This video masterfully distills the stochastic complexity of particle decay into a clear hierarchy of conservation laws and fundamental interactions. It is an essential primer that respects the rigor of physics while maintaining exceptional clarity.
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What Decides How Long a Particle Can Exist?
Added:Imagine two particles side by side. Both are fundamental. Both were born the same way in the same instant out of the same collision. From the outside, they look like siblings. But one of them will survive for essentially the entire age of the universe. The other will vanish before it has traveled a distance smaller than an atom. There is no clock ticking inside either one, no fuel gauge running down, no internal timer counting towards zero. And yet nature has already decided with astonishing precision [music] how long each of them gets to exist. Some particles live for billions of years. Some live for a fraction of a fraction of a second. And the strangest part is this. Identical particles created in identical ways still die at wildly different ages. What decides how long a particle is allowed to exist?
Before we go any deeper, if you're enjoying these journeys into the strange rules that shape our universe, a quick like or subscribe really helps the channel grow. It's a small thing for you, but it makes a huge difference for me. Also, we're now live on Spotify. The links in the description if you'd like to listen to us wherever you are. Now, let's begin. Picture a laboratory somewhere in the world. A particle accelerator is running. Inside, protons are being smashed together at nearly the speed of light. Out of the wreckage of these collisions, new particles pour forth. Hundreds of them, thousands of them. Some of them survive long enough to travel through detectors and leave visible tracks. Others vanish so quickly that we never see them directly. We only see the debris they leave behind. The daughter particles they decayed into.
Now imagine two of these new particles born in the same collision in the same instant. They emerge from the chaos side by side. Both are what physicists call fundamental particles. Neither one has any known internal structure. Neither one contains smaller parts. Both were created equally from pure energy following the same physical laws. In every important way that we can measure, they look like siblings. Their masses may differ. Their charges may differ.
But they are equally fundamental, equally basic. Neither one has any right to be considered older or younger than the other, or more or less complete, or more or less worthy of existence. And yet, one of them will live forever.
or at least so close to forever that the difference does not matter. [music] It will survive as long as the universe survives. It will still be there long after the last star has burned out. Long after the last galaxy has faded to dust, long after the cosmos itself has grown cold and dark. The other will disappear in a time so short that light itself traveling at 300,000 km/s cannot cross the width of an atom before it is gone. It vanishes in a fraction of a fraction of a fraction of a second. By the time your brain has registered its existence, it has already ceased to exist. It has left the stage before you were aware that a stage existed.
Same laboratory, same instant, same physical laws. Two particles equally fundamental. And nature has already decided before either of them has moved at all that one gets >> [music] >> essentially infinite time and the other gets almost none. That is the mystery we are going to explore. And to explore it properly, we first have to strip away almost everything most people assume about how unstable particles work.
Because when we hear the word decay, our minds reach for familiar images. A piece of fruit sitting on a counter slowly softening. A rusting car. A radioactive lump of material. In every one of these cases, we imagine some process happening internally. Something is being used up.
Some structure is breaking down bit by bit. The fruits cells are running out of something. The metal is losing atoms to the air. The uranium is somehow deteriorating from within like a candle burning down toward its final flicker.
And so we assume the same must be true for particles. We imagine that an unstable particle contains something that is slowly running down. that there is a little clock ticking inside it, counting down toward the moment of destruction. That the particle is aging in some way, growing more fragile with every passing nancond until finally it cannot hold itself together anymore and it falls apart.
This picture is wrong. It is not just slightly wrong. It is completely fundamentally wrong.
There is no clock inside a particle.
There is no fuel gauge. There is no counter ticking down. There is no internal structure that gradually weakens.
A muon that has existed for one nanocond is not one bit more likely to decay in the next instant [music] than a muon that was just born. The particle does not age. It does not get tired. It does not deteriorate.
It does not know how long it has been alive. And even if it did, [music] that information would not matter to its fate. This is what physicists mean when they say quantum decay is memoryless.
The universe does not keep track of how long a particle has been alive. Each moment is a completely fresh start.
The past does not exist as far as the particle is concerned. Every single instant, the question of whether it will survive the next instant is asked again from scratch with no reference to anything that has come before.
When physicists first began to work this out in the early 20th century studying radioactive materials, they found the result deeply disturbing. It clashed with everything classical physics had taught. In the older worldview, if you knew enough about the state of a system, you could, in principle, predict what it would do next. A perfectly detailed description of a uranium atom, they had assumed, should reveal exactly when that atom would decay. But no such detailed description was ever found. And eventually, the community was forced to accept that no such description exists.
The decay is not determined by anything hidden inside the atom. It is genuinely irreducibly probabilistic.
So if there is no clock and no aging [music] and no gradual deterioration, then what is actually going on? What actually decides when a particle disappears?
The answer, and this is the beginning of everything we are going to build tonight, is that decay is not a scheduled event. It is a probability, [music] a pure quantum probability.
Every unstable particle carries with it a specific unchanging chance of decaying in any given moment. That chance is fixed by nature. It never grows. It never shrinks. It never depends on the particle's history. It is simply there, built into what the particle is. The same way its mass and its electric charge are built into what it is.
Think about it like this. Imagine you have a very unusual coin. Every [music] second the coin flips itself. If it lands one particular way, nothing happens and the coin keeps flipping. If it lands the other way, the coin ceases to exist.
Now, the coin does not care how many times it has already flipped. It does not remember the previous outcomes. It does not become more likely to disappear because it has been flipping for a long time. Every second it just flips again.
And every flip is independent of every flip that came before. That is roughly what an unstable particle is doing.
Except instead of flipping once per second, it is being asked the question of survival continuously.
every possible fraction of time, in every possible instant, the question comes up. And the probability of decay in that fraction of time is completely determined by the type of particle it is. Some particles have an enormous probability of decaying quickly. For them, the coin lands the deadly way almost immediately.
They exist for a fraction of a second and are gone. Others have a much smaller probability.
For them, the coin has to flip an enormous number of times before it happens to land the deadly way. They can survive for micros seconds or milliseconds or seconds or years. And some have a probability so vanishingly small that we have never seen them decay at all. They might have some tiny chance of decaying or they might be truly stable, meaning the probability really is exactly zero.
In [music] either case, we can wait around forever without seeing it happen.
Now, because this is a probability rather than a scheduled event, we need a way to describe how quickly on average a given type of particle disappears.
And this is where two closely related but slightly different ideas come in.
One is called the mean lifetime. The other is called the half-life.
Both are used constantly in physics and both are trying to capture the same underlying reality from slightly different angles.
Let us start with the half-life because it is the more familiar of the two. The half-life of a particle is the amount of time it takes for half of a large collection of those particles to have decayed.
If you start with 1 million muons and the halflife of a muon is a certain number of micros [music] then after that many micros you will have roughly 500,000 muons left. After another half-life you will have about 250,000 left. After another about 125,000 and so on. Each successive half-life removes half of whatever was still there.
Notice that this is a statistical statement. It does not say that any particular muon lasts exactly that long.
It does not say that all of them die at the same age. It says that if you have a lot of them, half will be gone after one half-life.
Which half? Nobody can predict. Which particular muon lasts three half- livives and which one lasts only a hundredth of a halfife?
Nobody can predict that either. All you can say is what fraction of the total population will remain after a given time.
The mean lifetime is a slightly different way of describing the same thing. It is essentially the average lifespan of the particles in a large collection.
If you took every single muon in your sample, waited for each one to decay, wrote down how long each one lived, and then averaged all those numbers together, you would get the mean lifetime.
The two numbers are closely related, but they are not the same. The mean lifetime is a bit longer than the half-life by a specific mathematical factor.
The reason has to do with the shape of the decay curve. When you plot the number of surviving particles against time, you get a smooth curve that starts high and decreases forever, never quite reaching zero.
It falls quickly at first when most particles are still around and many of them are being lost to decay.
Then it falls more slowly as fewer and fewer are left.
The half-life measures how long it takes to fall to half its starting value. The mean lifetime is the average time each particle spends before decaying. And because a small number of particles happen to live for a very long time, they pull the average up slightly above the half-life.
Both quantities describe the same underlying probability.
Both are ways of translating a fixed per instant chance of decay into a number you can put on a chart and compare between particle types.
When physicists write down a table of particle properties, they usually list the mean lifetime.
But you can convert one into the other with a simple multiplication.
What matters and what I want you to hold on to is that both numbers are averages.
Neither of them predicts what any individual particle will do. They only describe the statistics of large populations.
And this brings us to something that used to bother physicists deeply and that still bothers philosophers today.
If nature has already decided the probability of decay for every particle but has not decided when any particular particle will decay, then what is actually happening in each individual case?
What makes the difference between the muon that lives for a nancond and the muon born in the same instant [music] that lives for a microcond? The honest answer according to our best theory is nothing. Nothing at all makes them different. They are in every measurable respect identical. There is no hidden variable inside them that distinguishes them. There is no secret set of instructions that one carries and the other does not. Nature simply produces a random outcome and the two particles happen to fall on different sides of that randomness.
This is one of the strangest and most unfamiliar features of quantum physics.
