“Why is the Planck Length important in understanding gravity and the universe? #PlanckLength #Gravity #UniverseExploration
– What exactly is the Planck Length and why is it considered the smallest measurement?
– How does the Planck Length relate to gravity and the speed of light in a vacuum?
– Is the Planck Length connected to the size of the universe before the Big Bang?
– What makes the Planck Length significant in scientific calculations and theories?
– How do the combination of numbers leading to the Planck Length impact our understanding of physics?”
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.
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.
(Edit to elaborate: Einstein says, “energy is mass.” Schwarzschild says “it takes *this* much mass packed into *this* small of a radius, to make a black hole.” Planck’s equation says, “the smaller a photon’s wavelength, the more energy it carries.” Together they say: “A photon THAT small, would basically be too energetic to exist.”)
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.
eta2: It’s important to add, these limits are at present purely theoretical. We really have *no idea* if the relativistic model is correct at sizes that small, or if quantum gravity is actually weirder and more complex than that. We don’t know if sub-Planck photons, super-Planck temperatures, &c. are actually forbidden by the universe, or if we would just need new physical laws to describe their behaviour. It’s not something we can even remotely approach experimentally yet.
>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.
It’s the point at which our understanding and ability to do calculations within physics stops being reliable.
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.
It’s mostly wishful thinking. Planck scale is far enough from our current capacities* that we can imagine anything happens there without having to worry about falsifiability
*At least from a particle physics perspective. From an astrophysics perspective, Planck mass black holes should be a thing, and should explode with a very particular spectrum. We have been looking for decades with no result.
Not an ELI5 question. But I’ll try. Planck length isn’t just smallest length measurement. It’s smallest meaningful measurement. It’s like pixel of the Universe. Anything beyond that limit becomes meaningless, or collapses into infinities or zeroes in math.
To measure things, you need to interact with them. In our mesa-scale world you can do measurements by just applying a ruler, but think of it this way – you don’t actually measure anything by ruler alone, you do it by detecting and interpreting light that comes from it with your eyes and the object you’re measuring. So, you need light, and eyes obviously. And light do interact with your object, though without any noticeable effects. In quantum world of elementary particles, though, the light interaction might and do mess up with a lot of things. And the visible light particles are enormous compared to Planck’s length, so you need something else, something smaller. But then quantum mechanics comes into play, and as you get your measurement particles smaller, they becomes less precise, so you have to have them at higher energies to increase precision. At some point, as you close up to Planck’s length, you have to have them at such a high energy at such small radius, that they essentially become a black hole and you physically cannot pump them with more energy. No matter what particles you use – electrons, photons, neutrinos maybe, anything have it’s limits. Usually, that limit is much much higher than Planck’s length. Except for light, for which Planck’s length is the limit. The smallest possible wavelength of light, with highest possible energy of a photon. Any higher than that would be a Kugelblitz, a black hole made of light, though at incredibly small size, and it would evaporate into photons of lower energy the very moment it’s created.
Now, what makes Planck’s length important is that it’s literally the cause and the root of quantum physics (meaning that quantum physics started as an attempt to explain this constant). It’s everywhere as a boundary of what’s possible. It saves our Universe from ultraviolet catastrophe (according to older theories, we should’ve been evaporated by cosmic ultraviolet light, which obviously not what happening), from femtoscopic Kugelblitzes, it’s tightly tied with the speed of light and defines causality, it sets the boundary between quantum uncertain world and our well-defined mesascopic world of wavefunction collapse (because Uncertainty principle is based on an equation that includes Planck’s constant), etc, etc. It’s literally everywhere in the quantum physics as one of the most if not the most important constants.
There’s nothing special about the Planck length. It’s just another unit that we could use to measure distances, like inches and meters. The Planck length is part of a family of units called the Planck units, and these were all chosen to make a bunch of physical constants have values of 1, so that doing calculations would be easy. For example, in imperial (American) units, the speed of light is about 671 million miles per hour. In metric units, it’s 300 million meters per second. In Planck units, it’s 1 Planck length per Planck time. It just happens that the Planck length is really short, so a lot of people ascribe it some mystical importance, but it really isn’t anything special. It’s no different than yards or kilometers, just shorter.
Planck length is a boundary of light wavelength. Shorter wavelengths would mean gravity would take over. Other than knowing it, it has had no significance to humans. It’s an extremely high energy density. No star comes even close to this number.
PS We produce higher temperatures than the suns core, but we are nowhere near Planck energy density. We can produce this energy in like 5 seconds. But for Planck length to be relevant, it has to already be there.
If you have too much mass in one spot, you get a black hole. Also in order to measure something very small, we have to bounce electrons off of it, and measure the returning electrons. To measure smaller and smaller with accuracy, you need higher energy electrons. Einstein discovered that mass and energy are equivalent to E=mc^2, so with enough energy in that electron going to a small enough space, you end up with enough mass in one spot to create a black hole. This means your electron won’t get bounced back and you can’t measure it, and that small length is the planck length.
This is just untrue. The wavelength of a photon is dependent on the relative velocity of the observer: if you move towards a photon, it will appear to have a shorter wavelength than if you move away from it. If you move fast enough towards a photon, you can observe its wavelength to be as short as you want, including as short as the Planck length. If the Planck length really was the limit at which a photon would turn into a black hole, then every single photon would immediately turn into a black hole because some reference frame would see it having a short enough wavelength.
You are correct that (some of) the Planck units are far beyond the scales we can currently measure, and this unfortunately leads to superstition and misinformation that they’re “special” somehow. As it stands currently, there is no evidence that Planck units represent any sort of limit on the universe. Maybe one day we’ll be able to measure the Planck length and find that is is important, maybe we’ll find out it isn’t, and maybe we’ll find it’s impossible to reach the Planck length because the limit is much higher. But for now, the Planck length isn’t special; it’s just math.
At first I left this as a comment to someone else’s response, but after seeing a lot of misconceptions in this thread I decided to make it a standalone comment.
First, there’s nothing that prevents us from explaining things that are smaller than Planck length. In fact, the Planck mass is on the microgram scale, and we routinely study things that are muchhhh less massive than that. In reality, the Planck length (and other Planck units) are a set of units such that a bunch of physical constants that routinely pop up in our equations are equal to 1.
As an example, in SI units (ie meters, seconds, kg, etc) the speed of lights is 3×10^(8) m/s. However, say we redefine our unit of length to be one light second (the distance light travels in one second). We then have, in this new set of units, that light travels exactly 1 light second per second, so in this set of units the speed of light is 1. We can see that there’s freedom in our units to make this happens (we could have instead taken our length unit to be light years and our time unit to be years and we’d also have c=1), so we can ask ourselves if there’s a choice of units that also allows for other quantities of interest (such as Planck’s constant) to simultaneously have a value of 1, and the answer is yes. The Planck units are a set of units such that the speed of light, Planck’s constant, Newton’s gravitational constant, and the Boltzmann constant all have a value of 1. That’s all that they are, and as we can see there’s nothing particularly fundamental about them that prevents us from studying things that are smaller than them.
Source: PhD in theoretical physics
Another Eli5 answer is that at planck length, there is 100% uncertainty. So you are (in theory) inserting so much energy into such a small region that what you try to measure will be pure bollocks.
There could be smaller things happening at faster times than planck time. But who knows? We don’t know if this is a hard limit, but we also don’t have any reason to think so.