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If time isn't real, then when you say "rate of change", I ask "rate of change with respect to what?"

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!

An illusion, if just a fancy one.

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.

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