When we look at large scale objects, we are used to the idea that if two things behave differently, it must be because they were somehow different to begin with. Two dice that land on different numbers had slightly different starting positions or slightly [music] different spin. Two apples that fall from a tree at different times were slightly different in how they were attached.
The differences were always there, hidden but real. And if we had complete information, we could have predicted the outcome.
Quantum mechanics tells us this is not true at the deepest level. Two truly identical particles can behave completely differently and there is no hidden difference that we are missing.
Nature itself is probabilistic.
The universe does not have a pre-ordained answer for when each individual particle will decay. It simply has a probability and the outcome unfolds moment by moment live in real time with no script.
Now this can feel unsettling the first time you really absorb it. It certainly unsettled the physicists who first discovered it. Einstein famously refused to accept it, insisting that God does not play dice with the universe. But the experimental evidence accumulated over more than a century now has pushed us further and further in the direction of accepting that at the deepest level this really is how nature works. Individual quantum events do not have determined outcomes. They have probabilities. That is all. And this has a strange elegance to it as well. It means that the story of any single particle is genuinely a story. It has not been written in advance. It is not a recording being played back. Each moment of the particle's existence is a real live event with an outcome that even the universe has not fixed until it happens.
It also explains something that would otherwise be a huge puzzle. Namely, why do identical unstable particles die at such wildly different ages?
If they were like batteries, all charged to the same level and all draining at the same rate, they should all die at more or less the same time. A few% variation maybe from small differences in manufacturing, but not the enormous range we actually see. In a real sample of muons, some will decay almost immediately. Others will last many, many multiples of the mean lifetime.
The distribution of lifetimes stretches out enormously from essentially zero at one end to a long tail that fades gradually into invisibility at the other. This makes complete sense once you understand that each moment is an independent chance.
It is exactly like watching a stadium full of people flipping coins. Every second everyone flips. If they get heads they stay. If they get tails they leave.
On average, half the people will be gone after one flip. But some particular person might get 20 heads in a row and stay for a long time. Someone else might get tails on the very first flip and leave immediately.
There is no reason for the difference.
It is just how the coins happened to fall. Multiply this over billions and trillions of particles and you get the smooth exponential decay curve that physics students learn to draw.
It is a statistical shape built up from countless independent quantum events, none of which has any memory of any other. Zoom in on any single event, and it looks completely random. Zoom out to see the population as a whole, and you get a shape as predictable as anything in physics. The randomness and the regularity are two sides of the same coin. You need enormous randomness at the individual level to produce such perfect regularity in the aggregate.
There is one more subtle point that follows from all of this and it is worth pausing on. Because decay is a probability per unit time, the survival curve never actually reaches zero.
Mathematically, no matter how long you wait, there is always some tiny fraction of the original sample that has by luck avoided decay.
In practice, once you have waited many multiples of the mean lifetime, the number remaining becomes so small that no experiment can detect [music] it. But in principle, the tail of the distribution goes on forever. There is always some minuscule chance that a particular unstable particle [music] just happens to last a very very long time. This is a signature of the quantum world. Nothing is ever truly ruled out.
There are only probabilities. Some are essentially certain. Some are essentially impossible. But the numbers are always finite. Always describing chances rather than certainties.
So let us step back and take in what we have arrived at. When physicists talk about how long a particle can exist, they are not describing a scheduled event or a mechanical countdown. They are describing a quantum probability that is baked into what the particle is.
That probability is constant over time.
It does not change as the particle ages because the particle does not really age. It is the same particle at every moment of its existence with the same fixed chance of decay in the next instant. This probability when applied across a large population produces a smooth statistical curve. From that curve, we extract two closely related numbers. The half-life, which tells us when the population has dropped to half.
The mean lifetime, [music] which tells us the average survival time. Both numbers are properties of the particle type, [music] not of any individual particle. And both numbers vary enormously across the different types of particles that nature has produced.
Some particles have mean lifetimes so short they defy easy description. The tiniest fractions of a second, so brief that even a beam of light moving through empty space would barely have time to cross the width of an atomic nucleus before the particle was gone. Others live long enough to be measured with ordinary stopwatches.
Others still are so stable that we cannot even confirm they decay at all.
And we simply set experimental lower bounds on how long they must live if they are unstable. Bounds that stretch across time spans dwarfing the entire history of the cosmos.
And the question that will occupy the rest of our journey tonight is [music] why? What actually sets that probability?
What decides when a particle comes into existence [music] whether it will get a lifetime of an eternity or the briefest possible flicker? We have established what a lifetime is not. It is not a clock. It is not a fuel gauge. It is not a schedule. It is not aging. It is not deterioration.
The picture of a particle slowly wearing out is simply wrong. We have established what a lifetime is. It is a statistical consequence of a fixed quantum probability of decay per unit time. It is the average shape of what happens when many independent quantum coins are being flipped. But we have not yet asked what actually determines that probability.
Why is the probability enormous for some particles and vanishingly small for others? Why do some particles have essentially no chance of decaying at all? What ingredients does nature use to set that number? That is where we go next. Because the probability is not arbitrary. It is not chosen at random.
It is the outcome of specific physical rules. Rules about what a particle is allowed to become, what forces can drive the transformation, and what room the particle has to move into.
Every unstable particle sits inside a landscape of possibilities.
>> [music] >> and its lifetime is determined by the shape of that landscape. Some particles sit surrounded by wide open doors leading to lower energy final states.
Those particles decay quickly because there are many easy ways out. Others sit in tightly constrained regions with only narrow paths available. Those live longer because the ways out are harder to reach. And some particles sit in a place with no doors at all, no permitted lower energy state they are allowed to reach. Those particles [music] cannot decay at all, no matter how long you wait, because there is nowhere for them to go.
The rules of the landscape are not something a particle chooses. They are enforced [music] by the deepest laws of nature. And the first of those rules, the one that decides whether a decay is even permitted to happen in the first place, is what we will turn to next.
So a particle sits there holding within itself a fixed probability of decay per unit time. That probability, we said, is not arbitrary. Nature does not just pick a number and stamp it onto the particle.
The number emerges from something deeper, from rules, from constraints, from the shape of the landscape that the particle finds itself in. And the very first rule before we even get to how strong the interactions are, before we get to how much room is available, is a rule of permission. A particle cannot decay unless the decay itself is allowed.
Not allowed in some vague sense, not allowed because there is enough time, but allowed in the strictest possible sense. The universe has bookkeeping rules that must be satisfied. Every decay is a transaction and every transaction must balance. If the books do not balance, the transaction never happens. It does not happen slowly. It does not happen rarely. It simply does not happen at all.
This is one of the most important and least understood ideas in particle physics. So let us take our time with it because once you really see how it works, so many other mysteries fall into place, why some particles are stable, why others are not, why certain decays that seem intuitive never occur in nature, why the world has the specific ingredients it has and not others.
Let us start with the most obvious rule.
Energy has to balance. If a particle is going to decay into other particles, the combined mass and energy of those other particles cannot be greater than what the original particle had. This is conservation of energy and it is one of the deepest principles in all of physics. Nothing has ever been observed to violate it.
Every experiment ever done at every [music] scale in every corner of the universe we can probe has confirmed it.
For a particle sitting at rest, this means that the mass of everything it decays into has to be less than its own mass. If a particle weighs a certain amount and the products it would supposedly decay into add up to more than that, the decay simply does not happen. There is not enough energy to create those heavier products. The universe has no way to loan the particle the extra energy it would need. So the decay path is closed, sealed, not available.
Think of it this way. Imagine you have a certain amount of money. You cannot spend more than you have. You cannot buy something that costs more than your total wealth. It does not matter how much you want it. It does not matter how long you save. If the price is more than your balance, you cannot make the purchase. That is exactly what is happening with energy in particle decays. Every particle [music] has an energy budget given by its mass and it can only decay into products whose combined mass fits within that budget.
Anything more expensive is off the table. Now, this alone already tells us something profound. It tells us that if a particle happens to be the lightest possible thing in its category, it has nowhere to go. There is no lower energy state for it to fall into. And so [music] if there is no other rule pushing it to change, it must simply sit there unchanging forever.
But energy is only one of the bookkeeping constraints. The universe keeps track of more than just how much mass and energy there is. It also keeps track of electric charge.
Total electric charge is conserved absolutely everywhere, always.
This is one of the most rigorously tested rules in all of physics. No experiment has ever seen the total charge of a system change during any process.
If you start with a total charge of zero, you end with a total charge of zero. If you start with a total charge of one, you end with a total charge of one. There is no exception.
This means that when a particle decays, the charges of the products have to add up to the charge of the original. A positively charged particle can decay into a positive particle plus some neutral particles or into two positive particles and one negative or into some other combination that sums to positive.
But it cannot decay into products that add up to zero or to negative or to any charge other than what it started with.
Now combine this with the energy rule and already the landscape of allowed decays starts to narrow. A particle needs to find products whose combined mass is smaller than its own and whose combined charge equals its own. Not every particle in the universe qualifies. In fact, most combinations do not qualify. Nature is picky about what final states it will permit.
