What this covers
On Oct. 7, 2015, Perimeter Institute Director Neil Turok opened the 2015/16 season of the PI Public Lecture Series with a talk about the remarkable simplicity that underlies nature. Turok discussed how this simplicity at the largest and tiniest scales of the universe is pointing toward new avenues of physics research and could lead to revolutionary advances in technology.
Perimeter Institute (charitable registration number 88981 4323 RR0001) is the world’s largest independent research hub devoted to theoretical physics, created to foster breakthroughs in the fundamental understanding of our universe, from the smallest particles to the entire cosmos. The Perimeter Institute Public Lecture Series is made possible in part by the support of donors like you. Be part of the equation: https://perimeterinstitute.ca/inspiring-and-educating-public
Subscribe for updates on future live webcasts, events, free posters, and more: https://insidetheperimeter.ca/newsletter/
facebook.com/pioutreach twitter.com/perimeter instagram.com/perimeterinstitute Donate: https://perimeterinstitute.ca/give-today
Source description (no synthesized summary yet).
The universe exhibits astonishing simplicity at both extreme scales—the tiniest (Planck scale) and largest (cosmic horizon defined by dark energy)—yet remains complex in between, suggesting undiscovered simple principles that unify quantum mechanics and relativity and potentially explain phenomena like dark energy through new symmetries.
- Recent cosmological observations show the universe requires only one number (one part in 100,000) to describe its large-scale structure, making it simpler than a single atom
- Both Planck-scale physics and cosmological-scale phenomena exhibit unexpected regularity and scale-invariance, hinting at deeper unified principles
- The cyclic universe and scale-symmetry models offer potential solutions to the dark energy puzzle without invoking untestable multiverses
This asset isn't compiled yet
You're seeing its claims, ranked. Compile it to build the argument threads, weight them, and check each claim against your library — the full view.
Einstein's theory of gravity (general relativity), which describes spacetime as curved by matter, automatically implies that space itself can expand or contract, leading to the possibility of an expanding or contracting universe, a consequence Einstein himself did not immediately recognize until Alexander Friedmann derived expanding universe solutions from Einstein's equations.
“as soon as you do that if you make space and time time malleable you bring into being the possibility that the whole that all of the space in the universe came out of something much much smaller okay... it took Alexander Freedman a young Russian to stare at Einstein's equations and to realize that actually they can describe an expanding universe”
The variations in temperature and density measured across the cosmic microwave background sky exhibit 'synchronicity'—all oscillations were excited simultaneously at the Big Bang and have oscillated in phase ever since, analogous to a bell struck once whose vibrations remain synchronized, which we observe through Fourier analysis of the CMB power spectrum.
“see if you take if you take a bell which vibrates at various tones and you strike it all those vibrations are synchronized because they all got excited at the same time and so if you look at the pattern uh in in the in the sound of a bell you would be able to detect that it was struck at one moment and that's what happens with these variations of temperature they were excited at the big bang and subsequent to that they're all they they have oscillated a certain number of times”
Probabilities must sum to one in any valid physical model, and this constraint is preserved under time evolution if the system uses Pythagoras's Theorem: representing probabilities as a point on a unit sphere in multi-dimensional space ensures the sum of probability squares remains one as the point evolves on the sphere's surface.
“probabilities have to add up to one... you pick a circle or in this many dimensional case of sphere with a unit radius single radius and you say I'm going to associate to uh some property uh a real number and an imaginary number X Plus i y and because this uh lies on a on a sphere the sums of the squares are guaranteed to be one okay”
Paul Dirac developed an equation describing the electron as a relativistic quantum entity, leading to the prediction of antimatter and the discovery that all particles have corresponding antiparticles—one of the deepest insights in physics emerging from demanding consistency between relativity and quantum mechanics.
“Durak went to Princeton uh where he met Richard feinan very famous young American physicist... durak was socially pretty inept and uh he said the only thing he could think of saying to Fineman is um do you have an equation knowing of course that he had an equation D had an equation which describes three quarters of the known particles in the universe okay the dra equation”
Mathematics is logic crystallized, and the most proven ideas in mathematics are those derived through rigorous proof, whereas physics applies logic to the real world by discovering which mathematical rules nature actually obeys.
