What is the true nature of time?

[DaveC426913]

Passionflower, conventional spacetime is defined as the 3 physical spatial dimensions and one timelike dimension.

It is not really open to interpretation or opinion.


There are theories that posit other numbers, and you are welcome to refer to them, or alternately, develop a paper for your own ideas and submit it to the appropriate forum.

But again, not really an opinion thing.


Perhaps when you are describing a path, you are referring to the fact that timelike dimensions are distinct from space-like dimensions in that timelike dimensions allow movement in only one direction - forward - and at a constant speed. We must travel through the time dimension.

 

[Passionflower]

It is not really open to interpretation or opinion.

Well so if we have one single time dimension then what is a path in spacetime according to you?

 

[DaveC426913]

Well so if we have one single time dimension then what is a path in spacetime according to you?

A path could go from [xyzt] to [x'y'z't'].

Because we have freedom in spatial dimensions, we could instead have chosen to go from [x'y'z't] to [xyxt'], but we cannot go from [x'y'z't'] to [xyzt].

 

[Passionflower]

A path could go from [xyzt] to [x'y'z't'].

Because we have freedom in spatial dimensions, we could instead have chosen to go from [x'y'z't] to [xyxt'], but we cannot go from [x'y'z't'] to [xyzt].

?

Are you going to explain what you think a path in spacetime repesents?

 

[DaveC426913]

No, I'm simply trying to stop you from violating PF guidelines in your attempt to freely interpret what you think spacetime and spacelike and timelike dimensions are.

You asked me what a path through 4D spacetime might be. I obliged. It will be defined by the connection between two points each defined by 4 coordinates.

 

[Passionflower]

violating PF guidelines

What guidelines am I violating?

So I take it you are not going to explain to me what you think a path in spacetime represents?

 

[DaveC426913]

What guidelines am I violating?

Not 'are', but are heading that way, or so it seems. You seem to be creating you own definitions for dimenion and spacetime.

The PF rules put a leash on overly-speculative posts. PF is about mainstream physics.

I'm not trying to be a heavy, I'm just cutting to the chase of the argument you've been having for about 20 posts. Spacetime is a well-known concept.

So I take it you are not going to explain to me what you think a path in spacetime represents?

You ask the oddest questions. Path is your word. Represent is your word. Why am I obliged to answer a question for which you frame the vocabulary?

 

[Passionflower]

You ask the oddest questions. Path is your word. Represent is your word. Why am I obliged to answer a question for which you frame the vocabulary?

Really that is odd?
You accuse me of creating my own definitions or being overly speculative and you are not familiar with paths in spacetime?

Despite you recognition as a 'Science Advisor' on this forum I am seriously questioning your expertise in this matter.

You accuse me of being overly speculative, what do I speculate about?

 

[DaveC426913]

You accuse me of creating my own definitions or being overly speculative and you are not familiar with paths in spacetime?

Who said I am not familiar?

You've gone from shouting down cshum00 to shouting at me. You are very confrontational in your discussion style.


I don't really have any contribution to the discussion, except my original point of order, which is that spacetime is a conventional concept.

 

[Passionflower]

You've gone from shouting down cshum00 to shouting at me. You are very confrontational in your discussion style.

I am not confrontational, the only person who is confrontational is you as you accuse me of something without any base.

 

[DaveC426913]

I am not confrontational, the only person who is confrontational is you as you accuse me of something without any base.

That must be difficult.

The point has been made. Keep closer to established science. Avoid over-speculation.

 

[Passionflower]

Avoid over-speculation.

What do you think I wrote is speculation?
If you accuse someone shouldn't you at least mention what you think I wrote is speculation?

 

[DaveC426913]

"...time is not a dimension..."
"Time is a path in spacetime not a dimension of spacetime."
"I think that time is a path in spacetime not a dimension of spacetime."

 

[Passionflower]

"...time is not a dimension..."
"Time is a path in spacetime not a dimension of spacetime."
"I think that time is a path in spacetime not a dimension of spacetime."

And you think that is speculative?

You do not think that you measure time by integrating the traversed path in spacetime?

Let's say we have 5 observers traveling between two events, their pathlenghts are different. Which dimension shows time for all those observers? The answer is no dimension, as the time for each observer is the length of their path in spacetime.

If you think that is speculative then I seriously question your understanding of relativity. That is not a problem by itself but then do not accuse someone of posting speculative postings.

 

[cshum00]

I have been keeping it quiet for a while. How about you answer my questions first.

