- 4438 - ATOMS - are mostly empty space? Practically all of the matter we see and interact with is made of atoms, which are mostly empty space. Then why is reality so... solid? Although, at a fundamental level, the Universe is made up of point-like quantum particles, they assemble together to create objects of finite sizes and masses, occupying specific amounts of volume, that is space..
------------------------- 4438 - ATOMS - are mostly empty space?
- The electron is a fundamental particle, but
the nucleus can be broken up into still smaller, more fundamental constituents.
Whether there are structures on scales smaller than the presently known
subatomic particles remains to be discovered.
-
- All of the macroscopic structures we see and
interact with are composed of the same few subatomic particles, whose
interactions are known. Yet the atom, the building block for all materials
solid, liquid, gas, and more, found on Earth and beyond, is mostly empty space,
with very little volume taken up by "substantive" particles. Our macroscopic reality is somehow just as
it seems, despite the minuscule nature of the components that make it up. How
is this possible?
-
- The physical objects you see, touch, and
otherwise interact with all occupy a volume of space. Whether in the form of
solid, liquid, gas, or any other phase of matter, it costs energy in order to
reduce the volume that any tangible material occupies, as though the very
components of matter themselves are capable of resisting to occupy a smaller
amount of three-dimensional space.
-
- And yet, the fundamental constituents of
matter occupy no measurable volume at all; they’re simply “point particles”. So
how, then, can substances made out of volume-less entities come to occupy space
at all, creating the world and Universe as we observe it?
-
- The size, wavelength, and
temperature/energy scales correspond to various parts of the electromagnetic
spectrum. You have to go to higher energies, and shorter wavelengths, to probe
the smallest scales. Ultraviolet light is sufficient to ionize atoms, but as
the Universe expands, light gets systematically shifted to lower temperatures
and longer wavelengths.
-
- If you want to understand volume, you have
to understand the way we make the measurements that reveal how large an object
is. The way you determine the size of a macroscopic entity is typically to
compare it to some standard of reference whose size is known: a ruler or other
measuring stick, the amount of force that a spring (or spring-like object) is
displaced by owing to that object, the light-travel-time it takes to cross the
span of an object, or even through experiments that strike an object with a
particle or photon of a particular wavelength.
-
- Just as light has a quantum mechanical
wavelength defined by its energy, particles of matter have an equivalent
wavelength, “de Broglie wavelength”, regardless of their other properties,
including their fundamental nature.
-
- When we break down matter itself, we find that
everything we’re familiar with is actually made of smaller constituents. A
human being, for example, can be broken down into their individual organs,
which in turn are made of individual units known as cells. A fully grown human
adult might have between 80-100 trillion cells in them all told, where only
about 4 trillion of them make up what you typically think of as your body: your
musculoskeletal system, connective tissue, circulatory system, and all of your
vital organs.
-
- Another 40 trillion or so are blood cells,
while fully half of the cells in your body do not have your genetic material at
all. Instead, they’re made of single-celled organisms such as bacteria that
live largely in your intestines; from a certain point of view, half of your
cells are not even you!
-
- Although human beings are made of cells, at
a more fundamental level, we’re made of atoms. All told, there are close to
10^28 atoms in a human body, mostly hydrogen by number but mostly oxygen and
carbon by mass.
-
- Cells themselves are relatively small,
typically spanning only 100 microns across and usually requiring a microscope
to resolve individually. However, cells aren’t fundamental at all, but can be
further broken down into smaller constituents.
-
- More complex cells contain organelles,
cell components that perform specific biological functions. Each of those
components is composed of molecules, which range in size from nanometers on up;
a single DNA molecule, although very thin, can be longer than a human finger
when stretched straight!
-
- Molecules, in turn, are made up of atoms,
where atoms are roughly just one Ångstrom across, and typically exhibit
spherical symmetry, having the same extent in all three dimensions.
-
- For a long time in the 19th century, it was
assumed that atoms were fundamental; their very name, atom, means “unable to be
cut.” But later experiments showed that atoms themselves were made of still
smaller constituents: electrons and atomic nuclei. Even today, electrons cannot
be broken apart into smaller constituents, but atomic nuclei have a finite
size, typically a few femtometers
across, existing on distance scales 100,000 times smaller than an atom itself.
