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Suppose I conjectured that, at some length scale, spacetime was discretized into "cells", Minecraft-style. For simplicity, I guess let's say they're cubes with side length $n$.

Presumably we can put an upper bound on $n$ from observation. For instance, myself and the table occupy the same $10 \text{m}^2$ cube of space, and we are two different objects, so $n < 10 \text{m}^2$. (Is this conclusion correct? Is my reasoning correct?)

Is there any experiment that would disprove this hypothesis for all $n$? My intuition is no, and I was using this as an example of a non-falsifiable hypothesis earlier today, but I was seized by doubt, as I have a math & computer science background without much physics.

Is my conjecture falsifiable?

Eli Rose
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If you want a falsifiable theory you must make a prediction about specific mutually exclusive ways the universe could be versus not be and then argue that one the groups must happen or cannot happen. Then when you investigate and find which one you get, you have falsified or not falsified the theory.

So ask yourself what you predictions are. Your predictions are a bit vague, but they sound like the predictions of a continuous theory. Why do I say that. It's because of the "at some level" part. It sounds like it means that at scales much larger than that hypothetical level every prediction agrees with the continuous theory.

So you could make the same predictions as a continuous theory and then whenever data is collected, no matter what data we see, the data was collected at some scale and you could just say that if only the scale was smaller things would have turned out differently.

But however small the scale is, you can pull the same trick. You never even need to bother making discrete predictions because whatever data fits the continuous theory also allows the discrete one to exist at the much smaller resolution without being exposed.

This freedom to wiggle out of any data is the hallmark of an unfalsifiable theory.

But if you claimed there was a discrete theory at a fixed level where experiments with a particular nonzero scale were small enough to require different predictions for the discrete theory. Now you have made a prediction that can be tested and thus your theory is falsifiable.

So you could have a whole family of theories, each predicting deviations at a different scale. And each one would be falsifiable. But the meta claim that at least one of them is correct, that meta claim is not falsifiable.

Timaeus
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Apologies for the late response. Also, I mean to post this as a comment to Timaeus's answer since this doesn't really answer your question, and I do not have 50 rep to comment.

A user in Phys.SE wrote this answer to similar question.

Seems like a rather simple thought experiment, with a conclusion that " no matter how much you reduce the scale, there's always a smaller distance possible". So, the universe has to prohibit movement along certain directions to preserve the smallest unit of displacement. Is this what actually the proponents of discrete spacetime believe?

Now, how would one claiming discretized spacetime get around this?

Community
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Will Graham
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I will state that specific models, regardless of scale as discussed in the other answers, can be falsified by not being able to incorporate the standard model of particle physics in its mathematics. The standard model represents innumerable measurements/data and any theory has to be able to demonstrate that the model emerges naturally from its formalism.

In addition, any model must obey Lorenz transformations, which also is validated by innumerable measurements. These have shown that the interactions of the particles in the standard model are local, and this has to be seen to emerge from the model naturally for it to have a connection to real data and not be a mathematical game.

There exist other gauges than scale , and these can invalidated the model.

anna v
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