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26/05/2013 01:19:08

### Author Topic: How many 'dimensions' is there to Time?  (Read 3830 times)

#### yor_on

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• on: 21/02/2011 01:25:24
If I look at the 'Many Worlds' scenario. Could I assume that time actually 'branch out' in more ways than only 'forward & backward? In it (MW) you have all those 'instants' in where probability is said to rule, branching out the most 'probable' for us, but what happen to the rest?

What do you think?

Imagine it as one and the same 'time', although 'split' to us, only having one arrow. How would it look from 'Time' itself? Does it see a ocean containing countless distributaries? A neural network. What would such a thing look like? Would it just 'grow' or is there some other way to catch that idea?
==

I presume that I alternatively can assume that all of 'SpaceTime' needs to 'grow' with time in such a scenario, or treat 'time' as being on its own. The scenario making most sense to me is the one in where all 'dimensions' hang together. Or should I assume them to 'bud off'? But then the question seems to become, why can't I notice it? Are we the 'first' from where all other bud off then, or could we be a distributary ourselves? If we ourselves was a secondary phenomena from an earlier budding would there be a difference?
« Last Edit: 21/02/2011 01:48:07 by yor_on »

#### Geezer

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• Reply #1 on: 21/02/2011 03:46:56
I don't think time has any dimensions. Space and time are inseperable, so time and space cannot have unique dimensions.

#### JP

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• Reply #2 on: 21/02/2011 04:38:51
Dimensionality has a very strict mathematical definition.  Within that definition, a single universe with space and time has 3 space dimensions and one time dimension.  The geometry of the universe means that moving objects have certain allowed trajectories and that the overall space-time has a certain geometry.  From the definition of dimensions, time is one-dimensional in the sense that the time coordinate of an event (at least from one observer's point of view) is given by a single number.  The spatial coordinates require three numbers, hence three dimensions.

Now, if the universes could branch, as in the MW interpretation, and you could somehow look down from above on all the branches, then you'd need additional dimensions to keep track of which universe you were in as well as the 3+1 dimensions within that universe.  I'm not quite sure how this would work, though.

However, the fact is that you can't look down from above.  The many worlds interpretation is, for any observer, indistinguishable from if there was only one dimension with the Copenhagen interpretation.  So in every case, you can simply treat the universe as only having one time dimension (which is one-dimensional, I suppose).  Questions about more dimensions due to multiple universes is essentially metaphysics, since none of it changes the 3+1 dimensional nature of the model we actually use to do calculations.

------------------
Though I suppose theories like string theory, which propose 10-11 dimensions do indeed have extra dimensions within our own which can be accessed by observers.  It's just that unless we look with a very powerful microscope (i.e. particle accelerator) we only see 3+1 of those dimensions.  I really don't know what those have to say about time as a dimension.

#### Geezer

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• Reply #3 on: 21/02/2011 05:12:54
The geometry of the universe means that moving objects have certain allowed trajectories and that the overall space-time has a certain geometry.

That's the point. Space-time has a geometry. Strictly speaking, because they are both functions of each other, neither space nor time have discrete geometries. If we can't define the geometry of something, I don't understand how we can define its dimensions.

(Unless we revert to a Newtonian model, which works for me  )

#### yor_on

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• Reply #4 on: 21/02/2011 11:30:10
Ahh, Jp, that's exactly what I'm doing in fact. Treating it as on 'its own' :)
After all, no matter how you define those 'dimensions' they are conceptual thingies. They are not to be weighted, neither can I take them 'apart'. So when I think of 'time' I do it as 'one concept', not several.
==

Well, with one exception. I differ the 'arrow' from the idea of 'time.
« Last Edit: 21/02/2011 13:21:26 by yor_on »

#### graham.d

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• Reply #5 on: 21/02/2011 14:35:10
Geezer, I think just because the x,y,z,t axes are not orthogonal (as in Euclidean space) doesn't mean that there are not 4 dimensions. It is considered that there are (at least, in fact). The surface of a sphere can be considered as 2 dimensional even though these dimensions are not orthogonal (longitude and latitude). As you say, it depends on the underlying geometry.

