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Particle Physics lesson

particles colliding LHC

Your job: Produce a document, with pictures, putting together what you have learned today. Ways that you can do this:

* Handwrite

* Create a PowerPoint presentation

* Google Docs (typing or voice-to-text)

* Create a poster – pencils, colored pencils, pens, markers.


Inside atoms we have protons, neutrons and electrons. Now we learn that protons and neutrons are not “solid”. They are built from smaller subatomic particles!

The particle zoo


Animation: Atoms to Quarks


Videos: Out Of Sight – Building From Quarks To Atoms to Molecules


CERN: Two protons collide and create new particles


CK-12 Chemistry Fundamental Particles


At the end of this website launch and explore the “CK-12 Interactive”


Advanced topics

Quarks are particles within protons and neutrons.

How do point particles create atoms with size?


Understanding Modern Physics. Electromagnetism to Relativity

I’m linking to some rather excellent lessons on modern physics from the School of Physics – The University of New South Wales, Sydney, Australia.

website – newt.phys.unsw.edu.au/einsteinlight/index.html

Gravity General Relativity warping The Elegant Universe

From “The Elegant Universe”, PBS series NOVA. 2003.

1. GALILEO – Mechanics and Galilean relativity (Multimedia above right, smaller html version here)

Related Links

2. MAXWELL – Electricity, magnetism and relativity (Multimedia above right, smaller html version here)

Related Links

3. EINSTEIN – The principle of Special Relativity (Multimedia above right, smaller html version here)

Related Links

4. TIME DILATION – How relativity implies time dilation and length contraction (Multimediaabove right, smaller html version here)

Related Links

5. E = mc2 – How relativistic mechanics leads to E = mc2 (Multimedia above right, smaller html version here)

Related Links

6. BEYOND RELATIVITY. (Multimedia version, or smaller html version)Related Links



How did we develop modern physics?

For over 2,000 years, great thinkers have studied the Heavens and the Earth, searching for unifying principles that explain how our universe works.

By time of the scientific revolution and the Enlightenment we began to discover a pattern of interconnected principles that apparently explained all phenomenon ever observed in our universe.

This tested, reliable description of our universe has come to be known as classical physics. By any measure, classical physics has been an extraordinary success. It includes the laws of optics, electromagnetic radiation, Newton’s laws of motion and the law of gravity, and the laws of thermodynamics.

By the late 1800s classical physics had been so successful at describing nearly everything observed, that many scientists had come to believe that we had discovered all that could be known, and that physics was nearly at an end.

The universe followed a set of basically comprehensible, classical laws, which worked like clockwork.


All that was left was for physicists to make ever-more-accurate measurements, and tidy up a few “loose ends” that couldn’t yet be explained.

A few scientists discovered, however, that these loose ends simply couldn’t be explained by any of the known laws of physics.  No amount of ingenious thinking could find a way to explain these odd phenomenon.

For instance

  • Electrons should not be able to orbit around an atom’s nucleus; they should give off radiation, lose energy, and spiral into the nucleus, thus causing all atoms in the universe to collapse in a nanosecond  Yet this obviously doesn’t happen.

  • Light was proven to travel in the form of waves, yet Einstein’s explanation of the photoelectric effect proved that light travelled as discrete particles (“photons”).  How could light be both a wave and a particle at the same time?

  • Radioactive elements would spontaneously break down into lighter weight elements, but in a random process that could only be described statistically, not deterministically.

  • When elements are heated, they give off only certain frequencies of light (“spectra”).  Why would some frequencies be given off, but not others?

  • Electrons around an atom could absorb or release certain amounts of radiation, of multiples of these amounts, but not any amount in between.  How could particles have one amount of energy, a higher amount, but not an amount in-between?

    • That’s like saying that a car can travel at 50 mph or 100 mph, but not at any speed in-between.  Cars would magically jump from 50 to 100 mph, without any speed in-between. Wouldn’t this be nonsense?  Yet for electrons it was observed to be true!

Three Failure of Classical Physics, Dr. Bradley Carroll

All of these odd phenomenon were observed more and more often. No explanation consistent with the known laws of physics could explain any of them.  Over a 40 year period, between 1880 and 1920, there was a tremendous revolution in science that produced what we now call modern physics: Quantum mechanics, Special Relativity, and General Relativity

Modern physics reveals a radically new understanding of the universe that, at its core, shows us that our everyday perception of reality is entirely wrong.