But the rules do not stop there.
Momentum has to be conserved. This is subtler than the previous two because momentum is a vector, [music] meaning it has both a magnitude and a direction.
But the principle is the same. Whatever total momentum a system starts with, it must end with. If a particle is sitting at rest, its total momentum is zero. So the [music] products of its decay must have zero total momentum, which means they cannot all fly off in the same direction. They have to arrange themselves so that their combined motion cancels out. This is why when a particle at rest decays into just two products, those two products always fly off in [music] exactly opposite directions, their momentum have to cancel. If they went off at some other angle, the total would not be zero and momentum would not be conserved.
Nature will not permit that. So the geometry of decay products is not a matter of coincidence. It is a consequence of a conservation law being enforced with perfect precision.
Then there is angular momentum.
Every particle carries a specific amount of intrinsic spin.
Spin is one of the strangest properties in quantum physics because it does not correspond to anything really rotating in the classical sense and yet it behaves mathematically as if it did. It has a magnitude and it has a direction and it obeys strict conservation rules.
When a particle decays, the total angular momentum of the products must equal the angular momentum of the original particle, taking into account both the intrinsic spins of the products and any orbital motion between them.
This can seem like an arcane detail, but it has real consequences.
It rules out entire categories of decays that would otherwise look perfectly reasonable on other grounds.
A particle with a certain spin cannot decay into products whose combined spins and orbital angular momentum cannot possibly sum to the same value. Nature will not allow the mismatch.
That decay channel is closed no matter how tempting it might seem.
So far we have four rules. Energy, charge, momentum, angular momentum. And already they are doing an enormous amount of work in shaping what particles are allowed to become. But there are more. Because as physicists studied particles more carefully over the decades of the 20th century, they discovered that nature was keeping track of quantities [music] that nobody had suspected existed.
Quantities that seem to have no analog in ordinary experience.
Quantities that were not obvious from the outside.
Yet they were being conserved with astonishing precision every time.
Consider a simple observation. The proton, the positively charged particle sitting inside every atomic nucleus, is heavier than an electron. Much heavier.
About 1,800 times heavier. If we look at the rules we already have, it would be perfectly allowed on energy grounds for a proton to decay into a posetron, which is the antimatter partner of an electron plus some radiation. The charges balance. The masses fit within the energy budget. Momentum and angular momentum can be arranged to work out.
And yet this decay is never observed ever. Physicists have watched enormous quantities of protons in giant underground detectors for years at a time, looking for even a single one to decay this way. They have never seen it, not once.
Whatever forbids this decay [music] is doing so with a strictness that dwarfs any experimental limit we have been able to set. If the proton does decay this way, its lifetime for doing so is longer than a number that already exceeds the age of the universe by many, many orders of magnitude.
So what is stopping it? Not the rules we have listed so far. Something else, something more subtle. The something else is that nature keeps a running count of what physicists call baron number.
Barons are a family of particles that includes the proton, the neutron and various others. Every baron carries a baron number of +1.
Every antibaron carries a barriion number of minus1.
Everything else has a barriion number of zero. And in every process ever observed, the total barriion number is conserved.
The proton has baron number one. The posetron being neither a baron nor an antibaron has barri number zero.
Radiation has baron number zero. So if a proton decayed into a posetron plus some radiation [music] the total baron number would go from one before to zero after.
That is not conservation. That is a violation and nature does not permit it.
This is why the proton is stable as far as we can tell. Not because it is somehow tougher than other particles.
Not because it has some special protective mechanism. It is stable because it is the lightest barriion.
There is no other barriion it could decay into that would have less mass.
And nature refuses to let the baron number change. So the proton sits there indefinitely held in place not by any force but by a conservation rule.
Similarly there is a quantity called leptton number. Leptons are another family of particles that includes electrons, muons and their more exotic cousins.
Every lepton has leptton number + one.
Every antilepton has lepton number minus1.
Everything else is zero.
And in every observed process, leptton number is conserved.
This is why the electron is stable. The electron is the lightest particle that carries negative electric charge. If it wanted to decay, it would need to find a product with less mass and with negative charge and with leptton number plus one.
But there is no such particle. The electron has nowhere to go. So it sits there forever protected by the combined weight of charge conservation [music] and leptton number conservation.
This is such an important idea that I want to underline it. When we say a particle is stable, we do not usually mean that it has some special property that makes it invulnerable.
We mean that it has no allowed exit. All the doors are closed. There is no lower energy state that satisfies every conservation rule simultaneously.
And because there is no permitted final state, the decay probability is exactly zero. Not small, not tiny, zero. [music] A stable particle is not one that has resisted decay for a long time. It is one that has never had the option to decay at all. Now, here is where things get subtle. Because the rule is not that particles decay whenever they can and refuse when they cannot. The rule is stricter than that. A forbidden decay is not something that happens rarely. It is something that does not happen at all.
There is no long wait during which it might occur. There is no small probability slowly ticking upward as time passes. If the decay violates a conservation law, the decay is simply not part of what the universe permits.
Waiting a longer time does not help.
Waiting a trillion years does not help.
Waiting forever does not help.
The path is not there.
Contrast this with a decay that is allowed. In that case, the probability per unit time is fixed. And given enough time, the decay will happen with essentially certainty.
A muon, if you wait long enough, will always decay because it has permitted exits available. Its lifetime is short.
But an electron, no matter how long you wait, will not decay because it has no permitted exits at all.
The difference is not a matter of degree. It is a matter of kind.
This distinction between allowed but slow versus completely forbidden is one of the sharpest lines in physics.
It shows up over and over again in nature.
Certain decays are seen, others are not.
The pattern of which ones happen and which do not turns out to be a beautiful map of the conservation laws that govern the world.
Let us look at one more example because it illustrates the point vividly.
The neutron which is the neutral partner of the proton is a barriion just like the proton. It has barriion number one.
When a neutron is bound inside a stable atomic nucleus, it is stable [music] because its energy is lower there than what it would take to escape.
But a free neutron, one floating on its own outside a nucleus, is unstable.
It decays with a mean lifetime of a little under 15 minutes. What does it decay into? A proton, an electron, [music] and an anti-utrino.
Let us check the books. Number one, the anti-utrino is an antilepton. So it has leptton number minus1.
The neutron had baron number one and leptton number zero. On the other side, we have baron number one and leptton number one minus one [music] which is zero. The books balance. The charge balances too because the neutron had zero charge, the proton [music] has +1, the electron has minus1, and the antiutrino has zero. Everything works out. And so the decay is permitted. It happens.
But notice what does not happen. A neutron does not simply decay into a proton and a photon. That would violate charge conservation because the proton has a positive charge and the photon has none. So the total on the right side would be + one but the total on the left was zero. It is forbidden. So it does not happen.
Nor does a neutron decay into two photons.
That would give a total lepton number and baron number of zero on the right side. But the left side had baron number one. So it is forbidden.
Nor does a neutron decay into a proton and an electron alone without the anti-utrino.
That would give total lepton number one on the right side. But the left had lepton number zero. Forbidden.
Only the specific combination that balances all the books is permitted.
Only that combination happens. And when we look at neutron decays in the laboratory, that is exactly what we see again and again and again.
The universe is meticulous.
The picture that emerges is this. Every particle sits in a landscape of possible decays, most of which are forbidden. A few of them are permitted, meaning they satisfy every conservation law. Those permitted decays are the ones that can happen. The forbidden ones simply cannot ever, regardless of how much time passes or what conditions you set up. The stable particles are the ones for which no permitted decay exists at all. the electron, the proton, as far as we can tell, certain neutrinos whose masses are so small that there is nothing lighter they could turn into while conserving leptton number. These particles are stable because the universe's conservation laws leave them nowhere to go.
This is a very different picture from the intuitive one. Intuitively, [music] we might think that particles are stable because they are sturdy or because they are simple. or because they have some special protective quality. But the actual reason is much cleaner and much more mathematical.
They are stable because the bookkeeping does not permit them to change into anything else that would have less mass.
That is all. That is the whole answer.
Take away one of the conservation laws and the same particles might become unstable.
Add a new conservation law and other particles might become stable that currently are not. This gives us an interesting way of seeing the universe.
The stable matter that makes up our world, the atoms, [music] the molecules, the stars, the planets, the living things is not stable because of any special mechanism inside them. It is stable because it happens to sit at a floor of the landscape of permitted transformations.
It has nowhere to fall further, no permitted way to become something simpler. So it [music] persists.
We live in a universe with a specific set of conservation laws. And those laws have produced a specific stable substrate on which everything else is built. Our existence is possible because of those exact rules.
The proton is stable. Because the proton is stable, hydrogen exists.
Because hydrogen exists, stars can burn.
Because stars burn, heavier elements can form. Because heavier elements form, planets and chemistry and biology can arise. And it all rests on a set of accounting rules that the universe follows with absolute strictness.
Now, physicists have not always known about all these conservation laws. In fact, several of them were discovered essentially by noticing what does not happen. Someone would look at a set of particles and think, "This decay should occur based on everything we know, but we never see it." Then they would look for a pattern. They would notice that all the decays we do see share some feature that the missing decays do not share. And from that pattern, they would extract a new conservation law. That is how barrier number was discovered. That is how lepton number was discovered.
