I’m not really into physics and what not, I just know the bare minimum. I’m a law student, so please believe I’m like 5 when it comes to this discipline of education.
Why is the Planck Length the “smallest thing in the world?” Or at least I hope I asked it right.
I’ve read that you cannot go smaller than this length, otherwise blackholes will occur and the world doesn’t make sense anymore.
Could you explain the main steps to understanding “length” and it’s relationship to energy before diving into the planks length? This concept is super interesting and I really want to understand it. From what I have read, understanding this concept is broken down like this:
(1) What is a wavelength actually?
(2) How are wavelengths and energy related?
(3) Why is the Plancks Length the smallest thing in the universe?
(4) What happens when something is smaller than a Planck Length?
Thanks!
In: Physics
The Planck length is literally nothing and completely meaningless. A lot of your other “answers” are complete bullshit, do not believe them. It has absolutely zero real world threshold or meaning. Pseudoscience “journalist” just blow it out of proportion as some special thing.
It’s just a number you get when you smash a couple constants together. Specifically the speed of light, the gravitational constant, the Planck constant, the Boltzmann constant, and the Coulomb constant. The Planck length is specifically the squareroot(h/G/c^3 ). That is h = Planck constant (reduced), G = gravitational constant, c = speed of light. Combining these constants this way happens to give you units of length. That’s all it is. End of story. There is literally nothing else to it. Anything anyone else is saying beyond this isn’t true and has no basis.
And you can get any unit from these, you just set these constants to equal 1 and see what pops out. The Planck mass for example is 0.02 milligrams. This is less than you, but more than one of your cells. It holds absolutely no physical limitation. Clearly, 0.02 mg has no significance, so expecting the Planck length to hold significance is complete nonsense and pseudoscience. If anyone tells you a Planck “whatever” is some fundamental limit, they are clueless.
So what is the Planck length them? Well, it’s an absurdly small length you get from throwing a few constants together. Unlike the Planck mass, it is way out of the realm of everyday human experience, and on the small side. Planck temperature on the other hand is also way out of everyday human realms, but on the high end. What significance does it hold? Well firstly, using the Planck length, and mass, and all the other Planck values is a unit system on its own. But because it is based on fundamental constant, those constants are 1. The speed of light is just 1 in Planck distance per Planck time. Kind of handy, better than metric in some situations where the speed of light is 300,000,000 m/s. 1 is a lot nicer number for sure. Secondly, we know with absolutely certainty our laws of physics are wrong at the very small scale. How wrong and at which scale do they become very wrong? We have no idea. What exists on a small scale like this? We have no idea. But this Planck length happens to be very small, so we can confidently say by the Planck length, our laws of physics are worthless. Not at it, probably some point well before it, but definitely by it they are worthless. It’s just the only thing we have at that small of scale to use as a threshold.
For 1 and 2, you need to understand the surprising and absolutely unintuitive fact that energy is quantized. What this means is that you can only have a value among a discrete set of values for energy. To explain it a bit further, let’s say you are counting some stuff on a macroscopic level. Measuring water is hard because (without getting into molecular level) it’s a continuous stream and the volume can have any value. Counting eggs(or fruits or chocolates, etc) on the other hand, is not. They are neatly segregated into “packets” and your count of them can have only whole number values. So you say they are “quantized” because their total amount should be a whole number multiple of some basic “smallest amount” of them(one egg or one chocolate, etc) while water is not so constrained.
For most of the history of science, we thought energy was like water in that regard. However, recently we’ve found that energy is quantized: there is some minimum amount of energy that all other energy is a multiple of. This can be explained by the concept of “wave particle duality”. Basically, matter show properties of particles ( like protons, electrons, neutrons, etc) for some things, but behaves like a wave for others. This wave is something like a sound wave or electromagnetic wave (radiation, light, etc)- a propogation of oscillations of some value. In sound this value is air density, in light it is electric and magnetic field, whereas for matter it is probability. Probability that the matter exists there that is.
See, matter in the microscopic level doesn’t “exist” like it does at the macroscopic level. It doesn’t have a fixed location that it inhabits. It has a region where it can be, but the only way to find out is by “measuring” it, which causes the probability function to collapse and give a value. But even then, by the Heisenberg uncertainty principle, we can’t be a 100% precise in calculating where it will be. Now, probability and uncertainty here doesn’t just mean that we don’t know where it is, it means we can’t know where it is because it doesn’t have a fixed location at all. The square of the probability gives us the wavelength, which gives us the energy of the particle. The more precise we want to calculate its position the more energy we’ll have to spend in measuring it. Energy is also equivalent to mass by Einstein’s equation. There comes a certain point, where the difference in distance is so small, that if we had to measure it with more precision, we’d have to put so much energy there that it would be so massive in such a small area, that the density would be that of a black hole. Therefore we can’t measure distances smaller than that without there being black holes. That length is the Planck length.