Yet do apples now fall up when dropped?  Does electricity no longer flow in circuits?  Of course not.  Since the universe still operates as it always has, there must be some link between the classical world and the relativistic, quantum world.

Consider Newton’s laws of motion.  In Newtonian, classical physics, the momentum of a moving object equals its mass x velocity.

p = m·v

Let’s say we have an electron moving at 0.98 c (98% of the speed of light.)  What is its momentum? According to classical physics it must be:

p = m·v = (9.11 x 10 –31 kg)·0.98·(3 x 10 8 m/s)

   = 2.68 x 10 – 22 kg·m/s

In particle accelerators we use very strong magnetic fields to accelerate charged particles; we can make electrons actually travel at such ultra-high speeds!  When we do so, we find that the momentum of an electron traveling at 0.98 c is five times greater than this!  This sort of thing has been tested again and again.  For very high speeds, Newton’s laws of physics fail to give accurate results!  Yet Newton’s laws obviously work extremely well for all practical purposes.  What is going on?

As discovered by Albert Einstein, Newton’s laws of physics are actually a mathematical subset of a more general law of physics, relativistic physics.  Relativistic physics always gives the correct answer at all speeds, while Newton’s laws are seen to be an approximation of relativity, an approximation that works extremely well.

The relativistic formula for momentum turns out to be this:

relativistic momentum formula

Image from the Hyperphysics website

That looks very different from p = m·v.  But look more closely.  What happens when v (the velocity of an object) is much less than c , the speed of light?   (And note that even 10,000 miles an hour is very small compared to c !)  In this case,  v2 / c2 becomes very, very small.  It becomes so small that we can treat it as zero.

Then the denominator for this equation becomes 1, and the equation reduces to the classical momentum equation!  So in this sense, Newton’s laws of physics are included in relativity!

Newton’s laws have a domain in which they are applicable (i.e. give correct results) and outside of this domain they don’t function. So we look for a wider theory that encompasses Newton’s laws, but with a wider domain of applicability.

Special relativity is the set of physical laws that include Newton’s laws of motion, but work in a wider domain of applicability.

General relativity is the set of physical laws that include Special Relativity, but work in a wider domain of applicability.

Quantum mechanics is the set of physical laws that include Newton’s laws of motion, and optics, but work in a wider domain of applicability.

Problem: The description of reality given by general relativity and quantum mechanics is incompatible. That’s bad.  But within their domain of applicability, they both have been fantastically accurate!  That’s good.  This means that there must be an even deeper, more fundamental law of physics that includes both relativity and QM.

Quantum gravity is the postulated fundamental law that includes both QM and relativity.   The search for a theory of quantum gravity is one of the great quests of 21st century science.


“If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.” – Neils Bohr

“We know nothing except through logical analysis, and if we reject that sole connection with reality, we might as well stop trying to be adults and retreat into the capricious dream-world of infantility.”

H.P. Lovecraft, in a letter sent to Robert E. Howard, 8/16/1932

Particle Detectors

A particle detector is a device used to detect, track, and/or identify ionizing particles.

These particles may have been produced by nuclear decay, cosmic radiation, or reactions in a particle accelerator.

Particle detectors can measure the particle’s energy, momentum, spin, charge, particle type, in addition to merely registering the presence of the particle.

Cloud Chamber

(Adapted from Wikipedia)

cloud chamber, also known as a Wilson cloud chamber, is a particle detector used for visualizing the passage of ionizing radiation.

A cloud chamber consists of a sealed environment containing a supersaturated vapor of water or alcohol.

An energetic charged particle (for example, an alpha or beta particle) interacts with the gaseous mixture:

it knocks electrons off gas molecules via electrostatic forces during collisions

This results in a trail of ionized gas particles. They act as condensation centers : a mist-like trail of small droplets form if the gas mixture is at the point of condensation.

These droplets are visible as a “cloud” track that persist for several seconds while the droplets fall through the vapor.

These tracks have characteristic shapes. For example, an alpha particle track is thick and straight, while an electron track is wispy and shows more evidence of deflections by collisions.