-I asked you several times what you mean by coordinates and yet you haven't answered that question to me.

You do not think that you measure time by integrating the traversed path in spacetime?

-You are saying that:
t(x, y, z, t) = \int_a^b \sqrt{ (\frac{\partial x}{\partial s})^2 + (\frac{\partial y}{\partial s})^2 + (\frac{\partial z}{\partial s})^2 + (\frac{\partial t}{\partial s})^2} \partial s
Then show us how you got there because i have no idea where that came from. (note that the fourth dimension in this integration is still time)
-I also told that spacetime means 3-spatial dimension and one time dimension.
-Yet, you keep using it as if spacetime has four dimensions and there are 3-spacial dimension and no time dimension. And yet, you never answered me what the fourth dimension would be if it is not time.

Let's say we have 5 observers traveling between two events, their pathlenghts are different. Which dimension shows time for all those observers? The answer is no dimension, as the time for each observer is the length of their path in spacetime.

-The answer is that you keep using Gallilean/General/Newtonian coordinates instead of transformed coordinates.

If you think that is speculative then I seriously question your understanding of relativity. That is not a problem by itself but then do not accuse someone of posting speculative postings.

-Ok, if ignoring the definition of spacetime is not speculative then what is?

 

[Passionflower]

-I asked you several times what you mean by coordinates and yet you haven't answered that question to me.

Coordinates, as opposed to spacetime, is like a map of spacetime, a projection while spacetime is the reality we live in. Each observer in this spacetime can have a unique measure of time, this is unlike a Galilean spacetime where all time is identical for all observers.

-Yet, you keep using it as if spacetime has four dimensions and there are 3-spacial dimension and no time dimension. And yet, you never answered me what the fourth dimension would be if it is not time.

Observers observe slices of spacetime as space while time is orthogonal to this spactial slice. But different observers observe different slices. There is no single dimension in spacetime that is time.

For instance consider an accelerating observer in spacetime, this observer's worldline is curved, at each point we can make a foliation of spacetime that is space and time, sometimes called 3D+1, for this observer but it pseudo rotates in spacetime at each moment of the acceleration.

 

[cshum00]

Ok, thanks for trying to explaining things. I am still confused so i need more details in order to get the picture you have in your mind.

-First, how are you defining spacetime? You keep using spacetime while i keep telling you that the word spacetime uses time as a dimension. Use another word because spacetime can't be the word you are referring to (if you think that time is not a dimension).

Coordinates, as opposed to spacetime, is like a map of spacetime, a projection while spacetime is the reality we live in. Each observer in this spacetime can have a unique measure of time, this is unlike a Galilean spacetime where all time is identical for all observers.

-Ok, let's forget about spacetime at the moment. Let me try it with just physical space not spacetime. A map of physical space would be 3 coordinates; which is exactly the mathematical concept of 3 dimension. Then how come you say that coordinate doesn't mean dimension?
-Then this brings me to the next question of how are you defining dimension?

Observers observe slices of spacetime as space while time is orthogonal to this spactial slice. But different observers observe different slices. The is no single common dimension in spacetime that represents time.

-Again, having something orthogonal to something else is the idea of dimensions so that you can have an extra coordinate to navigate on while you are denying that time is not a dimension.

-And here is the last question, if a coordinate system is not the same as a dimensional system. Then what is the difference?

 

[Passionflower]

-Again, having something orthogonal to something else is the idea of dimensions so that you can have an extra coordinate to navigate on while you are denying that time is not a dimension.

Yes but this is a chart for a particular observer of spacetime, e.g. a particular foliation of space and time. Try to distinguish between a chart or a map of something and the real thing.

 

[cshum00]

Please answer the other questions as well.

Yes but this is a chart for a particular observer of spacetime, e.g. a particular foliation of space and time. Try to distinguish between a chart or a map of something and the real thing.

The problem is that you just tell me to compare it when i don't see the difference. Rather than just tell me to compare it, tell me what is the difference. That way get to the point faster.

 

[Passionflower]

Please answer the other questions as well.The problem is that you just tell me to compare it when i don't see the difference. Rather than just tell me to compare it, tell me what is the difference. That way get to the point faster.