I feel I’ve done a really bad job of explaining it, there may be some parts that you can’t understand and even some mistakes, my physics is not very good and I’m a computer science student, not physics. So I hope someone who actually knows this physics properly can correct me and explain it better. But this is basically the gist of it I think.
Our “standard model” of particle physics does not take gravity into account, but it should work with weak gravity.
At lengths around the plank length a particle has so much energy density that it would form a black hole and thus definitely have strong gravity.
So the plank length is where our weak-gravity-assumption stops working and hence are no longer sure what happens.
>(1) What is a wavelength actually?
I’ll tackle this one.
First, think of a guitar string. When you pluck that string, it starts to vibrate back and forth. Now, imagine a point on the string somewhere down the middle. Picture that point going back and forth as the string vibrates. Now, let’s get out a piece of paper and draw two axes on it: the horizontal axis is time, and the vertical axis is distance. Let’s graph the dot’s position over time. It goes from one side to the other and then back, oscillating up and down and up and down. If you look at that line, you’ll see peaks and valleys, sort of like a wave! The wave “length” is the distance from one peak to the next.
Guitar strings are not the only thing that vibrates; on the atomic level, literally everything in the universe vibrates as well! Quantum mechanics is the science that deals with these waves and that describes particles such as electrons, protons, and neutrons by their wave functions.
Does that help a little?
Max Planck designated it as the smallest measurable length of consequence, by definition. that’s the definition of a Planck unit of distance. anything smaller is inconsequential in terms of physical distance. that’s it. that’s the definition.
>Why is the Planck Length the “smallest thing in the world?” Or at least I hope I asked it right.
It’s not. At least, no one is saying that we know it is. Rather, it’s the smallest length that we can *measure* (sort of). The short version is that quantum theory says to measure a length of distance precisely, one needs to put a lot of energy into a small space. As the distance gets smaller, then the energy requirements get bigger. Eventually, one puts so much energy into the space that it would become a black hole according to the rules of general relativity, and that happens at the Planck length. However, no one really thinks for sure that this would happen, but it is past the point at which our known rules of physics break down. It’s more like “we have no idea how the rules of physics work beyond that length of distance”.
(1) What is a wavelength actually?
A wevelength is the distance between identical points on a wave. So: the distance from peak to peak, or trough to trough. That kinda thing.
(2) How are wavelengths and energy related?
The higher the energy, the shorter the wavelength. For a somewhat intuitive sense of this, you can consider that a single wavelength (peak to peak) carries a constant amount of energy. If the wavelength is shorter, you can fit more waves into the same space, and thus you have a higher energy. This is not *actually* how it works, but hopefully provides a good intuitive feel for it.
(3) Why is the Plancks Length the smallest thing in the universe?
Strictly, the Planck length is not necessarily the shortest length possible. See my below point.
(4) What happens when something is smaller than a Planck Length?
Below the Planck length, our currently-understood laws of physics break down.
All our laws of physics apply to certain “regimes”, certain spans of energy. As we’ve seen above, wavelengths correspond to energies. Above a certain energy, none of our currently-understood laws of physics hold. In the same way that special relativity takes appreciable effect above a certain speed, so “something else” must take effect above this energy cutoff. The value of this energy cutoff corresponds to a length of the Planck length.
Paul Shillito (Curious Droid) just did an excellent video on scales from the very big (light-year) to the very small (Planck length): [The Scale of Everything](https://www.youtube.com/watch?v=ST7EP7xnriM). Worth a look!
He explains the Planck length as such:
>Think of a dot that has the same diameter as a human hair, about 0.1mm. This is about the smallest thing we can see unaided. If that 0.1mm dot were magnified to the size of the observable universe, all 93 billion light-years of it, then the Planck length would be the size of a 0.1mm dot in comparison.
When you see something, what you are actually seeing is the reflection of light particles which have reflected from that object into your eyes.
Think of Planck length as just a theoretical number. It is the limit for which we can focus light without having the amount of energy which you have focused into that area turning into a black hole. This makes it the smallest potential observable (and measurable) length.
The Planck length is a theory (has not been proven). In the Planck length theory it says, it could exist smaller particles/lengths. But everything smaller than a Planck length. Would not matter/ be relative in the universe, as anything more than just a practical/length.
So imagine the universe is a human, which can’t eat anything smaller than an apple and a Planck length is an apple. The human will not have any effect by any foods that are smaller than an apple.
So there for is, the Planck length the smallest length in theory.
Latest Answers