Cloud chambers played a prominent role in the experimental particle physics from the 1920s to the 1950s, until the advent of the bubble chamber.

This is a Diffusion Cloud Chamber used for public demonstrations at the Museum of Technology in Berlin. The first part shows the alpha and beta radiation occurring around us all the time, thanks to normal activity in the atmosphere. Then a sample of Radon 220 (half-life 55 sec) is inserted into the chamber and all hell breaks loose as an alpha-decay party ensues!

Source: Derek McKenzie, Physics Footnotes, http://physicsfootnotes.com/radon-cloud-chamber/


Here is an example of two particles colliding within an accelerator, and decaying into a variety of other products.



particles colliding LHC

Let’s look at some detailed examples. We’ll see photographs of the particle detector, then we’ll see cutaway diagrams showing us what is inside the detector.

While each detector is different – designed for a different task – they all have some basic elements in common. Each has a set of wires that make a signal if a particle flies through them. These wires are arrayed around the target area – the place where the particles are forced to collide.

When a collision occurs, some particles are broken free and fly outwards.

More remarkably, when a collision occurs, some particles are actually created – we generate particles that weren’t even there before. How is that possible? Short version, Einstein’s theory of mass-energy equivalence means that matter can be converted into energy, or vice-versa. The massive energy in these collisions creates many new sub-atomic particles. Some of these may be permanent, others might exist for only short periods of time.

ALICE, A Large Ion Collider Experiment in the LHC at CERN

This animation shows what happens when electrons and positrons collide in the ILD detector, one of the planned detectors for the future ILC. Many collisions will happen at the same time around the clock, producing a vast array of possible events. This shows one possible collision event involving the Higgs boson.



“With the uncertainty principle and the observer effects in mind, how do these devices measure both the position and momentum of sub-atomic particles with the kind of accuracy that they seem to get, with the beautiful color pictures?”

How do these devices measure both the position and momentum of particles without violating the Heisenberg Uncertainty principle?




how Particle Accelerators Work



The Particle Adventure app lets us discover: The Standard Model, Accelerators and Particle Detectors, Higgs Boson Discovered, Unsolved Mysteries, Particle Decays and Annihilations.

   Android – The Particle Adveture .   iOS (Apple) The Particle Adventure

Interactive website sims

The Particle Adventure

CPEP Contemporary Physics Education Project


Further reading

Symmetry Magazine (for high school students)


Learning Standards

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect. Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra. Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles.
Relativity, such as time dilation, length contraction, and mass-energy equivalence

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

Electromagnetic radiation can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. Quantum theory relates the two models…. Knowledge of quantum physics enabled the development of semiconductors, computer chips, and lasers, all of which are now essential components of modern imaging, communications, and information technologies.


Four types of multiverses

Most people believe that the universe began at the Big Bang, and that our universe is the only one that has ever existed. Others believe that the universe is cyclical, and that universes existed before ours: those universes, it is hypothesized, collapsed and were replaced by later universes.

When Georges Lemaître, a Belgian physicist and Roman Catholic priest, first began to develop the Big Bang Theory (in 1927), many scientists assumed the former – this is the only universe that has ever existed. In this view, it makes no sense to ask “what happened before the Big Bang?” as there was no before.

In more recent years, scientists have studied the possibility of a multi-verse. Our universe may not be the only one that has existed; perhaps others existed before our own, and others may exist after our own. Also, perhaps other universes  – in some way removed from our own – simultaneously exist.  In this view, one indeed may ask “what happened before the Big Bang?” as there was a time before our universe.

Is there evidence of a multiverse?

At the present time, most scientists say that we don’t have any direct evidence. However, astronomical and physics evidence, as interpreted through quantum mechanics and general relativity, may suggest that other universes may exist.

As such, physicists have developed models of how our universe may have been created, perhaps from the destruction of a previous universe, or perhaps ours branched off from some other.

On the other hand, some physicists hold that certain results of quantum mechanics experiments, indeed, are direct evidence of our universe physically interfering with other “nearby” quantum multiverse.

