What does the time coordinate represent in spacetime?by constantinou1 Tags: spacetime, special relativity, time 

#1
Jan1112, 07:43 PM

P: 7

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 cant 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. 



#2
Jan1112, 08:03 PM

PF Gold
P: 4,542

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




#3
Jan1112, 08:59 PM

P: 260

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).




#4
Jan1212, 11:46 AM

P: 5,634

What does the time coordinate represent in spacetime?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 : 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. 



#5
Jan1212, 12:33 PM

PF Gold
P: 4,542

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 xaxis. 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. 



#6
Jan1212, 01:38 PM

P: 5,634

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". 



#7
Jan1212, 02:02 PM

PF Gold
P: 4,542

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.




#8
Jan1212, 03:15 PM

P: 1,555

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. 



#9
Jan1212, 04:25 PM

P: 848





#10
Jan1212, 07:04 PM

P: 5,634

interpretations..... 



#11
Jan1212, 09:08 PM

PF Gold
P: 4,542





#12
Jan1312, 07:50 AM

P: 7

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 xaxis. Would it true that:  B will see A's clocks running slow and the xdimension contracted because relative to B, A is moving.  A will see B's clocks running slow and the xdimension contracted because relative to A, B is moving. Would both these statements correct, or am I missing something? 



#13
Jan1312, 07:58 AM

P: 848

"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). 



#14
Jan1312, 09:38 AM

P: 5,634

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 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.” 



#15
Jan1312, 09:44 AM

P: 5,634

You might find the first page of posts here of value:
http://www.physicsforums.com/showthr...me+coordinates 



#16
Jan1312, 10:03 AM

P: 5,634

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




#17
Jan1312, 12:02 PM

P: 5,634

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!] 



#18
Jan1312, 03:39 PM

P: 7

Ok, thanks alot guys for the good responses and links, it's made things a little more clear and got me alot 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? 


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