That is how strangeness another conservation quantity we have not talked about but which governs some heavier particles was discovered.
Let us actually take a moment with strangeness because its story is one of the most beautiful examples of how nature reveals its bookkeeping rules to us. In the middle of the 20th century, physicists studying cosmic rays and early particle experiments began noticing a strange class of particles.
That is not just a figure of speech.
That is literally what they called them at the time, strange particles because they behaved oddly.
They were produced abundantly in high energy collisions [music] which suggested they were being created by the strong interaction. Anything produced that easily by the strong force should also decay through the strong force, which would mean it should vanish almost instantly.
That is what everything else with strong force production did. But these particles did not vanish instantly. They lingered. Not for a long time by human standards, but for an eternity by particle physics standards. They lived for something like 10us 10 seconds. that is many trillions of times longer than a typical strong force decay.
Something was slowing them down.
Something was preventing the strong force from doing its usual work on them.
Physicists puzzled over this for years.
Eventually, they realized that the pattern of what happened [music] and what did not happen made sense if you assumed nature was keeping track of yet another quantity. a quantity that these particles carried, a quantity that the strong and electromagnetic interactions conserved absolutely, but that the weak interaction was allowed to violate.
So when a strange particle was produced, it always appeared in a pair with one carrying positive strangeness and the other carrying negative strangeness so that the total was still zero. That made the production allowed. But when a single strange particle wanted to decay into ordinary particles that had no strangeness, the total strangeness would have to change. And the strong force would not permit that. Neither would the electromagnetic force. So neither of those pathways was open. Only the weak interaction, which does not care about strangeness in the same way, could drive the decay.
And because the weak interaction is so feeble, the decay took an extraordinarily long time compared to a typical strong force process.
That is why the strange particles were strange. They lived so much longer than they should have because their only available exit was through the weak force.
And the reason their only available exit was through the weak force was because the strong and electromagnetic interactions were forbidden from breaking a conservation law they respected.
Strangess was a rule the universe was following. [music] Physicists just had not known to look for it. This kind of story has repeated itself several times in the history of particle physics.
Nature keeps track of more quantities than we initially suspected.
Each time we thought we had the full ledger, [music] the universe would show us another decay that did not happen and another decay that did. And the pattern of what worked and what did not would force us to conclude that yet another column existed on the books. Charm is another such quantity discovered in the 1970s.
Bottomness and topness are others associated with the heavier quarks. Each of these represents a piece of the bookkeeping that nature enforces with varying degrees of strictness.
Some of these numbers are conserved by the strong and electromagnetic interactions but violated by the weak.
Some are conserved by all three. The pattern is intricate. It took decades of careful experimental work to sort it all out and it is still an active area of research today because there are hints that some of these rules might be broken in subtle ways under extreme conditions.
Now let me turn to another beautiful example of a decay that does not happen because it teaches us something about how strict the bookkeeping really is.
Consider the muon again. The muon is a leptton. The electron is also a lepton.
So the muon has leptton number + one and so does the electron. When a muon decays into an electron, [music] lepton number is conserved. Good. But here is a question that puzzled physicists for a long time. Why does the muon not decay directly into an electron plus a photon?
The math works out beautifully. The muon is heavier than the electron plus a photon.
Charge is conserved.
Leptton number is conserved. Angular momentum can be arranged to balance.
Every rule we have listed so far is satisfied.
So why do we not see it? The answer is that nature is keeping track of something even more specific than just leptton number. It is keeping track of what physicists call [music] leptton flavor. A muon does not just have leptton number plus one. It has muon leptton number + 1. An electron does not just have lepton number + one. It has electron lepton number + 1. These are separate quantities and each of them appears to be conserved on its own. So if a muon tried to decay into an electron plus a photon, muon leptton number would go from +1 to zero and electron leptton number would go from 0 to + 1. both would change. Neither would be conserved and so the decay does not happen. This is why the actual muon decay involves not just an electron but also two neutrinos of specific types.
One is a muon neutrino carrying muon lepton number + one to balance the loss of the muon. The other is an electron anti-utrino carrying electron lepton number minus1 to balance the gain of the electron.
Each flavor of lepton number is separately conserved.
Every arrow of the transaction balances on its own row of the ledger. This is what I meant when I said the bookkeeping is meticulous.
It is not enough to balance the totals.
The universe is checking multiple columns at once and every column has to balance independently. If a decay would violate any single one of them, the decay does not occur.
There is something wonderful about this because it means that the specific pattern of decays we observe in nature is like a fingerprint of the underlying laws. If we only knew the totals, many decays would look possible that we never see. It is only when we look at the pattern of what happens and what does not that the deeper structure reveals itself.
The universe is showing us its books, one refused transaction at a time. And it is worth pausing to notice how nature has actually taught us these rules.
Physicists did not sit down at a desk and dream up the idea of baron number or leptton flavor or strangeness.
They did not derive these things from first principles and then check experimentally.
They discovered them the hard way by looking at what nature refused to do.
Every conservation law in this list was born from a puzzle.
Someone would look at a set of particles, calculate that a certain decay should occur, and then [music] find that in the laboratory it stubbornly did not. And after enough such puzzles piled up, the pattern would become undeniable.
There was something being conserved that no one had known about. This is a strange and humbling way to do science.
Usually we think of physics as a matter of building theories and testing them.
But in the case of these conservation laws, the theory came after the observation.
The universe was the teacher and physicists were the students trying to figure out what the lesson was.
Every missing decay was a hint. Every observed decay was a confirmation.
Slowly, painstakingly, the community assembled a picture of the ledger by watching what nature would and would not allow.
There is also something almost eerie about the strictness of it. When we say a conservation law is enforced, we do not mean that it is enforced 99% of the time, we do not mean that occasional violations happen and are quickly patched up. We mean that in every observation ever made at every scale across the entire visible universe and back through all of cosmic history, the law has held.
Barryon number has never been observed to change. Not once.
Charge has never been observed to change. Not once. And when a decay violates one of these laws, [music] it simply does not occur, no matter how favorable every other condition might be. This is a kind of enforcement that has no analog in human affairs.
Rules that are truly and completely inviable are rare in ordinary life. But in particle physics, we appear to be dealing with them. The universe has laws it does not break. And every unstable particle we study is living within the walls of those laws, allowed to transform only in the specific ways that the laws permit.
Now, physicists do continue to ask whether some of these apparent conservation laws are truly perfect or whether they might be broken under extreme conditions we have not yet probed.
There are theoretical reasons to suspect that some of them like baron number and leptton number might be violated by an incredibly tiny amount in processes we have not yet been able to observe.
Experiments are ongoing to look for such violations.
If they were found, it would rewrite parts of our understanding.
But for the vast majority of processes at the energies we can access, these laws hold with a strictness that leaves no room for argument.
Every time a decay does not happen that we thought should, we learn that there is another column in the ledger we had missed. But now we come back to our central question.
We wanted to know what decides how long a particle can exist. We now have the first big piece of the answer. Whether a particle can decay at all is determined by whether there exists any final state that satisfies every conservation rule.
If no such final state exists, the particle is stable and its lifetime is essentially infinite.
If at least one such final state exists, the particle is unstable and it will eventually decay. But we have not yet said how quickly because knowing that a decay is permitted is only the first step. Two particles might both have permitted decays, but one might decay in a fraction of a second while the other takes hours. Being allowed to decay does not tell you how fast it will happen. So what determines the rate?
What decides whether a permitted decay happens quickly or slowly? The answer is the strength of the force that drives the decay. Because it turns out that not every decay is powered by the same interaction.
Some decays are driven by the strongest force in nature, others by a much weaker one. And the strength of the force that has to do the work of transforming one particle into another has an enormous effect on how quickly the transformation happens.
That is where we go next. Because a decay that is fully [music] permitted by all the bookkeeping rules, but that has to be driven by an extremely weak force can end up taking an amount of time so much longer than a decay driven by a stronger force that the two lifetimes differ by 20 or more orders of magnitude.
Same rules of permission, same particle physics landscape, wildly different lifetimes because different forces are doing the work.
So, we have arrived at the second great ingredient in a particle's lifetime. The bookkeeping rules tell us whether a decay is even permitted, whether the doors are there at all. But two particles can have similarly promising doors open in front of them and still end up with lifetimes that differ by amounts almost impossible to describe in ordinary language.
Not by a factor of 10, [music] not by a factor of a thousand, by factors of 10 billion or 10 trillion or more. Two decays, both perfectly legal on the books, both fully consistent with every conservation rule the universe enforces.
[music] And yet, one happens almost instantly, while the other takes what feels, by the standards of particle physics like an eternity.
What is going on here?
Why does permission alone not settle the matter? Why does having the doors open not tell us how quickly the particle will actually walk [music] through?
The answer is that having a door is not the same as being pushed through it.
Every decay has to be driven by something. Something has to actually do the work of turning the initial particle into the final products.
