It's probably in jest to joke that the newly emptied out office spaces could be converted to vertical farming of cannabis for growers' clubs which are going to be legal from April 1st in Germany.
To be honest, if these growing clubs could cover rent + electricity + water in my opinion it is not really that bad of an idea to take over empty office buildings, most legal cannabis is already grown in very controlled environments, open plan offices would be pretty good for it.
It is true that there is no experimental evidence, but I think there are some convincing arguments that something must happen at the Planck scale (for very short distances) in a full quantum-gravity theory.
Here are some quotes from "Covariant Loop Quantum Gravity", Rovelli and Vidotto (slightly redacted). I suggest the whole chapter 1, in particular 1.2 to get an idea of why fundamentally spacetime may be discrete.
"In general relativity, any form of energy E acts as a gravitational mass and distorts spacetime around itself. The distortion increases when energy is concentrated, to the point that a black hole forms when a mass M is concentrated in a sphere of radius R ∼ GM/c^2, where G is the Newton constant. If we take L arbitrary small, to get a sharper localization, the concentrated energy will grow to the point where R becomes larger than L. But in this case the region of size L that we wanted to mark will be hidden beyond a black hole horizon, and we lose localization. Therefore we can decrease L only up to a minimum value, which clearly is reached when the horizon radius reaches L, that is when R = L.
Combining the relations above, [..] we find that it is not possible to localize anything with a precision better than the Planck length (~10^-35 m).
Well above this length scale, we can treat spacetime as a smooth space. Below, it makes no sense to talk about distance. What happens at this scale is that the quantum fluctuations of the gravitational field, namely the metric, become wide, and spacetime can no longer be viewed as a smooth manifold: anything smaller than the Planck length is “hidden inside its own mini-black hole”."
"The existence of a minimal length scale gives quantum gravity universal character, analogous to special relativity and quantum mechanics: Special relativity can be seen as the discovery of the existence of a maximal local physical velocity, the speed of light c. Quantum mechanics can be interpreted as the discovery [..] that a compact region of phase space contains only a finite number of distinguishable quantum states, and therefore there is a minimal amount of information in the state of a system. Quantum gravity yields the discovery that there is a minimal length lo at the Planck scale. This leads to a fundamental finiteness and discreteness of the world."
You're talking about minimum lengths, not discrete spacetime.
It may be the case that there's a minimum length beyond which "no meaningful laws of physics apply", but it really says nothing about whether real numbers are indispensable in the formulation of physics, or about whether spacetime is continuous.
There being a minimum length doesnt mean that everything is a discrete multiple of this length, or that space is broken into units of it, or that objects have to be aligned on grid boundaries defined by it.
Whenever people try to do philosophy of physics the inevitable place everyone lands at is a series of false equivocations, often caused by the language of physics being ambiguous and polysemous. But "minimum length" here does not mean a sort of grid length.
I agree with all your claims here in the literal sense, but suppose there's a minimum length, then it would seem to be at least theoretically possible to use discrete mathematics to formulate an approximation to the "real number formulation of physics"?
The fact that we don't have already a full system using discrete maths doesn't mean it is impossible, because our current system is based on a long tradition of belief in real numbers, and assuming physical space is continuous.
I'd argue (admittedly unhelpfully) that unless we have actually tried to formulate physics using discrete mathematics and found a barrier that we prove unequivocally that it is impossible to overcome, we can't claim that physics must be formulated using real numbers/continuous math. There's a difference between "we don't know how to do this" vs "we know we can't do this".
I don't understand your point, I never said that "everything is a discrete multiple of this length, or that space is broken into units of it, or that objects have to be aligned on grid boundaries defined by it", I just wanted to mention that "continuity of spacetime is a convenient approximation" may be a correct sentence in the context of quantum gravity.
Also, for what is worth, in QM the space of wavefunctions can also be finite dimensional (for instance the Hilbert space of a spin 1/2 particle).
And that's not what a "minimum length" in this case means. We're not talking about space having a minimum unit. We're talking, at best, about (presumably massive) objects having a minimum extension in space .
Even with a "minimum length" (in this specific sense), you have an object at position p, and can (move/observe) it at any p+dx continuously.
importantly, the question is whether the best theories of physics in a world with a minimum extension-in-space require continuous mathematics, and there's nothing about this plank length to suggest they wouldnt
Discreteness would mean that there exists some base distance p such that the distance between any two objects is Np, with N being a natural number (and any surface is some Mp^2 and any volume is Qp^3 and so on). Continuity is simply the opposite of that. It could be that objects can be at arbitrary real-valued distance d from each other, but that d > p is a precondition for any other law of physics.
By contrast, discretness has various unintuitive mathematical properties that mean it's not easy to fit into some other theories (particularly those relying on differential equations).