“what is what is mathematics after all mathematics is just logic it's the crystallization of logic the ideas which are considered proven in mathematics are the most proven things we know more or less by definition okay uh that's what what you mean by mathematical proof so physics is a little different okay physics is logic applied to the real world”
Art McDonald pioneered the Sudbury Neutrino Observatory and discovered that neutrinos from the Sun change their type (oscillate between flavors) during transit to Earth, proving neutrinos have finite mass and validating the precision of solar physics models—a discovery worthy of the Nobel Prize.
“he built the world's top laboratory for studying neutrinos in Sudbury and they discovered uh how neutrinos work how they they travel from the Sun to us how they change uh flavors on the way and this is really an incredible pointer to new physics beyond the standard model”
The universe is defined by two extreme scales: the largest scale is approximately 10^25 meters, defined by dark energy and the cosmic horizon beyond which we can never see due to accelerating expansion, and the smallest scale is the Planck length of approximately 10^-35 meters, the scale at which quantum gravity effects become dominant and space-time breaks down.
“there is a scale there's a fundamental scale in physics it's it's the scale defined by the dark energy which limits the region of the universe we will ever see and so that's the largest scale uh we know of it's about 10 ^ 25 U uh meters the tiniest scale we know of in the universe is what we call the plank scale”
Time dilation—the slowing of time for objects moving at high velocities—is a direct consequence of relativity: observers watching a fast-moving object will measure its internal time as passing more slowly than their own, a counterintuitive but empirically confirmed effect.
“if you want to stay young you travel a lot okay because then the uh time you between the Beats of your heart will will be much longer okay for somebody else watching you”
As a theorist, one should be happy when proven wrong because it means the idea was testable and worth discussing; if an idea cannot be proven wrong, it is not worth talking about, which makes supersymmetry predictions at the LHC valuable even if they are not detected.
“as a theorist you should be happy when you're wrong because at least it meant your idea was testable was worth talking about okay it was worth talking about I mean if you can't be proven wrong it's not worth talking about”
The Pythagorean theorem applies not only in two dimensions to triangles but also in any number of dimensions, such that for a three-dimensional box the sum of the squares of the three edge lengths equals the square of the long diagonal, and this multi-dimensional generalization becomes crucial for quantum mechanics.
“one thing I didn't tell you about Pythagoras's Theorem is it actually works in any number of Dimensions you might think it only works in two dimensions for triangles but actually if you made a box a three-dimensional box and you measured the long diagonal the Pythagoras Theorem would still work that the sums of the square of the three edges of the box would equal the square on the diagonal and actually works in any number of Dimensions”
Euler's formula—that the exponential of an imaginary number (e^(iθ)) equals cosine plus i times sine—connects differential equations (which give exponentials), algebra (the imaginary number), and geometry (circles and trigonometry) into a single unified statement, and has been called the most beautiful formula in mathematics.
“when you exponentiate the imaginary number it goes around in a circle... the exponential of an imaginary number times Theta... it gives you the trigonometric functions cosiness and signs... this formula here connects differential equations which give you exponentials to algebra which gives you I to Geometry which gives you these okay it's been called called the most amazing formula in mathematics”
In physics, everything is fundamentally a wave: particles like electrons obey wave equations, and every entity in nature possesses wave-particle duality, existing as both a traveling wave and a discrete particle, though humans do not typically feel this wave nature because our de Broglie wavelengths are extremely small.
“in physics everything is a wave because when particles like the electron um were understood better uh by uh Paul D who found out the equation describing the electron what did he do he tried to write down a wave equation uh that was the root to discovering the electron oyss a wave equation even though it's a particle uh every entity we know on of in nature has this dual facet it's both a wave it travels along like the waves I showed you um and it's also a particle and so uh uh every particle we know has this property in fact you have this property you probably don't feel like a wave but I can assure you you are a wave according to Quantum Mechanics you're a wave and it spreads”
Particles in the standard model are classified by their spin: spin-0 particles (Higgs boson) do not spin; spin-1/2 particles (electrons, neutrinos) have minimal angular momentum; spin-1 particles (photons) are light; and spin-2 particles (gravitons) describe gravity, with higher spins (e.g., spin-3/2) being problematic for field theory and requiring string theory for proper description, for which there is no evidence.