Two of the most well known adherents of this view are Max Tegmark (his work is the basis of this article) as well as David Deutsch.  See The Fabric of Reality by David Deutsch (Penguin, 1998)

A Physicist Explores the Multiverse Quantum Computers Predict Parallel Worlds by Susan Barber

David Deutsch’s multiverse carries us beyond the realms of imagination

New evidence for the multiverse—and its implications

Pilot wave theory really implies multiverse theory

Mag Tegmark Article – the four types of multiverse are


Summary: The simplest type of parallel universe is simply a region of space that is too far away for us to have seen yet. The farthest that we can observe is currently about 4 ! 1026 meters, or 42 billion lightyears—the distance that light has been able to travel since the big bang.  (The distance is greater than 14 billion light-years because cosmic expansion has lengthened distances.) Each of the Level I parallel universes is basically the same as ours. All the differences stem from variations in the initial arrangement of matter.

How far away parallel Universe multiverse Tegmark


Summary: A somewhat more elaborate type of parallel universe emerges from the theory of cosmological inflation. The idea is that our Level I multiverse—namely, our universe and contiguous regions of space—is a bubble embedded in an even vaster but mostly empty volume. Other bubbles exist out there, disconnected from ours. They nucleate like raindrops in a cloud. During nucleation, variations in quantum fields endow each bubble with properties that distinguish it from other bubbles.

Level II Multiverse Tegmark


Summary: Quantum mechanics predicts a vast number of parallel universes by broadening the concept of “elsewhere.” These universes are located elsewhere, not in ordinary space but in an abstract realm of all possible states. Every conceivable way that the world could be (within the scope of quantum mechanics) corresponds to a different universe.

Yet these parallel universes might make their presence felt in laboratory experiments, such as wave interference and quantum computation.

Level III multiverse Tegmark quantum

LEVEL IV: Mathematical universe hypothesis

Existing outside of ur space and time, they are almost impossible to visualize; the best one can do is to think of them abstractly. We can at least create static sculptures that represent the mathematical structure of the physical laws that govern them.

For example, consider a simple universe: Earth, moon and sun, obeying Newton’s laws. To an objective observer, this universe looks like a circular ring (Earth’s orbit smeared out in time) wrapped in a braid (the moon’s orbit around Earth).

Other shapes embody other laws of physics (a, b, c, d).

According to Max Tegmark, this paradigm solves various problems concerning the foundations of physics.

Level IV multiverse Tegmark mathematical

A Level IV multiverse comes from the idea that our physical world is a mathematical structure. It means that mathematical equations describe not merely some limited aspects of the physical world, but all aspects of it.


External resources

Max Tegmark multiverse website. MIT.Edu

Scientific American article:Parallel Universes

Infographic: Inflation Meets Many Worlds

Are Parallel Universes Unscientific Nonsense? Insider Tips for Criticizing the Multiverse. Scientific American

The Physics of David Deutsch (older version)

David Deutsch homepage, Centre for Quantum Computation, Oxford Univ

Related articles

What Is (And Isn’t) Scientific About The Multiverse, by Ethan Siegel, Forbes


Learning Standards

2016 Massachusetts Science and Technology/Engineering Standards
Students will be able to:
* respectfully provide and/or receive critiques on scientific arguments by probing reasoning and evidence and challenging ideas and conclusions, and determining what additional information is required to solve contradictions

Next Generation Science Standards: Science & Engineering Practices
● Ask questions that arise from careful observation of phenomena, or unexpected results, to clarify and/or seek additional information.
● Ask questions that arise from examining models or a theory, to clarify and/or seek additional information and relationships.

Warp drive

Through science fiction, most people are familiar with the idea of warp drive. It is a fictional form of FTL (Faster Than Light travel) Its most popular use is in the science-fiction series Star Trek.

According to the laws of physic could warp drive potentially be possible?

Enterprise at warp speed Star Trek

Warp drive in science fiction

first mention, “Islands of Space,” by John W. Campbell. 1931

Star Trek

Warping space in general relativity



Mass warping space gravitational lens



Gravity General Relativity warping The Elegant Universe

From “The Elegant Universe”, PBS series NOVA. 2003.

Warp drive in real physics

The Alcubierre drive is a speculative analysis of physics which shows that warp drive may in fact be possible. It is based on a solution of Einstein’s field equations in general relativity.  It was first proposed by Mexican theoretical physicist Miguel Alcubierre.

