Is Time a Dimension? Exploring the Differences

[boysherpa]

is time a "dimension"

I have been trying to figure this one out for some time now. I have read much on the subject, but it seems to be dealt with in such a cavalier fashion. So, here goes...

We speak of space-time as if it were something packaged. I have a problem with this. Let me list the difficulties I have:

Concerning position:
1. In physical 3-space, I can position an object anywhere I like, relative to an arbitrary (0,0,0) position.
2. After any arbitrary operation, the objects position can be anywhere in 3-space, including any previous position.
3. The object may be placed in + or - position relative to the origin.
4. Any operation changing the objects position instantiates or necessitates the creation of time. Without a change of position, there is no need to speak of time.
5. Changes in position may be made with an infinity of possible velocities and accelerations, positing "time"
Concerning time:
A. I have no control over the timing of an event - it always occurs at the present - dissimilar from item 1.
B. I can never reuse the present or a previous time - dissimilar from item 2.
C. Causality forces only forward motion in time - dissimilar from item 3.
D. The flow of time does not instantiate a change of position - dissimilar from item 4.
E. Time does not seem to have various rates of flow (relativity excepted) - dissimilar from item 5.

It would seem, then, that time is only superficially similar to 3-space, in that it operates in some mathematical models in a fashion similar to the spatial distances. However, A-E behaviors are distinctly different from 1-5 behaviors.

So, how can we group time with space? It would seem time is something wholly different, and perhaps not of the same substance.

Any help?

 

[Dale]

None of those things are relevant.

The term http://en.wikipedia.org/wiki/Dimension" has a specific mathematical meaning: "In mathematics the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it". A minimum of four coordinates are needed to specify every event in spacetime, so spacetime is a four-dimensional space. The fact one coordinate is different from the other three does not make it any less of a coordinate.

Having said that, you are absolutely correct that time is fundamentally different than space as can be seen from the Minkowski metric: ds²=-c²dt²+dx²+dy²+dz². Time is still a dimension, but that minus sign definitely singles it out.

 

[atyy]

For any person, there's always a time dimension that is separate from his space dimensions. But what is time for me may be space for you, which is why we imagine time and space together as spacetime.

 

[Fredrik]

We could define spacetime to be the set $\mathbb R^4$ and let functions of the form $C:\mathbb R\rightarrow\mathbb R^4$ represent an object's motion, even if we knew nothing about special relativity. It's this definition that turns time into a "dimension". Time is a dimension in that model, for the reasons DaleSpam explained.

In this model of spacetime, "space" is a subset of spacetime such that all the members of it are simultaneous (i.e. have the same time coordinate). The difference between SR and pre-relativistic physics is what atyy said: Each inertial observer would call a different 3-dimensional slice of spacetime "space" (assuming that they assign coordinates to events using a pretty obvious definition of simultaneity involving light, a mirror and a clock).

 

[Naty1]

Boy,
Don't be disallusioned that you don't understand "spacetime". In some sense, nobody does, but it EXPLAINS much of what we oberserve experimentally...so its a very useful set of rules/relationships/concepts...until a better one arrives.

Einstein published his general relativity and Minkowski subsequently formalized the idea of four dimension spactime...Einstein adopted it...And physicsts spent the next twenty years slowly discovering what general relativity really means...

 

[Fredrik]

Posting the same thing again so that the LaTeX can be seen...

We could define spacetime to be the set $\mathbb R^4$ and let functions of the form $C:\mathbb R\rightarrow\mathbb R^4$ represent an object's motion, even if we knew nothing about special relativity. It's this definition that turns time into a "dimension". Time is a dimension in that model, for the reasons DaleSpam explained.

In this model of spacetime, "space" is a subset of spacetime such that all the members of it are simultaneous (i.e. have the same time coordinate). The difference between SR and pre-relativistic physics is what atyy said: Each inertial observer would call a different 3-dimensional slice of spacetime "space" (assuming that they assign coordinates to events using a pretty obvious definition of simultaneity involving light, a mirror and a clock).

 

[Makep]

I have been trying to figure this one out for some time now. I have read much on the subject, but it seems to be dealt with in such a cavalier fashion. So, here goes...

