It is true from SR+Minkowski that space and time can be considered together as a manifold, where (relative motion) boosts rotate smoothly between the dimensions. The signature just decides the interval expression, but doesn't change physics.
But is also true (SR, esp GR) that the important thing about spacetime is the light-cone structure at each spacetime point. Space-like and time-like directions (2 for time-like, past and future) really are different. The forward and backward light cones define a null-surface with zero interval (everywhere, all at once, a la photon).
Relative velocities tilt light cones to bring the local and global views into agreement. Somehow...
However... Proper time is asymmetric, past and future really are different here and now. Local proper time seems to be inexorable, and ~independent of the universe. It is the clock tick we all feel. Proper time seems directed, but non-transformable. We always experience the same rate of 1s/s, looking at our local inertial atomic clocks.
It is confusing to hold all those ideas in my mind at the same time. I have not seen a good explanation that resolves the confusion (I have seen the equations :)
My guess is that local proper time is a real progression, perhaps by axiom, not dependent on cause-effect, or 2nd Law, or QM entanglement, or .. anything else. However, relative time is accurately described by SR, GR and some future QG.
Also, QM is fundamentally wrong, because it is background-dependent. GR showed us that the more profound approach is to include gravity, space, time, matter and energy as dynamic participants in the same framework of laws. QM (Schrodinger/Dirac/QED/QFT...) seems provincial, and provisional, because it assumes a spacetime background - which cannot possibly be true, as is.
I suppose I align with the GR-istas, especially Penrose, who seem to understand this conformal/twistor structure deeply, and use it to lead their intuition for speculative future theories, of cosmology, and also QG.
It is true from SR+Minkowski that space and time can be considered together as a manifold, where (relative motion) boosts rotate smoothly between the dimensions. The signature just decides the interval expression, but doesn't change physics.
But is also true (SR, esp GR) that the important thing about spacetime is the light-cone structure at each spacetime point. Space-like and time-like directions (2 for time-like, past and future) really are different. The forward and backward light cones define a null-surface with zero interval (everywhere, all at once, a la photon).
Relative velocities tilt light cones to bring the local and global views into agreement. Somehow...
However... Proper time is asymmetric, past and future really are different here and now. Local proper time seems to be inexorable, and ~independent of the universe. It is the clock tick we all feel. Proper time seems directed, but non-transformable. We always experience the same rate of 1s/s, looking at our local inertial atomic clocks.
It is confusing to hold all those ideas in my mind at the same time. I have not seen a good explanation that resolves the confusion (I have seen the equations :)
My guess is that local proper time is a real progression, perhaps by axiom, not dependent on cause-effect, or 2nd Law, or QM entanglement, or .. anything else. However, relative time is accurately described by SR, GR and some future QG.
Also, QM is fundamentally wrong, because it is background-dependent. GR showed us that the more profound approach is to include gravity, space, time, matter and energy as dynamic participants in the same framework of laws. QM (Schrodinger/Dirac/QED/QFT...) seems provincial, and provisional, because it assumes a spacetime background - which cannot possibly be true, as is.
I suppose I align with the GR-istas, especially Penrose, who seem to understand this conformal/twistor structure deeply, and use it to lead their intuition for speculative future theories, of cosmology, and also QG.