The question of scale

[Anonymous]

If I’ve understood correctly, based on experimentation and observation, broad scientific consensus exists around how the world functions at different scales – at a very large scale (planetary/cosmoliogical?), relativity theory; in our ‘ordinary’ world, classical physics; and, at very small scales, quantum theory. If this is the case, has science established any clear boundaries to these dimensions of scale, is it a hard boundary or some kind of spectrum?

[SciWiz]

Hi Richard, thanks for the question.

What you write is totally correct. The short answer is: there’s no hard boundary, the theories become increasingly inaccurate when applied outside of their proper domain.

When we will have a unified theory of quantum physics and gravitation (aka quantum gravity), general relativity and quantum physics will turn out to be an approximation of that theory – in the same way that Newtonian physics turns out to be an approximation of general relativity when masses and speeds are those typical of the macroscopic world around us.

To be more specific: Quantum physics can be applied to extremely small objects (e.g., processes at the molecular scale or smaller).

Relativity theory is the right theory to use when objects of large mass are involved (I’d say, roughly, from the size of a small moon onwards – so yes, on a cosmological scale) and/or objects moving at very high speed (roughly, you start getting noticeable effects from something like 5% or so of the speed of light upwards. The closer you get to light speed, the greater the effect). But there are theoretical complications when you try to combine it with quantum theory.

Outside these two domains (macroscopic objects, not extremely massive, and low speeds compared to the speed of light), Newtonian physics is a good approximation.

One of the necessary skills in science is to know what’s the best level of approximation that allows you to describe the phenomenon you’re interested in with the necessary accuracy, without focussing on unnecessary details: for example, if you want to study the motion of a bicycle, you don’t need to study the quantum wavefunction of each of its constituent particles, nor the way its mass distorts spacetime according to relativity theory: Newtonian laws of motions will provide you with the right tradeoff between accuracy and level of detail.

Best wishes, and good luck with your studies!
Marco

[Author]

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