What does the time coordinate represent in spacetime?

[constantinou1]

Hello PF,
I have just been given an introduction to special relativity and its postulates. One of the consequences of special relativity of course is that space and time are entangled and that in order to assign a coordinate to an event, you must give it spatial (x, y ,z) and temporal coordinates (t). My problem is that I can't get my head around what the temporal coordinate on its own stands for.
For example, the spatial coordinate represents the position of an event relative to the origin of the reference frame, but what does the time coordinate represent on its own? If I was at the origin and assigned an event the coordinates (100m,0,0,10s), for example, what does the time coordinate stand for?

Thanks in advance.

 

[ghwellsjr]

You have to imagine or actually have a clock at the spatial origin set to zero to begin with. It's an ordinary clock but you can't move it away. It has to stay at the spatial origin. Then the origin in spacetime is the event that has the coordinates (0m,0m,0m,0s). The event with coordinates of (0m,0m,0m,10s) is ten seconds later at that same location. It's not complicated

 

[elfmotat]

It's the time coordinate of an event. Say you start a stopwatch (with you standing at the origin) - this corresponds to an event at (0,0,0,0). Now say you snap your fingers some time later (at the same spot), for example 3 seconds after you start the watch. The event where you snap your fingers has coordinates (3 sec,0,0,0).

 

[Naty1]

My problem is that I can't get my head around what the temporal coordinate on its own stands for.

What do you think the distance coordinates stand for?? I'll bet you just haven't realized yet that what you think you know about spatial coordinates (distances) is incomplete.Try to express it...here or just to yourself. [This stuff IS hard to get your head around at first: That's why it took an "Einstein" to figure it out.]

In non relativistic theory, have you considered a plot of, say, d = vt...time on one axis, distance on another...that's where to start...in such a Newtonian setting both time and distance are fixed...that means they appear the same to everybody, they are "invarient"...but that's a low speed illusion...neither is fixed!

In special relativity the speed of light is the constant, neither space nor time! SPEED affects different observers measures of space and time in SR. In General Relativty, gravity with curved spacetime, gravitational potential also affects the passage of time and the measure of space.

For a nice introduction to relativity, try here:
http://www.jimhaldenwang.com/black_hole.htm

which includes :

In order for the speed of light to be constant in different inertial frames which are in motion relative to one another, Einstein realized that space and time cannot be absolute.

PS: "If I was at the origin and assigned an event the coordinates (100m,0,0,10s), for example, what does the time coordinate stand for?" It would depend on who measured those values: different observers would provide you different values!

As a next step try reading about "proper time" and "coordinate time"...have fun.

 

[ghwellsjr]

Opps, I didn't notice the first spatial coordinate was 100 meters, so I have to modify my answer:

The event with coordinates of (100m,0m,0m,10s) is ten seconds later at a location that's 100 meters away from the spatial origin along the x-axis. But now the issue is how do you determine the time at that remote location? According to Special Relativity, you need to imagine or actually have another immovable clock located at that position that had been previously synchronized to the clock at the origin in such a way that the time on its clock is later than the time it sees on the clock at the origin by an amount equal to how long it takes light to travel 100 meters at c.

 

[Naty1]

What george describes above is this:
http://en.wikipedia.org/wiki/Einstein_synchronisation

but that is only ONE interpretation of what the 'elasped time' means. Kind of like 'left' and 'right' so we can discuss things less ambiguously. That is merely a convention, not really what "the time means".

 

[ghwellsjr]

It's not an interpretation, it's the definition used in Einstein's Special Relativity. It is merely a convention but it is really what time means in Special Relativity.

 

[Passionflower]

I know some disagree but I think that time is a path in spacetime not a dimension of spacetime.

One can choose a coordinate system as such that the path in spacetime overlaps one axis (which we then call time) but such a coordinate would only be valid for user at rest to this coordinate system in flat spacetime. In curved spacetime even that is no longer true.

 

[bobc2]

I know some disagree but I think that time is a path in spacetime not a dimension of spacetime.

One can choose a coordinate system as such that the path in spacetime overlaps one axis (which we then call time) but such a coordinate would only be valid for user at rest to this coordinate system in flat spacetime. In curved spacetime even that is no longer true.

You may be on to something, Passionflower. Could you expand on that idea a little? For example, what is the 4th dimension then, if it is not always time? And is it different in curved spacetime?

 

[Naty1]

It's not an interpretation, it's the definition used in Einstein's Special Relativity. It is merely a convention but it is really what time means in Special Relativity.

It IS an interpretation...the 'right one'!...the one used in SR so it IS critical for clear communication...I was thinking about the fact that proper time and coordinate time are both
interpretations...

 

[ghwellsjr]

It's not an interpretation, it's the definition used in Einstein's Special Relativity. It is merely a convention but it is really what time means in Special Relativity.

It IS an interpretation...the 'right one'!...the one used in SR so it IS critical for clear communication...I was thinking about the fact that proper time and coordinate time are both
interpretations...

But the OP didn't ask about proper time. He only asked about coordinate time and in SR coordinate time is a very precise definition. (So is proper time and how you get from one to other but that's not what this thread is about.)

 

[constantinou1]

Thanks for all the replies, they are very helpful. So is it correct to say:
The spatial coordinate tells you the distance an event has taken place relative to your origin in your reference frame using the three dimensions (x,y,z).
The time coordinate tells you the time the event took place had there been a clock at the location of the event that 'ticked at the same rate' and started at the same time with a clock that is placed at the origin of your reference frame.

