Is time a dimension?

From school we remember that time is a coordinate - t, the uniform motion of some point is described by a function like x(t) = k*x, v(t) = k, a(t) = 0. And we imagined 3 space coordinates and one additional - the time, keeping in mind that we always move to the future, and never - back, to the past.

After 90s and the development of computer graphics everyone knows what "3D" means. We have 3 space dimensions. What does it mean? It is (possible) infinite set¹ of distinct "places" where objects can be located. And to understand what dimensions are, you should remember the main rule: dimensions are independent in the sense that a point or some body can move along one axis (the symbolic direction of the dimension, nothing more) without to move along others - the movement can be independent. Imagine movement of hockey players on the rink - intensive move to left, right, movement into the distance, towards the opponent and back: X, Y coordindates are changed but the height - the third Z is not, it is constant. Movement along one line parallel to some axis is similar - all other coordinates don't change. What about time?

We used to think about time in the same way - "idenendent time dimension". Well, movement along time axis is not free - you can move only forward with the same speed. Is it true?

Consider a cat crossing a street. To be crushed by a car, the cat's coordinates must match the car's coordinates:

                     ^^~
  ______             :   
 /|_||_\`.__         :   
(   _  o _ _\........✸   
=`-(_)--(_)-'              

Somebody could say: They may coincide, except for the time coordinate, for example, the cat passed in this place, but 5 minutes ago - it was saved!

Well, the cat is saved only if one of its space coordinates did not match, else - death. Think about independence of coordinates: the cat cannot survive without at least one coordinate to be different comparing to the car! The cat cannot seat on this place and to survive because X,Y,Z coordinates matched but the time - did not. Yes, the cat can independently change one of its coordinates: either X or Y, even Z (the last one often saves cats life!), but no way to change independently t coordinate!

Time is not real dimension. And no way to save the cat without to have at least one of its coordinates not matching the same coordinate of the car. Just no way.

If the cat is still alive, it is not because it was there, on this street, yesterday, but because today one of it coordinates are different. The surviving is not possible without the second, - and this is the proof that t is not independent dimension.

We can state it differently: it is not important what coordinates the cat had yesterday. They just don't matter. They could be absolutely any. Even the same of the car today. Only today's coordinates matter. So,

1. the cat cannot change its t coordinate - at least independently from its X, Y, Z and not equally to the t coordinate of the car
2. it seems the car and the cat always have the same t coordinate.

We can consider 2 different causes of cat's survival:

1. Different t coordinate of the car and the cat
2. One of space coordinates did not match

So, we should not reduce 1st to 2.

Should we take this objection into account? I think no. Otherwise, we have try to compare yesterday's cat with today's car which is strange: why not yesterday's cat and the yestarday's car as well as today's cat and today's car? A difference in only one coordinates gives survive.

cat: x₁, y₁, z₁, t₁
car: x₂, y₂, z₂, t₂
∀ t when the cat survives, all its life: x₁ ≠ x₂ ∨ y₁ ≠ y₂ ∨ z₁ ≠ z₂

and no such t in the cat's life when it is not right! Considering the opposite situation: to die the cat has to match all car's coordinates including the time. It means to be at the same place and the same time moment. If 1. is correct then the cat could quickly change its t coordinate after matching X, Y, Z coordinates - how it can do it?!

Another counterargument: to survive the cat has to change at least one of its coordinate. It means that it will not exist more on the previous place (x,y,z) and will be at (x+A, y+B, z+C). Let's say the car did not hit the cat at the time moment t1. Did it happen because the cat did not exist at the coordinate t1 when the car existed at this coordinate t1? It's wrong, it existed. But this logic work perfectly with space coordinates: if the car exists at (x, y, z) - the survived cat did not exist at (x, y, z) literally, it exists somewhere else. When the car did not hit the cat at t1 the cat exists at the t1 coordinate. It is alive because it does not exists at ill-fated (x, y, z) but it did not leave t1 and if the time is dimension - we will still find the cat at the sign "t1" on the line of time - where the car is too!

So, can we eliminate time?

What is the identity? In philosophy it's very complex problem and in general it was not solved. But in programming it is little bit simpler: for the identity of some software object we can use address: if addresses are the same - it is the same object. Identical. What is "address"? We can think about it as... X coordinate:

o-----------------> 0x axis

 Adr0 Adr1 Adr2
+----+----+---- -
|obj1|obj2|    |
+----+----+---- -
 obj3

obj1 and obj3 are the same object because 2 objects cannot fill the same memory cell. But obj2 is different object - it has a different address/identity criteria, or X coordinate.

And here we come to another understanding of coordinates and cats and cars: coordinates are identity criteria like the address for the computer memory: if all coordinates match then it is the same object! It's like a key in a map. So, does the identity of physical objects require the 4rd coordinate in the "identity" (x, y, z, t) tuple? Else cats... sometimes are cars.

How serious is the previous objection? Quite serious, it tells that (X, Y, Z) are not enough. Maybe missing part of identity is not one coordinate of time but something else - not one additional coordinate but more:

missing-coordinate = hash(unknown-parameter-1, unknown-parameter-2, ...)

Another possibility is to keep in mind - there is such categorie that cannot be understood but we have to accept that it is a potency to change coordinates during different motions.

So, these are 2 different mental visions:

1. We add to our object yet another ID (t, clock tick, etc)
2. We ignore it, because time ticks are behind the scene and we can focus only of potemcy of change coordinates - it is different and we call it "velocity" or "speed".

We always do the 2nd. Cats cannot become cars, they are always distinct: coordinates are not static, they always can change, with different intencity - ie, speed. Times is tightly connected with speed and vise versa, they are like the same phenomena but viewed from different points. Ability to change your coordinates requires speed which requires energy - another fundamental term (one of central terms in Indian philosophy). Is it possible to understand time/speed in static, without to consider energy?

