#planck time

omg cool question, just grab my two big interests and mash em up :3! so the answer is like... "maybe sorta", in relation to the "Planck time" and "chronon".

which is to say, there may be a smallest possible time interval below which (quantum something something), but the universe wouldn't be 'updated' at the same time all at once like a timestep in a computer simulation. relativity makes the concept of 'the same time' kind of tricky. but we're getting ahead of ourselves.

so, in physics, we model the universe with equations like the Schrödinger equation, which says "this is how the quantum wavefunction evolves" or "this is how electric and magnetic fields interact with charge". and these equations usually have some special numbers in them that are like, the basic parameters of the universe, which say for example how strong gravity and electromagnetism are, how fast light goes, that kinda thing.

these constants may be given by a more "fundamental" theory. for example, the speed of sound depends on the elastic properties of its medium, so you could theoretically work it out using the underlying model of electromagnetism, lattice vibrations etc. but some of these constants we have no way to calculate based on something else, we have to do an experiment.

now, theoretically, we have two approaches here:

we can do an experiment to measure them relative to something we do know, like a particular metal bar, and say that is the "metre". so we can say, the speed of light appears to travel 299792.4562±0.0011 metres long (the best measurement in 1972)

alternatively, we can define our measurement system based on the constant. so now instead of the metre being a metal bar, a metre is exactly 1/299792.458 of the distance light travels in a second. now the uncertainty is in the precise length of the metre.

the latter may seem weird and counterintuitive, but it's considered more rigorous, since the speed of light is available to anyone anywhere, and keeping a metal bar an exact length turns out to be surprisingly difficult. (along the way, the metre was defined based on radiation.) the SI has since done their best to define all the units using this kind of "explicit constant", the last one being the kilogram, which stopped being a lump of metal in Paris a few years ago.

anyway, that's all a little tangential... the point is, when you do this sort of definition, it's natural to say, well that fraction feels a little arbitrary, right? what if we measured everything in, say, the length light goes in a second? but wait, the second is also very arbitrary (a certain number of exact caesium transitions). can we come up with a unit system where all the important fundamental constants end up with the value 1?

this is already a pretty standard thing in certain areas of physics. in relativity, it's common to say we'll measure space and time with the same unit (treating them as having the same dimension) so the speed of light is exactly 1, a system which we call "natural units". this may sound weird but the maths is just fine. this has interesting consequences, like energy and mass now have the same dimension (which is why you might often see physicists discussing masses of particles in energy units like electron-volts), and speed is dimensionless, but it's fine! however, we still have to have some unit of space or time to use as the basis of our measurement system.

so what if we took it further, and set more constants to 1, eliminating all dimensions? in other words, measuring everything against products of the fundamental constants? to make this work, we need to choose a suitable set of fundamental constants. this is where we go into Planck units. the idea dates all the way back to 1899, when Max Planck proposed doing it based the following four constants...

the speed of light in a vacuum, c, (which is the fastest speed that anything can go relative to any observer in special relativity)

the gravitational constant, G, (measures the strength of gravity)

the reduced Planck constant, ħ, (used throughout quantum mechanics)

the Boltzmann constant, kB (used in thermodynamics pretty much any time temperature is relevant)

to this we could also add electromagnetism by adding the electric constant (aka vacuum permittivity), ε0.

to make a Planck unit, you basically shove these together until they have the right dimensions. for example, say we want to measure energy which has dimensions [mass][distance]/[time]^2. well, the Planck constant has dimensions [mass][distance]/[time], the gravitational constant has dimensions [distance]^3/([mass][time]^2]). the speed of light has dimension [distance]/[time]. so if you mash then together as sqrt(ħc^5/G) you get units of energy. which turns out to be about 2×10^9J in SI units, which is a huge amount of energy.

the thing about Planck units is that they tend to be either really big or really small. of interest to this post is the Planck time, sqrt(ħG/c^5), which comes out as about 5.3×10^-44 seconds. this is basically unimaginably brief. written out in positional notation it's 0.00 000 000 000 000 000 000 000 000 000 000 000 000 000 0053 seconds. we apparently have not yet been able to measure time to within an uncertainty of less than 10^-19 seconds, and while someone has an idea of an experiment that could detect effects as brief as 10^-33 seconds, this is still way way slower than the Planck time.

so we can define a really small time, but why is this important? well, physics has - for most of the last century - been struggling with a puzzle of "quantum gravity". tl:dr is we have an amazing theory of small things called quantum field theory that has made some truly amazingly accurate predictions; we have an amazing theory of gravity called general relativity that has also made some truly amazingly accurate predictions; if you try to combine the two, it starts throwing out infinities and getting really logically confused.

so, physicists believe, there must be a more fundamental theory of 'quantum gravity', to which general relativity and the standard model of quantum field theory are just approximations, just like newtonian mechanics is an approximation of relativity that works well at small speeds. this theory is nicknamed the 'theory of everything'.

