# How do Dimensions make up Space and Time?

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55 minutes ago, Frostedwinds said:

I was trying to discuss how dimension make up time and space in the confines of the system I first stated. As for how I define a dimension. It would be a vector of sorts that explains the function inside a system.

Thank you.

This suggests (to me) you are trying to describe some sort of vector space as the construct.

Are you aware of the conventional rules relating to vector spaces vis a vis dimensions and bases ?

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Posted (edited)
27 minutes ago, Strange said:

If we can only observe / measure  one dimension of time, how is that different from there being only one dimension of time?

if these other time dimensions are not detectable then they may as well not exist.

You seem to agree that your idea is not testable and therefore it is not science.

It is testable because it works in a system of mathematics. It’s not observable at the moment. Observable science is always changing. We use to think the earth was the center of the universe or that it was flat because we couldn’t observe otherwise. Also it was posted under a theoretical physics page not a applied physics page.

theory is a contemplative and rational type of abstract or generalizing thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking often is associated with such processes like observational studyresearch. Theories may either be scientific or other than scientific (or scientific to less extent). Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.

In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for, or empirically contradict ("falsify") it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge,[1] in contrast to more common uses of the word "theory" that imply that something is unproven or speculative (which in formal terms is better characterized by the word hypothesis).[2] Scientific theories are distinguished from hypotheses, which are individual empirically testable conjectures, and from scientific laws, which are descriptive accounts of the way nature behaves under certain conditions.

Theories guide the enterprise of finding facts rather than of reaching goals, and are neutral concerning alternatives among values.[3]:131 A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.[4]:46

The word theory or "in theory" is more or less often used erroneously by people to explain something which they individually did not experience or tested before.[5] In those instances, semantically, it is being replaced for another concept, a hypothesis. Instead of using the word hypothetically, it is exchanged for a phrase "in theory". In some instances the theory's credibility could be contested by calling it "just a theory" (implying that the idea has not even been tested).[6] Hence, that word "theory" is very often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for doing, which is opposed to theory.[6] A "classical example" of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.[a]

In reality, there is a long and a thorny process for an idea or hypothesis to become a theory. And even after it becomes one, it is constantly being tested for validity. Among notable and long discussed theories are Darwinism(or other related to Creation–evolution controversy), flat Earth and others.

2 minutes ago, studiot said:

Thank you.

This suggests (to me) you are trying to describe some sort of vector space as the construct.

Are you aware of the conventional rules relating to vector spaces vis a vis dimensions and bases ?

I’m suggesting both spatial and temporal vectors being define mathematically in a system as a dimension. To answer your question, no would you elaborate. Also thank you for having a genuine conversation with me.

Edited by Frostedwinds

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Posted (edited)
12 minutes ago, Frostedwinds said:
12 minutes ago, studiot said:

Thank you.

This suggests (to me) you are trying to describe some sort of vector space as the construct.

Are you aware of the conventional rules relating to vector spaces vis a vis dimensions and bases ?

No would you elaborate. Also thank you for having a genuine conversation with me.

A vector space is a mathematical generalisation of the idea of a plot or graph with axes and a function connecting or detailing (your explaining?) the relationship between the axes.

In this terminology, the axes are called 'basis vectors'.
In truth they are just lines like any other lines on the graph and we could plot the graph relative to any pair of non parallel lines.

Edited by studiot

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11 minutes ago, Frostedwinds said:

It﻿ ﻿is testable becaus﻿e it works in a system of mathematics. It’s not observable at th﻿e momen﻿t.﻿

So, again, what testable predictions does your model make?

13 minutes ago, Frostedwinds said:

In﻿ modern﻿ scienc﻿e, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature﻿﻿, ﻿﻿

Therefore, you do not have a scientific theory.

Also, when you copy and paste text you should provide a source. Otherwise it is plagiarism.

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1 hour ago, Strange said:

So, again, what testable predictions does your model make?

Therefore, you do not have a scientific theory.

Also, when you copy and paste text you should provide a source. Otherwise it is plagiarism.

You haven’t read any of the things I cited earlier have you. The contain all the information you would need. But regardless I’m going to state one last time. The question adheres not to whether or not you agree with how the system functions with three dimensions of time but instead what order the system functions with three dimensions of time. Please just leave the chat.