From one point of view we can think about time as additional identity component but then we have open question: how do changes of identity components ("coordinates") happen?! The answer is exactly the time, so I think it's wrong to treat it as an identity component - it is potency to change/modify them. Then we have simple scheme like in computers, memory can be imagined as a "space" with coordinates. The physical space can be seen in the same way: objects are "located" at some multicomponent "addresses"/"identities". The space is a storage of cells and reminds memory. Human memory is just neuron-based snapshot of the state of the larger memory, called "space". The physical space keeps a state. The state is a configuration of objects, nothing more. Real memory has refresh frequency, refreshing the state of cells, without it physical degradation processes will erase memory. Do we have something like this in the "real" physical world? Yes, all objects consist of elementary particles that are called sometimes "oscillators". They remind super-small flip-flop particles, by the way, quantum physics tells us that we will never see them. So, we can think about space and time like about a computer memory and memory refresh rate. Some objects move faster, they need lesser refresh clocks to change their "address" (space coordinates)!

In reality, memory is hardware:

            S P A C E
             +------+
             | M    |
 address     | E  C |
   or   x,y,z| M  H |    object:
 object ---->| O  I |--> set of
identity     | R  P |   attributes
             | Y    |
             +----o-+
                  |
time/clock -------'

It pushes us to the Simulation Hypothesis using about our world the metaphor of computational device, some kind of mega-computer: refresh clock is needed not only to keep a persistent state of memory but also it is needed to change the memory, and it restricts the highest speed of data saving - you cannot save (move) faster. Wow! Light speed! Physics teaches us that this is the limit of movement! And it reminds the refresh clock rate very much.

You shouldn't be confused by the three coordinates; the first two can address the cascading inclusion of memory blocks or form a hash.

We saw many times the usage of time t in physics and mathematics. Physics is not so abstract as math, it deals with real things (if to foget about theoretical physics with its black holes, etc). School physics even. And if to ask - where the time is then? No answer: there is only one t: now. When we can find an object 1 second ago? Or where is it when it's t is bigger then \( t_{now} \) ? Time looks as very imaginary concept, a "dimension" having only one coordinate: now. How long is it now²?

Now turns out to be a very elusive and brief moment, like a point in geometry---reality barely has time to appear out of nowhere before it instantly disappears into the past. And the duration of its real existence is elusive. And this understanding of time looks too fragile, too poetic.

So fundamental concept (categorie) as time is undefinable so much.

It is full of debates and it has very long history: Space and Time in Philosophy. And there are a lot of theories about time but they are often groupped in 2 categories: A-theories and B-theories. And by the way, one of them claims that time does not exist, it is illusion (kind of). If time does not exist, then the Theory of Relativity mostly stops to exist too because time (Spacetime) is key concept there - no time, no t in their formulas, at least they need adding of other arguments, maybe instead of t.

Philosophers and scientists denied the existence of time totally are:

• John McTaggart Ellis McTaggart: he introduced A-series and B-series, wrote a book called The Unreality of Time (1908)³ where he explained his ideas ("time is unreal")
• Julian Barbour: physicist and a philosopher, wrote The End of Time (1999)⁴, Barbour recounts that he read a newspaper article about Dirac's work in which he was quoted as saying: "This result has led me to doubt how fundamental the 4-dimensional requirement in physics is". The nature of time as a 4 dimension or something else became the topic of research.

Before them, some schools of Indian philosophy, including Buddhism also claimed that the time is not real but mental construction⁵.

In the Theory of Relativety everything is more complex even: no one "time": every atom, elementary particles have their own "local" times, their own "ages", simultaneous events can be non-simultaneous events in own "time system", this theory is full of paradoxes, some contradictions and hard, 100% experimental proving (existing proofs can be treated in different ways without resorting of the Theory of Relativety), but today it's accepted as true theory, and academic science ignores some problems around it (GPS expert Ron Hatch about the theory of relativety - well it also has problems but debates continue and "paradoxes" still look assymetrical). But another crush can come from the "Theory" of Simulation: computed world needs common clock and it means there is a global common time system. Simulation hypothesis is little from from sci-fi, but not more too much: modern science treats the Universe as a mathematical object, and Stephen Wolfram promotes exactly this theory - the theory of computational Universe. Sure, such theories do not mean 100% that the time is global, but especially in the case of simulated Universe - it is the obvious "approach", it's typical for computers.

If time is not a dimension, then it cannot be a coordinate. It's a problem: then what is t in the formulas? Obviously, it's "instrumental" argument needed for ordering of "events". Then:

1. If the order of independent events can be different in different time systems (by the Theory of Relativety) then what is the sense of this t?! Initially, it was introduced in physics just to describe differential (speed, acceleration) when we describe motion of a point. So, it is "tooling", "instrumental" argument needed to see changed coordinates as a chain of points beloning to some continuous function (so we can do differentiation of a function).
2. What is "event"?

Event, in general, seems to be a point on that graph of the motion's function. And the key feature of it is its horizontal coordinate: mystical t. Where do events exist? In our memory. Because tries to find them in the reality lead to a lot of logical, philosophical problems.

But we feel the time! We are getting old! As before: everything is about motion :) We get older not because of time magically moved us from "now" to "yesterday", but because molecules inside our biological cells are moved al the time, and their "good configuration" when we were young becomes "bad configuration" - DNA defects and so on. So, infinite movement of small particles inside us leads to death. Time does not magically affect us, time allows particles, molecules to move and to change the configuration (state!) of our organisms. It is again the cat and the car.

On the other side of the theories of time there are also its own radical ideas reaching even the concept of multidimensional time. But it will be one of next posts.