# What exactly the time is?

What exactly the "time" is?

Is it just like other spatial dimension?
It is very confusing for me to understand.

It is quite confusing to everyone. In many ways it acts as another spatial dimension, but the ways in which it doesn't are what makes it strange. For example, why is it that things that have no mass are locked to travel at C through space and not at all (from their reference) through time? Why do massive things conversely HAVE to travel through time? and why always forward? Hard questions that no one has the answers to...

It is easier for me to think of time as actually being the 2nd Law of Thermodynamics.
This manner of viewing time may be only be part of the picture and have many flaws (and probably does) but looking at it that way makes a lot more sense to me.

We could easily convert all distance measurements into time measurements, in other words: the time it takes light to travel to an object along each of the x, y and z axes, for example.

That means we would have removed distance as a dimension and replaced it with time. But doing so would imply that we could regard time as no longer necessarily only a scalar but requiring it to be also a vector since it is often enough that a Laplacian is taken of functions of distance. And then we get to the strange notion of time changing with time which may or may not have validity.

Fredrik
Staff Emeritus
Gold Member

I'm quoting myself from a similar thread:

We could define spacetime to be the set $\mathbb R^4$ and let functions of the form $C:\mathbb R\rightarrow\mathbb R^4$ represent an object's motion, even if we knew nothing about special relativity. It's this definition that turns time into a "dimension". Time is a dimension in that model, for the reasons DaleSpam explained.

In this model of spacetime, "space" is a subset of spacetime such that all the members of it are simultaneous (i.e. have the same time coordinate). The difference between SR and pre-relativistic physics is what atyy said: Each inertial observer would call a different 3-dimensional slice of spacetime "space" (assuming that they assign coordinates to events using a pretty obvious definition of simultaneity involving light, a mirror and a clock).

Regarding the definition of time...

We can define a coordinate system in Newtonian mechanics, SR and GR as a function $x:M\rightarrow\mathbb R^4$, where M is spacetime, and then define "coordinate time" as a component of that function. In SR and GR it's also necessary to define "proper time", which is the integral of $$\sqrt{-g_{\mu\nu}dx^\mu dx^\nu}$$ along a curve.

That takes care of the definitions in the mathematical models used in these three theories, but the theories must still include postulates that tell us how these things are related to what clock's measure. In Newtonian mechanics, clocks measure coordinate time. In SR and GR, a clock measures the proper time of the curve that represents its motion.

Regarding the "is it like the spatial dimensions" question... The answer is yes, if we only consider the vector space structure (or affine space structure or manifold structure) of spacetime. Then it's exactly the same, but the bilinear form (often called "inner product" or "scalar product" even though it doesn't quite satisfy the definition of an inner product) that we use to define "distances" gives a different meaning to time.

Hawking in his books, "a brief history of time" explains about arrow of time. There is three different kinds of arrow of time:
1. Thermodinamic time. The direction in which disorder or entropy increases
2. Cosmological time. This is the direction of time in which the universe is expanding rahter than contracting
3. psychological time. this is the direction in which we feel time passes, the direction in which we remember the past but no future.

Is it just like other spatial dimension?
It is very confusing for me to understand.

Yes, time has multiple dimensions, just like space.

3 coordinates in space specify the spacial position.
3 coordinates in time specify the time position.

You can view time like the following:

Time dimension 1:
Timeline - easy to understand....we're all living through our timelines.

Time dimension 2:
Timeplane - think of parallel universes (infinite number of timelines forming a plane)....infinite versions of ourselves living out infinite versions of our lives.

Time dimension 3:
Timespace - infinite number of timeplanes....an extension of the parallel universe concept into the realm of non-parallel universes. Think of it as infinite versions of ourselves living out infinite versions of infinitely different lives.

When you specify the three time coordinates, you are defining a specific point in a timeline, of a specific universe and a specific set of conditions (that somehow define whether or not two timelines are parallel or non-parallel with respect to the specified conditions). That last one is hard to imagine. An example is this: let's say we define our condition as hair color. You can say that all timelines that exist where you live your life as a blonde are considered parallel.....and those timelines that you live as a brunnette is non-parallel to the "blonde timeplane" ----> hahaha.

You take the cross-section of one of those timelines, and you have your normal spacial dimensions (that we all know and love) that resides in that time position.

I hope that helps you understand multi-spacial time in a non-mathematical way.

WP

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