive stable
particles in nature. The list will include a particle called the
positron (which is known as the antiparticle of the electron), and a
particle called the antiproton (known as the antiparticle of the
proton). Note that both positrons and antiprotons are completely
stable particles which will stay around forever when they exist by
themselves undisturbed in nature. In actual practice, however,
positrons and antiprotons tend to be quickly destroyed in our
universe because a positron is converted to energy whenever it comes
in contact with an electron, and an antiproton is converted to energy
whenever it comes into contact with a proton. (Conversely, an
electron and a positron can be produced by a collision of two energy
particles called photons, and a proton and antiproton can be produced
by a collision of two photons.)
So here is the table listing the
stable massive particles in nature that can exist by themselves (throughout
this discussion I am going to ignore the “ghost particles” called
neutrinos):
Particle Name | Mass | Charge |
Electron | 9.10938291 X 10-31 kg | -1.60217657 × 10-19 coulombs |
Positron | 9.10938291 X 10-31 kg | 1.60217657 × 10-19 coulombs |
Neutron | 1.674927351 X 10-27 kg | |
Proton | 1.672621777 X 10-27 kg | 1.60217657 × 10-19 coulombs |
Antiproton | 1.672621777 X 10-27 kg | -1.60217657 × 10-19 coulombs |
I list these figures to ten decimal
places, because the observational studies described here and here
verify that these masses and charges have been determined to ten decimal places.
Looking at the table above, your first
impression will be that there are a number of coincidences. The
coincidences can be listed as follows:
- The absolute magnitude of the charge of the electron, the proton, the positron, and the antiproton are all exactly the same. (An absolute magnitude is the number you are left with after you remove any negative sign. For example, the absolute magnitude of -22 is 22, and the absolute magnitude of 23 is 23).
- The mass of the electron is exactly the same as the mass of the positron.
- The mass of the the proton is exactly the same as the mass of the antiproton.
There is one way (at least in theory)
that we might be able to explain some of the coincidences in the list
given above. If we can prove that these coincidences are due to a
“simple integer combination” situation, then it might make one or
more of the coincidences seem not very coincidental.
Let me give an example of what I mean
by a “simple integer combination” situation. Imagine if two men
equipped with empty bags go up to a barrel of tiny gold nuggets. The
men both fill the bags with as much gold as they can carry, and then
go home and weigh how much is in each bag. They find that both bags
contain exactly the same weight of gold, to a tenth of an ounce. That would be a huge
coincidence, with a very low likelihood. But
imagine that instead of little nuggets the barrel contains only big
50 kilogram gold bars. Such bars would be so heavy that each of the
men could carry no more than 2 or 3 of them. It would therefore be
not much of a coincidence at all if the men then came home, weighed
their bags, and found that both bags weighed the same. Since we would
expect that both bags would be a simple integer combination of 50
kilograms (50, 100, or at most 150) then the likelihood of both men
coincidentally carrying the same weight would be relatively high,
around 1 in 3. This example shows how a “simple integer
combination” situation can get make a coincidence seem not very
unlikely.
Looking at the situation in regard to
fundamental particles, we can imagine a universe in which a simple
integer combination might explain away the coincidence of the proton
mass matching the antiproton mass. Protons are believed to be made
up of particles called quarks. The two main types of quarks are
called the up quark and the down quark.
The following table (omitting
antiquarks) shows the relation between the charges in the fundamental
particles that have charges (in this table e refers to a
charge of 1.60217657 × 10-19 coulombs):
Particle | Charge |
Proton | 1e |
Antiproton | -1e |
Up Quark | 2/3 e |
Down Quark | -1/3e |
Electron | -1e |
Positron | 1e |
Protons are believed to be made of two
Up quarks and one Down quark. This gives them a charge of 2/3e
+2/3e + -1/3e, which equals 1e.
Now we can imagine a universe in which
a simple integer combination might explain away the coincidence of
the proton charge equaling the antiproton charge. It would be a
universe in which antiprotons were made up of three Down quarks. Then
we would explain the -1e charge of the antiproton without having to
believe in any big coincidence. Since there are 4 ways in which you
can make 3 combinations of an Up quark and a Down quark, we would
then have a minimal coincidence with a likelihood of only 1 in 4 –
not very unlikely at all.
The only problem is: that is not an
accurate description of the antiproton. When we look at what
antiprotons are made of, the coincidences don't become smaller and
more likely – instead they become greater and more unlikely.