That something is a force. one of the fundamental interactions of nature and nature has provided us with different forces of vastly different strengths and the force that happens to be responsible for a particular decay makes all the difference in how quickly it unfolds.
There are, as far as we can tell, four fundamental interactions in the universe. Gravity is one of them. But gravity is so unbelievably weak at the scale of individual particles that it plays essentially no role in decays. We can set it aside for now. The other three, the ones that actually drive the transformations of unstable particles are the strong interaction, the electromagnetic interaction, [music] and the weak interaction.
Each one has its own character. Each one has its own strength and each one when it drives a decay does so at a completely different pace.
Let us start with the strong interaction because it is the most powerful of the three by a wide margin. The strong interaction is what holds atomic nuclei together. It is what binds quarks into protons and neutrons. It is the reason the world does not fly apart at the seams.
At the scales where it operates, which are the scales of the atomic nucleus and smaller, it is enormously more powerful than electromagnetism, which is in turn enormously more powerful than the weak interaction.
When a particle decays through the strong interaction, the decay happens with astonishing speed. And I do not mean fast by human standards. [music] I mean fast by any standard. The typical lifetime of a particle that decays through the strong interaction is somewhere around 10 to the minus 23 seconds. That is a decimal point followed by 22 zeros followed by a 1. It is a time so short that it defies intuition.
It is roughly the time it takes light moving at 300,000 km/s to cross the diameter of a proton, which is to say essentially no time at all by any measure a human being can grasp.
Particles that decay this way, and there are many of them, do not really live in any meaningful sense. They are almost more like transient patterns than persistent objects.
They come into being and are gone before any conceivable detector could see them directly.
What we see when we study these particles are not the particles themselves but the residue they leave behind. The daughter products, the traces in the detector.
We infer the existence of the parent particle by reconstructing the properties of what came out.
Why does the strong force act so quickly?
because it is strong because the interaction when it is available to drive a decay does so with overwhelming vigor. There is a probability per unit time that the interaction will trigger the transformation. And that probability is enormous.
So enormous that the particle almost certainly transforms within the smallest fraction of a second that has any physical meaning in this context.
Now the electromagnetic interaction is the next one down. It is the force that holds electrons in orbit around atomic nuclei. It is responsible for chemistry, for light, for magnetism, for most of the phenomena of everyday life. It is far weaker than the strong force at nuclear scales, but it is still by particle physics standards quite powerful. And so decays driven by the electromagnetic interaction happen [music] quickly too, though not as quickly as those driven by the strong force.
A typical electromagnetic decay lifetime is around 10 -6 seconds. Compare that to the strong decay lifetime of 10us 23 seconds.
The electromagnetic decay is around 10 million times slower, which sounds like a lot until you realize that both numbers are absurdly short by human standards.
Both lifetimes are so brief that they might as well be instantaneous from our perspective.
But from the perspective of particle physics, 10 million times is an enormous difference.
An example of an electromagnetic decay is when a particle sheds its excess energy by emitting a photon.
The photon carries away the energy. The particle transitions to a lower energy state.
This kind of transition happens through the electromagnetic interaction and it happens fast but not as fast as a strong force decay.
And now we come to the weak interaction which is where things get interesting.
The weak interaction is the runt of the litter. It is the weakest of the three by an enormous margin. At the energy scales relevant to most particle decays.
The weak interaction is roughly a million times feebler than the electromagnetic one and vastly vastly weaker than the strong. When the weak interaction has to drive a decay, it is like asking someone to push a heavy object with almost no strength at all.
It happens eventually, but it takes much, much longer.
Particles that decay through the weak interaction have lifetimes that range from around 10us3 seconds up to hundreds of seconds or more. That is a range spanning 15 orders of magnitude. And within that range, they are still much slower than either strong or electromagnetic decays.
Even the fastest weak decays are billions of times slower than typical strong decays. And the slowest weak decays can be almost human in their duration.
A free neutron, as we saw earlier, has a mean lifetime of nearly 15 minutes.
15 minutes. You could time it with a wristwatch.
Compared to a strong force decay, that is essentially an eternity.
This is the astonishing thing about the weak interaction.
It is so feeble that decays it drives happen at speeds you can measure with ordinary clocks. Nothing else in fundamental particle physics gives us that. If you want to see a decay in real time with your eyes on a scale you can experience, you need the weak interaction to be involved.
Let me put this in perspective with an example that makes the difference vivid.
Consider two particles that seem at first glance to be very similar. Both are called pions.
Pons are particles made of a quark and an anti-quark and they come in a few varieties. There is a neutral pion with no electric charge and there are charged pions with plus or minus one unit of charge. The neutral pion and the charged pions have very similar masses. They are made of the same kinds of building blocks. They are in many ways cousins.
If you looked at them side by side without knowing more, you might expect them to have similar lifetimes.
They do not. Not even close.
The neutral pion has a mean lifetime of about 10 -17 seconds. That is 100 quintilionth of a second roughly. Very fast. The charged pion has a mean lifetime of about 10us 8 seconds about 26 n roughly. The charged pion lives roughly a billion times longer than the neutral one. A billion. from two particles that look superficially like siblings.
Why? Because the decays are driven by different forces. The neutral pion being electrically neutral [music] can decay through the electromagnetic interaction.
It sheds its energy by emitting photons and this happens quickly because electromagnetism is a fairly strong force. The charged pion cannot decay electromagnetically the same way. its electric charge has to go somewhere and the electromagnetic interaction alone cannot arrange that in a permitted way.
So the decay of the charged pion has to proceed through the weak interaction and the weak interaction is so much fee than the electromagnetic one that the whole process is dragged out by a factor of about a billion. Two particles nearly identical in almost every respect. One driven by electromagnetism, the other driven by the weak force.
Result, a billionfold difference in lifetime. That is the influence of interaction strength on decay rate. And this pattern shows up over and over again throughout particle physics.
Whenever you see a particle with a lifetime that is surprisingly long compared to others of similar mass and character, you can almost always trace it back to the weak interaction.
The weak interaction is the reason there are particles that live long enough for us to work with. It is the reason certain kinds of experiments are even possible. Without the weak interaction, unstable particles would essentially all vanish before we could do anything with them. Consider the muon. The muon is a particle that behaves almost like a heavy version of the electron. It has the same electric charge as the electron. It has the same intrinsic spin. It behaves in most ways like a heavier sibling, but it is unstable. It decays and when it decays, it turns into an electron and a couple of neutrinos.
Now, this decay is fully permitted by the conservation rules. Charge is conserved because the muon and the electron both have charge minus1.
Lepton number is conserved because the muon carries a certain kind of leptton number and the products [music] carry the same kind. Energy is conserved because the muon is heavier than the sum of the electron and neutrino masses.
Momentum is conserved because the three products can arrange themselves to balance out. Everything checks out on the books. But the decay happens through the weak interaction because turning a muon into an electron plus neutrinos is a transformation that changes the type of leptton involved.
And that kind of change is precisely what the weak interaction does. And because the weak interaction is so weak, the muon has a mean lifetime of about 2.2 micros, 2.2 millionth of a second. That is quite short by human standards, but it is enormously long by particle physics standards. It is long enough that muons produced high in Earth's atmosphere by cosmic rays can actually reach the ground before decaying, which is remarkable given how briefly they exist.
In fact, given their mean lifetime and their speed, muons should not really be reaching the ground at all. They are created about 15 km up in the atmosphere when cosmic rays collide with air molecules. And in 2.2 microsconds, they can only travel a fraction of that distance before decaying. But they do reach the ground in enormous numbers every single second. The reason is that they are moving so fast that time itself passes more slowly for them, stretching their lifetimes as we observe them from below. The weak interaction sets the clock and relativity gives it just enough time to matter. It is long enough that experiments in laboratories can capture muons, hold them, study them, use them as probes of other phenomena.
All of that is possible only because the weak interaction is so weak that it takes a long time to do its work. The point is not just that different particles have different lifetimes. The point is that when we understand which interaction drives a given decay, we get a rough sense of how quickly it will happen.
Strong force decays are essentially instantaneous.
Electromagnetic decays are very fast but measurable in principle. Weak force decays span a huge range but even at their fastest they are slow compared to strong or electromagnetic decays and at their slowest they can last minutes or longer. Now I want to be careful with the word strength here because it can be misleading. When physicists [music] say the strong force is strong, they do not mean it is like a strong wind blowing particles around with mechanical force.
They mean that the probability per unit time for a transformation driven by the strong interaction is high. When they say the weak force is weak, [music] they do not mean it is like a gentle breeze.
They mean the probability per unit time for a transformation driven by the weak interaction is low. So strength in this context really refers to how likely it is that the interaction will trigger a transformation in a given moment. A strong interaction will trigger transformations with high probability so they happen fast. A weak interaction will trigger transformations with low probability so they happen slowly. The end result is what we perceive as fast versus slow decays.
But the underlying reality is a difference in the fundamental probability per unit time [music] that each interaction contributes to. Let us pause here and ask something that might have been nagging at you. When we say that an interaction drives a decay, what does that actually mean physically? What is the interaction doing? How does it turn one particle into another? The answer takes us into one of the deepest and most beautiful ideas in modern physics.
