So I get that a Planck length is the smallest length measurement that we have. But why?

I know it has something to do with gravity and speed of light in a vacuum. But why? Is it the size of the universe as early as we can calculate prior to the Big Bang? What is significant about it?

All the videos I see just say it’s a combination of these three numbers, they cancel out, and you get Planck length – and it’s really really small. Thanks in advance!

In: Physics

Planck length and related constants, represent quantities beyond which the laws of physics as we currently understand them, kind of hit a wall and cease to give reasonable answers. Those laws say we can’t have EM radiation (aka “light”) whose wavelength is the Planck length, for instance, because at that wavelength, Einstein and Schwarzschild’s equations say the energy carried by a single photon, would be enough to collapse the photon into a black hole.

And because of all our laws which connect different physical units to each other, there’s a host of interrelated prohibitions which fall out of this. You can’t have matter that’s hotter than the Planck temperature, because if you did, then its thermal radiation would have a wavelength shorter than the Planck limit, and so on.

Nothing. It’s not important at all. It’s way smaller than anything we can measure. Absurdly, radically smaller than anything we could dream of measuring.

Now, it is approximately the smallest length that our known physics applies. Very approximately. This is just because it’s around the distance that gravity’s influence should become significant, and we don’t know how gravity works at such small scales.

The length itself is a cool idea. The length of a meter, or a second, is arbitrary. Why is light speed 299,792,458 metres per second? What if we said the speed of light is “1”. Let’s repeat this for several different numbers, like the gravitational and planck constants. Now every other unit, like distance and time, can be derived from one of these. By combining these constants, we can derive other units. For instance, in this system, a unit of time will be sqrt(hG/c^5 )

Now in our regular units h and G are very small, while c^5 is *insanely big* so the resulting time unit is ludicrously small.

>So I get that a Planck length is the smallest length measurement that we have.

Misconception. It is the smallest measurement that we can do anything with with accuracy because once your go smaller, quantum uncertainty kicks in.

>I know it has something to do with gravity and speed of light in a vacuum.

It is calculated using 3 constants. Gravitational Constant, Speed of Light and Planc’s constant.

>Is it the size of the universe as early as we can calculate prior to the Big Bang? What is significant about it?

No, has nothing to do with it. It is just a threshold to tell us we can’t calculate things with accuracy if the length is smaller than a Planc length.

Have you ever heard of [Zeno’s Dichotomy Paradox?](https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Dichotomy_paradox). It basically asks the question of how you could ever arrive at a destination when you always have to pass through a halfway point between where you currently are and where you want to go?

The Planck Length is basically the universe’s answer to that paradox, which is to impose a minimum amount of time that must elapse and a minimum amount of distance that can be traveled during that time. Because that minimum amount of distance per time can be greater than the halfway point between you and your destination, Zeno’s paradox doesn’t exist in the real world and objects can move meaningfully in space.

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