“there are particles which don't have any spin the higs boson is one... they're these kind of particles that spin half like the electron and neutrinos... photons which have spin one and gravity happens to have spin two... three halves is a little bit of a problem... essentially this is all that's possible... Spins Beyond two seem to be uh not possible with field Theory you need strength theory for which there is no evidence”
Theories that cannot be proven wrong through any conceivable experiment describe untestable and therefore likely meaningless concepts; such theories violate the principle of economy in science and are likely signs that the underlying formalism is fundamentally flawed.
“the one thing we've learned in physics is that if you talk about Concepts which are untestable through any conceivable experiment you're probably not making sense okay it's at the very least it's uneconomical because you're having to talk about stuff which could never in principle ever be probed but it is more likely a sign that your whole formalism is wrong”
Planck's constant can be empirically determined by measuring the Sun's temperature, the wavelength of visible light it emits, and knowing the relationship E = hf, then calculating h directly—demonstrating how nature itself reveals fundamental constants through observable phenomena.
“we know the um we know the temperature of the sun we know the energy which is carried by the uh by uh by each uh light wave it's given by the temperature and uh we also know the frequency of visible light just take the ratio and you get planks constant okay so the sun directly tell if we know the temperature and we know the wavelength of light we just read off planks con from the Sun”
Some physicists propose the multiverse hypothesis to explain dark energy fine-tuning: if infinite universes with different physical constants exist, observers inevitably find themselves in a universe fine-tuned for life, making the observed fine-tuning unsurprising rather than mysteriously fortunate, but this approach sacrifices predictability and is called by some 'the end of physics'.
“some people propose a Multiverse and this is called by some the end of physics that they say look there some basically what they're saying is some things we'll never explain so let's just postulate that there are infinite number of possible universes and we happen to be in one that came out like this okay... the problem with this theory is that it can't make any predictions nobody can Define probabilities there's no Pythagoras theorem in this Theory it really is just wild Randomness”
The fundamental equation of physics (the Lagrangian of the standard model) summarizes nearly all known physical phenomena in a single mathematical expression containing Einstein's theory of gravity (spacetime curvature), Maxwell's electromagnetic theory, the weak and strong nuclear forces, and Dirac's equation for electrons, making it the most compact summary of known physics.
“these ideas of quantum mechanics and relativity led to this equation this is the equation which summarizes all the physics we know uh uh it is a simple equation I can assure you it is amazing that there are almost no phenomena in nature which we know of which cannot be described by this equation”
Atomic clocks using optical lattices—arrays of atoms trapped and cooled by lasers—can now reach accuracies of one part in 10^18, making them more than 10 times more precise than the best traditional atomic clocks, and these devices enable construction of extremely sensitive detectors for fundamental physics.
“clocks using atom Atomic uh Optical luses atoms in Optical luses can now reach accuracies of um better than 1/10th of a second over the age of the universe so these clocks are accurate to one part in 10 to the 18 in precision”
Measurements of vacuum stability using the LHC-measured Higgs mass show that our universe's vacuum is stable for approximately 10^500 years before potential quantum tunneling to a lower-energy state could occur, a timescale so enormous that it is not a practical concern for the future of our universe.
“according to the measurements at LHC the vacuum we're in is stable for 10 to the^ 500 years okay it's a long time um do we take that seriously iously I don't know”
A sinusoidal wave—used to model oscillatory phenomena like the motion of pendulums, vibrating strings, and light waves—emerges directly from Euler's formula and trigonometry through the relationship e^(iθ), demonstrating that the real part traces out oscillatory motion as the angle θ increases.
“if I use that real part to model a wave which is traveling which is also traveling upwards as its amplitude is going back and forth I get what we call a sinusoidal wave so the wave is now following this function which came out of trigonometry through this uh construction”
Neutrino masses, tiny though they are, provide tantalizing clues toward unification of physics at the Planck mass scale where quantum gravity becomes relevant, but current experiments are far too low-energy to directly probe this regime of unification.