Let's take an example, suppose we have an inertial observer who uses a chart of spacetime that maps his spatial dimensions the way he measures it and orthogonal to that he maps his time. He, for the sake of argument, defines that time in spacetime is orthogonal to his space. Now he accelerates, what will happen? Well the original chart no longer maps onto his space and time foliation. He could Fermi walker transport this chart so that at all times his foliation of space and time is as he measures it but then the chart pseudo rotates (pseudo because spacetime is a Minkowski spacetime and not an Euclidean spacetime) wrt spacetime. The one real dimension in spacetime he defined as time before acceleration is no longer time for him.

Spacetime as it exists in nature has four dimensions, it is however a mistake to claim that one of these dimensions is time, as I said before each observer can have a different view of what represents space and time and what for one observer is time may be a combination of space and time for another observer.

In general relativity the difference between a chart and spacetime itself becomes even more painful, especially in spacetimes that are non-stationary. Think in this context about the background independence of GR, something which distinguishes GR from QM.

 

[ghwellsjr]

Ever since your first post on this thread, you have not used the term "spacetime interval":

In Galilean spacetime time is surely a dimension, but is that the case in relativity?

I think in relativity time is the length of a path between two events in four dimensions. You think I am wrong?

Is that because you are talking about something entirely different?

 

[matheinste]

As I said before I think that time is a path in spacetime not a dimension of spacetime. Feel free to introduce mathematics to show how wrong I am.

Excuse the lack of rigor but Mathematically the definition of the dimension of a vector space is the least number of coordinate terms required to uniquely define the "position" of any (maybe abstract point) object within that vector space. However, when dealing with vector spaces modelling physical situations there are practical restrictions involved. We choose three spatial and one time axis, orthogonal to the spatial subspace, to suit our needs.
These axes are usually taken to be our physically defined dimensions althouggh they are really coordinate axes. So a dimension is really just a number describing a certain property of a vector space. We need to choose four coordinate to obtain four coordinates for the event we wish to define and we usually call these axes dimensions to suit our idea of what a dimension is physically.

A timelike interval, or path in spacetime can be regarded as a coordinate axis if the time axis is taken as part of the usual coordinate system asigned by an observer at rest with respect to that coordinate system. Of course in this somewhat special circumstance the other three coordinate numbers required as the spacetime coordinate of events along the time axis are all zero. But for non inertial observers this is not a practical proposition.


In the case of physical dimensions, for an observer at rest and so having the time dimension as one of his coordinate axes, each dimension for that observer is usually taken as being mutually orthogonal to the others, but this is really to suit physics and is not necessary mathematically where the only requirement is for the coordinate axes to be not linearly dependent.

Matheinste.

 

[Passionflower]

A timelike interval, or path in spacetime can be regarded as a coordinate axis if the time axis is taken as part of the usual coordinate system asigned by an observer at rest with respect to that coordinate system. Of course in this somewhat special circumstance the other three coordinate numbers required as the spacetime coordinate of events along the time axis are all zero. But for non inertial observers this is not a practical proposition.

A coordinate axis is not the same as a dimension of spacetime. Same story here, a chart used to map spacetime is mistaken for spacetime itself.

Again if we assume for the sake of argument that a particular dimension of spacetime is time then all observers would have to agree this dimension represents time but that is not the case as different observers are oriented differently in spacetime. What is time for one observer is a mixture of space and time for another observer.

 

[Dale]

There seems to be a lot of confusion on this thread with people "talking past" each other. In relativity treminology can often be confusing and the same word can be used to identify different concepts. So I hope the following helps:

1) Spacetime is a 4-dimensional pseudo-Riemannian manifold with a (-+++) signature. The dimensionality and the signature of the manifold are coordinate-independent properties of the manifold. One of these dimensions is singled out from the others (in a coordinate independent sense) by the signature and is called the "timelike" dimension. In this sense "time is a dimension of spacetime".

2) On the other hand the reason that spacetime is 4D is because at each point in the manifold you can construct an orthonormal basis (for the tangent space) with 4 basis vectors. One of these basis vectors will be timelike and the others will be spacelike. You can call the timelike basis vector "time", but it is not unique. There are an infinite number of possible sets of basis vectors at each point. So none of these individual time basis vectors can be said to be "the" time basis vector in a coordinate independent sense.

3) At each point along a worldline in spacetime it is possible to construct a tangent vector. This tangent vector can be classified as timelike, spacelike, or lightlike (null). If the tangent vector is timelike at every point along a worldline then the whole worldline is said to be timelike and it can represent the motion of a massive particle. The length of a timelike worldline is the called the proper time, and it is a coordinate independent scalar quantity.

Most of the confusion on this thread seems to be that everyone is using the same word for all three distinct concepts.