unfortunately, despite decades of trying and some really abstruse mathematical apparatus, nobody has figured out anything that looks like the answer. sure, there's ideas, most (in)famously string theory, but there's nothing which has shown the predictive power we demand of a good physical theory.

why is this relevant to time, and the Planck time especially? well, the 'Planck scale' is considered to be where our existing theories break down - it's where gravitational and quantum effects are on about the same scale. it's thought that to understand physics at times as brief and distances as short as the Planck scale, we'll need that new theory of quantum gravity.

but we might not have to go down that far. apparently one of the mathematical ideas that physicists have been trying on is that time might be 'quantised', i.e. coming in discrete steps like animation frames. the name given to this step is a 'chronon', although i don't know if you could exactly call it a particle despite the name.

some sources, including that article, seem to speak of the Planck time as the "smallest possible time interval" between two events. but I'm not really sure why this is said - and it's covered in citation neededs so it seems a little dubious.

unfortunately, QFT and especially quantum gravity is way above where i got to when i mental illnessed out of undergraduate physics, so i can't really explain why a chronon would be a useful concept or why the Planck time might be thought to be the smallest time. in the Schrödinger equation, in special and general relativity, and indeed in classical Newtonian physics, time is fully continuous - but this might be an approximation!

if there is a chronon, it's going to play in interesting ways with the relativity of simultaneity and quantum collapse and all that. like it seems you could very easily find a reference frame where events that are simultaneous in one frame are half a chronon apart in another. but the relationship between relativity and quantum interpretations is a subject i am not really able to address when I'm this sleepy lol.

Ask Ethan: Why is there a limit to what physics can predict?

"Why are there these units (Planck units) which you can't further divide?"

There are fundamental limits to the Universe, in the sense that there are scales where our laws of physics break down. You can't break matter or energy up into infinitely small pieces, and the same goes -- we think -- for space and time. But is that necessarily all true, and is that what the Planck scale means? Not quite. Rather, these are scales at which our laws of physics stop giving reliable predictions, as we make these mass, energy, length and time scales out of three constants fundamental to our physical theories: the gravitational constant, the speed of light and Planck's constant. They do have strong physical implications, but they don't necessarily mean these scales can't be divisible further. After all, every particle in existence has a mass far below the Planck mass!

Episode 2 of my series on cosmology has been uploaded on the socials!

https://youtube.com/shorts/EX4DDqgcpeU?si=LR4VNRkVXyDDVSF4

If reading Planck vaguely tickled your memory, it’s probably from the Planck Length, the shortest unit of distance we know of, and/or the Planck Time, the shortest unit of time we know of.

Now, it’s important for you to know, when I say shortest, I mean shortest.

The Planck Length is equal to 1.616255(18)×10^-35 meters long, or, as it says in the Wikipedia article “About 10^-20 times the diameter of a proton.” That’s 1 followed by twenty 0’s, or, 100 000 000 000 000 000 000 times smaller than the diameter of a proton.

THATS INSANE!

A Planck time is just as incomprehensibly small as the Planck length is, seeing as it’s the amount of time it takes for light to cross a Planck length, about 5.39×10^-44 seconds.

It’s important that you know how impossibly tiny these units are, because in the section “Analysis of the units”, directly after these two measurements is this.

Do you see that? Do you see that measurement?? What the hell is that???

Why is the Planck energy so much bigger than the other ones? Why are they using how much fuel is in a car as an example of how much energy it is?! What is this!?

Planck time is the smallest measurable interval and equals t-43 second.

In that first instant of the Big Bang, the universe consists of pure energy at a temperature of 1032 Kelvin. It is smaller than an atom. And so, in this first instant, the cosmos exists as a quantum event, which means that this inconceivable intensity of energy is not actually a point but a probability cloud – the original wave function.

An interval later, at 10-35 second after the Big Bang, inflation expands three-dimensional space faster than light by a stupefying factor of 1050!

But before this happens, the entire content of the Big Bang – all the energy that will eventually express the hundreds of billions of galaxies of the universe – exists in a space smaller than an atom and therefore subject to quantum uncertainty.

So, at t-43 second, everything that ever will be is There as pure energy.

What might ‘time’ mean in this First Instant just prior to inflation?

The ‘quantum jitters’ happening at t-43 second are now visible, writ large in the cosmic microwave background as the irregularities among the incandescent galactic filaments and vast vacuoles devoid of stars.

Within that quantum event at t-43 second are all the possible ‘universes’ that could ever exist (the renowned ‘sum-over-histories’).

The peculiar nature of energy, of light, is that it has no rest mass, hence is time-free.

Einstein’s famous thought experiment about riding on a beam of light reveals that a photon arrives at its destination instantly – with no passage of time for the photon – and no distance traveled from the photon’s perspective.

Therefore, at t-43 second, when all that ever-will-be is light, is every thing and every place that will be already happening?

Are we, in truth, There now, at t-43 second, still entangled with Everything?