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We all know that space and time are the fundamental units, means no mathematical expression can express their relation to other variable fundamentally. But as we know that moving rod has a contracted length and dilated time which depend on the velocity of that rod w.r.t. an inertial frame in which the motion is happening. So it's a natural question that space and time measurements are not alone to be measured in any inertial frame but one has to specify velocity also. It sounds like 3d space and 1d time have another dimension (velocity) to be included in their totality. So velocity is also a form of space and time. So what is wrong here?

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The units of space are meters (and square meters and cubic meters)
The units of time are seconds
The units of velocity are meters per second

So the units of velocity are not independent of the units of space and time.


In classical mechanics, we can measure the position of an object using only three dimensions, for example distances x, y and z in some cartesian frame of reference. We can measure the speed of an object by measuring how those distances change after some interval of time. We have only needed four dimensions x,y,z and t but two separate measurements. We can measure the length of an object using only one dimension - though we make separate measurements (along that one dimension) of each end.

In special relativity, all the above is also true and is exactly the same.

What special relativity tells us is that two observers will disagree about the measured length of an object if one is moving relative to the object and one is stationary relative to the object. The Lorentz equation describes how those two observers' measurements disagree. Each observer still only needs one spatial dimension to measure the length of the object in their own frame of reference.

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it was in classical mecanics too so why did it not arise there? –  Abhinav Anand Nov 24 '12 at 20:08
    
@AbhinavAnand: I'm not sure which concept you mean by "it" in your comment. I have expanded my answer. Maybe that helps? –  RedGrittyBrick Nov 24 '12 at 20:31
    
i have something to say to you in good length,but u don`t mention email id,please if u could. –  Abhinav Anand Nov 24 '12 at 21:34
    
How about The h bar chat room? –  RedGrittyBrick Nov 24 '12 at 23:46
    
Well I have to wait then,need more reputation points. –  Abhinav Anand Nov 26 '12 at 14:04
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As I have said space should include velocity in itself as extra dimension and same is true for time.Now as our saying if velocity is a form of space and also of time then the space and time both can be expressed in terms of velocity also. so what comes now that we will have two equations one expressing space-velocity relationship and other time-velocity relationship and inquiring these two spacial relativity expressions one can eliminate velocity from them and the only reality lefts behind and that is space time amalgamation which is a characteristic of relativity both special and general. so i think in this way we reach our satisfaction.

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