So consider a case where A moves with a constant velocity relative to B along the x-axis.
Would it true that:
- B will see A's clocks running slow and the x-dimension contracted because relative to B, A is moving.
- A will see B's clocks running slow and the x-dimension contracted because relative to A, B is moving.

Would both these statements correct, or am I missing something?

 

[bobc2]

...For example, the spatial coordinate represents the position of an event relative to the origin of the reference frame, but what does the time coordinate represent on its own?

There are a couple of ways to interpret your question, constantinou1. Most of the posts have approached it one way, and I'll approach it as though you're searching for more of an external physical reality answer to what is the 4th dimension... although I really can't answer your question. But I'll just give you a quote from Hermann Weyl (Einstein's friend and colleague and one of the great mathematicians and physicists).

"The objective world merely exists, it does not happen; as a whole it has no history. Only before the eye of the consciousness climbing up in the world line of my body..."

He seems to be giving us a picture of physical structures literally extended along the 4th dimension for billions and trillions of miles with the passage of time associated with the consciousness moving along the world line of the body at the speed of light (...no history. Only before the eye of the consciousness...).

To try to engage further in this type of discussion would violate the rules of the forum, since the position of the forum is that this type of discussion has no physics content. So, here, you should be content with limiting your understanding of the 4th dimension as just representing time. Events are located with the specification of four coordinates, one of which is time (units of seconds, years, ... or whatever units you prefer for a given situation).

 

[Naty1]

The spatial coordinate tells you the distance an event has taken place relative to your origin in your reference frame using the three dimensions (x,y,z).
The time coordinate tells you the time the event took place had there been a clock at the location of the event that 'ticked at the same rate' and started at the same time with a clock that is placed at the origin of your reference frame.

That looks ok, but I'll bet there turn out to be issues with it that I can't think of right now. sounds ok to get you started.
I think it's ok for special relativity (flat space time) but not for general relativty.

you should be aware of the standard "Einstein" type synchronization explained in Wikipedia

So consider a case where A moves with a constant velocity relative to B along the x-axis.
Would it true that:
- B will see A's clocks running slow and the x-dimension contracted because relative to B, A is moving.
- A will see B's clocks running slow and the x-dimension contracted because relative to A, B is moving.

ok.

Here are a couple of closely related insights that may be helpful for both SR and GR:
Via Lorentz transform:

1) time and space are not entirely separate entities but one frame's time gets split into another frame's space and vice versa. [time dilation;length contraction]
2) there is a notion of "distance" called the spacetime interval which also mixes space and time together and is agreed upon by all reference frames (i.e. is invariant under the Lorentz transform).


"The proper time for a given observer is measured by the clock that travels with the observer. Then the clock is always at rest relative to the observer in question and thus travels the same worldline.”

 

[Naty1]

You might find the first page of posts here of value:

https://www.physicsforums.com/showthread.php?t=563230&highlight=spacetime+coordinates

 

[Naty1]

contant...: By coincidence I just came across this from a book written by a poster here, BenCrowell, and thought you might find it interesting:

In 1971, J.C. Hafele and R.E. Keating of the U.S. Naval Observatory
brought atomic clocks aboard commercial airliners and went
around the world, once from east to west and once from west to east.
Hafele and Keating observed that there was a discrepancy between the times measured by the traveling clocks and the times measured by similar clocks that stayed
at the lab in Washington. The result was that the east-going clock lost an amount of time
tE = -59 +/- 10 ns, while the west-going one gained
tW = +273 +/- 7 ns. This establishes that time is not universal and absolute.

more here:http://www.lightandmatter.com/genrel/genrel.pdf

 

[Naty1]

I happened to come across this interpretation from my notes, I think from DrGreg in these forums..it's neat capsule:

[It's a much clearer insight into convention, and proper time and it's relation to coordinates.

Note the dimensions of length (ct) for the time coordinate!]

What we would like is a convenient way to keep things organized so that we can easily keep track of the things that everyone agrees on and easily determine how any frame sees something. This is exactly what the four-vector approach accomplishes. If we take our normal space coordinates that we have all seen since introductory physics, (x,y,z), and we add a time coordinate, (ct,x,y,z), then we have four-vectors and spacetime. Now we can write the Lorentz transform as a matrix and easily switch between reference frames. This is very useful for figuring out how different frames look at times and distances.

We can also consider the spacetime interval (aka Minkowski norm) as the length of the position four-vector. One important use of this approach is that in an object's rest frame all of the space coordinates are 0, so the spacetime interval is immediately seen to be the time in an object's rest frame or its "proper time". Since the interval is invariant then we see that all frames agree on the proper time along any worldline...

 

[constantinou1]

Ok, thanks a lot guys for the good responses and links, it's made things a little more clear and got me a lot more interested in the subject .
Also one last question, would any of you happen to know of a book that gives a good introduction to special relativity?

 

[Naty1]

You have book links to two online (free) sources in my previous posts...plus wikipedia...

 

[ghwellsjr]

Ok, thanks a lot guys for the good responses and links, it's made things a little more clear and got me a lot more interested in the subject .
Also one last question, would any of you happen to know of a book that gives a good introduction to special relativity?

Does it have to be a book? I think the best introduction to special relativity is Einstein's original 1905 paper:
http://www.fourmilab.ch/etexts/einstein/specrel/www/