What is the difference between proper time and coordinate time in relativity?

[monty37]

i know i have asked this before
but please..my teacher says time is a scalar quantity,my physics book also says so.
but time moves forward,why should it be a scalar?

 

[russ_watters]

"Forward" is not a vector, it is a plus sign. A vector needs a direction in space, not just a positive or negative.

 

[atyy]

If you have only one spatial dimension, then left and right can be denoted by plus and minus signs, and there is not much of a difference between a scalar and a vector. This changes in 2 or more spatial dimensions. In Newtonian physics, there is only one time dimension/direction, so time is a scalar/vector. In relativity "time" and "space" rotate into each other, then people talk about time-like vectors.

 

[monty37]

well can i not say time moves in the forward direction,now forward ,the future very
much applies to direction,right.so according to einstenian physics,time is a vector
and according to Newtonian physics,time is a scalar,right?

 

[Chrisas]

Einstein Physics: Time is not a vector. Time is one component of a 4-vector.

 

[atyy]

Time is the only "direction" in which a "stationary" observer moves. Any observer moving with constant velocity can be considered "stationary". Every "stationary" observer has a "velocity" in spacetime. Different "stationary" observers have "velocities" which point in different directions in spacetime. For each "stationary" observer, the spacetime direction in which his "velocity" points is his "time" direction, so the "time" direction of different "stationary" observers is different.

The elapsed time of a "stationary" observer is the "length" of his "velocity" vector integrated along his path in spacetime. This elasped time can be generalised for arbitrarily moving observers.

Maybe try looking up "4-velocity" and "proper time".

 

[monty37]

what is this 4-vector?
now,putting it directly,if someone asks you if time is a scalar?
yes is the answer,right?

 

[tiny-tim]

now,putting it directly,if someone asks you if time is a scalar?
yes is the answer,right?

Hi monty37!

Short answer: Proper time is a scalar.

Observed time is neither a scalar nor a vector … as Chrisas says, it's just a component of a vector …

Time is not a vector. Time is one component of a 4-vector.

 

[DrGreg]

Hi monty37!

Short answer: Proper time is a scalar.

Observed time is neither a scalar nor a vector … as Chrisas says, it's just a component of a vector …

Tiny-Tim's answer is technically the correct answer, but I suspect it will go over the head of Monty37. I suspect he may not know the difference between proper time and coordinate time, and I'm pretty confident he hasn't studied tensors and therefore won't appreciate the tensor interpretation of "scalar" as "invariant".

Loosely speaking, yes "time is a scalar", in the non-tensor sense of a one-dimensional real number.

 

[atyy]

Time is what you read on your clock, so it is a scalar.

A bit more correctly: Proper time is the elapsed time as read by a standard ideal clock, so it is a scalar. Standard ideal clocks moving at different velocities read different proper times.

 

[monty37]

DrGreg is right! can someone tell me difference between proper time and coordinate
time?provide me a link, if you can on this.Also elaborate on tensors.

 

[Fredrik]

DrGreg is right!

He usually is.

can someone tell me difference between proper time and coordinate
time?

See post #21 here.

Also elaborate on tensors.

Tensors are pretty difficult to understand, and not very important here. But see e.g. post #3 here. There's a lot more to be said about tensors, but I'm afraid it would mostly be gibberish to you if you haven't even studied linear algebra yet. You probably feel that way about the post I linked to as well, but maybe it's better than nothing.

 

[atyy]

DrGreg is right! can someone tell me difference between proper time and coordinate
time?provide me a link, if you can on this.Also elaborate on tensors.

If a person carries an ideal clock (like an atomic clock), and walks about, flies about, swim about etc, proper time is the time elapsed as read by the clock he is carrying. People carrying identical clocks, but moving in different ways, will have different proper time.

If we fill all of space with clocks that "do not move relative to each other", and define some "time" at which all the clocks are set to zero, then coordinate time at that location is the proper time on the clock at that location, ie. coordinate time is the proper time of a specific set of clocks moving in a specific set of ways.

If we are in Newtonian, non-relativistic physics, and we define one place to be the "origin" of a set of axes. Then for an object located away from the origin, there is a position vector from the origin to the object. The distance between the origin and the object is the "length" of the position vector. In this sense, "distance" is a function that takes a vector as input and produces a number as output. A tensor generalizes this idea: it is a function that takes one or more vectors as inputs and produces a number as output. In relativity, the vectors are vectors in spacetime, not just space alone.