What are the Requirements for Time to be Considered a Vector?

[romsofia]

Is time a vector?

I don't think so, because we can't go back in time therefore it can't follow vector rules.

However, I'm not sure this works in all cases (such as in a cases where v is close to c).

Thanks for the help.

 

[BruceW]

In relativity, time is one component of the spacetime 4-vector.
Also, it is theoretically possible to go meet your former self according to general relativity.

 

[Naty1]

You can make time a scalar or a vector in a particular theory...the test is whether such a formulation matches observations and leads to any predictions. Is it useful??

While time is a vector in relativity it is not in Newtonian physics.

...because we can't go back in time therefore it can't follow vector rules.

A vector has magnitude and direction...it doesn't have to point everywhere nor is our ability to "go" with a vector a criteria...for example, you also cannot "go" where an acceleration vector does.

 

[romsofia]

In relativity, time is one component of the spacetime 4-vector.
Also, it is theoretically possible to go meet your former self according to general relativity.

Oh I think I've seen that somewhere, but I thought we took the time out. E.G. $${S(x,y,z,t)}$$ and then we did something like $${S(x,y,z)*e^{-i\omega t}}$$ but I doubt that is what you're talking about haha.

Anyway, thanks for the help!

A vector has magnitude and direction...it doesn't have to point everywhere nor is our ability to "go" with a vector a criteria...for example, you also cannot "go" where an acceleration vector does.

A vector also has to follow basic laws (addition, subtraction, etc). If you can't go back in time, then you can never have a negative time value which is possible following the laws of subtraction.For example, $${C=B-A}$$ with $${B=1}$$ and $${A=2}$$ then $${C=-1}$$ which wouldn't make sense to me.

Anyways, thanks for your input and help!

 

[BruceW]

Oh I think I've seen that somewhere, but I thought we took the time out. E.G. $${S(x,y,z,t)}$$ and then we did something like $${S(x,y,z)*e^{-i\omega t}}$$ but I doubt that is what you're talking about haha.

Anyway, thanks for the help!

No problem. It looks like you're talking about some quantum energy eigenstate. This can't be done for a general quantum state. Also, I was talking about relativity, not quantum mechanics.
In relativity, we can talk about each spacetime event being specified by 4 components (i.e. a 4-vector). We only know which is the time component when we define it ourselves. So time is not a separate entity from space in relativity.

 

[romsofia]

No problem. It looks like you're talking about some quantum energy eigenstate. This can't be done for a general quantum state. Also, I was talking about relativity, not quantum mechanics.
In relativity, we can talk about each spacetime event being specified by 4 components (i.e. a 4-vector). We only know which is the time component when we define it ourselves. So time is not a separate entity from space in relativity.

Brain fart on my part haha, I guess when I was typing that I forgot that you were talking about general relativity >.<!

Thanks for all the help though, I have little knowledge of relativity so I guess I have to start studying some of it :D!

 

[Dale]

A vector also has to follow basic laws (addition, subtraction, etc).

The laws that a vector must satisfy are listed here.
http://en.wikipedia.org/wiki/Vector_space#Definition

There is no requirement that you be able to "go" backwards in time for time to be a vector. A negative time simply means that one thing happened earlier than another.