-
- Although, by volume, an atom is mostly
empty space, dominated by the electron cloud, the dense atomic nucleus,
responsible for only 1 part in 10^15 of an atom’s volume, contains 99.95% of an
atom’s mass.
-
- But even atomic nuclei aren’t elementary
particles; they’re composed of still smaller entities. Each atom’s nucleus is
made of either a single proton or a mix of protons and neutrons, where an
individual proton (or neutron) has been measured to be between 0.84 and 0.88
femtometers in diameter.
-
- Protons and neutrons themselves can be
further broken down into components: quarks and gluons. According to current
best experimental results we’ve come to the fundamental entities that make up
most of the normal matter we interact with in our daily lives: electrons,
gluons, and quarks.
-
- High-energy physics experiments involving
particle colliders have placed the tightest constraints on how large-or-small
these elementary particles can be. Owing to the Large Hadron Collider at CERN,
we can definitively state that if any of these particles do have a finite size,
and are made up of still-smaller constituents, our most powerful
accelerator-and-collider has been unable to crack them open. Their physical
sizes must be smaller than 100 zeptometers, or 10^-19 meters.
-
- Somehow, the fundamental constituents that
make up everything we interact with have no measurable size at all, behaving as
truly dimensionless point particles, and yet they bind together to produce the
full suite of entities we find at all scales: protons and neutrons, atomic
nuclei, atoms, molecules, cell components, cells, organs, and living beings
among them.
-
- The scale of quarks and gluons is the limit
to how far we’ve ever probed nature.
-
- How can point-like particles — particles of
possibly an infinitesimal size — combine together to make physical objects that
have a positive, finite, non-zero size?
-
- The first is fact that there’s a quantum
rule — the Pauli Exclusion Principle — that prevents any two identical quantum
particles of a certain type from occupying the same quantum state. Particles
come in two varieties, fermions and bosons, and while there are no restrictions
on how many identical bosons can occupy the same quantum state in the same
physical location, the Pauli Exclusion Principle applies to all fermions.
-
- Given that each type of “quark” and every
electron is a “fermion”, this rule excludes even infinitesimally small
particles from coexisting in the same volume of space. Just based on this rule
alone, you can see how multiple particles, even if they don’t have a “size”
themselves, are required to be separated from one another by a finite distance.
-
- The second aspect is that these particles
have fundamental properties inherent to them, and those properties include
things like electric charge, weak isospin and weak hypercharge, and color
charge.
-
- Fermionic particles, the ones subject to
the Pauli Exclusion Principle, that possess an electric charge will experience
the electromagnetic force, coupling to the photon. Fermionic particles with
weak isospin and weak hypercharge experience the weak nuclear force, coupling
to the W and Z bosons. And Fermionic particles with a color charge experience
the strong nuclear force, coupling to the “gluons”. Wow, that's a mouthfull.
-
- As it turns out, quarks and electrons
(along with the electron’s two heavier, fundamental cousins, the muon and tau
particles) all have electric charges to them, meaning they all experience the
electromagnetic interaction.
-
- In electromagnetism, like charges (either +
+ or – -) repel, while opposite charges (either + – or – +) attract, with the
force getting stronger the closer the objects get.
-
- All of the quarks possess a color charge,
meaning they all experience the strong nuclear force. The strong nuclear force
is always attractive, but behaves in a less intuitive fashion: at very small
particle separations, the strong force goes to zero, but increases the farther
away two color-charged objects are from one another.
-
- If two composite objects are color-neutral
overall but made up of entities that possess a color charge — like the proton
and neutron — they exhibit what’s called a residual strong force: a force that
attracts nearby objects with color-charged components, but that drops to zero
very quickly as the distance between them rises.
-
- The Pauli exclusion principle prevents two
fermions from coexisting in the same quantum system with the same quantum
state. It only applies to fermions, however, like quarks and leptons. It does
not apply to bosons, and hence there is no limit to, say, the number of
identical photons that can coexist in the same quantum state.