We speak of space-time as if it were something packaged. I have a problem with this. Let me list the difficulties I have:

Concerning position:
1. In physical 3-space, I can position an object anywhere I like, relative to an arbitrary (0,0,0) position.
2. After any arbitrary operation, the objects position can be anywhere in 3-space, including any previous position.
3. The object may be placed in + or - position relative to the origin.
4. Any operation changing the objects position instantiates or necessitates the creation of time. Without a change of position, there is no need to speak of time.
5. Changes in position may be made with an infinity of possible velocities and accelerations, positing "time"
Concerning time:
A. I have no control over the timing of an event - it always occurs at the present - dissimilar from item 1.
B. I can never reuse the present or a previous time - dissimilar from item 2.
C. Causality forces only forward motion in time - dissimilar from item 3.
D. The flow of time does not instantiate a change of position - dissimilar from item 4.
E. Time does not seem to have various rates of flow (relativity excepted) - dissimilar from item 5.

It would seem, then, that time is only superficially similar to 3-space, in that it operates in some mathematical models in a fashion similar to the spatial distances. However, A-E behaviors are distinctly different from 1-5 behaviors.

So, how can we group time with space? It would seem time is something wholly different, and perhaps not of the same substance.

Any help?

As one comes to think of it, it is really impossible to exist without time and space - everything becomes oblivious. As you have rightly stated, time begins with the beginning of motion. The characteristic of time is two-fold:
a. Linear time
b. Oscillating time
A body moving in a linear motion will generate linear time. On the other hand, a body moving in rotatory motion will generate an oscillating time.Whatever the case is, time is a measure of space in motion while space is a measure of space at 'rest'. It would be better to think of time as having intrinsic and extrinsic qualities.
Intrinsic qualities of time play on the elements of a body as classical physics would have us believe. The Galileian coordinates of space and time with respect to an entity's own inertial frame generates its intrinsic qualities of time.When this system becomes a relativistic system, space changes at some predictable rate. This rate of change generates the extrinsic qualities of time that can either be linear or oscillating in nature.
Thus, time is a dimension of space that is changing and therefore, is a dimension.

 

[Naty1]

So, how can we group time with space? It would seem time is something wholly different, and perhaps not of the same substance.

I think time can be logically grouped with space even if it's something wholly different. Did Minkowski set d= ict for a fourth dimension...seems ok...

Regardless of how you want to think of the relationship, we believe space/time/energy/mass all emerge simultaneously,or close to it, from a random fluctuation, or if you prefer, big bang...it appears they are intrinsicly linked "at birth" but of course nobody knows precisely why or how...maybe a theory of everything will plumb that depth...

You have a number of suppositions which you are of course entitled to, but if you depend on statements/hypothesis contrary to current science you can't expect to end up with results consistent with current science. For example:

Time does not seem to have various rates of flow (relativity excepted)

makes no sense since 1905 or so and special relativity...sure it seems that way in everyday life, but physics should take you beyond your senses...

 

[boysherpa]

This has been a great discussion! I have spent many years reading in this area, and have noted some of the discussion points above. A couple of the replies have hit home at what I think causes my confusion with time.

I am mostly curious about the need for time to explain displacements in space (or oscillations, good point), and whether this defines time or whether time exist independently. Maybe another way to put this is that we humans need time but the universe doesn't. Notice that I am purposefully avoiding details because this is a top-level issue.

Some of the posts seem to be unable to separate the mathematical modeling from "reality" - time and space has nothing to do with mathematics. Mathematics is our tool to represent these things. If we cannot explain these items without mathematics, then we do not understand them. This is the situation with quantum mechanics. We have a wonderful predictive tool with QM, but no ability to answer questions like "why" or "how".

 

[Fredrik]

Some of the posts seem to be unable to separate the mathematical modeling from "reality" - time and space has nothing to do with mathematics. Mathematics is our tool to represent these things. If we cannot explain these items without mathematics, then we do not understand them.

That's definitely not true. You can only understand things that you have a theory for, and you need mathematics to make the theory unambiguous.

 

[Vanadium 50]

If we cannot explain these items without mathematics, then we do not understand them.

Just the opposite. If you can't describe something quantitatively, you don't understand it.

This is the situation with quantum mechanics. We have a wonderful predictive tool with QM, but no ability to answer questions like "why" or "how".

