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
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.
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