-
- It’s why fermion-containing stellar
remnants, like white dwarfs and neutron stars, can hold themselves up against
gravitational collapse, as the Pauli Exclusion Principle limits the volume that
a finite number of fermions can occupy.
-
- Meanwhile, all of the fundamental fermions
have some type of “weak charge" (isospin and/or hypercharge), but that
force can safely be ignored when considering the size of an object.
-
- Finally, the third aspect that governs the
sizes of objects in the Universe is a different fundamental, quantum property
inherent to all fermions (and some bosons) in the Universe: mass. If an object
is massless, its mass is zero, it cannot remain still, but rather must always
remain not only in motion, but in motion at the fastest speed allowable in the
Universe: the speed of light.
-
- Photons are massless, gluons are massless,
and gravitational waves are massless. They can all carry energy, but have no
mass inherent to them, and as a result, they always move at the maximum speed
allowable: the speed of light. 186,000
miles per second.
-
- Thankfully, there are many entities in the
Universe that do have mass, including all of the quarks, the electrons, and the
(heavier) cousins of the electron: the muon and tau particles. Electrons are
extremely light particles, while quarks range from “somewhat heavier” than the
electron in the case of the up-and-down quarks to “the heaviest known
fundamental particle of all” in the case of the top quark.
-
- Having a mass mandates that particles move
slower than the speed of light, and even enables them to come to rest under the
right conditions. If it weren’t for the massive nature of the quarks and
electrons — and for the Higgs field that gives these particles their masses —
forming bound states out of these objects like protons, atomic nuclei, atoms,
and everything that’s subsequently built out of them would be entirely
impossible!
-
- The “strong force”, operating as it does
because of the existence of ‘color charge’ and the exchange of gluons, is
responsible for the force that holds atomic nuclei together. This force,
governed by the exchange of massive gluons, is bounded by the speed of light.
-
- With those three aspects firmly in mind:
-
---------------- no two identical fermions can occupy the same
quantum state in the same location,
-
---------------- particles have charges and those charges
dictate the type and magnitude of force(s) that they experience,
-
------------------- some particles have a finite, positive,
non-zero rest mass,
-
- We can finally begin building objects of
specific, finite sizes out of even infinitesimally-sized constituents, starting with protons and neutrons: entities
made out of quarks and gluons. The quarks inside each proton and neutron have
both electric and color charges. The electric force between similar quarks
(up-up or down-down) causes repulsion, while the electric force between
differing quarks (up-down or down-up) is attractive.
-
- When quarks get very close together, the
strong force is negligible, meaning that if they were moving toward one
another, they’ll simply “coast” past one another. However, the farther apart
they get, the greater the attractive force between them gets, preventing them
from getting too far apart. In fact, once the quarks inside a proton or neutron
reach a critical separation distance from one another, the strong force causes
them to “snap back” toward one another, just like a stretched spring would.
-
- Because the quarks within a proton and
neutron have non-zero masses, those quarks must always move slower than the
speed of light, enabling them to accelerate, decelerate, and even (temporarily)
come to rest within this composite structure.
-
- Combined, the strong and electromagnetic
forces between quarks create protons and neutrons of finite sizes, under 1
femtometer apiece, while the binding energy between the quarks, due to the
strong force, winds up being responsible for the majority of a proton’s and
neutron’s total mass. Only 1% of a proton’s/neutron’s mass arises from the
quarks inside it, while the other 99% comes from this binding energy.
-
- Individual protons and neutrons are
colorless entities: the only type of quark state admissible in the Universe
today. Although the strong force is mediated by massless (gluon) particles, the
only force that exists between individual bound states are due to mesons, which
themselves are all quite massive, limiting the strong force’s range severely.
-
- Atomic nuclei are a little simpler: the
volume of an atom’s nucleus is approximately equal to the volume of its
constituent protons and neutrons combined together. But for atoms themselves ,
the atomic nuclei orbited by electrons the electromagnetic force is now the one
responsible for the size of an atom, as the positively charged, massive nucleus
anchors the atom, and the negatively charged, much less-massive electron(s)
orbit the nucleus.