QM is no better and no worse than classical mechanics in this regard. The only difference is that classical mechanics is intuitive and QM is not.

 

[boysherpa]

Concerning Fredrick and Vandadium's posts:

Good points, from the quantitative perspective. I will concede that. I was thinking in a rather limited sense. The "how" and "why" questions are separable from the quantitative questions. Oh, and I don't think we should believe that understanding something only means quantitative modeling. Equating the universe to a mathematical model seems, at least to me, a tenuous concept (and there are excellent mathematical reasons for this position, such as self-consistency arguments).

I will take issue with this statement from Vanadium's post (forgive my quoting technique):

<boysherpa>'This is the situation with quantum mechanics. We have a wonderful predictive tool with QM, but no ability to answer questions like "why" or "how".'
<vanadium> "QM is no better and no worse than classical mechanics in this regard. The only difference is that classical mechanics is intuitive and QM is not."

Actually, the last sentence is the key here. "Every action has an equal and opposite reaction" is quite different from "I have no idea what is inside the box, but I can predict quite exactly what should happen over a large number of outcomes". It's not at all that it is intuitive. Rather, there are two important differences. First is that reductionism still applies in classical mechanics, and the underlying mechanisms are accessible to the observer. Second, classical mechanics is to a high degree deterministic in nature. Of course, we could argue til the cows come home that these qualities are merely approximations...

 

[Dale]

Some of the posts seem to be unable to separate the mathematical modeling from "reality" - time and space has nothing to do with mathematics.

This is a very common claim, but it is simply wrong. Math is the language of logic; if the universe behaves logically then it can be described mathematically. It is as simple as that.

IMO, a non-mathematical treatment of physics is like reading an English translation of Tolstoy. You can get the plot and understand the story, but you miss all of the subtle things that make him great. As divorced from "reality" as our mathematical models are, our verbal descriptions and plain-language models are far worse.

 

[Vanadium 50]

Classically, you can ask what the value of an unmeasured (and unmeasurable) quantity is. Quantum mechanically, you cannot. What makes one of these "better" than the other? I maintain it's personal preference - maybe based on comfort, maybe on philosophy, maybe on something else. But just that - preference.

 

[atyy]

Some of the posts seem to be unable to separate the mathematical modeling from "reality" - time and space has nothing to do with mathematics. Mathematics is our tool to represent these things. If we cannot explain these items without mathematics, then we do not understand them.

Yes, the answer I gave was only for a particular model of reality. Maybe someday a more powerful theory than general relativity will be found, and we will get yet another notion of "space" and "time". At the same time, mathematics is just an extension of everyday language - after all the number 7 is already a mathematical concept. Many mathematicians and physicists do look for the simplest ways to think about things correctly.

Thurston, http://arxiv.org/abs/math/9404236

 

[Fredrik]

The "how" and "why" questions are separable from the quantitative questions.

Not really. Scientific answers are always in the form of a theory that agrees with experiment, regardless of whether the question is "how" or "how much". A theory can't even be stated unambiguously without mathematics.

Equating the universe to a mathematical model seems, at least to me, a tenuous concept (and there are excellent mathematical reasons for this position, such as self-consistency arguments).

There may be good reasons why we shouldn't believe that the universe is a particular mathematical model, but we're not arguing that it is. At least I'm not.

 

[CaptainQuasar]

boysherpa, observe that you are using inaccurate mathematical models in your own statements about the universe. You speak of "3-space" but that is a simplified mathematical model that does not correspond to reality: look at the precession of the perihelion of Mercury. Within a cube-shaped boundary around the Sun at 2 million km per side, in flat space there would be 2³ × million³ = 8 × 10²⁷ km³ of "three dimensional space" but experimental observation shows there's more than that.

There isn't any real "3-space". Reality is some funky thing where time is integrally connected to length, width, and depth and gets correspondingly distorted when they get distorted. Thinking that there's a "3-space" in reality is a projection of your local perceived environment upon the rest of the universe, the way that people used to think that the Sun revolves around the Earth.

⚛​

 

[john 8]

Hi everyone.

I am new to this forum, but not new to science forms. I would like to participate in this discussion on time, but before I do I want to make sure that everyone’s definition of time as it is being used here is agreed upon by all participants. I have run into many snags on this topic because of all the people in a discussion on time have their own definition on what time is. What it always comes down to is that there are those people who say time is just a consideration of man, and there are those that say time is a real physical something.

