How is time a dimension?

[Keen]

My understanding of relativity is very limited, so I'd appreciate if someone could help me understand this concept. When it comes to an object, I can move it in space by applying forces change direction etc... I can even make an object stop moving altogether in a certain frame of reference, but when it comes to time, it seems to me that there is little control over how an object moves in time. It always goes forward, I can't make the object stop etc... so how is it helpful to think of time as a dimension when it behaves very separately from the others?

[Strange]

13 minutes ago, Keen said:

My understanding of relativity is very limited, so I'd appreciate if someone could help me understand this concept. When it comes to an object, I can move it in space by applying forces change direction etc... I can even make an object stop moving altogether in a certain frame of reference, but when it comes to time, it seems to me that there is little control over how an object moves in time. It always goes forward, I can't make the object stop etc... so how is it helpful to think of time as a dimension when it behaves very separately from the others?

You are correct that the time dimension is different. One difference is that we cannot stop "moving through" the time dimension and we can only go forward. But that is what makes it a time dimension rather than a spatial dimension.

The reason it is a dimension is because of the independent information we need to specify an event. For example, if you are meeting someone for lunch, you need to specify the place (as 3 spatial dimensions; for example latitude, longitude and altitude; or som equivalent) but you also need to specify the time you are meeting. So you need four dimensions (independent values) to arrange the meeting.

[Mordred]

To add to Strange comment time is treated as an interval that is given units of length via the ct coordinate. This allows us to graph time as a vector with which the vector length can contract due to the Lorentz transforms. ie length contraction which affects both the length scale of the x and ct axis. The main term dimension as Strange mentioned is an independent variable. Ie a variable that can change without affecting any other variable in an equation. The spatial dimensions qualify but they are not the only possible independent variables/dimensions in an equation. Not all dimensions are spatial, they are simply the most commonly known examples.

The key is the math definition of dimension as an independent variable.

Edited July 4, 2018 by Mordred