# Independent Continuum

1. Apr 14, 2007

### paradoxical67

"Independent Continuum"

Can anybody please explain to me what this actually means. My understanding in very vague terms is that something is constant, with reference to Einstein's The Special and General Theory book, where he says that we often think of time (and space i think) as "independent continuums". Any help wil lbe appreciated. Peace.

2. Apr 14, 2007

### MeJennifer

With respect to relativity, it means that only an observer's view of space and time taken together make an independent continuum. In relativity, space and time are covariant entities, not invariant entities. That means that different observers do agree on the combined measurement of space and time but they do not agree on the separate measurements of space and time.

Last edited: Apr 14, 2007
3. Apr 14, 2007

### paradoxical67

hmm ok. When you speak of the combined values, is this due to the fact that as time dilates, space also contracts? So one would not notice the change..? :s

4. Apr 14, 2007

### MeJennifer

Time dilation and space contraction are the consequences of the symmetry pattern of space and time.

You can translate the separate values of space and time into another form by using the Lorentz transformations. The form changes but the meaning is the same, each observer simply has a different perspective on this one, combined, reality called spacetime.

Last edited: Apr 14, 2007
5. Apr 14, 2007

### reilly

Independent just means that an event can have any time assigned to it, and any spatial point as well. In general knowing a time tells you nothing about where, and vica versa. That's independence.
Regards,
Reilly Atkinson

6. Apr 14, 2007

### MeJennifer

The whole point is that in relativity time and space are no longer independent but co-dependent. "Time is robbed of its independence", as Albert Einstein formulates it.

7. Apr 14, 2007

### paradoxical67

s

right ok. This is comlicated. :grumpy:

im going to stick to 'constants' for now. I am writing a research paper on special relativity, clearly i havent understood a great deal!!

Thanks for the help though guys, i semi understood what youre saying.

8. Apr 14, 2007

### JesseM

Basically I think the main thing to understand is that although different frames can disagree on the time interval $$\Delta t$$ and the spatial distance $$\Delta x$$ between any two events, they will always agree on the invariant spacetime interval $$c^2 \Delta t^2 - \Delta x^2$$

9. Apr 14, 2007

### paradoxical67

ok thanks.

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