In his analysis, a spacecraft could effectively achieve a kind of FTL travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.

Alcubierre Warp Drive

From a demo on Wolfram.com by Thomas Mueller.

Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel.

In this analysis, objects still cannot accelerate to the speed of light within normal spacetime; therefore it doesn’t violate the laws of General Relativity.

Instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space.

“Space-time bubble is the closest that modern physics comes to the “warp drive” of science fiction. It can convey a starship at arbitrarily high speeds. Space-time contracts at the front of the bubble, reducing the distance to the destination, and expands at its rear, increasing the distance from the origin (arrows). The ship itself stands still relative to the space immediately around it; crew members do not experience any acceleration. Negative energy (blue) is required on the sides of the bubble.” – Ford and Roman


Lawrence H. Ford and Thomas A. Roman. Sci Am article.


Negative energy warp bubble


Although the metric proposed by Alcubierre is consistent with the Einstein field equations, it may not be physically meaningful. We are not certain that the mathematical solutions are possible in the real world. If so then this warp drive will not be possible.

Even if it is physically meaningful, that does not necessarily mean that a drive can be constructed. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter. So if exotic matter with the correct properties can not exist, then the drive could not be constructed.

Problematic requirements

This section is from “NASA –Faster-than-Speed-of-Light Space Travel? ‘Will ‘Warp Bubbles’ Enable Dreams of Interstellar Voyages?’ ” DailyGalaxy. com
Posted on Sep 21, 2018

In general relativity, one often first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it; but it is also possible to run the Einstein field equations in the other direction, first specifying a metric and then finding the energy-momentum tensor associated with it. This is what Alcubierre did in building his metric.

This practice means that the solution can violate various energy conditions and require exotic matter. The need for exotic matter leads to questions about whether it is actually possible…

Yet another problem according to Serguei Krasnikov is that it would be impossible to generate the bubble without being able to force the exotic matter to move at locally FTL speeds, which would require the existence of tachyons. Some methods have been suggested which would avoid the problem of tachyonic motion, but would probably generate a naked singularity at the front of the bubble.

Dr. White believes that advances he and others have made render warp speed less implausible. Among other things, he has redesigned the theoretical warp-traveling spacecraft — and in particular a ring around it that is key to its propulsion system — in a way that he believes will greatly reduce the energy requirements. But ”We’re not bolting this to a spacecraft,” he said of the technology.

Richard Obousy, a physicist who is president of Icarus Interstellar, a nonprofit group composed of volunteers collaborating on starship design, said “it is not airy-fairy, pie in the sky. We tend to overestimate what we can do on short time scales, but I think we massively underestimate what we can do on longer time scales.”

… Still, one of the most dubious is Dr. Alcubierre himself. He listed a number of concerns, starting with the vast amounts of exotic matter that would be needed. “The warp drive on this ground alone is impossible,” he said. “At speeds larger than the speed of light, the front of the warp bubble cannot be reached by any signal from within the ship,” he said. “This does not just mean we can’t turn it off; it is much worse. It means we can’t even turn it on in the first place.”

… As Caltech physicist Sean Carroll notes: “In short, it requires negative energy densities, which can’t be strictly disproven but are probably unrealistic; the total amount of energy is likely to be equivalent to the mass-energy of an astrophysical body; and the gravitational fields produced would likely rip any ship to shreds. My personal estimate of the likelihood we will ever be able to build a ‘warp drive’ is much less than 1%. And the chances it will happen in the next hundred years I would put at less than 0.01%.”


Spaceship design

The IXS Enterprise is a theory fitting concept for a space warping ship. It’s designed by Mark Rademaker with NASA scientist Dr. Harold White and used in his presentations as an extra. Mike Okuda also brought input, and designed the Ship’s insignia.

IXS Enterprise / IXS-11

IXS Enterprise (Wikipedia)


Further reading

Negative Energy. Wormholes and Warp Drive. Scientific American Jan 2000

Faster-than-light (FTL) Travel in Science Fiction. Dan Koboldt

Alcubierre warp drive, Wikipedia

Faster Than Light, Wikipedia

Negative Energy, Wormholes and Warp Drive, Scientific American, Jan 2000

By Lawrence H. Ford and Thomas A. Roman

Learning Standards

2016 Massachusetts Science and Technology Curriculum Framework
Appendix VIII: Value of Crosscutting Concepts and Nature of Science in Curricula

ETS3. Technological Systems.  5.3-5-ETS3-1(MA). Use informational text to provide examples of improvements to existing technologies (innovations) and the development of new technologies (inventions). Recognize that technology is any modification of the natural or designed world done to fulfill human needs or wants.