“there are a few other little details neutrino masses uh I already pointed to these are Clues towards unification these neutrino masses are pointing towards unification at the plank Mass I mean it's it's very tantalizing but it's also very remote from any current experiment”
Violating unitarity in physics—allowing probabilities to diverge from a sum of one—is the most fundamental violation possible in theoretical physics, causing a physicist who violates unitarity to be 'in big big trouble'.
“if you're a physicist and you violate unitarity you're in big big trouble okay”
Maxwell's equations of electricity and magnetism predict that light exists and travels at a specific speed determined by the electromagnetic constants, and this prediction was validated experimentally to within a few percent, making it the greatest discovery in physics because it shows how to predict entirely new phenomena from first principles.
“when Maxwell discovered the equations of electricity and magnetism the astonishing he Discovery he made as a as a consequence of figuring out the right equations was that he could describe light and... Maxwell showed the known laws of electricity and magnetism gave rise to light and they predicted its speed and it was correct within a few percent uh so that I call the the greatest discovery in physics of all time”
If light were purely a wave as Maxwell's theory suggests, the sun and all hot objects would radiate all their energy into infinitely short wavelengths (a problem called the ultraviolet catastrophe) because there are infinitely many possible short wavelengths and thermal equilibrium would distribute energy equally among all modes, causing the sun to cool instantly—but the sun exists stably because light carries energy only in discrete packets (quanta).
“if Maxwell was right was absolutely right that light was a wave and that was the end of the story none of the world we know would work... the trouble is that if you allow waves of arbitrary wavelength you can fit an arbitrary number of those waves into any volume of space... the trouble is If there really was this Infinity of possible short waves they would carry the heat of the Sun away in an instant... if Maxwell was true the sun couldn't exist”
The vacuum of quantum chromodynamics contains gluon fields everywhere, and these gluons are responsible for holding together atomic nuclei; without this vacuum structure, nuclei would fall apart—demonstrating that 'empty' vacuum has real physical energy.
“what holds particles together in atomic nuclei is something called qcd Quantum chromodynamics... it has Fields called gluons which do this and they're everywhere in the vacuum and if these things weren't there in the vacuum then nuclei would fall apart so we know the stuff is there we know it has energy”
The vacuum energy density calculated from quantum field theory (energy contributions from electron fields, electromagnetic fields, Higgs field, and gluon fields in quantum chromodynamics) sums to an incredibly tiny number—0.0000...0001 with 120 zeros—yet because vacuum permeates all space, this tiny density dominates the universe's energy budget.
“if these things weren't there in the vacuum then nuclei would fall apart... we know the stuff is there we know it has energy we can calculate the energy in these fields in the vacuum and it's a large number it's a very large number... somehow all of these vacuum energies add up to this okay they add up to 0.0000 with 120 zos one so the vacuum energy is Tiny in any sensible units it's ridiculously small but because there's so much of it it fills all of space it overwhelms everything else in the universe”
In an expanding universe where space itself stretches, light waves emitted in the early universe have their wavelengths stretched along with spacetime, causing them to become increasingly redshifted as space expands, which is how we observe the light from the Big Bang today as the cosmic microwave background.
“in an expanding universe space itself expands what I've drawn here is light coming out of the big bang and those light waves as the universe stretches their wavelength is stretched along with space they get longer and longer”
The imaginary number i, whose square equals negative one, was initially discovered as a trick to solve polynomial equations in 16th-century mathematics competitions, but once introduced, it reveals a profound truth: any polynomial equation of degree n has exactly n solutions in the complex numbers, known as the fundamental theorem of algebra.
“there was a guy uh who um at the time who discovered that if he imagined a number whose square was minus one then he could actually solve lots of equations... this number I the imaginary number came into being... once you've introduced it you can solve all equations okay... any equation which say I wrote down x^ 23 plus some number time x 22 and so on equals z there will be 23 Solutions of that equation”
Niels Bohr resolved the classical paradox that electrons orbiting nuclei should radiate energy and collapse by proposing that electrons occupy standing wave modes around the nucleus with discrete wavelengths fitting integer numbers of wavelengths in the orbit, giving rise to quantized energy levels that match observed atomic spectra.