1 hour ago, studiot said:

A vector space is a mathematical generalisation of the idea of a plot or graph with axes and a function connecting or detailing (your explaining?) the relationship between the axes.

In this terminology, the axes are called 'basis vectors'.
In truth they are just lines like any other lines on the graph and we could plot the graph relative to any pair of non parallel lines.

What I was trying to gauge was what is the relation between the two parts graphing out space and time. How would you label them in an order that fits the function of a balanced system? Does it even matter what order they are in to create a balance and etc.

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5 hours ago, Frostedwinds said:

What I was trying to gauge was what is the relation between the two parts graphing out space and time. How would you label them in an order that fits the function of a balanced system? Does it even matter what order they are in to create a balance and etc.

Not sure I understand what your trying to express here but the order of spatial coordinates and time axis isn't important. The importance is the symmetry basis between them for example I can write x,y,z,t or place time as the first coordinate which is the current accepted convention of the four momentum. (t,x,y,z). All four coordinates are othogonal 90 degree to each other in Cartesian coordinates.

I can't say anything about your application of three time dimensions as you haven't really defined this yet.

I myself use an important definition of dimension (that definition applies to both mathematics and Physics) an independent variable\value or other mathematical object that can vary without varying any other mathematical object.

In essence a degree of freedom. Studiot has commented before that I follow and oft stress proper definitions. LOL.

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7 hours ago, Frostedwinds said:

You﻿ haven’t ﻿read any of the things I cited ﻿earlier have yo﻿u﻿﻿.﻿

I did. They have no evidence to support your claims.

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Posted (edited)
13 hours ago, Frostedwinds said:

What I was trying to gauge was what is the relation between the two parts graphing out space and time.

A very good question.

In order to discuss this let us try to simplify and just use x;y coordinates for the moment.

Are these unique representations?

No they are not, but they have certain desirable characteristics.

Notably that the physical dimensions of x and y are the same.

So when we consider a (differential) variation with time, these differentials have the same form of physical dimensions (they are both velocities)

$\dot x = \frac{{dx}}{{dt}};\dot y = \frac{{dy}}{{dt}}$

This allows us to combine the two to form a vector describing the overall change over time.
That is they are the components of that vector.

BUT CONSIDER

If we use polar coordinates, r and θ then these refer to the same point and their time derivatives to the same change

but they do not have the same physical dimensions.

$\dot r = \frac{{dr}}{{dt}};\dot \theta = \frac{{d\theta }}{{dt}}$

So we cannot combine these directly to establish the overall change.

The angular derivatives are not components of a vector.

I see you are in a very different time zone from myself so I guess that English is not your first language.

If this is true we can help you choose the correct English words for what you want to say.

Edited by studiot

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9 hours ago, studiot said:

A very good question.

In order to discuss this let us try to simplify and just use x;y coordinates for the moment.

Are these unique representations?

No they are not, but they have certain desirable characteristics.

Notably that the physical dimensions of x and y are the same.

So when we consider a (differential) variation with time, these differentials have the same form of physical dimensions (they are both velocities)

x˙=dxdt;y˙=dydt

This allows us to combine the two to form a vector describing the overall change over time.
That is they are the components of that vector.

BUT CONSIDER

If we use polar coordinates, r and θ then these refer to the same point and their time derivatives to the same change

but they do not have the same physical dimensions.

r˙=drdt;θ˙=dθdt

So we cannot combine these directly to establish the overall change.

The angular derivatives are not components of a vector.

I see you are in a very different time zone from myself so I guess that English is not your first language.

If this is true we can help you choose the correct English words for what you want to say.

How about describing it as a direction and not a vector particularly. Direction through three dimensional space makes up x,y,z so let’s say directions through time makes up t1,t2,t3. They work in contrast to each other playing a part as equal parts space and equal parts time.

