# Something Strange Happens When You Trust Quantum Mechanics - Channel: [Veritasium](https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA) - Published: 2025-03-05 - Source video: [Watch on YouTube](https://youtube.com/watch?v=qJZ1Ez28C-A) - Read on ReadTube: https://www.read.tube/p/videos/qJZ1Ez28C-A - Language: Original (source language) ## Summary **Quantum Particles Explore All Paths Simultaneously** 量子力学表明，物体并非沿单一行径运动，而是同时探索所有可能的路径。这是因为微观粒子的作用量极小，导致不同路径的相位发生干涉，只有在作用量极小值附近的路径才会相长干涉并最终显现出来。 Contrary to the traditional view that particles follow a single, well-defined path, quantum mechanics reveals that particles explore all possible trajectories simultaneously. This behavior is fundamentally described by the principle of least action. - The path a particle takes is determined by the interference of all potential trajectories, each associated with a phase proportional to its action. - For macroscopic objects, the action is so large relative to Planck's constant that paths deviating from the classical trajectory destructively interfere, leaving only the path of least action. - For quantum particles, the action is small, allowing for observable wave-like behaviors such as interference patterns in the double-slit experiment. - This framework serves as a unifying principle in theoretical physics, where the Lagrangian is used to derive the laws governing different physical systems. ## Article As a 42 year old who's spent most of my life studying physics, I must admit that I had a big misconception. I believed that every object has one single trajectory through space, one single path. But in this video, I will prove to you that this is not the case. Everything is actually exploring all possible paths all at once. #### The Fastest Path So let's start with a simple thought experiment. Say you're at a beach when all of a sudden you see your friend struggling out in the water. You want to go help them as quickly as possible. So which path should you take to get there? The shortest path is a straight line, so you could head directly towards him. But you can run faster than you can swim, and this path requires more swimming. So alternatively, you could run down the beach to minimize the distance through the water. But now the total distance is longer than it needs to be. So the optimal path, it turns out, is somewhere in between. To be precise, it depends on the speeds at which you can run and swim. Now, you might recognize this mathematical relationship because it is the exact same law that governs light passing from one medium into another. So light also takes the fastest path from point A to point B. What's weird about this is that as humans, we can see where we want to go and then figure out the fastest route. But light, I mean, how does light know how to travel to minimize its journey time? #### Local Rules vs. Global Optimization Now here is where my misconception comes in. I shine a laser beam. The light just goes in one direction. I throw a ball. The ball just goes in one direction, you know? I would have answered, there is nothing strange about this. Light sets off from point A in some direction. And then a little while later it encounters a new medium. And due to local interactions with that medium, it changes direction, ending up at point B. If you later find that of all the possible paths, light took the shortest time to get from A to B, I wouldn't think it was optimizing for anything. I would just think that's what happens when light obeys local rules. But now I will prove to you that light doesn't set out in only one direction. Instead, it really does explore all possible paths. And the same is true for electrons and protons. All quantum particles. So the fact that we see things on single, well-defined trajectories is, in a way, the most convincing illusion nature has ever devised. And the way it works all comes down to a quantity known as the action. In a previous video, we showed how an obscure scientist, Maupertuis, made an ad hoc proposal that there should be a quantity called action, which he defined as mass times velocity times distance. And he claimed that everything always follows the path that minimizes the action. Hamilton later showed that this action is equivalent to the integral over time of kinetic energy minus potential energy. Action was useful and an alternative way of solving physics problems, especially when Newton's laws get too cumbersome. #### The Birth of Quantum Mechanics But then, around the turn of the 20th century, action showed up at the heart of a scientific revolution: the birth of quantum mechanics. It all started with electric lighting in Germany. Think about what it's like in the 1890s. Electricity being more widely available, at least in urban sectors. And things like light bulbs. They were new. They were literally the hot new thing. Germany wanted to replace all their gas street lights with electric light bulbs. So an important question was how do you maximize the visible light given off by a hot filament? Scientists at a German research institute, the PTR, studied how much light different materials emitted as a function of temperature. At low temperatures, each material gave off its own characteristic spectrum, mostly in the infrared, but above about 500°C all materials started to glow in the same way, with an almost identical distribution of light. The hotter the object, the more energy was emitted at every wavelength, and the peak of the distribution shifted to the left. They started by imagining the simplest object possible, one that would absorb all light that falls onto it and perfectly emit radiation based on its temperature. They came up with a hole in a metal cube. This hole is a perfect blackbody because any light that shines onto it will go straight in, bounce