“Neil's bore was uh trying to think about the atom the atom didn't make any sense from a classical point of view because the electron which is orbiting the nucleus would emit radiation and spiral inwards... so um the one thing you know about waves is they have standing waves... waves naturally come in these discrete U modes... Neil's B did did he imagined the hydrogen atom... when it goes around it can go around in a certain number of wavelengths... he conjectured were the energy levels of the hydrogen atom”
The constancy of the speed of light for all observers (predicted by Maxwell's equations) contradicts Newtonian mechanics, which predicts that relative velocities should add, and this paradox led Einstein to develop special relativity by recognizing that time and space are not absolute but depend on the observer's motion.
“if I know the speed of light that immediately doesn't make any sense in Newtonian theory of mechanics... in the Newtonian Theory which is the common sense theory if something is traveling at a certain speed and I travel afterwards its speed will go down... but it's absolutely wrong okay because light travels at the speed of light no matter how fast you chase after it... from Maxwell's equations Maxwell's equations predicted the speed of light... the only reason you can predict a speed is because that speed is the same for anybody... that gave rise to the theory of relativity”
Einstein's photoelectric effect explanation confirms Planck's quantization hypothesis: when light of a specific frequency strikes a metal surface, it ejects electrons all with the same energy determined by Planck's constant times the light frequency, demonstrating that light energy comes in discrete, indivisible packets (photons).
“the experiment is called a photoelectric effect you shine light at some frequency onto the surface of a metal... and the light hits the surface of the metal and it kicks out these electrons... what happened in the experiment was a very strange thing is that if you shun a certain wavelength and frequency of light onto the metal you got off you got out electrons of only one energy okay and the energy was given by the same constant Plank's constant times the frequency of the light”
Within the next two years, gravitational wave detectors will image black hole mergers and collisions, and within five years will detect gravitational waves from neutron star mergers, ultimately enabling detection of gravitational waves reaching back to the Big Bang itself.
“we're seeing black holes uh within the next two years we will have images of black holes I think you saw those on the slide before this lecture from a young researcher here and we're going to see gravitational waves within the next 5 years gravitational waves telling us what happens when black holes merge uh and and uh Collide and and also with neutron stars and ultimately we'll be able to use these gravitational waves to look back to the Big Bang itself”
Quantum computers using qubits (quantum bits) instead of classical bits exploit the quantum properties of individual particle spins to explore a superposition of computational states simultaneously, potentially making quantum computers vastly more powerful than digital computers for certain problems.
“we're all excited about quantum computers and manipulating uh cubits instead of bits so instead of the the closest analog to the zeros and ones in your computer uh the simplest element of quantum reality is a single spin of a particle... if you build a computer out of these things it will be vastly more powerful uh than uh anything built out of digital technology”
Black holes form when matter collapses under gravity to create a singularity, and it is possible that singularities within black holes represent the birthplace of new universes—a speculative but mathematically permissible possibility.
“there's also the question of when you make a black hole you know when matter collapses to make a black hole inside the black hole you get a singularity and we don't yet know what happens there it could be that that's the birthplace of a new universe uh we we don't know enough”
The simplicity of mathematical theorems like Pythagoras's theorem is connected historically to the development of justice and proof in ancient Greece, because mathematical proof and the requirement to produce conclusive evidence before convicting someone are logically parallel concepts, suggesting that logic, mathematics, and justice are deeply intertwined.
“a friend of mine in Africa once told me that this uh the significance of proof mathematical proof it's a African mathematician mathem medical proof is connected to Justice because in ancient Greece one of their Innovations was that you couldn't just accuse someone of something without showing without arguing without conclusively producing evidence that they've done something wrong so idea of proof came along at the same time as mathematical proof so logic and Justice are actually very closely interconnected”
The universe exhibits astonishing regularity and predictable behavior on the largest and smallest scales, which physics does not yet understand, but this behavior points toward undiscovered simple principles that will eventually be discovered.
“I hope to share with you the some of the most amazing discoveries we have made recently about the universe and the fact they're pointing Us in new directions for our understand understanding of the universe uh which is extremely exciting... the universe has regular um predictable Behaviour which we do not yet understand and so this is pointing us as at new simple principles which we're trying to discover”
The ishango bone, carved 22,000 years ago in the Congo with 60 notches on each side in particular arithmetical patterns, represents the earliest evidence of mathematical thinking and the study of number patterns by humans.
