One experiment suggests that time is an emergent property of quantum entanglement. [1]
"A static, entangled state between a clock system and the rest of the universe is perceived as evolving by internal observers that test the correlations between the two subsystems. We implement this mechanism using an entangled state of the polarization of two photons, one of which is used as a clock to gauge the evolution of the second: an "internal" observer that becomes correlated with the clock photon sees the other system evolve, while an "external" observer that only observes global properties of the two photons can prove it is static."
I'm working in a field where m=1 and hbar as a semiclassical scale is given as order of N (number of bosons or fermions), i.e. I don't do actual real physics...
But.... a thought experiment:
If a particle experiences time differently dependent to its speed in relative to a frame of reference, i.e. that time experienced is scaled according to its speed. Since speed is definitely not discrete, scaling it with time, even though time in itself is discrete as you claimed, still makes the time experienced for said particle to be continuous, no? Is this not a contradiction?
Slightly unrelated but your comment led me to actually learning what the Planck length is, and the Wikipedia article for it has a great section on how to visualize it [1].
I am unconvinced that time is a real dimension, sure we can model movement/interactions of particles as a 4th dimension, but nothing in our understanding of physics requires it being a physical reality. IMO it's less space-time and more just space, it's just the rate of change slows with more mass.
There's at least one prominent physicist [1] who is working on showing that time is an emergent property of quantum physics rather than a fundamental one.
He's not claiming time isn't real, which the definition of "real" is difficult and troubling to define in itself.
I think he doesn't consider time to be 4th (or part of 3+1 or \R^3 \times \R ) dimension... or in heat equation language: that the domain is a not parabolic cylinder.
Check out "The Order of Time" by Carlo Rovelli! You might find it interesting. He explains (WAY more eloquently than I could) that time is most likely an interpretation of underlying physical law, rather than a fundamental part of it!
I have a hard time buying that, given the Lorentz Transform. Time is just as much a real dimension as space is. (Or are the dimensions of space also "an interpretation of underlying physical law"?)
I believe the Lorentz Transformation more than I believe eloquent arguments.
Very much not correct. The Plank time is a rough scale at which we know that our theories do not work. That might mean that a new discrete theory appears there (which is frankly quite probable), but we most certainly do not know whether that is the case and it is just as possible that the underlying theory is continuous.
"A static, entangled state between a clock system and the rest of the universe is perceived as evolving by internal observers that test the correlations between the two subsystems. We implement this mechanism using an entangled state of the polarization of two photons, one of which is used as a clock to gauge the evolution of the second: an "internal" observer that becomes correlated with the clock photon sees the other system evolve, while an "external" observer that only observes global properties of the two photons can prove it is static."
[1] https://arxiv.org/abs/1310.4691