Space = Time

x,y,z = t1,t2,t3

direction through time we can state as a change in momentum from a point in time

direction through time we can state as a change of perspective from a point in space

now that would mean that we have to quantify space without time and time without space

the place of intersection being the an area where a point in space and a point in time exist together

now take as example the ability to preform motion as kinetic energy that energy is yet to choose a direction (a point in time)

now take as example matter as being an object with mass and volume (making up an area of space)

Matter with kinetic energy has yet to chose a direction but is an area in space that is at a point in time.

a point in space has zero dimensions, so a point in time also would have zero dimension (or no direction)

the intersection would be at that zero dimension as well then

then matter that expends the kinetic energy moves into the first dimension of time (or moves in one direction through time)

if there is only one direction through time then the system is unbalanced and x,y,z=t1

momentum measured as a direction through time would allow kinetic energy being a point in time to move in multiple direction

such as: you have two apples on a table, before you decided to pick one up you the potential to pick all three up meaning there are two options of the direction for you to chose from

the potential energy is a point in time and the two directions are t1, and t2

now let’s say you chose apple one or apple two, they are both motions of a t1 direction through a plane of t2

that would suggest that you can also rotate the plane of time (t2) perpendicular again and create and area of time (t3) that makes up all the possible directions your hand could have traveled including towards apple one or apple two

that would create a balance system where x,y,z=t1,t2,t3

That would also state that space(x,y,z) is matter and that time(t1,t2,t3) is energy in all directions.

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I am making a effort to respond to what you say,  I hope helpfully.

None of your last post responds to mine.

In particular I said

20 hours ago, studiot said:

I see you are in a very different time zone from myself so I guess that English is not your first language.

If this is true we can help you choose the correct English words for what you want to say.

Now I am just trying to make beter communication between us.

Here is an example

10 hours ago, Frostedwinds said:

now take as example matter as being an object with mass and volume (making up an area of space)

I think the correct word here is a region of space.

'Area' has a particular specialist meaning in Science and I do not think you mean that.

Before you asked specifically about the relationship or the connection between the coordinate axes (if any) and I am trying to work through that.

But I am receiving no indication if you are following this or not.

When we have laid the groundwork I propose to explore your very interesting suggestion that travelling (I won't call it motion or movement as they again has specific meanings in Science)

in time requires multiple time dimensions.

But can we lay that aside until we have discussed axes, dimensions and the relationships between them first?

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11 hours ago, Frostedwinds said:

How about describing it as a direction and not a vector particularly. Direction through three dimensional space makes up x,y,z so let’s say directions through time makes up t1,t2,t3. They work in contrast to each other playing a part as equal parts space and equal parts time.

Space = Time

x,y,z = t1,t2,t3

direction through time we can state as a change in momentum from a point in time

direction through time we can state as a change of perspective from a point in space

Kinetic energy depends on speed. Speed is ds/dt, where s is the displacement

Which t do I use here?

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Purpose of this post is to allow participants to decide if the papers I referenced* are applicable to this discussion or not.

On 8/6/2019 at 9:34 PM, Frostedwinds said:

The question was pertaining to a system of relevance that the theory in question if functioning within a system where time is explained by three separate dimensions in the same way that space is.

I might have misunderstood the context so that my answer* was not applicable to the actual question.

On 8/6/2019 at 9:37 PM, studiot said:

This question and the subsequent discussion depends crucially on what the participants consider a dimension to be and also what properties it posses and its relationships to any other dimensions included in the discussion.

Here are some short notes about dimensions used in my post.

The geometric model Spacetime has 3 spatial and on time dimension. A dimension is an independent variable or value that can change without affecting other mathematical objects**.

In Minkowski space (referenced in the articles I linked to), the metric signature have same sign for the three spatial dimensions and sign for the one time dimension is opposite ***: (+ − − −) or (− + + +).

My point was that, according to the papers, physical laws that works for (+ − − −) does not hold at all for instance for (+ + − −) or (++ − − −). There may only be one (time) dimension holding the opposite sign. So my comment may be out of scope if other definitions or connections between time and space are intended.

*) scienceforums.net/comment1112894
**) Borrowed some formulations from @Mordred
***) Hopefully correctly expressed; I do not yet master this kind of math

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On 8/5/2019 at 11:58 PM, Frostedwinds said:

dimension zero (a point in space)

You have mentioned several times that you consider a point to have no dimensions.