around inside, and eventually be absorbed. But this also makes it a perfect emitter. Any radiation inside the cube can escape through the hole unimpeded. Theorists reasoned that electrons in the walls of the cube would wiggle around, emitting electromagnetic waves. These waves would then bounce off the other walls. When you have two waves of the same frequency, where one travels to the right and the other to the left, they can interfere in such a way that they create places where there's no wave amplitude—those are nodes—and places where there is maximum wave amplitude, the anti nodes. Waves like this are called standing waves because they don't really move left or right and inside a cavity, given enough time and reflections, it is only these standing waves that survive. All the other ones just cancel out. So a sort of order emerges from the chaos. For shorter wavelengths or higher frequencies, you can fit more and more different vibrational modes inside this cube, so that in three dimensions, the total number of modes is proportional to frequency cubed, or one over lambda cubed. The expectation was there would be more and more waves inside the cube, the shorter the wavelength. This led directly to the Rayleigh-Jeans law. At longer wavelengths, it matched the experimental data pretty well, but at shorter wavelengths the theory diverged from experiment. In fact, it predicted that at the shortest wavelengths, an infinite amount of energy would be emitted. This, for obvious reasons, became known as the ultraviolet catastrophe. #### Planck's Constant The person to solve this problem was Max Planck. By 1897, he was a professor himself, and for the next three years he struggled to find a theoretical explanation for blackbody radiation. In an 'act of desperation', he did something no one had thought to try. According to classical physics, the energy of an electromagnetic wave depends only on its amplitude, not its wavelength or frequency. And it could take any arbitrary value. So any atom could emit any wavelength of light with an arbitrarily small amount of energy. But Planck tried restricting the energy so that it could only come in multiples of a smallest amount. A quantum. And he made the energy of one quantum directly proportional to its frequency. $E = hf$, where $h$ is just a constant. With this approach, Planck got a new formula for the radiation spectrum. He introduced what we now call Planck's constant, and it has the units of action. Planck's constant, $h$, is a quantum of action. Planck later proposed that any time any change happened in nature, it would be some whole multiple of this quantum of action. #### De Broglie and Wave Mechanics In 1905, Albert Einstein claimed that Planck's theory was telling us that light actually comes in discrete packets, or photons, each with an energy $hf$. Eight years later, Niels Bohr was trying to understand how an atom is stable. He realizes that as the electron goes around the nucleus, it has an angular momentum (mass times velocity times radius). So angular momentum has the same units as action. Bohr decides to discretize the orbital angular momentum. He imagines the electron can only be in one unit, two units, three units of the same quantity $h$. And because it's talking about motion in a circle, the factors $2\pi$ come in. So it is really $nh / 2\pi$, what we now call an $\hbar$. Then, for his PhD, Louis de Broglie proposed that everything—electrons, basketballs, people—has a wavelength. And he defined this wavelength analogously to light as Planck's constant divided by the particle's momentum ($p = mv$). If an electron is a wave, the only way it could stay bound to a nucleus in an atom is if it exists as a standing wave. That requires that a whole number of wavelengths fit around the circumference of the orbit. $$2\pi r = n \lambda$$ Substituting de Broglie's expression for the wavelength: $$2\pi r = n \frac{h}{mv}$$ Rearranging this to get angular momentum ($mvr$): $$mvr = \frac{nh}{2\pi}$$ That is precisely Bohr's quantized angular momentum condition. #### Feynman and the Sum Over Histories It is this wave nature of quantum objects that means they no longer have a single path through space. Instead, they must explore all possible paths. If you believe in the double slit experiment that you can't tell which of the two slits the particle went through, then you have to consider the possibility that it goes through both. By that same logic, any time any particle goes from place one to place two, you have to consider all the possible paths it could take to get there. According to Feynman, any time a particle moves from point 1 to point 2, it has some chance to take any path. To find the probability, we assign a phase (represented by a stopwatch) to each path. As the particle wave follows a path, its phase increases. When we add up the arrows (amplitudes) for all possible paths and square the result, we get the probability. Mathematically, the phase depends on the action. The phase increase is the integral over time of (kinetic energy - potential energy), which is the classical action. Because $\hbar$ is so tiny (about $10^{-34}$ joule seconds), the phases of ordinary objects on ordinary paths spin around zillions of times, eventually pointing in random directions and cancelling out. The only exception is for paths closest to the path of least action, where the phases constructively interfere. This is how classical mechanics emerges from quantum mechanics. Everything explores all possible paths. It's just that massive particles have large actions compared to $\hbar$, so that only paths extremely close to the true path of least action survive. If you go to much smaller particles like electrons or photons, there's more of a spread in which trajectories they actually end up taking.