-
- Because they have opposite charges to one
another, atomic nuclei and electrons always mutually attract, but because each
individual proton is 1,836 times as massive as each individual electron, the
electrons move rapidly around each atom’s nucleus. The simplest atom is
hydrogen, where only one electron orbits around a solitary proton, held
together by the electromagnetic force.
-
- Now, remember the Pauli Exclusion
Principle: no two identical fermions can occupy the same quantum state in the
same location. The hydrogen atom is small because its electron is in the
lowest-energy state allowable, the ground state, and only has one electron.
Heavier atomic nuclei, however — like carbon, oxygen, phosphorus, or iron —
have more protons in their nuclei, requiring greater numbers of electrons
within them.
-
- If the lower-energy quantum states are all
full of electrons, then subsequent electrons must occupy higher-energy states,
leading to larger electron orbits (on average) and “puffier” atoms that occupy
greater volumes. Carbon atoms each have six electrons, oxygen atoms have eight,
phosphorus atoms have fifteen, and iron atoms have twenty-six electrons apiece.
-
- The more protons you have at the core of
your atom, the more electrons you have orbiting within the outskirts of your
atom. The more electrons you have, the greater the number of energy states that
must be occupied. And the higher the energy state of the highest-energy
electrons within your atom, the greater the amount of physical volume your atom
must occupy. A hydrogen atom might be only about 1 Ångstrom in diameter, but
heavier atoms can be substantially larger up to multiple Ångstroms across.
-
- The energy levels and electron
wavefunctions that correspond to different states within a hydrogen atom,
although the configurations are extremely similar for all atoms. The energy
levels are quantized in multiples of Planck’s constant, but the sizes of the
orbitals and atoms are determined by the ground-state energy and the electron’s
mass.
-
- Only two electrons, one spin up and one
spin down, can occupy each of these energy levels owing to the Pauli exclusion
principle, while other electrons must occupy higher, more voluminous orbitals.
When you drop from a higher energy level to a lower one, you must change the
type of orbital you’re in if you’re only going to emit one photon, otherwise
you’ll violate certain conservation laws that cannot be broken.
-
- Although atoms frequently assemble to form
larger structures, the volume occupied by most objects can be mostly accounted
for by understanding the volume occupied by an object’s constituent atoms
themselves. The Pauli Exclusion Principle, stating that no two identical
fermions can occupy the same quantum state, prevents the electrons from
adjacent atoms from infringing on the volume that the other one occupies.
-
- Using a human being as an example, we’re
made mostly of carbon, oxygen, hydrogen and nitrogen, with phosphorus, calcium,
iron, and other modestly heavy elements comprising the majority of the rest.
Given that there are approximately 1,028 atoms in a typical adult human body,
if you assume that a typical atom is about 2 Ångstroms on a side, that
translates into a volume of around 80 liters for an adult human: about the size
of a 180 pound adult.
-
- Under exceptional circumstances, of course,
these rules can vary slightly. In a white dwarf star, for example, there are so
many atoms packed together in one location that the electrons in orbit around
their atomic nuclei actually get crushed by the compressive gravitational
forces surrounding them, compelling them to occupy substantially smaller
volumes than normal.
-
- In muonic atoms — where an atom’s electrons
are replaced by the electron’s heavier cousin, the muon — atoms are only about
1/200th the diameter of electron-based atoms, as muons are approximately 200
times more massive than electrons. But for the conventional matter that makes
up our familiar experiences, it’s the cumulative effects of:
-
----------------- the low but non-zero mass of the electron,
-
------------------ the strong, negative electric charge of the
electron,
-
------------------ the massive, positively charged atomic
nucleus,combined with the Pauli Exclusion Principle, that give atoms, and all
objects here on Earth, the volumes they occupy. From fundamental quantum entities
all the way up to the macroscopic world we inhabit, that’s how fundamentally
tiny, perhaps even point-like objects wind up occupying so much space!
-
April 21, 2023 ATOMS
- are mostly empty space? 4438
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--------------------- --- Sunday, April 21, 2024
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