Or Why time must be a dimension?
There are at least two clear proofs for it.
Time dilation and bending of space-time.
Both of which verified to great accuracy by countless experiments and observations.
It should be very clear that if time was an artificial human invented concept neither would be possible.
In fact any kind of verification of special/general relativity should be seen as a time being a dimension.
That is because all relativity calculations based on time being accepted as the fourth dimension.
By looking at all kinds of clocks used in daily life it is easy to get the idea that time is just a human invented concept.
So that it can set set and measured in any way wanted.
But scientists today also have atomic clocks which are extremely precise.
And it really easy for them to see and measure time dilation due to changes in speed and/or gravity.
And what they clearly see is those time dilation measurements match to calculations (to extreme precision) using equations of relativity!
Hopefully someday costs of atomic clocks will be cheap enough so that verifications of time dilation could be done in high school physics labs.
The experiments could be like start with two atomic clocks next to each other.
Make sure the clocks are calibrated to match exactly (synchronized).
Later move one the clocks around so that it will experience different speed and/or gravity and bring it back to its starting point.
Measure the changes in speed and/or gravity with enough precision using suitable measurement devices.
Later compare the difference in the clocks with the time dilation calculations using equations of relativity.
What will become clear is the results match extremely closely within the error margin(s) of the measurements.
I want to speculate that I think Universe could be really some kind of cellular automata operating in Planck scale.
(Meaning made of Planck length cells which updated every Planck time steps.)
If so it would mean both Quantum and Relativity are emergent properties,
But even if that is true, dimensions of both space and time would still be dimensions.
Only with difference that whereas dimensions in math have infinite size and scale (continuity), real dimensions of the Universe have neither.
When physicists see infinities in calculation results they interpret it as breakdown of the theory.
I do not believe that Universe really has any real infinity anywhere, neither in its dimensions nor in centers of Black Holes.
Because it is very clear from known physics is that Universe is based on extremely advanced mathematics.
I think mathematics is based on calculation, so the Universe must be calculable.
(Because we clearly see Universe is a dynamical system; it is not a static mathematical structure.)
That means it must be digital. That means it must be some kind of computer.
And the simplest and thus the best candidate would be some kind of computer called Cellular Automata.
(But it may still be a more advanced CA probably nobody thought/studied before.
Especially considering entanglement (which is non-local) property it must have to be compatible with Quantum Mechanics.)
What if it turns out there are real infinities in the Universe?
I think Universe would still need to be calculable.
That means infinities in the calculations need to be treated as special values.
(Many computer programming languages today allow setting a constant/variable to positive/negative infinity and use it in calculations as specially treated values.
For example using rules like infinity plus or minus any non-infinite number is infinity; any positive non-infinite number divided by zero is infinity, etc.)