Time, Space, and Dimensions: Exploring the Measure of Length

[petm1]

Would I be correct in thinking of time as the measure in length of a single point. If we take into account one second of this measure of time, would a photon be the longest and the shortest a cesium atom? Would I be correct in thinking of space as the measure in length between two points, using a photon as the ruler? Thinking of this measure for time can we see a need for time to have three dimensions just as we do for space?

 

[FunkyDwarf]

Time is a non-event between events. The 'duration' of this non-event can only ever be measured in proportion to events, ie some standard candle.

 

[Mentz114]

can we see a need for time to have three dimensions just as we do for space?

Some theories introduce extra space dimensions ( see Kaluza-Klein and string theories ) and I know of at least one attempt to add 2 extra time dimensions ( ref supplied if you want it).
But the theories that agree with experiment use one time and three spatial dimensions.

 

[pervect]

Time, as measured by a clock, is generally regarded as an interval. Much as distance measures the length of spacelike curves, time measures the "length" of timelike curves. Rulers are used to measure spacelike intervals, clocks are used to measure timelike ones.

It doesn't make a lot of sense to talk about the "interval" or "length" of a point, it would be equal to zero.

 

[Chris Hillman]

That was easy!

Would I be correct in thinking of time as the measure in length of a single point?

No, you would not.

(At least, not unless you explain very carefully your nonstandard usage of "time", "measure", "length", "single", and/or "point".)

 

[petm1]

Time is a non-event between events. The 'duration' of this non-event can only ever be measured in proportion to events, ie some standard candle.

I've always read that time was the continuum, with the key being that it has continuity, but I can see how you might call it a non-event, I think of time as the dimensionless point myself. As for our "standard candle" it is the cesium atom, with its 9,192,631,770 events per second.

 

[petm1]

Some theories introduce extra space dimensions ( see Kaluza-Klein and string theories ) and I know of at least one attempt to add 2 extra time dimensions ( ref supplied if you want it).
But the theories that agree with experiment use one time and three spatial dimensions.

I would like to read those references please. I never said that one and three dimensions didn't agree with experiments, I am just cheering for time to have as many dimensions as space.

 

[petm1]

Time, as measured by a clock, is generally regarded as an interval. Much as distance measures the length of spacelike curves, time measures the "length" of timelike curves. Rulers are used to measure spacelike intervals, clocks are used to measure timelike ones.

It doesn't make a lot of sense to talk about the "interval" or "length" of a point, it would be equal to zero.

Your right I should have called it a point in geometry and not the point where two lines meet as mathematicians use it.

 

[Mentz114]

Here is a reference to an article proposing a 6D space-time model.

"Modified Kaluza-Klein Theory, Quantum Hidden Variables and 3-Dimensional Time"
Xiaodong Chen
arXiv:quant-ph/0501034v2

 

[robphy]

Here is a reference to an article proposing a 6D space-time model.

"Modified Kaluza-Klein Theory, Quantum Hidden Variables and 3-Dimensional Time"
Xiaodong Chen
arXiv:quant-ph/0501034v2

In my opinion, further discussion along these lines doesn't belong in S&GR
...but maybe in "Beyond the Standard Model" https://www.physicsforums.com/forumdisplay.php?f=66 .

 

[Mentz114]

Robphy, the reference was given in response to the OPs question. I don't intend discussing it here (or anywhere for that matter).

 

[Chris Hillman]

I beg to differ!

Your right I should have called it a point in geometry and not the point where two lines meet as mathematicians use it.

That comment is a bit startling, since you might find some respectable mathematicians thinking of "a point" as "the intersection of two lines" back in 18th century France, and this point of view remains valuable in certain contexts even today (see in fact recent issues of John Baez's This Weeks Finds), but in general I doubt this has ever been the first thing most mathematicians are likely to think of when someone says "point". Note however that "point" has generally been taken to be an undefined term since the ancient Greeks. These days a point is an element of a "space", but the intuition of what the "neighborhood" of a point looks like depends critically upon the nature of the "space", and there is a tremendous variety of spaces considered in mathematics since the 19th century, most quite different in many ways from three dimensional euclidean space.

 

[petm1]

First if this thread does not belong here, I am sorry. please feel free to move or lock at any time, thanks in advance. jeff

Originally Posted by petm1 View Post
Would I be correct in thinking of time as the measure in length of a single point?

No, you would not.

(At least, not unless you explain very carefully your nonstandard usage of "time", "measure", "length", "single", and/or "point".)

Time: the continuum or the continuous passage of existence, or the dimensionless point that we exist within.

measure: compare, an extension of a point on a line used to show length.

Length: for time we call it a duration or interval, and as compared to a clock we express it seconds.

single: one.

Point: has two sides in and out.

Time, as measured by a clock, is generally regarded as an interval. Much as distance measures the length of spacelike curves, time measures the "length" of timelike curves. Rulers are used to measure spacelike intervals, clocks are used to measure timelike ones.

Time like curves, looks like a continuous line of a single dimensional point(s) to me. I'm thinking that time is the points and our second is measuring the motion of and through them.

It doesn't make a lot of sense to talk about the "interval" or "length" of a point, it would be equal to zero.

Without relative movement it is equal to zero.

 

[pervect]

Time like curves, looks like a continuous line of a single dimensional point(s) to me. I'm thinking that time is the points and our second is measuring the motion of and through them.

This is getting too philosophical for the GR forum (and not in a good way).

I'll respond to a few points, though, before I lock this. Points in space-time are events. Events are not time.

You might give an event a time coordinate, which is a number. But a coordinate is a label for the time - the time coordinate is not really the time.

Time is the structure of the points - the topology. The fact that you can arrange points into a line by assigning a single number to them would suggest that time has the topology of a line.

However, this is ignoring one very important fact that comes out of SR. Time and space are not separate entities. What we really have is not a 3-dimensional space and a 1-dimensional time, but a 4-dimensional space-time. The splitting of space-time into space and time requires an arbitrary, human decision.