9. Influence of Engineering, Technology, and Science on Society and the Natural World

In grades 9–12, students can describe how modern civilization depends on major technological systems, such as agriculture, health, water, energy, transportation, manufacturing, construction, and communications. Engineers continuously modify these systems to increase benefits while decreasing costs and risks. New technologies can have deep impacts on society and the environment, including some that were not anticipated.

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect

Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra. Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles. Relativity, such as time dilation, length contraction, and mass-energy equivalence.

College Board Standards for College Success: Science

Enduring Understanding 1D: Classica mechanics can not describe all properties of objects.

How do point particles create atoms with size?

This article is archived for use with my students from Ask Ethan: If Matter Is Made Of Point Particles, Why Does Everything Have A Size?

Forbes, Stars With a Bang, by Ethan Siegel 9/16/17

Proton Structure Brookhaven

Proton Structure Brookhaven National Laboratory

The big idea of atomic theory is that, at some smallest, fundamental level, the matter that makes up everything can be divided no further. Those ultimate building blocks would be literally ἄ-τομος, or un-cuttable.

As we’ve gone down to progressively smaller scales, we’ve found that molecules are made of atoms, which are made of protons, neutrons, and electrons, and that protons and neutrons can be further split into quark and gluons. Yet even though quarks, gluons, electrons, and more appear to be truly point-like, all the matter made out of them has a real, finite size. Why is that? That’s what Brian Cobb wants to know:

Many sources state that quarks are point particles… so one would think that objects composed of them — in this instance, neutrons — would also be points. Is my logic flawed? Or would they be bound to each other in such a way that they would cause the resulting neutron to have angular size?

Let’s take a journey down to the smallest scales, and find out what’s truly going on.

Magdalena Kowalska Nuclear Scale to quarks

Magdalena Kowalska / CERN / ISOLDE team

If we take a look at matter, things behave similar to how we expect they should, in the macroscopic world, down to about the size of molecules: nanometer (10-9meter) scales. On smaller scales than that, the quantum rules that govern individual particles start to become important.

Single atoms, with electrons orbiting a nucleus, come in at about the size of an Angstrom: 10-10 meters. The atomic nucleus itself, made up of protons and neutrons, is 100,000 times smaller than the atoms in which they are found: a scale of 10-15 meters. Within each individual proton or neutron, quarks and gluons reside.

While molecules, atoms, and nuclei all have sizes associated with them, the fundamental particles they’re made out of — quarks, gluons, and electrons — are truly point-like.

Standard-Model Quarks Leptons Bosons

E. Siegel / Beyond The Galaxy

The way we determine whether something is point-like or not is simply to collide whatever we can with it at the highest possible energies, and to look for evidence that there’s a composite structure inside.

In the quantum world, particles don’t just have a physical size, they also have a wavelength associated with them, determined by their energy. Higher energy means smaller wavelength, which means we can probe smaller and more intricate structures. X-rays are high-enough in energy to probe the structure of atoms, with images from X-ray diffraction and crystallography shedding light on what molecules look like and how individual bonds look.

Electron density map of protein

Imperial College London

At even higher energies, we can get even better resolution. Particle accelerators could not only blast atomic nuclei apart, but deep inelastic scattering revealed the internal structure of the proton and neutron: the quarks and gluons lying within.

It’s possible that, at some point down the road, we’ll find that some of the particles we presently think are fundamental are actually made of smaller entities themselves. At the present point, however, thanks to the energies reached by the LHC, we know that if quarks, gluons, or electrons aren’t fundamental, their structures must be smaller than 10-18 to 10-19 meters. To the best of our knowledge, they’re truly points.

quark-gluon plasma

Brookhaven National Laboratory

So how, then, are the things made out of them larger than points? It’s the interplay of (up to) three things: Forces, Particle properties, and Energy.

