List Mathematical properties of time that differs from space

[Secret]

What is the full list of properties in terms of formulating time mathematically that is differ from space

I am aware of only 2
1. 4 velocity vectors are future directing (pointed out by one of my GR maths professors)
2. the sign for time in the metric signature is opposite to the of space

But is there more, particularly those that is related to the daily life notion of "time elapsed/flows"?

[ICN5D]

Time elapsed is purely relative, according to metabolism and body size. It's more biological than mathematical. A recent study was done on body size to time scale proportions, and there is more or less a direct relation. They studied about 40 wildly different species, so it was thorough. It was found that a common housefly perceived time at 4x our rate. They can easily see your hand coming for them in slow motion. An elephant was something like 1.5 or 1.75 times slower. And, if you could imagine a sugar ant, those ultra-tiny little guys, they sense about 5-6x our rate. But, there's still some math involved in the biology here. One must account for the larger distances that the electrical neuron pulses have to travel in a larger body. We still can't escape relativity.

[Prashantkrishnan]

Time elapsed is purely relative, according to metabolism and body size. It's more biological than mathematical. A recent study was done on body size to time scale proportions, and there is more or less a direct relation. They studied about 40 wildly different species, so it was thorough. It was found that a common housefly perceived time at 4x our rate. They can easily see your hand coming for them in slow motion. An elephant was something like 1.5 or 1.75 times slower. And, if you could imagine a sugar ant, those ultra-tiny little guys, they sense about 5-6x our rate. But, there's still some math involved in the biology here. One must account for the larger distances that the electrical neuron pulses have to travel in a larger body. We still can't escape relativity.

Does this mean that as our size changes, our time scale changes? Would the time scale of a small baby and that of the same person after a few years be different due to size change?

[ICN5D]

To some degree, most likely. We're born much smaller than an adult, which makes time go by slower. Other than time spent alive to judge elapsed time, this would be the biological factor as well. But, a baby or small child won't perceive much faster if a fly was 4x human. Maybe 1.2x adult perception rate would be reasonable.

[anderscolingustafson]

One difference between time and space is that the universe has basically the same structure throughout space at least on the cosmic scale but the universe but the universe is radically different at different times. For instance in the early universe the weak force was unified to electromagnetism and all particles were massless but today the weak force has separated from electromagnetism and particles have mass but no matter how far you go in space electromagnetism and the weak force will remain separated and particles will have mass. Also the average temperature of the universe increases as you go back in time but it is pretty much the same no matter what direction of space you go in. Also the universe most likely has no edge in space but it has an edge in time known as the big bang. Also the total amount of energy, angular momentum, and electric charge remains constant through time but can vary through different parts of space.

[Teragon]

An event in relativity is a point in spacetime defined by x, y, z and t.

Events separated only by space may not cause each other, while events separated only by time may do so, if they're close enough in space. If the distance between two events in spacetime x²+y²+z²-c²t² is larger than zero, they may not be causally related.

If time was visualized as a coordinate of space (even without considering the longterm inhomogenity) the universe would look very different in this direction... "spaghettified".

The laws of the universe are the same if x, y or z is reversed, but are hughely different / violated, if t is reversed.

You can stand still in space relative to other events, but you cannot stand still in time relative to them. Inside the event horizon of a black hole, time and the radial coordinate of space change their roles!