 

[Passionflower]

One of these dimensions is singled out from the others (in a coordinate independent sense) by the signature and is called the "timelike" dimension.

Ok, so which one is the one singled out?

I am asking because I do not agree there is such a singled out dimension, I think 'rotating' our manifold gives us the same physical description, any direction can represent the timelike dimension.

You say in a coordinate independent sense, so let's say we have 5 observers going from event A to B with different path lengths. How, in a coordinate independent way, do they determine this singled out "timelike" dimension?

Do you agree or disagree that time for each of those observers is the length of the path on this manifold and that this is not represented by one single dimension of the manifold?

 

[Dale]

Ok, so which one is the one singled out?

The one with the negative signature.

I am asking because I do not agree there is such a singled out dimension, I think 'rotating' our manifold gives us the same physical description, any direction can represent the timelike dimension.

You can't rotate a manifold, that doesn't make sense.

You say in a coordinate independent sense, so let's say we have 5 observers going from event A to B with different path lengths. How, in a coordinate independent way, do they determine this singled out "timelike" dimension?

By looking at the signature. The observers have nothing to do with it. Remember, this refers to the dimensionality of the space, not some specific direction or vector within the space.

Do you agree or disagree that time for each of those observers is the length of the path on this manifold and that this is not represented by one single dimension of the manifold?

Yes, I agree that proper time (see 3 above) is the length of a timelike worldline. But there are other usages of the word "time", as I pointed out above.

 

[Passionflower]

Yes, I agree that proper time (see 3 above) is the length of a timelike worldline.

Ok, I am glad you agree.

But there are other usages of the word "time", as I pointed out above.

I must be slow. So in what way do you think the "timelike" dimension of the manifold is time?

 

[cshum00]

Let's take an example, suppose we have an inertial observer who uses a chart of spacetime that maps his spatial dimensions the way he measures it and orthogonal to that he maps his time. He, for the sake of argument, defines that time in spacetime is orthogonal to his space. Now he accelerates, what will happen? Well the original chart no longer maps onto his space and time foliation. He could Fermi walker transport this chart so that at all times his foliation of space and time is as he measures it but then the chart pseudo rotates (pseudo because spacetime is a Minkowski spacetime and not an Euclidean spacetime) wrt spacetime. The one real dimension in spacetime he defined as time before acceleration is no longer time for him.

The problem is that this not only happen to the time dimension. It also happens to the spatial dimensions. There is also length contraction when traveling at speed close to light, the observers won't agree on the distance seen to be traveled. In that case, not only time won't be a dimension but also space would be dimensionless according to your analogy.

Spacetime as it exists in nature has four dimensions, it is however a mistake to claim that one of these dimensions is time, as I said before each observer can have a different view of what represents space and time and what for one observer is time may be a combination of space and time for another observer.

If time is not the fourth dimension in the spacetime, then what is? Don't just tell me that "if time is the fourth dimension, what is its' length?" Tell me, in your analogy; what is the fourth dimension in spacetime if time isn't the one?

 

[Passionflower]

The problem is that this not only happen to the time dimension. It also happens to the spatial dimensions. There is also length contraction when traveling at speed close to light, the observers won't agree on the distance seen to be traveled. In that case, not only time won't be a dimension but also space would be dimensionless according to your analogy.

What is a spatial dimension for one observer can be a mixture of time and space for another observer.

If time is not the fourth dimension in the spacetime, then what is?

Not one single dimension of spacetime is space or time since this would imply an absolute space and time as in the case of Galilean spacetime.

As I wrote, by now like four times or more, what for one observer is time is a mixture of space and time for another observer or what for one observer is a spatial dimension is a mixture of space and time for another observer. While for an accelerating observer this constantly changes. Why does that seem so hard to understand?

 

[cshum00]

As I wrote, by now like four times or more, what for one observer is time is a mixture of space and time for another observer or what for one observer is a spatial dimension is a mixture of space and time for another observer. While for an accelerating observer this constantly changes. Why does that seem so hard to understand?

It is almost impossible to understand you for me because you keep using words that have solid definitions in a totally different meaning.

What is a spatial dimension for one observer can be a mixture of time and space for another observer.

Not one single dimension of spacetime is space or time since this would imply an absolute space and time as in the case of Galilean spacetime.

Ok, so you are saying that neither space or time are dimensions? I agree with you that in Galilean spacetime thinks of absolute time and space but even if you are in Minkowski spacetime you still uses both space and time as dimensions.