The quarks that we know don’t just have an electric charge, but also (like the gluons) have a color charge. While the electric charge can be positive or negative, and while like charges repel while opposites attract, the force arising from the color charges — the strong nuclear force — is always attractive. And it works, believe it or not, much like a spring does.

Warning: Analogy ahead!

Caution analogies

Here we go:

Quarks and Gluons

How did the Proton Get Its Spin? Brookhaven National Laboratory

Above: The internal structure of a proton, with quarks, gluons, and quark spin shown. The nuclear force acts like a spring, with negligible force when unstretched but large, attractive forces when stretched to large distances

When two color-charged objects are close together, the force between them drops away to zero, like a coiled spring that isn’t stretched at all.

When quarks are close together, the electrical force takes over, which often leads to a mutual repulsion.

But when the color-charged objects are far apart, the strong force gets stronger. Like a stretched spring, it works to pull the quarks back together.

Based on the magnitude of the color charges and the strength of the strong force, along with the electric charges of each of the quarks, that’s how we arrive at the size of the proton and the neutron: where the strong and electromagnetic forces roughly balance.

Quarks and protons

APS/Alan Stonebraker

The three valence quarks of a proton contribute to its spin, but so do the gluons, sea quarks and antiquarks, and orbital angular momentum as well. The electrostatic repulsion and the attractive strong nuclear force, in tandem, are what give the proton its size.

On slightly larger scales, the strong force holds protons and neutrons together in an atomic nucleus, overcoming the electrostatic repulsion between the individual protons. This nuclear force is a residual effect of the strong nuclear force, which only works over very short distances.

Because individual protons and neutrons themselves are color-neutral, the exchange is mediated by virtual, unstable particles known as pions, which explains why nuclei beyond a certain size become unstable; it’s too difficult for pions to be exchanged across larger distances. Only in the case of neutron stars does the addition of gravitational binding energy suppress the nucleus’ tendency to rearrange itself into a more stable configuration.

Nuclear Force GIF

Wikimedia Commons user Manishearth

And on the scale of the atom itself, the key is that the lowest-energy configuration of any electron bound to a nucleus isn’t a zero-energy state, but is actually a relatively high-energy one compared to the electron’s rest mass.

This quantum configuration means that the electron itself needs to zip around at very high speeds inside the atom; even though the nucleus and the electron are oppositely charged, the electron won’t simply hit the nucleus and remain at the center.

Instead, the electron exists in a cloud-like configuration, zipping and swirling around the nucleus (and passing through it) at a distance that’s almost a million times as great as the size of the nucleus itself.

Wavefunctions of the electron of a hydrogen atom PoorLeno Wikipedia

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.

There are some fun caveats that allow us to explore how these sizes change in extreme conditions. In extremely massive planets, the atoms themselves begin to get compressed due to large gravitational forces, meaning you can pack more of them into a small space.

Jupiter, for example, has three times the mass of Saturn, but is only about 20% larger in size. If you replace an electron in a hydrogen atom with a muon, an unstable electron-like particle that has the same charge but 206 times the mass, the muonic hydrogen atom will be only 1/206th the size of normal hydrogen.

And a Uranium atom is actually larger in size than the individual protons-and-neutrons would be if you packed them together, due to the long-range nature of the electrostatic repulsion of the protons, compared to the short-range nature of the strong force.

Planet's axes are tilted at different angles axis

Image credit: Calvin Hamilton.

The planets of the Solar System, shown to the scale of their physical sizes, show a Saturn that’s almost as large as Jupiter. However, Jupiter is 3 times as massive, indicating that its atoms are substantially compressed due to gravitational pressure.

By having different forces at play of different strengths, you can build a proton, neutron, or other hadron of finite size out of point-like quarks. By combining protons and neutrons, you can build nuclei of larger sizes than their individual components, bound together, would give you. And by binding electrons to the nucleus, you can build a much larger structure, all owing to the fact that the zero-point energy of an electron bound to an atom is much greater than zero.

In order to get a Universe filled with structures that take up a finite amount of space and have a non-zero size, you don’t need anything more than zero-dimensional, point-like building blocks. Forces, energy, and the quantum properties inherent to particles themselves are more than enough to do the job.


Ethan Siegel is the founder and primary writer of Starts With A Bang!


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