“somebody in the Congo carved these markings on a bone the ishango bone um there are 60 notches on either side of the bone in very particular arithmetical patterns and uh so and people who've uh analyzed the bone have concluded that that this is not a coincidence they weren't they weren't just uh playing with notches they were studying uh patterns in numbers so that's uh that's the beginning of mathematics”
Dark matter comprises 25% of the energy density of the universe and clusters around galaxies, but its composition is completely unknown; experiments at the SNO lab are searching for various candidate particles to identify dark matter, making it one of the great mysteries of physics.
“we have the dark matter there's 25% of the energy in the universe is in stuff which clumps around galaxies and we don't know what it is... experiments at Art MacDonald's lab snow lab are searching for all different different candidate many different candidates of Dark Matter”
A new theoretical model proposes that the universe can bounce: it contracts with light waves overlapping into a singularity, then bounces back and expands, and this is mathematically consistent because light has no intrinsic scale—the universe's shrinking is invisible to light due to the scale-invariance of Maxwell's equations.
“we've just put a paper out describing how a universe can Bounce It uh it can contract with the light waves going down and bounce again uh mathematically this is allowed um it looks pretty bad when all the light is on top of itself but you'll remember that light doesn't have a scale you see so whereas we would look at the universe and say it's shrinking in fact the light doesn't see the shrinking it's due to the scale independence of Maxwell's equations”
Most theoretical physicists are dismayed by recent discoveries showing the universe is simpler than predicted models, because the models were predicting specific features that didn't materialize—for example, the Higgs boson was found to be 'lonely' without the many companion particles most theorists predicted would accompany it.
“most theorists I know are dismayed by this because it means that most of the models have turned out wrong because the models were all predicting oh you should get this or that or this specific feature or that specific feature and uh what's happened is the universe has surprised everyone that it's it's simpler than any of our models can explain the same thing happened at the large hron collider and I'm not going to dwell on it but they were looking for the higs boson they found the higs boson most of the theorists in the world were predicting lots of other particles would come along with the higs boson uh but the higs is pretty lonely”
Theoretical physicists pursuing fundamental physics should expect to sacrifice practical career flexibility for the opportunity to work on the deepest questions; however, this sacrifice is not wasted because the rigorous thinking and sophisticated mathematical training developed during theoretical physics research make practitioners highly capable in almost any field, so few theoretical physicists face unemployment after leaving the field.
“I would probably say what I was advised which was only go into this if you don't mind uh sacrificing your career... he well knew that... the truth is theoretical physics is deliberately you know when you go into it you're deliberately taking on the most difficult challenging impossible problems... in the process of doing that you learn a vast amount of stuff... you just have to look at the career trajectories of people who leave theoretical physics and I don't know a single one of them who's unemployed”
The universe to describe its large-scale structure requires only one number—the variation in density across space is one part in 100,000—which is fewer parameters than needed to describe a single hydrogen atom, making the universe the simplest object we know of.
“the whole universe is as simple as an as the simplest atom if you think about a hydrogen atom you know how many numbers do you need to describe an atom an atom is a pretty simple thing... well it turns out the universe to describe the structure you need one number which is this number one part and 100,000 that number describes the structure of the universe uh fewer numbers than you need to describe a single atom so the universe turns out to be the simplest thing we know”
In the first billionth of a second after the Big Bang, smooth acoustic waves filling space evolved into sharp shocks through nonlinear dynamics, and these shocks then collided to generate interesting physical effects including vortices and potentially gravitational waves.
“this is trying to calculate what happened in the first billionth of a second after the big bang... the beginning of the movie are these smooth waves filling space... but as they evolve you see they form shocks sharp edges and these shocks then collide and they will generate all kinds of interesting effects”
The fundamental question of physics is: 'How did everything come out of nothing?'—a profound puzzle that is astonishingly difficult to address because we lack observational access to the boundary conditions of the universe itself.
