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
My seven year old is extremely into numbers and space so I read him this ELI5 to see if he knew the answer. What stood out to him is that “Black holes don’t form if something is smaller than a Planck’s Length; they form if something is hotter than the Planck’s Temperature.”
1) picture a regular wavy line, google ‘sinusoid’ to get the right idea.
The line wiggles up and down, creating a series of ‘bumps’. All the ‘bumps’ pointing up, we call ‘peaks’ (like a mountain peak), the ones pointing down we call ‘troughs’ (like a pit animals eat from).
The wavelength is the distance between one peak and its nearest other peak, if you measure it with a ruler. It’s the length of one ‘cycle’ of the wave.
The wavelength tells you how big a single ‘cycle’ of a wave is.
2) waves with shorter wavelengths carry more energy. It takes more energy to pack those wave cycles closer together.
Waves also have a feature called ‘frequency’ which is related to wavelength.
The ‘frequency’ is the number of cycles that pass a specific point in a period of 1 second.
Frequency x wavelength = the speed of the wave.
For light, which always has the same speed called ‘c’, wavelength x frequency = c.
The energy carried by a wave of light is just its frequency multiplied by a constant, called ‘Planck’s Constant’, denoted by the letter ‘h’.
A wave with double the frequency carries double the energy.
Energy = frequency x h
Energy = h x (c/wavelength)
Waves carry energy from one place to another.
Sound, light, ocean waves, earthquakes and tremors (seismic waves), they’re all described in this same way.
3) the planck length isn’t exactly the smallest ‘possible’ unit of length.
There are other good comments explaining it better than I could do.
4) we don’t really know. It’s hard to test our current theories of physics on scales that small.
You can go infinitely big and infinitely small its just a way of saying, like miles or kilometers
It’s just the unit that makes quantum mechanics and general relativity stop having poles. Do you really think the universe is as simple as a variety of vector fields? The Planck units are a base for our *approximations* and the fact that they arise at all from our equations could mean either that the universe is discrete (unlikely) or that our physics can’t capture continuous space yet.
It’s the smallest mathematically significant distance, anything smaller than a Planck is so small we don’t have the tools or formulae necessary to use it
“Why is the Planck Length the “smallest thing in the world?”
its not, its the smallest distance that we can measure based on our current understanding of Physics, based on this we just accept that anything below this distance doesn’t really possess any notable properties regarding energy, therefore is not detectable with current methods that wouldn’t interfere with the experiment.
basically attempting ot measure a distance smaller than planck’s length with our current method would place too much mass/energy in a small space causing it to collapse into a black hole(which shouldn’t be a thing based on your understanding of physics, so its said that distance below plancks’s length physics sorta break down as nothing with such small perceived mass shouldn’t possess that sort of gravity).
If you’re looking for an intuitive way to consider the Planck units, divide the Planck length by the Planck time to get the fastest possible way to travel the shortest possible distance, and it naturally works out to be the speed of light. Since information cannot be packed further or faster into these basic units, that limiting factor naturally pops up
Follow-up question: Our understanding of physics can only take us back in time to a tiny amount of time after the Big Bang (call that duration T). Is the Planck Length how far light can travel in T?
It is the minimum “size” of an object that physics can affect. If it were smaller than this, things begin to break down and become unpredictable.
Plank’s constant is a relation (aka. a ratio) or how certain one can be about the position of a thing and a destination (velocity) of a thing (*h-bar = <certainty of position> x <certainty of velocity>*). This put a limit on how certain we can be [about many things](https://en.wikipedia.org/wiki/Natural_units#Planck_units):
* length (Plank length)
* time (Plank time)
* mass (Plank mass)
* etc
Essentially Plank length is [super-mega-uber smaller than the smallest sub-atomic particle](https://www.htwins.net/scale2/) we’ve found so far. So this limit is really far from reach at this point. But on a theoretical level (math) this is the limit at which any object can move. If the universe is a digital “grid” the Plank Length smallest move anything can make.
How did we find this value? By developing a [hyper accurate](https://en.wikipedia.org/wiki/Quantum_electrodynamics) (like 19 significant figures!!!) model for the electron and determined this constant was connected to energy levels (orbits) of electrons in an atom. Then we started finding it everywhere. Kinda like how we (humans) determined the smallest electric charge was by experimenting with different [drops of oil](https://en.wikipedia.org/wiki/Oil_drop_experiment) and factored out the differences to find the fundamental electric charge.
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