As far as the implications of many-worlds ideas are concerned, I am unsure of the implied differences that may result between spacial dimensions and a time dimension, but I'll have a go at answering anyway :-). If you think of an "event" in spacetime resulting in one of several possible outcomes (one of two other events, say) this is limited by being geometrically confined by "lightcones" due to the finite speed of light. Our perception of such events is also confined by the same physics limitations. It is not time branching per se, but the whole of spacetime adopting a different state. We perceive this event in time because we are part of spacetime and we are used to cause and effect being time directional; in fact a definition of time in a local environment. I have been interested recently in what a blackhole would look like after passing the event horizon. Mathematically this is problematic (and can't be done) using a shwartzchild metric as the maths breaks down at the horizon, but it is possible to analyse with a coordinate transform and can be visualised using a Penrose diagram. Inside the BH the region is "timelike" rather than "spacelike" and your view of the singularity is actually equivalent to looking forward in time to the end of the universe. I am not sure how this helps except to show that in some senses time and space dimensions are interchangeable. I can't say I understand this or the implications, but I'm trying to :-)

#### yor_on

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• Reply #6 on: 21/02/2011 15:10:01
Good on you Graham :)

Spooky stuff, black holes. But you make a very nice point in lifting them up. They too should have a 'times arrow' and we do say that they are singularities. Should I see this as a proof of 'time' budding off? Or should I consider it a 'bifurcation/split path', somehow still connected to our own 'time' outside the singularity?
« Last Edit: 22/02/2011 06:03:16 by yor_on »

#### Geezer

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• Reply #7 on: 21/02/2011 19:01:39
Geezer, I think just because the x,y,z,t axes are not orthogonal (as in Euclidean space) doesn't mean that there are not 4 dimensions. It is considered that there are (at least, in fact). The surface of a sphere can be considered as 2 dimensional even though these dimensions are not orthogonal (longitude and latitude). As you say, it depends on the underlying geometry.

Ah, but you can't define the position of a moving object in terms of those four dimensions that all observers will agree on. (At least I don't think you can.)

#### JP

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• Reply #8 on: 22/02/2011 05:06:25
There's a nice analogy between time as a dimension and 3D dimensions.  In 3D Euclidean space, you can label your axes up/down, left/right, front/back.  But then if you rotate your point of view, what now looks front  to you might be a mixture of what before was left and front.  Anyone can still define these axes from their point of view, but those might not agree due to a rotation.  Though quite clearly, if I rotate my point of view, I still see space as three-dimensional, even though each one of those dimensions might not be the same as previously.

In space-time, when you change speed, you're doing the equivalent of a rotation that mixes space with time (a Lorentz boost). So when you speed up, you're mixing your time axis with the other axes in terms of measurements.

So I think you have a point, Geezer.  :)  You can't simply separate time from the other axes, since they mix if you change speeds.  However, I think you're wrong that time isn't a dimension.  It surely is to any given observer.  Just as any observer sees three space dimensions, no matter how much you rotate them, they still see one time dimension no matter how much you speed them up.  Not all observers agree on the definition of this time dimension, but each still has a single (1D) time dimension.

#### yor_on

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• Reply #9 on: 22/02/2011 05:55:26
Very nice JP.

The best explanation I've seen to a 'geometric rotation' of SpaceTime. You made it understandable there.

#### Geezer

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• Reply #10 on: 22/02/2011 06:02:34
However, I think you're wrong that time isn't a dimension.  It surely is to any given observer.  Just as any observer sees three space dimensions, no matter how much you rotate them, they still see one time dimension no matter how much you speed them up.  Not all observers agree on the definition of this time dimension, but each still has a single (1D) time dimension.

Yes, but , wouldn't the purpose of assigning spacetime four dimensions be to permit an unambiguous definition for a location in spacetime that all observers can agree on? It seems that won't work unless we add more information.

Maybe we need to add another dimension to fix it

#### yor_on

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• Reply #11 on: 22/02/2011 06:03:57

I wrote " Should I see this as a proof of 'time' budding off? Or should I consider it a 'bifurcation/split path', somehow still connected to our own 'time' outside the singularity?"

If a Black Hole is a 'singularity' how do a entanglement find its way, 'communicating' with its twin? And how do a 'tunneling' know where to go?

#### yor_on

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• Reply #12 on: 22/02/2011 06:33:26
However, I think you're wrong that time isn't a dimension.  It surely is to any given observer.  Just as any observer sees three space dimensions, no matter how much you rotate them, they still see one time dimension no matter how much you speed them up.  Not all observers agree on the definition of this time dimension, but each still has a single (1D) time dimension.

Yes, but , wouldn't the purpose of assigning spacetime four dimensions be to permit an unambiguous definition for a location in spacetime that all observers can agree on? It seems that won't work unless we add more information.

Maybe we need to add another dimension to fix it

Very sweet Geezer. To me that Q. also asks what a 'zero motion' is? It's the same phenomena expressed differently. If there is no 'gold standard' for position and motion, except the way we find them able to translate into each other, when comparing arbitrarily defined 'slices' of SpaceTime, (frames of reference). Then you have two main solutions as I see it. Either there is a need for something 'Xtra' for the universe to define itself, and keep 'count'. Or we are looking at it from the wrong point of view?

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