“I want to end just by talking about something I'm most interested in which is this guy the tiniest puzzle in science uh how did everything come out of nothing uh it's very puzzling indeed”
Light exhibits wave-particle duality: it behaves as a wave during propagation (showing interference patterns through two slits) but collapses into a particle and delivers energy in discrete quanta at the moment of detection, acting as a 'possibility wave' that explores all options but is choosy about when and where it delivers energy.
“light is neither a wave nor a particle it's a little bit of both I like to think of the wave part of it as the exploratory part okay so it spends all of its time exploring all its options but it's pretty choosy about when and where it delivers and when it does it can only deliver in uh fixed amount and so it's a possibility wave that's what the waves are”
Physics transitioned from determinism (classical mechanics' mechanical worldview) to probabilism (quantum mechanics), but quantum probabilities are precisely predictable and not random: one can predict probabilities with extraordinary precision, making quantum mechanics deterministic at the probabilistic level rather than at the individual event level.
“physics made this jump from determinism or the classical picture of the world as a machine to another picture which is that physics is about probabilities but these probabilities when you say probability you you tend to think of Randomness and chaos and you know unpredictability it's not like that it's actually beautifully precise um the probability is is You can predict the probabilities with extraordinary Precision okay so it's not uh total chaos by any means”
The Large Hadron Collider probes scales of 1 billionth the size of an atom (13 TeV energy scale) and is searching for dark matter candidates and new particles beyond the standard model, with results expected within the coming years, representing humanity's most direct probe of physics beyond current theory.
“here is uh LHC it's running again this year it's tremendously exciting it's probing scales of 1 billionth the size of an atom uh 13 teev and they hope to see new particles we may we're waiting with baited breath”
A theoretical physicist is 'an imaginary person' while an experimental physicist like Art McDonald who 'builds things' is a 'real person,' reflecting the distinction that theoretical physicists work with abstract mathematical structures while experimentalists construct material apparatus to test reality.
“I'm what I call an imaginary person and I'll explain that more in the talk... art art really builds things and in many ways he pioneered what we're trying to do at Perimeter he built the world's top laboratory”
The simplicity Turok discusses refers to concepts that unify diverse ideas and knowledge, allowing physicists to explain maximum phenomena from minimum assumptions—not simplicity in the sense of surface-level ease, but rather elegant unification and compression of knowledge.
“for a physicist Simplicity means or simple concepts are Concepts which unify they bring together dis disperate ideas and disperate knowledge make sense of them and simplify I often like to say that uh theoretical physicist is somebody who has a terrible memory and therefore the they want to make sure they're on top of everything while they remember nothing and or it's little as possible so simple concepts are ones which uh which allow us to explain the most we possibly can from the least possible number of assumptions”
In a right-angled triangle, when a perpendicular is drawn from the right angle to the hypotenuse, the two smaller triangles created share angles with the original and with each other, making all three triangles similar in shape; since areas scale with the square of lengths for similar shapes, this forces the relationship a² + b² = c².
“if two angles are the same in two triangles the third angle is fixed okay so it means that all three angles in all three triangles have to be the same therefore the triangles must be the same shape... the area of this triangle is b^ 2 * some number the area of this one is c^ 2 time the same number and a s * the same number... you see immediately that because the areas of the two smaller triangles are the same as the bigger triangle you must have this formula”
Extending numbers to include both real and imaginary parts (X + iY) creates a two-dimensional space of complex numbers, allowing geometric visualization of algebraic relationships and providing the mathematical foundation for describing oscillatory phenomena in nature.
“we have a number X which could be any number from minus infinity to Infinity an ordinary number and then we have another kind of number which is a multiple of I so uh and we put the two things together we say I'm going to allow numbers which are have a real part the X part and the imaginary part which is the multiple of I okay so the dimension suddenly I've gone to numbers not being on a line then they're now in two Dimensions”
The exponential function—where the rate of change of a quantity equals the quantity itself (dy/dx = y)—is the simplest differential equation and has solution y = e^x, where e ≈ 2.718 is Euler's number, and this function describes any naturally occurring exponential growth or decay.
“the derivative of a function meaning the slope is equal to the function so it's telling you that how much the function will change as you increase uh the go along in X the change in the function is proportional to the function solution of that equation is this exponential function”