Hmmm, I'm intrigued by your response. I found that mathematics is incapable of proofing some math is nonsense in the real world. Like for example, I can divide anything mathematically into parts, and when added up the result is always one whole. Try doing that in the real world with objects, and living things.... Divide a cow into 12 pieces, add them together again and you have... a pile of meat. Twelve pieces to be exact. That's because math is - unlike programming languages - not typed. It's a flawed language. Take for example infinity or zero or even negative vaules. They just don't exist! Show me zero cows. Show me -4 cows. Show me an infinite number of atoms. The facts we can't count them does not mean the number is not finite. We can only use these concepts in mathematics as a 'hack' to deal with problems we can't otherwise solve. We only use negative values because we want to use an arbitrary reference point in space (any space, even vector spaces) from which we can go in all directions. But every value is always a positive one, in which direction you travel. Likewise with money, if I owe you money it's a negative post on my balance but it still is a positive amount of hard earned cash. Only the direction in which it flows changes. So the minus sign is only to indicate a direction.
Same with time, time is a measure of ticks on a man made device to measure, and I don't need to prove this, because there are no clocks in nature, only proxies (sun, moon, pendula's, etc). Hah, you say, we have atomic clocks. Well, these only work because of a feedback loop provided by... man made equipment.
In unscientific to assume time is fundamental because we experience time. We experience time because we have a consciousness and a memory. Take the memory out and there is no experience of time. We can only infer the notion of time via proxies like the sun or a man made device.
To proof 'time' as in 'universal time' exists, we must provide a mechanism that dictates and communicates the 'ticks' in the whole universe. There are only two ways to have multiple objects behave the same way, either you govern their behavior centrally but must provide a mechanism to communicate and force the behavior, or the behavior is intrinsic to the object, so it can only behave that way, meaning every subatomic particle has it's internal clock, and they all happen to run at the exact same speed. That all particles in the standard model have intrinsic values like charge and spin is one thing and something we can measure, but to assume they have an internal clock or obey an external clock is a far stretch. Both mechanisms raise more questions than they answer and add complexity to the very fundamental particles and forces. And the question is, will we ever be able to prove it.
Since we can not provide a mechanism that is remotely probable, we simply MUST assume that time is emergent.
Finally space. We only think of spacetime as something 'real' because of Einstein, but what about this thought experiment? Take a cold, dead, solid planet an drill a hole to the center. Excavate a kind of chamber there and go in there. Is there mass? Yes, a lot, a mass (you) within mass. Is there gravity? Errrrm, no. You float, like in empty space, you're weightless. Why? The planet pulls at you from every direction equally. Is there time dilation or distortion of spacetime? No, not according to general relativity. No pull, no distortion of spacetime. So does bend mass 'spacetime'? In this case, apparently not. Or is general relativity wrong? Apparently the spacetime distortion 'spikes up' within a given mass, all the way up to zero distortion at the center of mass. Could this also be the reason they calculate the rotation of galaxies wrong. You know, matter within matter.
As long as general relativity gives us these weird outcomes AND is incompatible with quantum physics, we can not assume 'spacetime' is real, only a proxy to some underlying reality.
