# Visualizing the Planck Length. Why is it the Smallest Length in the Universe?

## Arvin Ash

Visualizing the smallest size in the universe – Planck Length & why you can’t go smaller

Visualizing Planck length – why is it the smallest in the universe? Graphics courtesy of Michael and Cary Huang: http://www.htwins.net/

The scale of the universe is bigger than you can imagine. It is also smaller than you can imagine. The smallest lenth theorized to be possible, the Planck length is about 4 X 10^-35 meters. Just imagine things that are about the size of your body. Things like the giant earthworm that lives along streams in Australia. Or a big beachball, which can be found near oceans and beaches all across America.

Now, lets go smaller by one order of magnitude, so now we are looking at things that are on the scale of about 10 centimeters. These are things like the shrew, or a chicken egg.

Now let’s go a thousand times smaller than the scale of a human being, on the order of 1 millimeter or one thousand of a meter. Here, you’ll find things like a grain of sand or dust mites.

Let’s go 1000 times smaller than this scale. Now we are going a hundred times smaller than the width of a human hair. And ten times smaller than even bacteria. Here, we are going to find things like large viruses.

Let’s keep going to 1000 times smaller this. This is nanometers, or one billionth of a meter. Now we are exploring a universe that we can’t see with optical telescopes. This is on the scale of the size of molecules like DNA and the glucose molecule, that your body uses as its source of energy. And the scale of the biggest atom – cesium.

Let’s go 1000 times smaller than this. This is one trillionth of a meter. This is on the order of the wavelength of gamma rays. This is the highest energy electromagnetic radiation, consisting of the most energetic photons.

Let’s go 1000 times smaller than this. This is 1X 10^-15 or one quadrillionth of a meter. This is the size of particles that make up the nucleus of all atoms, protons and neutrons. The size of a typical atom is however is 100,000 times bigger than its nucleus.

You would think that we are getting close to the smallest size theorized to exist – the plank length. But we are nowhere close. You have to go a quadrillion times smaller than one quadrillionth of a meter, or 1 X 10^-30 of meter….and you would still need to go another 100,000 times smaller than that, or 1 X 10^-35 meters. Then you would be at the plank length. In fact, if an atom was the size of the earth, a planck length would be smaller than the size of an atom – it would be about the size of a proton.

But What exactly is a Planck length and why is it the smallest length?

Planck length is actually derived from the fundamental constants of the universe that define the properties of space-time: The speed of light – c which signifies the maximum speed of communication in the universe. The gravitational constant – G, which signifies the magnitude of gravitational force between two massive objects. And the reduced Planck Constant – h bar, which links how much energy a photon carries depending on its electromagnetic frequency.

These are really the only constants that define the fundamental properties of the universe and all its contents. By taking different mathematical combinations of these constants, and reducing their units, you can get a length. By similar mathematical manipulation, you can also get planck time and planck energy.

But what does this length mean? Why is it significant?

It is the smallest length at which gravity would have an effect. It is the scale and size of the strings in string theory. It is also the scale at which space-time is theorized to become quantized in Loop quantum gravity theory.

So why is it the smallest length? In 1964, C Alden Mead determined that using the known laws of quantum mechanics and laws of gravitation, it is impossible to determine the position of an object to a precision smaller than the Planck length. So from what is currently known about quantum mechanics, a length smaller than the Planck length has no meaning.

Note that I said “known” laws. It is possible that at lengths smaller than the Planck scale, gravity or quantum mechanics behaves completely differently, that we may not yet know about. This is quite possible. So until we find out what happens at such small scales, we will need to wait for a future Einstein to reveal this to us.

One of the remarkable things about Planck length is that since it is derived from the fundamental constants of the universe, which by definition applies to everything, it will be the same no matter what language you might speak, what units you might use, or even what planet you might come from.

Ao, if we ever come across aliens from another world and compare notes, we both will have the same length for the smallest length possible in the universe.

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