[geordief (OP)]

The level of resolution to achieve that seems formidable. Are there any possible techniques that might amplify any differences that might be expected if one model or the other was truer?

For what it is worth I lean to nature actually being fundamentally discrete .

Is the whole "fundamental" idea just airy fairiness in the first place and we just have to accept that all our models will only apply to the level they are pitched at?

[alancalverd]

Planck and Millikan demonstrated the quantum nature of light and charge. Particles other than the electron are a bit more difficult to demonstrate directly, but the whole of chemistry depends on the discrete and invariant nature of atoms.

[geordief (OP)]

Planck and Millikan demonstrated the quantum nature of light and charge. Particles other than the electron are a bit more difficult to demonstrate directly, but the whole of chemistry depends on the discrete and invariant nature of atoms.

Does that imply that spacetime should also  have a discrete nature when examined closely enough?

Are there any possible methods that could be used to test this?

edit:I realize spacetime is a only part of a model .I am wondering if it is attempting to model something that might turn out to be ,at least in part discrete.In other words might  a theory of quantum gravity  need to be a "discrete " rather than a "continuous" theory?

[Bill S]

Does that imply that spacetime should also  have a discrete nature when examined closely enough?

Obviously, spacetime includes time, and we looked quite extensively at time at

https://www.thenakedscientists.com/forum/index.php?topic=73398.0

[alancalverd]

No.Spacetime is a mathematical concept used to model the observed universe, and for the most part it works best as a continuum. It's easy to plot discrete events on a continuum, but very difficult to do so on a granular surface.

[evan_au]

Looking back, discrete energy levels for electrons in atoms did explain some things: Why light from glowing gas emitted specific wavelengths, and why the whole Earth didn't immediately collapse into tightly bound protons+electrons.

After we discover granularity in some other effects (like space or time), we may discover why some other things are the way they are...

The great successes of quantum theory over the past century lead many physicists to think that most of the universe is quantised (eg gravity quantised in gravitons - but they are just very tiny).

But these arguments date back at least as far as Zeno, in 400 BC.
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes

[yor_on]

I would say it's a matter of taste. Any continuous flow can be broken up into chunks. The chunks size will depend on your instruments capacity of resolving. Planck scale is not resolvable, and most probably never will be either. You are free to turn it around and assume that a granularity exist on some level of scale unresolvable for any future instruments, making it a 'flow' to those experiments able to resolve. For the moment I'm thinking of it as some weird sort of duality  :) Mostly because I keep changing my mind thinking of it. I seem to remember some idea in where you could use SpaceTime itself to test it astronomically, but I can't remember where I saw it. Then you have this one  https://phys.org/news/2016-04-universe-space-time-discrete.html.  If 'gravity' would be gravitons, where does that leave relativity, The second postulate in the equivalence principle states that there is no way for an observer to distinguish locally between gravity and acceleration. That means that GR in the case of 'free falling' reverts to SR

And in the link I gave, do notice " One of the problems to be solved in this respect is that if space-time is granular beyond a certain scale it means that there is a "basic scale", a fundamental unit that cannot be broken down into anything smaller, a hypothesis that clashes with Einstein's theory of special relativity.

Imagine holding a ruler in one hand: according to special relativity, to an observer moving in a straight line at a constant speed (close to the speed of light) relative to you, the ruler would appear shorter. But what happens if the ruler has the length of the fundamental scale? For special relativity, the ruler would still appear shorter than this unit of measurement. Special relativity is therefore clearly incompatible with the introduction of a basic graininess of spacetime. Suggesting the existence of this basic scale, say the physicists, means to violate Lorentz invariance, the fundamental tenet of special relativity."

[evan_au]

But what happens if the ruler has the length of the fundamental scale? For special relativity, the ruler would still appear shorter than this unit of measurement. Special relativity is therefore clearly incompatible with the introduction of a basic graininess of spacetime.

Not if you also introduce the other significant component of quantum theory: uncertainty.

In our familiar world, we might measure the length of a macroscopic object as one meter±0.001m
- But in the probabilistic quantum world, we might measure the length of a quantum-length object as 50% one, 25% zero and 25% two.
- If you then travel at relativistic speeds compared to this object, you may then measure the length of this quantum-length object as 50% zero, 30% one,  and 20% two.

So I don't think that Special Relativity is inherently incompatible with quantised space.

[yor_on]

You know Evan, I've more or less presumed that relativity must be 'compatible' for the longest time but I'm not sure any more. Although I got this notion recently of 'scale dependencies' existing, just as 'observer dependencies' does, and in such a manner it might be compatible, to me that is :) And if you consider the equivalence principle between uniform accelerations and 'gravity' it seems to me that 'gravitons' then would need to support not only 'gravity' but also its relativistic equivalence, uniform acceleration. That should make it quite tricky to construct, shouldn't it?

there are some new ideas called 'emergence's' and maybe scale dependence is just another side of that coin.

[yor_on]

But yes man :)
A beautiful way of thinking of it, indeterminacy. And you can apply it to the question of discreteness versus a flow too. There are no clear answers.

[yor_on]

Thinking of it, I'll stick with Einstein. So it's a 'flow' :)
Or a scale dependent 'emergence' ::))
Or both ....
=

Why I would stick with him is because his theory is truly imaginative. Statistics aside, where is the imagination?
They call it being outside the box, don't they :) although there's a lot of 'black boxes' involved in Einsteins thought experiments he's still outside to me.