Walking the Planck: the weird world of the littlest measure
Can there be a distance too small to measure or a moment of time so brief that it can’t be timed? Welcome to the weird quantum world of Planck measurements, where being “small” means the rules of physics themselves break down.
The tagline of this page is “Big (and little science) at STFC”. The “big” might include the study of insanely immense cosmic structures, such as stars, galaxies and black holes — stuff so large that they literally bend the fabric of the Universe to their will.
The “little” might include the brain-blending world of the unimaginably small — the quantum world of the atomic and subatomic, where our macroscopic view of reality is rendered impotent and the illogical reigns supreme.
But, beneath all of this there lurks another level of reality where our ability to quantify reality breaks down and being ‘small’ takes on a whole new meaning…
Distance: How short is too short to measure?
In theory, measuring extreme distances is limited only by how far you are willing to go — keep doubling a distance and there is no limit to how far your measurement can stretch.
But does it work the other way around?
Surely, it stands to reason that if you take a ruler and keep dividing it by half, there is no limit to how small the measure can go, but, as is so often the case in the quantum world, reason has precious little to stand on.
Let’s say you were to take a ruler (which for some bizarre reason measures 1.6 metres in length) and divide it into ten pieces and you take one of those ten pieces and divide that into ten pieces and so on.
In theory, you could repeat the exercise 35 times, but that is as far as you could go and no force in the Universe enable you to divide it further. This ‘last word’ in measurement units is called the Planck length.
The Planck length is 1.6metres divided by ten 35 times (1.6 x 10 ⁻³⁵), or 0.000000000000000000000000000000000016 metres, which, aside from being really very small indeed, is a measurement that is, as it turns out, as small as it is possible to go.
At this scale, the laws of physics we used to describe gravity and space and time become useless.
If two somethings were to be separated by less than one Planck length, there would be no way to determine which something was where.
Planck length: wave goodbye to measurability
We experience the Universe, for the most part, through our interaction with the electromagnetic spectrum (light waves, radio waves, x-rays etc) — our eyes can see where something is because they collect light photons that have interacted with the object (by bouncing off or being emitted).
All of the electromagnetic spectrum is transmitted by packets of energy called photons that have particular wavelengths — photons with more energy, like X-rays, carry more energy and have shorter wavelengths than light photons.
The shorter the wavelength of the photon, the smaller the object that photon can interact with — if it can’t interact, you can’t detect it.
The Planck length is so short that we could never create a photon with a short enough wavelength to interact with it — therefore, we can never measure anything smaller than it.
Even if we could create a photon with a wavelength shorter than Planck, it would carry so much energy, in such a small area, that it would collapse into a black hole before it could return any useful information.
Planck time: When the clock stops ticking
Time, theoretically, can tick onwards forever, but, wind it back to its smallest increments — past the second, the microsecond, and the picosecond — and eventually you come up against the smallest possible increment: the Planck time.
The Planck time is the smallest unit of time that can, in theory, be measured. One Planck time is the amount of time it takes a photon of light (traveling, naturally, at the speed of light) to cross a distance of one Planck length.
One unit of Planck time is equal to about 10 ⁻⁴³ seconds (or, 0.0000000000000000000000000000000000000000001seconds) — it is so short that the humble second is much (much, much) closer to the age of the Universe (13.8 billion years) than the Planck time is to the second.
Anything that happens before the hands of the Planck clock move on by one unit is, by definition, unmeasurable — a quality that allows all sorts of quantum mechanical weirdness to take place.
According to Quantum Theory (in particular Heisenberg’s Uncertainty principle), if you can’t see it happen, then anything can happen — in other words: if the Universe doesn’t see it happen, it didn’t happen (a concept that naughty children sometimes try to apply to the non-quantum world).
In this ‘grey’ zone of accountability, particles of matter can ‘borrow’ energy from the quantum vacuum and ‘pop’ into existence from literally nowhere.
As long as the particles ‘pop’ back out of existence and return their borrowed energy before the Planck time limit expires, the laws of ‘conservation of energy’ (which state that energy can’t be created or destroyed) haven’t been violated.
The land that time forgot
Perhaps the strangest byproduct of the Planck time is this: because time can’t be measured within the Planck unit, time as we think of it doesn’t exist in the quantum realm at all.
Even those who look after the planet’s atomic timekeepers, whose job it is keep our clocks ticking as accurately as possible, admit that they don’t ‘measure’ time — they just ‘define’ it.
The vacuum: When empty is far from empty
The discovery that space and time can’t be broken down beyond a certain point had bizarre implications for the way we understand the Universe. It showed that, because time and space each have a minimum dimension, at its most fundamental level the Universe is built from tiny quantifiable units, or quanta, which is where the science of ‘quantum’ mechanics gets its name.
Even the most featureless expanses of the Universe (the void, or the vacuum) are built from these quanta. At the quantum level, ‘empty space’ is never truly ‘empty’ and the concept of a vacuum being a complete absence of something falls apart.
A vacuum just appears empty to us because there is no energy or matter that we can measure. But beyond the measurable, in the quantum vacuum, empty space is seething with virtual particles that bubble up, live very (very, very, very) briefly on borrowed energy, and pop off again — something that physicists call ‘the quantum foam’).
A big deal for the Big Bang
Our inability to comprehend space and time at these scales has implications for our understanding of the origins of the Universe.
We are pretty certain that the Universe began life as an infinitely tiny, infinitely massive speck of energy known as the singularity (or, the primeval atom) that inflated and expanded in the Big Bang to become the Universe we know today.
Thanks to theoretical physicists and experiments like the Large Hadron Collider, we can chart the Universe’s development all way the back to almost the beginning, but the moments before it expanded to the Planck length remain a mystery. We have no idea what was going on because scientists don’t have anyway of describing it.
At the Planck length, the laws of general relativity, which we use to describe gravity and the geometry of spacetime (the fabric of the Universe combining time with the three dimensions of space), fall apart.
This is why you might hear of scientists trying to come up with a ‘grand unified theory’ — a new theoretical framework that will ‘unify’ the physics of the very big (relativity) with the physics of the very small (quantum theory).
Story by: Ben Gilliland
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