10 Mar 08
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 the same metric as the two previous ones. Time doesn't behave like simply adding this extra dimension. Even is special relativity , it enters as (-1) in the metric, not (+1).
To make things more complicated, time is our basic reference frame to perceive difference in interactions. We're intrinsically defined by time, so understanding it as another "dimension" in the metric of the universe is really strange.
10 Mar 08
2 edits
Originally posted by serigadoMetrics are pure convention.
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 o understanding it as another "dimension" in the metric of the universe is really strange.
For a given point in time, to pinpoint something's position in space, you need three dimensions. Yet, the same thing can be somewhere else in another point in time, therefore it's perfectly justifiable to think of time as an additional axis as you need the additional referent in an universe where the initial position may change along with time.
10 Mar 08
1 edit
Originally posted by Palynka[Metrics are pure convention
Metrics are pure convention.
For a given point in time, to pinpoint something's position in space, you need three dimensions. Yet, the same thing can be somewhere else in another point in time, therefore it's perfectly justifiable to think of time as an additional axis as you need the additional referent in an universe where the initial position may change along with time.
What do you mean by that? It appears to me that you are wrong but I want to understand why you are saying this and pinpoint it.
For a given point in time, to pinpoint something's position in space, you need three dimensions. Yet, the same thing can be somewhere else in another point in time, therefore it's perfectly justifiable to think of time as an additional axis as you need the additional referent in an universe where the initial position may change along with time.
All true but there are very fundamental differences between spacial dimensions and the time dimension and one should really understand them. First of all in spatial dimensions you can go back and forth as you please in time you just can go forward. Just like serigado said time is experinced and you can't put yourself out of time to better study it. One other thing is that a lot of scientits still wonder if time is real or just a handy fiction. Einstein prefered the second view. One other thing that normal people don't realise when discussing this things is that we are so used to the Euclidean metric, even if one doesn't know what that is, that one is always carrying that type of reasoning to other situations and that isn't applied. For instance we can all imagine curved spaces, a balloon for example, but we always embedd the ballon in a room. The room is the higher dimensional spance and guess what is metric is Euclidean. In general relativity the usual way of explaining that the metric changes from point to point is to introduce the rubber sheet and heavy balls analogy. For wjhat I'm worth as a physicist I'd say that that analogy is pretty $hitty. For one it uses gravity to explain gravity and it also gives bad representations habits. People get used to think in 2-d deformations and then translate things 2 a fourdimensional deformation. ANd that is wrong and get ´very bad results. I for one prefer to say that the metric isn't constant in general relativity and don't bother if I can or can't visualize things. I prefer that tpo $hitty visualisation.
And if thinking of time just as an aditional axis is so straightforward and logic whyt didn't guys like Newton or Huygens first done it in the early days of mechanics? Bear in mind that those two are intelectual giants. If you ask meNewton is the greatest physicist of all times. Why Einstein himself didn't like the concept so much when Minkowskii, is former math teacher, introduced it to math? If you read Einstein original article you'll see no mention of all future refinements on Special relativity. He only fully accepted the idea of a 4-dimensional continuum when he was very clodse to finishing general relativity and in there it was really needed.
10 Mar 08
Originally posted by PalynkaYes, you can see things that way. Each 3D configuration of space in function of time. In that view, time can be added as an extra-axis. But it really doesn't teach us anything new. It's just a new way of representing things.
Metrics are pure convention.
For a given point in time, to pinpoint something's position in space, you need three dimensions. Yet, the same thing can be somewhere else in another point in time, therefore it's perfectly justifiable to think of time as an additional axis as you need the additional referent in an universe where the initial position may change along with time.
When we talk time at 4th dimension, it has nothing to do with that representation. Time has actually something to do in how far things are!
10 Mar 08
But when you do try and treat time as a dimension, and you end up with something like the four-vector version of Maxwell's equations...it's so neat it's really difficult to dismiss it, in my opinion.
Mind you, my intuition never did work very well in four dimensions. That's why I ended up doing continuum mechanics rather than general relativity. 🙂
10 Mar 08
1 edit
Originally posted by adam warlockI never said the properties of that dimension are the same or even similar. Why should that even be a requirement? All I'm saying is that any representation on a 3D axis is subject to particular point in time. Therefore, to identify that representation properly, you would need a time dimension or you'd find yourself with the one set of vectors representing possibly different things.
[b][Metrics are pure convention
What do you mean by that? It appears to me that you are wrong but I want to understand why you are saying this and pinpoint it.
For a given point in time, to pinpoint something's position in space, you need three dimensions. Yet, the same thing can be somewhere else in another point in time, therefore it's perf was very clodse to finishing general relativity and in there it was really needed.
10 Mar 08
Originally posted by adam warlockI call this Sherlock Holmes' simplicity. They are seemingly straightforward when presented to you but are often hard to discover beforehand.
And if thinking of time just as an aditional axis is so straightforward and logic whyt didn't guys like Newton or Huygens first done it in the early days of mechanics?
10 Mar 08
Originally posted by PalynkaI never said you did. I just stated the differences.
I never said the properties of that dimension are the same or even similar. Why should that even be a requirement? All I'm saying is that any representation on a 3D axis is subject to particular point in time. Therefore, to identify that representation properly, you would need a time dimension or you'd find yourself with the one set of vectors representing possibly different things.
10 Mar 08
Originally posted by Palynkabut normalization isn't essential. It is just a way to neat things up. Saying that metrics is conventional based on this argument is wrong. Metrics can be a lot more fundamental than that.
The way you divide any axis is subject to normalization.
I see your point in normalization though. If we use different base vectors distances will differ from one base to another but it isn't the point. Metrics can tell you stuff about the space being considered itself.
10 Mar 08
1 edit
Originally posted by adam warlockYour 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.
I never said you did. I just stated the differences.
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.
10 Mar 08
1 edit
Originally posted by adam warlockWhat do you mean by metrics if not the way you "divide" a dimension?
but normalization isn't essential. It is just a way to neat things up. Saying that metrics is conventional based on this argument is wrong. Metrics can be a lot more fundamental than that.
I see your point in normalization though. If we use different base vectors distances will differ from one base to another but it isn't the point. Metrics can tell you stuff about the space being considered itself.
10 Mar 08
Originally posted by PalynkaOh! I think we are indeed discussin things from two different view points. I'm using the word metric as short for metrics tensor one thing that physicists usually do. http://en.wikipedia.org/wiki/Metric_tensor_%28general_relativity%29
What do you mean by metrics if not the way you "divide" a dimension?
Maybe you are speaking about it in a more mathematical definition?
In this the metric tensor tell us how the given space behaves. I think I'm using very bad language here but this is the best I can do.
10 Mar 08
Originally posted by PalynkaJust to add a bit. Dimensions for physicist also have their flexibility. Degrees of freedom are the best way to put this since they don't have to be spatial dimensions. For instance if you are studying the movement of a body in a 3-D space one natural to do it is using a phase diagram. in this case this phase diagram would have six dimensions. And we can also work on infinite dimensional spaces. With discrete or continous spectra. But I'm guessing you guys certainly have more refined defintions of dimensions.
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 hyperspaces or sometimes even infinite-dimensional ones. For me a dimension is a very flexible concept.
Just a musing about our little disagreement here.