I am one of those people that say time is actually a consideration based on our perception of the movement of objects. Time does not move or cause things to move. It is this perception of motion which gives us the idea of time. There may be some of you that disagree with this. This is fine, I would really like to hear your argument against this idea of time.

I have browsed this science forum and found that the people that participate in this forum are sticklers for facts that are backed up by scientific evidence, this is a good thing, the way all science forums should run.

So I just want to make sure that everyone is on the same page on this subject of time, or at least announce a definitive statement of your personal idea of time, that way there is no misunderstandings.


If there is anyone who thinks that time is a real thing whether it be a solid, liquid, gas, or some form of energy, I would really like to hear your explanation of this that has some scientific observational evidence.


Thanks.

 

[Dale]

IMO, time is simply the "t" in the "d/dt" terms from all the physics equations. As far as observational evidence goes, every clock is based on some physical mechanism that has a "d/dt" term in it somewhere, so there is probably evidence on your wrist.

 

[Makep]

This has been a great discussion! I have spent many years reading in this area, and have noted some of the discussion points above. A couple of the replies have hit home at what I think causes my confusion with time.

I am mostly curious about the need for time to explain displacements in space (or oscillations, good point), and whether this defines time or whether time exist independently. Maybe another way to put this is that we humans need time but the universe doesn't. Notice that I am purposefully avoiding details because this is a top-level issue.

Some of the posts seem to be unable to separate the mathematical modeling from "reality" - time and space has nothing to do with mathematics. Mathematics is our tool to represent these things. If we cannot explain these items without mathematics, then we do not understand them. This is the situation with quantum mechanics. We have a wonderful predictive tool with QM, but no ability to answer questions like "why" or "how".

You are correct. An entity without consciousness is devoid of the ability to discern change. Human beings require time as an instrument to understand and communicate the concept of change. Aging is a process of change. So too is displacement. We cannot say that the universe does not need time, as we do not yet know whether other elements of the universe, apart from humans, are also conscious. A conscious entity is aware, and through awareness, has the capacity to discern changes.
We have yet to device experiments or even prove that entities apart from humans are conscious or not. Perhaps our being alive is the culmination of millions of processes that are perpetually changing according to the laws of our inertial frame - the Earth - perhaps gravity.

 

[Fredrik]

Regarding the definition of time...

We can define a coordinate system in Newtonian mechanics, SR and GR as a function $x:M\rightarrow\mathbb R^4$, where M is spacetime, and then define "coordinate time" as a component of that function. In SR and GR it's also necessary to define "proper time", which is the integral of $\sqrt{-g_{\mu\nu}dx^\mu dx^\nu}$ along a curve.

That takes care of the definitions in the mathematical models used in these three theories, but the theories must still include postulates that tell us how these things are related to what clock's measure. In Newtonian mechanics, clocks measure coordinate time. In SR and GR, a clock measures the proper time of the curve that represents its motion.

 

[Dale]

You are correct. An entity without consciousness is devoid of the ability to discern change.

No, this is incorrect. Even simple single-cell organisms will react to changes in their environment by swimming towards new food sources or away from toxins. This is called chemotaxis, and it is very common.

 

[Makep]

No, this is incorrect. Even simple single-cell organisms will react to changes in their environment by swimming towards new food sources or away from toxins. This is called chemotaxis, and it is very common.

I disagree. Chemotaxis is the process where living entities respond to chemical stimuli, not such things as changes in inertial frames and hence time and space, in relativistic sense. There is another concept in which this can be aptly placed - the concept of trophism, as in phototrophism, geotrophism, hydrotrophism, etc.
But this trophic changes are demonstrable in all living things on earth. By some unexplainable phenomena, lower and simple animals can respond to physical changes. Do the chemicals in them 'sense' the need to change or are they compelled to change for which the observable behavior are the result and proof? I wonder.

 

[Dale]

Your post is confusing. First you disagree with what I said:

I disagree.

And then you agree with what I said:

By some unexplainable phenomena, lower and simple animals can respond to physical changes.

 

[Makep]

Your post is confusing. First you disagree with what I said:And then you agree with what I said:

To be exact, I do not agree with the usage of the word

chemotaxis

. It is reserved for chemical responses by basic life forms. Not to changes in space and time.