Each of these fundamental interactions works by exchanging carrier particles.
When the strong interaction acts, it acts through the exchange of particles called gluons.
When the electromagnetic interaction acts, it acts through the exchange of photons.
When the weak interaction acts, it acts through the exchange of particles called the W and Zed Bzons.
These carrier particles are the messengers of the interactions. They are what actually get swapped between the particles involved in a decay and the properties of these messengers turn out to be crucial for understanding why the interactions have such different strengths. [music] Here is the striking difference. Photons and gluons have no mass. They are massless carriers. They can in a certain quantum mechanical sense travel any distance without penalty. But the W and Zed Bzons, the carriers of the weak interaction, are enormously massive. Not just a little massive, astonishingly massive by the standards of particles that appear in ordinary decays. The W Bzon has about 80 times the mass of a proton. The Z Bzon is even heavier.
These are among the heaviest particles the standard model contains.
Why does the mass of the carrier matter?
Because in quantum mechanics, when you try to exchange a very heavy particle to mediate a process, that exchange is enormously suppressed. Nature can borrow the energy for a heavy carrier particle only for a very brief instant and it can do so only across a very short range.
Every time a weak interaction happens, it has to pay this heavy cost. And so weak force processes are dramatically slower than they would be if the W and Zed were light.
Photons, by contrast, are massless. They cost nothing to exchange over any distance. That is a huge part of why the electromagnetic interaction [music] can act quickly and across long ranges.
Gluons are also massless though they have a peculiar property of only being able to travel very short distances due to another quirk of the strong interaction.
But within their range they act with tremendous vigor. So the strengths of the three interactions which we described earlier as facts of nature actually trace back in significant part to the masses of the carriers.
The weak force [music] is weak in large part because its carriers are heavy. If the W and Z bzons were as light as photons, the weak force would not be weak at all. It would act at a rate comparable to electromagnetism and free neutrons would decay in fractions of a second rather than nearly 15 minutes.
Stars would burn differently. The universe would have a completely different history. The heaviness of the weak force carriers is one of the most important numerical facts in all of physics. It sets the time scales of a huge fraction of the processes that shape the universe. It is why radioactive decay happens on human time scales rather than instantly. It is why nuclear fusion in stars proceeds slowly enough to power stellar evolution across billions of years.
It is why we are here to think about it.
Now let us look at another beautiful case where these ideas come together.
Earlier I mentioned that strange particles have lifetimes far longer than they should if the strong force could act on them. Let us look at one specific strange particle to see the pattern clearly. Consider the kon. The kon is a particle made of a strange quark and an ordinary quark. It comes in a few varieties, some charged and some neutral. And the charged kons have a mean lifetime of about 10 the minus8 seconds, about the same as the charged pion. Actually, think about that for a moment. The kon is a particle that participates in the strong interaction.
It is made of quarks. It is produced abundantly in high energy collisions by the strong force.
By all the reasoning we developed a moment ago, its decay should be blazingly fast on the order of 10 theus 23 seconds.
That is what strong force decays look like. But it is not blazingly fast. It is roughly a thousand trillion times slower than that. Something is stopping the strong force from acting. That something is strangeness. The ka carries strangess. If it tried to decay through the strong interaction [music] into ordinary particles that have no strangeness, the total strangeness of the system would change and the strong interaction refuses to allow that.
Neither will the electromagnetic interaction. So both fast pathways are blocked. The only interaction available to drive the decay is the weak interaction which does not respect stranges the same way. And the weak interaction with its heavy carrier particles is dramatically slower than the other two. So the kon lingers not because it is intrinsically stable, not because it lacks a permitted decay, but because the only interaction that can perform its permitted decay is the feeble weak one. The result is a lifetime that is roughly a thousand trillion times longer than you would naively expect for a particle made of quarks. This is a perfect illustration of how the conservation rules from earlier and the interaction strengths we are discussing now work together to shape a particle's fate. The rules of permission determine which interactions are even allowed to act. And then the strength of the allowed interaction determines how quickly it does its job.
Take away either piece and you miss the picture.
The kon was in fact one of the particles that led physicists to discover stranges in the first place. It was a beautiful piece of scientific reasoning and it opened the door to our modern understanding of the quark model and the standard model of particle physics.
There is another aspect of this that is worth mentioning. When we say that the strong force cannot change strangeness, [music] we are really saying something about the carrier particles. Again, the gluons that mediate the strong interaction cannot convert one flavor of quark into another. They can bind quarks together. They can hold them in place.
They can exchange energy between them, but they cannot turn a strange quark into an up quark or a down quark into a charm quark. They simply do not have that capability built into them. The W Bzon, on the other hand, can do exactly that.
The W Bzon is the great flavor changer of particle physics. When it is exchanged, it can turn one flavor of quark into another or one flavor of leptton into another. That is precisely what the weak interaction does at the deepest level. It changes the identity of the particles involved. And the changes it enables are the ones that drive the vast majority of decays we observe in the world.
So when we say the weak force drives the decay of the neutron or the muon or the kon or the charged pion, what we really mean is this.
Inside the parent particle, [music] one flavor of quark or leptton has to change into another for the decay to proceed.
That kind of change can only happen through the exchange of a W bzon. And the W bzon is very heavy. So the exchange is dramatically suppressed.
That suppression is what we experience as the slowness of weak decays.
The picture that emerges from all of this is remarkably unified. The differences in interaction strengths are not arbitrary facts. They trace back to the masses of the carrier particles.
The differences in which decays are allowed trace back to the specific abilities of those carriers.
Together, the carriers and their properties determine which pathways are open, how quickly those pathways can be traversed, and therefore how long any given unstable particle can survive.
There is another subtlety worth noting.
The three interactions do not work in isolation.
In principle, if a decay is not forbidden by conservation laws, it could happen through any interaction that is compatible with the transformation.
But the fastest available interaction dominates.
If a particle can decay through the strong force, the strong force will do it. Even if the weak force could also technically do the job, it does not get a chance because the strong force decay happens so much faster that the particle is gone before the weak force has any opportunity to act. This is why when we see a decay happening on a time scale characteristic of the weak interaction, we can be quite confident that the stronger interactions were not available for that particular transformation.
Something about the particles involved must be blocking the electromagnetic or strong pathways, leaving only the weak one as an option. And the specific reasons why the stronger pathways are blocked often come back to those conservation laws we talked about earlier. The neutron is a striking illustration.
Even though it is built from quarks bound together by the strong force and even though the strong force is right there inside it holding it together, that force [music] cannot drive its decay. The transformation the neutron needs to undergo is one only the weak force can perform. [music] And so despite being a hadron in every other respect, the neutron's fate is handed over to the feeblest of the three interactions.
That is the reason its lifetime is measured in minutes rather than in fractions of a second. Not any special toughness, just the [music] fact that all the faster options were closed to it. This connection between conservation rules and interaction strengths is one of the most beautiful patterns in particle physics.
The conservation rules tell us which pathways are open. The interaction strengths tell us how quickly the particle will travel down those pathways. Together, they give us the outline of what a particle's lifetime will be. Not the exact number yet because there are more factors we have not gotten to, but a rough shape.
If a particle has strong force pathways available, it lives essentially no time at all. If it has only electromagnetic pathways, it lives longer, but still very briefly.
If it has only weak force pathways, it can live long enough to be studied in real time. And if it has no permitted pathways at all, it is stable and it lives forever.
There is one more aspect of interaction strength that I want to touch on because it deepens the picture. It is the fact that at very high energies the strengths of the different interactions actually change.
This is one of the most surprising discoveries of 20th century physics.
What we call the strengths of the fundamental forces are not really constants. They depend on the energy scale at which you probe them. At low energies, the ones we experience in ordinary life and in most laboratory experiments, the strong force is much stronger than the electromagnetic force, which is much stronger than the weak force. But at very high energies, these numbers get closer together. The electromagnetic and weak forces in particular at high enough energies become nearly equal in strength. In fact, they can be understood as two facets of a single unified interaction called the electroeak [music] interaction.
It is only at lower energies that they split apart into what seem like two separate forces.
So the picture we now have is this. A particle is created. [music] It has a certain probability per unit time of decaying and that probability is fixed [music] by nature. Whether the probability is large or small depends first on whether any decay is permitted at all that is set by the conservation laws. If nothing is permitted the particle is stable [music] and the probability is zero. If something is permitted then the probability depends on which interactions can drive the transformation.
The strong interaction, if available, produces enormous probabilities and consequently very short lifetimes.
The electromagnetic interaction produces smaller but still substantial probabilities and short lifetimes.
The weak interaction being feeble produces small probabilities and correspondingly longer lifetimes.
This gives us a rough hierarchy.
Strong decays are essentially instantaneous.
Electromagnetic decays are very fast.
Weak decays are slow by comparison.
That accounts for a huge amount of the variation we see in particle lifetimes.
It explains why some particles disappear in 10us23 seconds and others last for hundreds of seconds. Different forces are doing the work. And it explains at last some of what puzzled us at the very beginning.
