How is the “Plank Length” the absolute limit of how small something can be?

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How is the “Plank Length” the absolute limit of how small something can be?

In: Physics

It’s not. That is a commo pop science description of the Planck Length but it isn’t the real picture. The Planck Length is the base unit of length in the Planck Unit system, this is a system of units (like metric or imperial) defined so that certain constants like the speed of light are equal to 1. This makes doing mathematics easier as you can mostly ignore these constants.

The reason the Planck Length is often referred to as the shortest length comes from a misunderstanding about quantum mechanics. At scales below the Planck Length our modern understanding of physics breaks down, we don’t yet have a good understanding of how gravity interacts with quantum mechanics and at these scales both gravity and quantum mechanics will be important. This means to accurately describe physics at scales smaller than the Planck length we need a theory of quantum gravity, which we don’t currently have.

Basically the Planck length is around where our understanding of physics ends, but it isn’t a sharp cutoff just a gradual loss of accuracy and it doesn’t imply the Planck length is important physically for how small things can be. It is just a limitation of our theories.

Planck length is not the absolute limit of how small something can be.

There are many units of measurement. Meters, inches, light years etc.

Speed of light in meters per second is 299792458 m/s. That is not very nice number.
It would be nice if it was “1 some length/some time”.

Enter [Planck units](https://en.wikipedia.org/wiki/Planck_units#List_of_physical_equations).

The Planck units are defined in such way that many useful physical constants are “1” in them.
In planck units the speed of light is 1 planck length/planck time.

This makes math easier.
It does not have any deep “absoulute smallest unit of anything” at all.

the planck length is the absolute limit of how small something can be and still be detectable.

when you get to Quantum phenomena (aka when you go REAL small), things dont behave in a “classic” manner. everything in this world has both a “wave” side and a “particle” side. for stuff like you, your chair, your food, etc, that wavepart is so small that it’s essentially “not there” because it has no effect on anything.

but when you get to smaller and smaller stuff, that wave-part becomes (relatively) bigger and more important. and when you try to plot the speed or position of something it is no longer a “point” or “pillar” in your graph, but this “washed out area” and what makes quantum physics so weird is that that’s not because you dont know where the object is but because the object is in all of that area to varying degrees at the same time as long as you dont look too closely.

and you “looking closely” means you interact with that thing you’re looking at and influence it. and if you try to look so closely that you can pinpoint its position to something close to the planck length then you’d need so much energy that the thing you’re looking at is accelerated to lightspeed. and at that point all – even theoretical – attempts to be more precise break down

It’s not how small something can be, it’s how small we can see. To see something the wavelength of what were looking with has to be smaller than what we want to observe. Otherwise, the wave can just cruise on by unaffected, and to us observers an unaffected wave means “I didn’t see anything happen”.

At extremely small scales, we stop being able to do that forever. We need to get so much energy into what we’re using to look at what happens that E=mc^(2) becomes noticeable and we’re pumping mass into what we want to observe. At the Planck length we need so much energy to observe what’s there that we’ve added enough mass that it becomes a black hole, and by definition we can’t see what happens in a black hole.