why is time called 4th dimension?

[swaha]

we can see only three mutually perpendicular st line in space at a pt. if time was another dimension either we have to imagine it only or we must shrink the angles. but what is the reason of shrinking the angle? infact what is the significance of another dimension? pls explain.

[insane_alien]

time is perpendicular to the three spatial dimentions, you don't shrink any angles.

 

the dimention numbering system is arbitrary, you could call it the first second or third if you really wanted but since everybody calls it the fourth you're better sticking with that.

 

the significance of a fourth dimension is that you need 4 coordinates to locate an object, the first three for the spatial location of the object and the fourth for the time it is at that location.

 

like if i wanted to meet you i would have to give both a place AND a time otherwise we'd probably miss each other even if we stood in exactly the same spot.

[swaha]

thanks. i get it. we probably cant imagine it geometrically.

[insane_alien]

we can actually. look up tesseract and/or hypercube these are geometrical representations of a 4 dimentional object.

[Sisyphus]

we can actually. look up tesseract and/or hypercube these are geometrical representations of a 4 dimentional object.

 

That's not really the same thing as "imagining" it, though. You have to distort them in some way to represent them, usually by distorting the angles. You can, however, take a series of undistorted 3D "slices."

[Bob_for_short]

we can see only three mutually perpendicular st line in space at a pt. if time was another dimension either we have to imagine it only or we must shrink the angles. but what is the reason of shrinking the angle? infact what is the significance of another dimension? pls explain.

 

Time is time, it is not a forth space dimension in a usual sense.

 

In a usual geometry there is a notion of distance L=|r1-r2|. It is numerically the same (invariant) whatever reference frame you use.

 

In reality it is not invariant - it depends on the reference frame. The invariant quantity is the so called interval that includes time. In this sense it serves as a forth coordinate r4=i*ct in a four-dimentional space (r,i*ct). It was described for the first time in a H. Poincaré's paper (1905) and extensively applied later on in Minkowsky works.

 

On a two-dimesional plane (x, i*ct) the inter-axe angle is still 90° and the Lorentz transformations are just rotations in this plane that preserve the "length" determined as S=√[x^2+(i*ct)^2].

Edited July 21, 2009 by Bob_for_short

[swaha]

The invariant quantity is the so called interval that includes time. In this sense it serves as a forth coordinate r4=i*ct in a four-dimentional space (r,i*ct

But time also vaiers in different reference frames. wasnt it the light velocity that remained invariant? got confused again. help.

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i beg ur pardon for i had to copy paste what mr bob has written. i dont know how to use this quoting stuff here. sorry.

[insane_alien]

to quote someone just hit the big buttin at the bottom of their post labeled 'quote'

[swaha]

ok thanks. let's focus on the problem now.

[Bob_for_short]

The invariant quantity is the so called interval that includes time. In this sense it serves as a forth coordinate r4=i*ct in a four-dimensional space (r,i*ct).

 

But time also varies in different reference frames. wasn't it the light velocity that remained invariant? got confused again. help.

 

Yes, the time intervals (t2-t1) and distances or lengths L are not invariant - they change from one RF to another, but their combination S^2 = L^2 +[i*c(t2-t1)]^2 is invariant in our world. Here c is just a numerical constant common to all RF. In this sense x4 = i*ct is a forth independent variable (1D distance) in a four-dimensional (Minkowsky) space.

[Tolmosoff]

What can a dimension be called say if way beyond our universe where time and space don't exist ? Can that have a dimension ?.

[swaha]

please define what is meant by S, L here.

[Bob_for_short]

please define what is meant by S, L here.

 

Everything was defined above: L is a distance, S is an interval.

[swaha]

does it mean that L should vary with t2-t1 to keep S a constant?

[Bob_for_short]

does it mean that L should vary with t2-t1 to keep S a constant?

 

Yes, it does. Time intervals are relative, space distances too, the intervals are invariant.

[Eric 5]

we can see only three mutually perpendicular st line in space at a pt. if time was another dimension either we have to imagine it only or we must shrink the angles. but what is the reason of shrinking the angle? infact what is the significance of another dimension? pls explain.

 

Just to be clear. When you say we see only three dimensions, do you mean that light is being reflected off these dimensions so that the light percieving organs (known as eyes) can "see" dimensions?

 

What do you mean see?

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time is perpendicular to the three spatial dimentions, you don't shrink any angles.

 

the dimention numbering system is arbitrary, you could call it the first second or third if you really wanted but since everybody calls it the fourth you're better sticking with that.

 

the significance of a fourth dimension is that you need 4 coordinates to locate an object, the first three for the spatial location of the object and the fourth for the time it is at that location.

 

like if i wanted to meet you i would have to give both a place AND a time otherwise we'd probably miss each other even if we stood in exactly the same spot.

 

This is all about a mathmatical model. Not physical reality. Nothing in what you said describes a real physical thing. I only point this out so no one thinks that dimensions are a real physical entity.

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we can actually. Look up tesseract and/or hypercube these are geometrical representations of a 4 dimentional object.

 

not real things. Just imagination.

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Time is time, it is not a forth space dimension in a usual sense.

 

In a usual geometry there is a notion of distance L=|r1-r2|. It is numerically the same (invariant) whatever reference frame you use.

 

In reality it is not invariant - it depends on the reference frame. The invariant quantity is the so called interval that includes time. In this sense it serves as a forth coordinate r4=i*ct in a four-dimentional space (r,i*ct). It was described for the first time in a H. Poincaré's paper (1905) and extensively applied later on in Minkowsky works.

 

On a two-dimesional plane (x, i*ct) the inter-axe angle is still 90° and the Lorentz transformations are just rotations in this plane that preserve the "length" determined as S=√[x^2+(i*ct)^2].

 

BOB. Is time a physical thing as defined by physics or any science?