The two particles that emerged from the same collision, one lasting essentially forever and the other vanishing almost immediately.
Now we can start to see the reasons behind the mystery. Perhaps the immortal one has no permitted decay at all because the conservation laws leave it nowhere to go. It is stable.
Or perhaps it can only decay through the weak interaction which is so slow that within any reasonable observation time it appears essentially permanent.
Meanwhile, the short-lived one has a strong force decay available and so it vanishes as fast as the strong force can act which [music] is unimaginably fast.
Same universe, same laws, same instant of creation. But different landscapes of permitted decays and different forces available to drive them produce lifetimes separated by more orders of magnitude than we can easily grasp.
Yet even this is not the whole story because knowing which interaction drives a decay tells us the rough scale of the lifetime, but it does not tell us the exact number.
Within a given interaction, lifetimes can still vary enormously.
The weak interaction, for example, drives decays that range from around 10us3 seconds up to nearly 15 minutes. That is a [music] spread of 15 orders of magnitude.
All of those decays are driven by the same interaction. The strength of the force is roughly the same in all of them. So, what accounts for that huge variation within a single interaction category?
That brings us to the last piece of the puzzle. The piece that [music] adjusts the lifetime up or down within the range set by which force is at work. It is a subtler ingredient than the ones we have already met. It has to do with the amount of energy available for the decay and the number of different ways the decay can play out and the room the products have to distribute themselves in. This is what physicists call phase space. And even though the name sounds technical, the idea behind it is beautifully intuitive. It captures the fact that a decay does not just need to be permitted and driven by some force.
It also needs somewhere to go. It needs configurations in which the products can actually arrive. And the more room there is, the more different configurations, the more energy separating the initial and final states, the faster the decay proceeds.
Squeeze the room and the decay slows down. Even for the same interaction and the same conservation rules, the pace changes dramatically based on how much space is available in the final state.
That is what we turn to next. Because when we bring in phase space, we finally have the complete picture. The conservation laws set the doors. The interaction strengths set the rate at which the doors are opened. and phase space sets how much room lies on the other side.
Combine all three and you have the answer to what decides how long a particle can exist.
So we have arrived at the last great ingredient. Not the loudest one, not the most immediately obvious, but in many ways the most delicate [music] and the most surprising.
Because even when a decay is permitted and even when we know which interaction is going to drive it, the actual lifetime can still stretch or shrink by enormous factors [music] depending on one further consideration.
How much room the decay has to happen in? That may sound like an odd thing to say. What does room have to do with anything? A particle sits there and it either decays or it does not. Where would the room come from? And why would it matter? The room, it turns out, is not room in ordinary space. It is room in a more abstract sense. Room in the sense of how many different ways the products of the decay can arrange themselves.
How many different configurations of energy and momentum they can take when they emerge, how much variety there is in what the final state can look like.
Physicists have a name for this. They call it phase space. And I want to unpack that idea slowly because it is one of the most beautiful concepts in this whole story. And it is often glossed over or left mysterious.
Imagine you are a particle that is about to decay. You have some fixed amount of energy given by your mass. You have some fixed momentum which we can assume is zero if you are sitting still. and you are about to transform into a set of daughter particles.
Now those daughters have to share your energy. They have to add up to your total momentum. Their individual energies and momenta cannot be arbitrary. They are constrained by what you had to start with. But within those constraints, [music] there is still typically a range of choices. The daughters can fly out in slightly different directions. They can carry slightly different fractions of the total energy. One of them can be moving quickly and another slowly or they can share the energy more evenly.
As long as the totals balance, the individual details can vary.
Every possible combination of directions and energies for the daughters is what we call a configuration of the final state. And the total number of such configurations is what we call the phase [music] space of the decay.
Here is the key point. The larger the phase space, the more different ways the decay can happen. And the more ways it can happen, the higher the probability that it happens in any given moment. If there are only a few available configurations, the decay is like trying to thread a needle. There are not many ways for it to succeed. It happens slowly. If there are many available configurations, the decay is like trying to jump into an ocean. There are countless ways for it to succeed. It happens quickly.
So phase space acts like a multiplier on the base rate set by the interaction.
Given the same interaction driving the decay, a decay with a lot of phase space happens faster than a decay with only a little. And when phase space becomes very restricted, even a decay driven by a normally fast interaction can be dramatically slowed down.
Now what determines how much phase space is available? Two main things. The energy difference between the initial particle and the final products and the number of different final states that satisfy all the conservation rules.
Let us start with the energy difference.
Here is the principle. If the particle you start with has a mass much greater than the combined masses of the products it decays into, there is a lot of leftover energy. That leftover energy becomes kinetic energy for the products.
And that kinetic energy can be distributed among them in many different ways with many different momenta and directions.
Lots of freedom, lots of phase space.
The decay happens quickly.
But if the initial particles mass is only slightly greater than the combined masses of the products, there is very little leftover energy. The products barely have room to move. They come out almost at rest with hardly any variety in their momentum or directions.
There are only a few configurations that work. Phase space is small and the decay slows down enormously.
This is one of the most important levers in all of particle physics. A small energy difference between initial and final states can throttle a decay so severely that a particle which by all rights should disappear in a fraction of a second ends up lingering for minutes or hours or longer.
The classic example and the one that makes this vivid is the free neutron. We have already met the neutron. We know it decays into a proton, an electron, and an anti-utrino.
We know the decay is permitted by every conservation law. We know it happens through the weak interaction, which is why it takes a while. But we have not yet asked why it takes quite so long.
Why nearly 15 minutes? Why not fractions of a second? The answer is phase space.
The neutron and the proton have almost the same mass, nearly identical. The neutron is slightly heavier by a tiny amount. And that tiny amount is essentially all the leftover energy the decay has to work with. After you subtract the mass of the proton, you are left with a very small energy budget.
Some of that goes into the electron's mass. The rest becomes kinetic energy split between the electron, the anti-utrino, and a very slow recoiling proton. Because the energy budget is so small, the products have almost no room to distribute their momentum in different ways. There is very little variety in the final state. The phase space is tightly compressed.
And because phase space is small, the decay rate is much slower than it would be if the neutron were significantly heavier than the proton.
The nearly 15minute lifetime of the free neutron is a direct consequence of that near equality of masses between it and the proton. If the neutron were noticeably heavier, its lifetime would drop by many orders of magnitude.
Because the two masses are so close, the neutron lingers. This is a stunning example of how a subtle numerical accident. The fact that these two particles happen to have nearly the same mass has a gigantic effect on how the universe behaves. It is one of the reasons stars can burn as slowly and as steadily as they do because the weak interactions inside stars which involve transformations between protons and neutrons are throttled by exactly this kind of tight phase space. Without that throttling, stars would burn through their fuel in vastly different ways and the universe as we know it would not exist.
A tiny difference in mass produces a large difference in phase space which produces a large difference in decay rate [music] which produces the time scales on which stars evolve.
So a small energy gap between the initial and final states can lengthen a lifetime enormously.
Now let us look at the other side. What happens when there is a large energy gap? A particle much heavier than its decay products has a large energy budget. That budget can be distributed among the products in many many different ways. Each product can take on a wide range of possible energies and momenta [music] as long as the totals balance. The phase space is enormous and the decay proceeds much more quickly than it would if the gap were smaller. This is why heavier unstable particles tend to have shorter lifetimes all else being equal. Not always because interaction strength [music] also matters and conservation rules matter. But as a general trend, a heavy particle with a large mass difference between itself and its allowed decay products has plenty of phase space to work with and it uses [music] it. Its lifetime is short.
Now let us turn to the other main contributor to phase space. The number of different final states that satisfy all the conservation rules. Because it is not only about how much energy is available. It is also about how many distinct pathways the decay can take.
Some particles have only one way they are allowed to decay. Given the conservation rules and the available energy, only one combination of products is permitted. So all the phase space goes into that single channel. Whatever probability the interaction produces per unit time, it is all channeled through one exit.
But some particles have several allowed decay channels. Multiple different sets of products, each of which satisfies all the conservation rules. Each of these channels has its own phase space, its own set of possible configurations, and they all contribute to the total probability that the particle will decay in a given moment. The total decay rate is the sum of the rates through each individual channel. So, a particle with three permitted decay channels tends to decay faster than a similar particle with only one because there are more ways for the decay to happen. Adding channels adds rate. Adding rate shortens lifetime.
This is why some heavy particles with many possible decay products available to them have surprisingly short lifetimes even when each individual channel is not especially fast. The channels add up. Many small contributions become one large one and the particle disappears more quickly than any single channel would suggest.
Now, physicists have a compact way of packaging all of this together into a single number. They call it the decay width. The decay width of a particle captures both how fast it decays and how spread out its energy is in a certain quantum mechanical sense. A particle with a large decay width has many channels or lots of phase space or strong interactions driving its decays or some combination of these. and it has a short lifetime. A particle with a small decay width has few channels or restricted phase space or weak interactions and it has a long lifetime.