 

[Dale]

Huh? How can you have a concentration gradient (dC/dx) without space (x), and how can a cell move (dr/dt) along it without time (t)?

This whole discussion about consciousness is off topic. If you wish to continue it then you should start a new thread.

 

[Makep]

Huh? How can you have a concentration gradient (dC/dx) without space (x), and how can a cell move (dr/dt) along it without time (t)?

This whole discussion about consciousness is off topic. If you wish to continue it then you should start a new thread.

Good point. Don't you think space can also be concentrated such that there is a gradient for matter to move along? If not, then why not? If it is possible then how? Is there any mechanism available to allow matter to become aware of such changes?

 

[CaptainQuasar]

Makep, your comments make it look as though you're simply saying anything that comes to mind to try to get people to respond to you, which other people will probably perceive as trolling. People will get annoyed and frustrated with you if you keep doing that sort of thing.

⚛​

 

[john 8]

IMO, time is simply the "t" in the "d/dt" terms from all the physics equations.

Yes in physics equations the concept of time is symbolized with the letter t. So let me ask you, in all physics equations, does this symbol "t" represent a real physical thing or a concept?

As far as observational evidence goes, every clock is based on some physical mechanism that has a "d/dt" term in it somewhere, so there is probably evidence on your wrist.

Since this is a science forum I am going to take what you said literally and not assume a thing. This will point out how what you stated as observational evidence of time is faulty.

Yes we can observe a clock or wristwatch. What is being observed is a physical thing called a clock or a wristwatch. No observation of a thing called time.

I have owned many clocks and wristwatches. I have disassembled some clocks and wristwatches and have never observed a physical thing you describe as a "d/dt term" somewhere in these time pieces. I know that what I just said may seem a bit silly, but you said that a clock has a "d/dt" term in it somewhere.

Do you see how what you said is not a description of any observation of a physical thing called time, you just talked about equations.

So I will have to ask you again, what does the symbol "t" in physics equations represent?

Is it a representation of a physical universe thing or phenomenon, or is it representing a concept?



Clocks are a man made device operating as man designed it, counting off man made increments that man gave a numeric significance to that results in a man made concept called time. Clocks are designed to give numbers, to which man assigns a significance or importance to. A clock could be considered to be a device or machine that generates a number or numbers in a regulated manner that was pre-determined by man. A clock is akin to a regulated number generator that converts mechanical, electrical, or the motion of an object to a number through pre-determined engineering of the device, and these numbers are delivered at a rate that follows the set standards that man has agreed to be universal in all such machines.

If you think that clocks actually measure a physical thing called time please share with me your definition of a clock and time that shows that clocks actually measure anything outside of its immediate construction. What outside influence would a clock be measuring?

 

[john 8]

Regarding the definition of time...

We can define a coordinate system in Newtonian mechanics, SR and GR as a function $x:M\rightarrow\mathbb R^4$, where M is spacetime, and then define "coordinate time" as a component of that function. In SR and GR it's also necessary to define "proper time", which is the integral of $\sqrt{-g_{\mu\nu}dx^\mu dx^\nu}$ along a curve.

That takes care of the definitions in the mathematical models used in these three theories, but the theories must still include postulates that tell us how these things are related to what clock's measure. In Newtonian mechanics, clocks measure coordinate time. In SR and GR, a clock measures the proper time of the curve that represents its motion.

What do you think time is? You gave examples of time used in math, but do you think time is more than an equation.

 

[BWV]

In economics you have lots of arbitrary dimensions that are really just categorizations - like 10 different economic sectors (finance, industrials, energy etc.) which could be used in regressions. So I get that, but in spacetime you have the concept of orthogonality between these dimensions correct? This does not really apply to the category-dimensions that I am more familiar with. How does orthogonality work with 4 dimensions and how is time orthogonal to the three space dimensions and does it make sense to think of y being orthoganal to x,z &t ?

 

[Fredrik]

What do you think time is? You gave examples of time used in math, but do you think time is more than an equation.

