## Time as a vector

…but hey time is scalar!

I was browsing topics related to real-life applications of vectors when I stumbled upon the free-space diagram of a simple pendulum. And when you think of a pendulum, the next thing that comes in to your mind is…what? Yes, that’s right! A clock!

So before I even realized what I was searching on Google, I have already typed “vector quantity application in clocks .” It makes no sense but that is how I saw this interesting Quora question- “Why are we looking at time as scalar and not a vector, do you know of a method to display time as a vector?” And surprisingly, someone answered that it is indeed possible to measure time as a vector. Specifically, it is possible through the Minkowski diagram which is used for Einstein’s theory of special relativity. So what is this all about?

Time is absolute. Space is absolute. One hour for you is the same as an hour for me. One meter for you is a meter for me. But what if…

You are walking by the sidewalk when you see a car pass by. Assume that the car is moving equal to the speed of light, and you are walking half as fast. You say that the car is moving twice faster than you, but for the person inside that car you are seemingly walking half as fast. This is a contradiction since we know from our Physics class that the speed of light is ALWAYS equal to 3×10^8m/s wherever we are. But how is it that the speed of light could be twice as fast or half as fast? Well…

They say that when you are enjoying what you are doing, time flies by fast. And when you are bored, it goes oh so slow. Taking this into account, we can think that time is relative depending on our reference.

Now, Physicists thought of combining time and space into “one continuum of spacetime” where in time and space are not absolute. Now we say that a time for you is not the same time for me. And a meter for you is not a meter for me.

There are a lot of technicalities happening here so if you want to know the details, you can watch the source video below.

So where does time as a vector come in to play?

By graphical representation we can see that there a lot of time and space axes plotted over each other depending on the frame of reference. But still, we measure time in seconds, and space in meters. But since they are now contained in spacetime, we can measure both as one unit. Time can now be represented in meters since 1s*3×10^8m/s = 3×10^8m, and space can be measured as seconds!

And that’s it! I don’t want to go blabbing about the really technical stuff since I am not well versed in this theory. And I am not even sure if i understood it correctly (so do tell me if there are any mistakes.)

Source:

https://www.khanacademy.org/science/physics/special-relativity/minkowski-spacetime-2016-01-18T22:56:14.718Z/v/introduction-to-special-relativity-and-minkowski-spacetime-diagrams

https://www.quora.com/Why-are-we-looking-at-time-as-scalar-and-not-a-vector-do-you-know-of-a-method-to-display-time-as-a-vector

## Michelle Dela Rosa 3:03 pm

onFebruary 2, 2017 Permalink |Really interesting!

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