Time as 4th dimension

Originally posted by adam warlock
Maybe you are speaking about it in a more mathematical definition?

Originally posted by Palynka
I meant metrics in the "system of measurement" sense. But I'm now almost fully convinced of what I said at 20h14. 🙂

Originally posted by adam warlock
But I'm guessing you guys certainly have more refined defintions of dimensions.

Originally posted by adam warlock
I almost positive then that we talked about different things under the same name.

But what did you say at 20h14? 😕

Edit: I get it now. In my time zone it were 18h14.

Originally posted by Palynka
I don't think they're more "refined". In the mathematics we use we just tend to think of a dimension as, say, the values for one variable. Any subspace in a multidimensional space just represents a certain set of combinations of those values across different variables... Restrictions on values for certain variables can be represented by considering only a su ...[text shortened]... of the complete hyperplane.

In that sense, anything can be represented as a dimension...

humans cannot perceive any dimensions higher than thew third. and since they cannot know for sure at least now, whatever explain their equations better will do.

Originally posted by mtthw
I don't think this is that different from the concept of a phase space that Adam mentioned. That generalises the concept of dimension to include momentum as well as position...but phase spaces in general can go even further. They just represent the set of possible values of whatever it is that describes your physical system.

Originally posted by Palynka
It isn't different at all. All I'm saying is that it wouldn't surprise me if a mathematician found it very intuitive to see time as a 4th dimension.

Originally posted by Zahlanzi
a dimension that would have different properties that the other three might not be very nice for their equations.

Originally posted by Palynka
It isn't different at all. All I'm saying is that it wouldn't surprise me if a mathematician found it very intuitive to see time as a 4th dimension.

Originally posted by sonhouse
Why couldn't they see time as the 1st dimension? Does dimensioness have to exist in order for time to exist? Can't time exist outside dimensions?

Originally posted by sonhouse
Why couldn't they see time as the 1st dimension? Does dimensioness have to exist in order for time to exist? Can't time exist outside dimensions?

Is time a dimension or is it not?

As I see it, time may very well be treated as a dimension.
I asked a nice girl for a date. She asked me Where? A answered You know the romantic little restaurant at the corner of Main street (1st dimension) and Kings street (2nd dimension)? Yes, she said, I've heard the second floor (3rd dimension) has a wonderful view over the square! Yes, would you like to be there with me? Oh, yes, she said!
How did our little date of ours went? Not well, we forgot the 4th dimension - the When.
Conclusion, to have a nice date, you have to have 4 dimensions to be sure to meet at the right spatial position as well as the right temporal dimension.

Which one is the which? Which one is most important? How do we number them? Doesn't matter.

We have two classes of dimensions: The spatial ones (3 of them) and a temporal one (only 1). Do we hae more dimension classes? (A matter of disussion.)

An important difference between the spatial dimensions and the temproal one is that you can move in any direction in the spatial ones, but only forward in the temporal one.

An interesting question is: Does the future exist already? Is the future fixed and we're entering it by the time?
Another interesting question is: Does the past remain?

Originally posted by serigado
I hear/read many times the interpretation that universe is not 3D, that there is one extra dimension -> time.
I personally think that interpretation is WRONG. Time is an additional variable, but it can't be said to form an extra dimension, in analogy to ant living 2D in 3D world.
Why? Because in the jump we make from 2D to 3D we're adding a dimension with ...[text shortened]... o understanding it as another "dimension" in the metric of the universe is really strange.

Originally posted by Palynka
Your previous comments made me think that this maybe comes from the difference between the way a mathematician and a physicist see the concept of dimensions.

For example, I'm used to work with n-dimensional hyperplanes or sometimes even infinite-dimensional ones. For me a dimension is a very flexible concept.

Just a musing about our little disagreement here.

Edit: Hyperplanes, not hyperspaces Mr. Spock.