Scientists say that an antiproton is
made up not of quarks but particles called antiquarks. Rather than
being made of three Down quarks, an antiproton is made up of two Up
antiquarks and one Down antiquark. So there is not at all any
“simple integer combination” which explains why the proton charge
is exactly the opposite of the antiproton charge.
When we list all of the particles and
component particles, we have quite a list of coincidences to explain.
Here is the expanded table (in this table e refers to a
charge of 1.60217657 × 10-19 coulombs):
Particle | Charge | Composition |
Proton | 1e | 2 Up quarks, 1 Down quark |
Antiproton | -1e | 2 Up antiquarks, I Down antiquark |
Up Quark | 2/3 e | N/A |
Down Quark | -1/3e | N/A |
Up Antiquark | -2/3 e | N/A |
Down Antiquark | +1/3e | N/A |
Electron | -1e | N/A |
Positron | 1e | N/A |
So now we have 8 fundamental particles,
all of which have charges that are simple integer multiples (either
negative or positive) of the charge 1/3e ( one third of 1.60217657 ×
10-19 coulombs).
It is not an unlikely coincidence that
the proton charge has a simple numerical relation to the Up quark
charge and the Down quark charge, because the proton is made of two
Up quarks and one Down quark.
It is not an unlikely coincidence that
the antiproton charge has a simple numerical relation to the Up
antiquark charge and the Down antiquark charge, because the
antiproton is made of two Up antiquarks and one Down antiquark.
However, all of the following are
coincidences incredibly unlikely to occur if there is no underlying
principle that explains them:
- The coincidence that the electron charge is the exact opposite of the positron charge.
- The coincidence that the absolute magnitude of the charge of the Up quark is exactly twice the absolute magnitude of the charge of the Down quark.
- The coincidence that the absolute magnitude of the charge of the Up antiquark is exactly twice the absolute magnitude of the charge of the Down antiquark.
- The coincidence that the absolute magnitude of the charge of the Up quark is exactly the same as the absolute magnitude of the charge of the Up antiquark.
- The coincidence that the absolute magnitude of the charge of the Down quark is exactly the same as the absolute magnitude of the charge of the Down antiquark.
- The coincidence that the absolute magnitude of the proton charge is exactly the same as the absolute magnitude of the electron charge.
- The coincidence that the electron mass exactly equals the positron mass.
- The coincidence that the proton mass exactly equals the antiproton mass.
So that leaves us with a total of eight
fundamental numerical coincidences in nature – cases where two
numbers match exactly, even though the chance of them matching in a
random universe would seem to be very, very low. When I say “exactly
match” in the above list, I mean to ten decimal places.
Do We Know of Some Explanation for
the Match Between Antiparticles and Particles?
I'm sure that some people will try to
explain most of these coincidences simply by evoking an “every
particle has an antiparticle” principle. But “every particle has
an antiparticle” is an empirical generalization, not an
explanation.
Some may claim that there are
theoretical reasons why there need to be antiparticles. They may
claim that physicist Paul Dirac predicted the existence of an
antiparticle (the positron) before it was discovered. So doesn't that
show that there is some theoretical reason why antiparticles must
exist?
Not really. The situation in regard to
Dirac and the positron is more complicated than it is usually
described. Dirac's “prediction” of the positron came in 1931, one
year before the official discovery of the positron in 1932. But he
did not plainly say that the particle exists – he basically just
said that it might exist. So it wasn't really a prediction. Also, at
the very time that Dirac made this supposed prediction, another
scientist named Patrick Blackett was accumulating photographic
evidence that the positron exists – evidence he had not yet
published, but which Dirac was familiar with. This calls into
question whether Dirac deduced the positron's existence on purely
theoretical grounds. Another interesting fact is that Dirac's
“prediction” of the positron was made within the context of a
larger theory that is not widely accepted today – ideas such as
negative mass, negative energy, infinite charge density, the theory
that the universe is filled with an infinitely dense sea of negative
energy particles, and that there are “holes” in this sea. So the
theoretical basis that Dirac advanced for suspecting the existence of an
antiparticle doesn't seem to have been an explanation that still
holds up today.
In 1986 physicist Richard Feynman gave
some extremely complicated lecture called The Reason for
Antiparticles. However, according to this analysis by a
physicist, Feynman's explanation for the existence
of antiparticles was very different from Dirac's. Feynman's
explanation for antiparticles is based on the idea that an
antiparticle is a regular particle traveling backward in time, but
that curious idea is subject to criticism and is doubted by quite a
few. Commenting on his lecture, one physics buff says, “Funny that
Feynman, who is normally perceived as a master of exposition, is not
able to come up with a convincing story here.”