That is indeed the view of the Ancient Greeks (whom you also mentioned)

But the Ancient Greeks knew little of trigonometry and nothing of coordinate geometry and later developments in geometry (such as  latitude and longitude) and in Physics.

So is that view tenable today?

Let us explore this, because other respondents here are using dimension in quite a different way, for example:-

On 8/7/2019 at 6:24 AM, Mordred said:

I myself use an important definition of dimension (that definition applies to both mathematics and Physics) an independent variable\value or other mathematical object that can vary without varying any other mathematical object.

and

On 8/6/2019 at 8:08 AM, Strange said:

Times a fourth dimension. You can tell, because you need to specify four bits of information: where (3 spatial coordinates) and when (1 time coordinate). For example, two men meet on a street corner and decide to meet up again later for lunch at a restaurant,  on the tenth floor of a building 5 blocks East and 7 blocks North of where they are, in 3 hrs.

A point in space becomes a line in spacetime. A line in space becomes a plane in spacetime. And so on.

Now in both these views, a point has four dimensions (three spatial and one temporal)

This is because you require a value for each of Mordred's independent variables.

But modern thinking goes much further than this.

Consider

A point has no volume.

But a point can have mass, velocity (a noted by swansont) , spin and many other properties.

For every such property the point requires another 'dimension' or alternatively a relationship (such as an equation)to other coordinates.

We call these 'generalised coordinates'.

Every set of such coordinates form a space.

In Physics we call this 'Phase Space'.

I have underlined a comment above becasue it is the introduction to a mathematical technique called parametrisation.

This is important because Time can be used as a parameter.

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On 8/8/2019 at 5:53 AM, studiot said:

I am making a effort to respond to what you say,  I hope helpfully.

None of your last post responds to mine.

In particular I said

Now I am just trying to make beter communication between us.

Here is an example

I think the correct word here is a region of space.

'Area' has a particular specialist meaning in Science and I do not think you mean that.

Before you asked specifically about the relationship or the connection between the coordinate axes (if any) and I am trying to work through that.

But I am receiving no indication if you are following this or not.

When we have laid the groundwork I propose to explore your very interesting suggestion that travelling (I won't call it motion or movement as they again has specific meanings in Science)

in time requires multiple time dimensions.

But can we lay that aside until we have discussed axes, dimensions and the relationships between them first?

I live in America and yes English is my first and only language. So with words like Area, Motion, or Movement what are the specifics requirements of their use. I’m only using these words as general references to what I mean. Thank you again for the help with this.

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On 8/9/2019 at 7:08 PM, Frostedwinds said:

I live in America and yes English is my first and only language. So with words like Area, Motion, or Movement what are the specifics requirements of their use. I’m only using these words as general references to what I mean. Thank you again for the help with this.

Thank you for this useful reply.

What would also be useful would be some feedback about my thoughts on your posts.

I really have no idea what you have understood or agreed.

Also some idea of the level of maths you can cope with would be useful. You can't do this without some maths.

So consider again a simplified 2D x-y system.

Now let

x = Acos(t)

and

y = Asin(t)

I have used t, since it is conventional.

t is known as a parameter or sometimes a running variable.

t is used because the running variable is often time.

What it does is reduces a 2D system to a 1D system at the cost of introducing conditions by way of the two equations.

And time is used to link the (spatial) dimensions as you requested.

Conventional time has the same properties as a parameter vaiable.

It 'runs' evenly, with no gaps or jumps - the same property as real numbers and the calibration on our x and y axes.

But do real objects behave in this manner?

Well the East Coast Main (railway) line in Scotland is single track, North of Edinburgh.

This means that if an express train is 'stuck' behind a slow train it has to follow at the speed of the slow train.
It cannot pass.

In fact all the trains on the railway must follow at same speed to avoid collisions.

This must also be the case with a single time axis.
Everything travels at a constant even rate through the single time axis.

Perhaps this is why you have proposed more than one?

Of course in space different objects can travel at different speeds without collisions because a faster object can move sideways around a slower one,
and also because there are relatively enormous gaps between objects in space.

So far as I know we have never observed this type of behaviour involving the single time axis we can observe.

In fact it seems choc-a-bloc with objects.