The width and the lifetime are two sides of the same coin. Mathematically they are inversely related. Multiply them together and you get a fixed quantum mechanical constant. A large width means a short lifetime. A small width means a long lifetime. They are the same physical fact expressed in different units. The reason it is called width has a lovely origin. When physicists measure the energy of a short-lived particle, they find it is not a perfectly sharp value. It has a spread, a range of energies that the particle can seem to have when observed. and the size of that spread, the width of the peak on the energy chart, corresponds exactly to how quickly the particle decays.
Short-lived particles have broad energy peaks. Long lived particles have narrow energy peaks. The particle's fuzziness in energy is a direct mirror of its fuzziness in existence. The less time it exists, the less well-defined its energy is, and vice versa.
I do not want to get lost in this technicality. What matters is the underlying idea. The lifetime of a particle is not just a matter of what interactions can drive its decay. It is also a matter of how much room those decays have to happen in. Restrict the room and you slow things down even for the same interaction.
Open up the room and you speed things up.
So now finally we have all the pieces.
Let us bring them together. A particle sits in the universe. It has some fixed properties. Mass, charge, spin and other quantum numbers that we sometimes only detect by their absence. It is either alone in space, at [music] rest or moving. From the moment it exists, it faces the possibility of decay. Whether it can decay at all is decided by the conservation rules. If no combination of lighter particles exists that satisfies every rule, the particle cannot decay.
It is stable. It sits there indefinitely, unchanging, protected not by any special property, but by the fact that the universe's bookkeeping refuses to permit any transformation.
The probability per unit time of its decay is exactly zero. Not tiny, not almost zero, zero. If at least one combination of products is permitted, the particle can decay. The probability per unit time is greater [music] than zero. What that probability actually is depends on which interaction drives the decay. If the strong interaction can do the work, the probability per unit time is enormous and the particle vanishes in something like 10 - 23 seconds.
If only the electromagnetic interaction can do the work, the probability is smaller but still substantial [music] and the particle vanishes in perhaps 10 -16 seconds or so. If only the weak interaction can do the work, the probability is much smaller and the particle may last anywhere from 10 theus3 seconds to hundreds of seconds or more. And within whichever interaction is at work, the actual number is further [music] shaped by phase space.
How much energy is available for the products to share? How many different configurations can they take? How many separate channels are permitted? The more room, the more channels, the more energy, the faster the decay. The less room, the fewer channels, the smaller the energy budget, the slower. Together, these three factors, which decays are permitted, [music] which force drives them, and how much phase space is available, determine the probability per unit time. And that probability running silently and continuously in each moment of the particle's existence is what we call its decay rate. It sets the mean lifetime. It sets the half-life. It sets the entire statistical shape of when we should expect the particle to disappear.
And this is why identical particles do not all decay at the same age. Because although the probability per unit time is the same for every one of them, the outcome of that probability in any individual case is a genuine roll of the quantum dice.
Two particles created in the same instant with the same probability of decay per unit time still go on to have wildly different actual lifetimes because they are each undergoing an independent series of quantum events and the outcomes just happen differently.
There is something poetic in this picture. I think the particle is not doing anything to bring about its own end. It is not aging. It is not deteriorating.
It is not working its way toward a scheduled expiration.
It is simply existing moment by moment.
And each moment carries a fixed [music] chance that this will be the moment it transforms into something else.
The chance is set by three things. the doors that the conservation laws leave open, the force that stands ready to push the particle through those doors, the room on the other side of the doors waiting to receive whatever comes through. And these three ingredients multiplied together are the whole answer. There is nothing else. Not really. Every unstable particle in the universe has a lifetime that emerges from exactly this recipe. And every stable particle owes its stability to the fact that at least one of those ingredients is missing. No doors or no force to drive the transformation [music] or no room on the other side.
Let us go back one last time to the two particles we imagined at the very beginning. Born in the same instant from the same collision, side by side, both apparently fundamental.
And nature has already decided that one will live essentially forever and the other will vanish almost immediately.
Now finally we can see what nature has actually done. It has looked at the two particles and asked for each of them what does the landscape of possible decays look like? For the one that lives forever the landscape is empty. There are no permitted transformations. The conservation laws leave no exit. The particle [music] is trapped at the floor of what is possible. It has nowhere to go. And so it stays.
For the one that vanishes almost immediately, the landscape is full.
Doors everywhere. A strong force pathway available, ready to drive the transformation almost as fast as physics allows.
Large mass differences between it and its products, giving generous phase space. multiple channels each contributing to the total rate. Every ingredient conspiring to make the decay probability per unit time as large as it can possibly be. And so the particle is gone in a time so brief [music] that light can barely cross an atomic nucleus in its lifespan.
Same instant of birth, same physical laws, same universe, but radically different landscapes.
And that is why nature has assigned them such radically different fates.
There is one more thing I want to say before we close. [music] It is about how strange and beautiful this whole picture actually is when you step back from it.
Because think about what we have described.
Every unstable particle in the universe is at every moment of its existence undergoing a genuine quantum event.
[music] It is not a countdown. It is not a slow burn. It is a fresh evaluation moment by moment of whether or not the transformation will occur. The universe is not remembering how long the particle has been alive. [music] It is not tracking its age. It is not preparing it for some scheduled end. Each moment is entirely fresh. Each moment carries the same probability.
And the fact that particles do on average decay in a predictable pattern is entirely a consequence of many independent fresh moments adding up statistically to give a smooth curve.
There is something almost eerie in that idea. It means that the past does not causally reach forward to determine the future of the particle. The particle is not being pushed toward its decay by anything from before. It is just existing right now with a certain chance of transforming right now.
And then in the next instant it is just existing right now again with the same chance freshly.
Nothing accumulates, nothing builds up.
And yet statistically the pattern is inevitable. And it means that the differences in lifetimes we see across the particle zoo from the essentially eternal to the almost instantaneous are not really differences in how sturdy or fragile the particles are. They are differences in the landscape of possibilities that surrounds each of them. [music] Each particle is exactly what it is with no internal timer. What varies is how many exits nature has provided and how firmly those exits are guarded and how wide the paths are that lead out through them. Some particles find themselves in wide open planes, doors everywhere, forces ready to push them through and plenty of room on the other side. They vanish almost as soon as they arrive.
Some particles find themselves in tight rooms with narrow doors, a feeble force just barely able to nudge them through and hardly any room on the other side.
They linger for surprisingly long stretches, sometimes long enough to be timed with a wristwatch.
And some particles find themselves in perfectly sealed chambers with no doors at all. They stay forever. Not because anyone is holding them there, not because they are fighting to stay.
Simply because the universe's rules of transformation permit them no way out.
That is what decides how long a particle can exist. Not a clock, not a fuel gauge, not deterioration, not aging, but the shape of the landscape of possibilities that surrounds it moment by moment freshly from the instant of its birth until the instant of its transformation.
A particle's lifetime is a story written not in advance but in real time. It is a story shaped by which endings the universe permits, which forces are willing to bring those endings about, and how much room those endings have to unfold in. And out of this vast quantum machinery running silently across every corner of the universe, emerge the specific numbers we measure in our laboratories. the nanconds, the micros seconds, the minutes, the essentially infinite lifetimes of the stable particles that make up the ordinary matter of the world. The next time you hear that some particle has a lifetime of a certain fraction of a second or that some other particle is stable or that some third particle lasts for exactly the amount of time it does, you will know what that number is really telling you. It is telling you about the doors nature has left open or closed.
about the forces standing ready to act [music] or absent about the room available on the other side or the crushing tightness of it. It is telling you about a probability running moment by moment in a [music] landscape shaped by the deepest rules of the universe. A probability that is already answered before the particle can even ask the question of how long it gets to exist.
Every particle carries within it from the instant of its birth the whole story of its own possible endings. Not written as a fate, not scheduled as an event, but laid out as a landscape of chances waiting for the quantum universe to run its course [music] and to decide in real time which of those chances will be the one that is realized.
That is what decides how long a particle can exist. Not what is inside it, but what surrounds it in the space of possibilities, the permissions of the conservation laws, the strength of the forces available, the room in the final state.
Three ingredients multiplied together giving the entire answer. And it is out of this quiet ceaseless quantum accounting [music] going on right now in every particle in every corner of the universe that all the persistence and all the impermanence of matter itself emerges.
The atoms that make up your body, the stars that fill the sky, the brief flickers of unstable particles that come and go inside every collision, every reaction, every burst of cosmic energy.
All of it at the deepest level comes down to the same three questions being asked over and over.
Is the decay permitted? Is there a force to drive it? [music] Is there room for it to happen?
Answer those three questions for any particle in the universe and you will know how long it gets to exist.
Not to the exact instant, never to the exact instant, but to the shape of its lifetime, to its mean, to its statistical fate. That is the whole answer. And it is nothing less than the story of why matter in the form we know it persists at all. Why some pieces of the universe stay and why others come and go so quickly that they leave only traces.
Why the world around us has the specific texture it does made of the specific stable ingredients it is made of arranged in the specific ways it is arranged.
All of it in the end comes from a quiet quantum landscape of doors and forces and rooms shaping the lifetimes of every particle in existence. [music] Good night and may you never look at an unstable particle the same way again.
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