In his book Symmetry and the Beautiful
Universe (page 234), physicist Leon M. Lederman offers this attempt
to give a reason for antiparticles:
Quantum theory forces electrons to
have both positive and negative energy values for any given value of
the momentum. We would say that the negative-energy electron is just
another allowed quantum state of the electron. But this would be a
disaster as well, since it would mean that ordinary atoms, even
simple hydrogen atoms, could not be stable. The positive-energy
electron could emit photons, adding up to an energy of 2mc2,
and become a negative-energy electron and begin its descent into the
abyss of infinite negative energy. Evidently the whole universe could
not be stable if negative-energy states truly existed.
But this does not seem to be an
explanation for why antiparticles have to exist. It's
basically just a statement saying that it is convenient for
antiparticles to exist.
It is often claimed that special
relativity implies the existence of antiparticles (or that the
combination of special relativity and quantum mechanics implies the
existence of antiparticles). One sees statements such as this:
antiparticles are needed because of very subtle reasons buried deep
in the fabric of special relativity and quantum mechanics. But
virtually no one who makes such a claim explains what such reasons
are, and as a general principle one should perhaps be suspicious
about reasons described as deeply buried very subtle theoretical
reasons.
In the book Mathematical
Quantization (page 159), Professor Nik Weaver at the very
prestigious Washington University at St. Louis makes these statements: "A related argument claims that
relativity implies the existence of antiparticles.. This argument is
wrong...Thus the most that one can say is that relativity implies the
existence of phenomena that are reminiscent of multiple particles or
antiparticles. But even this seems misleading."
We can't explain the coincidences between the masses and charges of antiparticles and particles just by saying that they are required by the Standard Model or predicted by the Standard Model. The Standard Model evolved after the discovery of different types of antiparticles, so in this regard it simply reflects the coincidences that had already been discovered.
We also cannot explain any of the above
coincidences by evoking some principle of symmetry, whether it be a
CPT theorem or any other principle of symmetry. Such reasoning would
be circular. Certain types of symmetry in nature may be possible
because of the near-exact correspondence of the features of particles
and antiparticles, but that does not explain such a near-exact
correspondence. If X makes Y possible, we generally don't explain X
by mentioning Y. For example, a student's high SAT scores may
explain his admission to Harvard, but his admission to Harvard
doesn't explain his high SAT scores.
We might have some explanation for why
the masses and charges of antiparticles match the masses and charges
of their corresponding particles if we knew of some mechanism for
charge flipping, the changing of a negative charge into a positive
charge. Then a scientist could say, “Why, of course the absolute
magnitude of the charge of the positron is the same as the absolute
magnitude of the charge of the electron, and of course their masses
are identical – it's because the charge of one particle just flips,
and then you have the antiparticle.” But no such thing happens.
Scientists do not believe that particles ever change into
antiparticles, nor do they believe that antiparticles change into
particles. Scientists believe that what happens is that both a
particle and an antiparticle are created from a collision of
high-energy photons.
It seems that there are really no theoretical a
priori reasons why a universe has to contain any antiparticles.
If one were to cite some formula or equation that implies the
existence of antiparticles, that really would not be equivalent to
showing any necessity behind the existence of antiparticles. Such an
equation would merely reflect that we happen to live in a universe
in which antiparticles exist. Given a million external random
universes with a million random characteristics and a million random
set of laws, it would seem there is no reason to think even one of
them would be a universe in which there are only a few stable
particles with every particle having an antiparticle that is exactly
the same in mass but with an exactly opposite charge.
I may conclude
this section by noting that even if one were to have some completely
convincing explanation for antiparticle/particle coincidences, we
would still be left with no explanation for items 2 and 6 on my
previous list of coincidences, both of which are not really explained
by any widely accepted theory.
Other Coincidences
In this post I
have merely discussed the coincidences involving stable particles,
particles with a very long lifetime. There are also many similar
coincidences involving unstable particles which I have not even
mentioned. I may also note another coincidence involving the apparent
net electric neutrality of the universe. Protons are 1836 times more
massive than electrons. Judging from the intuitive principle that
smaller things tend to be more common than more massive things, we
might expect that electrons would be perhaps one or two thousand times more
common than protons. But instead the number of protons and electrons
in the universe seem to be equal, a fact referred to as the net
electric neutrality of the universe.
All in all, there
are too many mysterious exact numerical coincidences here, which
may suggest that a deeper or more complete explanation of things is needed.
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