Time is certainly more than that mathematical expression, but any answer to the question of what time "is", will always be in the form of a mathematical model and a set of instructions about how to use that model to make predictions about the real world. The best answer we have so far is the one provided by general relativity. The relevant "instruction about how to use the model to make predictions" says that what a clock measures is the proper time of the curve that represents the clock's motion. I don't think anyone has a better answer than that at this time.

Note that two definitions of time are needed. First we have to define time in a mathematical model (in this case as a certain integral), and then we have to define it operationally (as "what a clock measures"). Then we postulate how the two are related.

 

[Fredrik]

So I get that, but in spacetime you have the concept of orthogonality between these dimensions correct?
...
How does orthogonality work with 4 dimensions and how is time orthogonal to the three space dimensions and does it make sense to think of y being orthoganal to x,z &t ?

You should think of the spacetime manifold as the set of all events, and a coordinate system as a function that takes a point in spacetime to an ordered 4-tuple (t,x,y,z) of real numbers. The direction in which t is increasing is not necessarily orthogonal to the direction in which x is increasing for example.

That being said, in special relativity there's a class of coordinate systems that are "special" in a certain sense. They are called "global inertial frames" or just "inertial frames". If we use an inertial frame, then the t direction is orthogonal to the x direction in the sense that if u and v are two vectors in the t and x directions respectively, we have g(u,v)=0, where g is the metric.

So what does that have to do with orthogonality? Consider the definition of a "scalar product" (a.k.a. "inner product"). It's a function $(x,y)\mapsto\langle x,y\rangle$ that takes two vectors to a number and satisfies the conditions (i) <x,y>=<y,x>, (ii) <ax+by,z>=a<x,z>+b<y,z> and <x,ay+bz>=a<x,y>+b<x,z>, (iii) <x,x>$\geq$0 and <x,x>=0 only when x=0. The Cauchy-Schwarz inequality tells us that

$$\frac{|\langle x,y\rangle|}{\|x\|\|y\|}\leq 1$$

and that means that we can define an angle between any two vectors in an inner product space by

$$\cos\theta=\frac{\langle x,y\rangle}{\|x\|\|y\|}$$

That angle is zero when <x,y>=0. Now, a metric isn't exactly the same as a scalar product, because it doesn't satisfy condition (iii) above. (g(u,u) can be negative, and it can be zero for non-zero u). That means that it doesn't satisfy the Cauchy-Schwarz inequality, and that the "angle between vectors" isn't well-defined. But if we want to, I suppose we can ignore that and say that u and v are "orthogonal" if g(u,v)=0. If we choose to do that, then the t and x directions (defined by an inertial frame) are orthogonal.

 

[Dale]

Yes in physics equations the concept of time is symbolized with the letter t. So let me ask you, in all physics equations, does this symbol "t" represent a real physical thing or a concept?

Obviously a real physical thing. How can you get more physical than a physical variable measured by a physical device that operates according to a physical principle?

I have disassembled some clocks and wristwatches and have never observed a physical thing you describe as a "d/dt term" somewhere in these time pieces.

Then you didn't understand what you were looking at.

 

[meteor9]

That's true that we should rely on maths to have a quantitative explanation of everything we want to be 'logic'. But I think that mathematic equations, formula and theories are just good for the train of the 'daily life' , to manage things and predict the phenomena. Our brain , our memory is something much more sophisticated than some formula and it escapes the 'limits' of mathematic language which is just a tool . Do animals have the same conception of time ? Does time have any meaning to them? So I deduce that our brain is designed on such an unknown basis which enable us to 'perceive' and 'measure' time. Another example, it is about the conceptual ability of some primitive tribes around the world about the 'time' : for them the concept of 'tomorrow' doesn 't exist AT ALL , they don't see the 'future' , they just live in some 'momentum' , they can't anticipate the things which could happen in the 'future'. At this moment i write this and i experience it like all the other billion alive people around the world , 'yesterday' along with million million years ago are the same ,e.g. an 'illusion'. What in the world can prove that we don't 'live' in a sort of 'Closed Matrix' where time and space are static , and all we perceive as motion and movement are nothing but a static time? When we dream , we are motionless ourselves, but we 'see' the scenery in motion and we are unable to determine the time flown , we can dream just in few minutes some scenery and events as if they took some years, and vis-versa , we can dream a dream within 24 hours and having the impression that it last just few minutes. How can we quantify such a mysterious phenomenum which is the Time?