What is the true nature of time?

[cshum00]

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?

I think you are right. In the contents of your speech, you are clearly referring that the "length of a path" of the "four dimensions" that you are working on. Your thinking actually resembles to a filmstrip where each strip of the film is a point of the time path and inside each strip instead of a 2-D space dimension picture, you have a 3-D dimension picture.

Edit:I think that "path" is good enough. "Length of a path" would be more like the total amount of time specific time-frame.

 

[Passionflower]

I think you are right. In the contents of your speech, you are clearly referring that the "length of a path" of the "four dimensions" that you are working on. Your thinking actually resembles to a filmstrip where each strip of the film is a point of the time path and inside each strip instead of a 2-D space dimension picture, you have a 3-D dimension picture.

Edit:I think that "path" is good enough. "Length of a path" would be more like the total amount of time specific time-frame.

So it appears that you agree.
If that is so then time cannot be something else as well right? Thus do you agree that time is not a dimension?

 

[cshum00]

So it appears that you agree.
If that is so then time cannot be something else as well right? Thus do you agree that time is not a dimension?

I am confused. How does agreeing that time is one of the 4 dimensions you mentioned leads to that time is not a dimension?

 

[Passionflower]

I am confused. How does agreeing that time is one of the 4 dimensions you mentioned leads to that time is not a dimension?

Where did I write that "time is one of the 4 dimensions"?

 

[cshum00]

Where did I write that "time is one of the 4 dimensions"?

Ok, then what are those 4 dimensions then? If time is not one of those 4-dimensions then i would disagree. I guess that i did not get the right picture for your statement.

 

[Passionflower]

Ok, then what are those 4 dimensions then? If time is not one of those 4-dimensions then i would disagree. I guess that i did not get the right picture for your statement.

Ok, so let's assume that one of the 4 dimensions is time then what is the length of a path between two events in those 4 dimensions?

 

[cshum00]

Ok, so let's assume that one of the 4 dimensions is time then what is the length of a path between two events in those 4 dimensions?

Ok, it would be like i mentioned before on my edit:

Edit:I think that "path" is good enough. "Length of a path" would be more like the total amount of time specific time-frame.

In other words, it would be the total amount of time that it takes from one event to the second event.

 

[Passionflower]

Ok, it would be like i mentioned before on my edit:


In other words, it would be the total amount of time that it takes from one event to the second event.

Yes and that is not time?

 

[DrGreg]

Passionflower, are you aware of the difference between coordinate time, which is one of the 4 dimensions of spacetime (for a given choice of coordinates), and proper time which is the "length" of a 4-dimensional curve or line (and is independent of any choice of coordinates)?

 

[cshum00]

@Passionflower
Ok, i think i got the root of our problem and the solution.

Let's start with your original statement:
"I think in relativity time is the length of a path between two events in four dimensions."

-First, i will modify your statement to: "Time is a path between two events in four dimensions."
-I remove the word relativity because i am not sure in which relativity you are referring to; the general or special. Also, specifying special relativity will make one of the four dimensions to time which in our case we don't want to.
-It is not length because they are two different things. For example, length would be like: it took five minutes for me to write my essay. While for time i would be saying, according to Easter Time clock, i finished my essay at 10:42AM.
...
-This will require us to look at dimension not as the scientific meaning of dimension but the mathematical one. When i say this, i mean anything CAN be a dimension.
-Saying that, we will look at event as a dimension. For example, e₁ (event1), e₂ (event2) and so on.
-So, according to the modified statement we are looking at time as t(e, x, y, z) where e=event, x=spacial-dimension1, y=spacial-dimension1, z=spacial-dimension3.
-In other words, time is a function of event, and 3 spatial dimensions. And length of the path of 2 points of time would be how much time lapsed between two events.
-This support the filmstrip idea where each event would be each snapshot on the film, and the difference in length between two film strips is the total time it took for those two events to happen.

Now, the next problem is when i said that time is one of the four dimensions.
-In the case of viewing time as part of the dimension, i would actually be defining event as a function of time and the 3 spatial dimensions or e(t, x, y, z).
-So, if we see time as a function of event, we would intuitively make event as a dimension.
-And if we make time as a dimension, we intuitively create an event function instead.
-Next, is what is the length of the path between two events? It is NOT the total amount of time between two events. I was wrong. Yes, sorry and i apologize. I don't know what it means unless we give a meaningful value to each point of event.

 

[Passionflower]

Passionflower, are you aware of the difference between coordinate time, which is one of the 4 dimensions of spacetime (for a given choice of coordinates), and proper time which is the "length" of a 4-dimensional curve or line (and is independent of any choice of coordinates)?

Coordinate time is a dimension on a chart of spacetime. But mapping an observer's proper time onto the coordinate time axis of a chart is not the same as claiming that one single spacetime dimension represents time. It does not, time is represented by a path between two events inside this spacetime. For a Galilean spacetime you would be correct but not for a Minkowski spacetime.

While proper time always describes what a physical clock measures, coordinate time may or may not do that. Clearly coordinate time cannot be a dimension of time because if we have a simple spacetime with two observers taking a different path with a different length between two events then clearly coordinate time cannot represent time for both observers, time for each observer is the path length between the events not the coordinate time. Yes we can use different coordinates for each observer but then we are not talking about dimensions of spacetime but observer dependent charts where the proper time is modeled by using the time dimension of the coordinate chart for that particular observer.

Don't mix up a coordinate chart of spacetime with spacetime itself.

 

[cshum00]

I am but what is the point?

While proper time always describes what a physical clock measures, coordinate time may or may not do that. Clearly coordinate time cannot be a dimension of time because if we have a simple spacetime with two observers taking a different path with a different length between two events then clearly coordinate time cannot represent time for both observers, time for each observer is the path length between the events not the coordinate time. Yes we can use different coordinates for each observer but then we are not talking about dimensions of spacetime but simply observer dependent maps where the proper time is modeled by using the time axis of the coordinate chart for that particular observer. But then we mix up the chart with spacetime itself.

I am confused. Unless you mean something else by coordinate, isn't time as a coordinate the same as time being a dimension?

About the problem of two observers not being represented in a single graph is because each observer's coordinate system is shifted with respect to each other. For example, if my origin is not your origin but shifted on a certain way, then when i say this point of space, it won't be the same point of space in your coordinate system. That is why we need to do transformations.

Edit: BTW, did my previous post clear our misunderstandings.

Just because we are defining time as a function of other coordinates, it doesn't mean that time is not a dimension. For example, i would define a function to be z(x,y); but it doesn't mean that z is not a dimension. And most importantly, time is a fundamental quantity which adds the requirement of being a dimension for science.

 

[Passionflower]

I am confused. Unless you mean something else by coordinate, isn't time as a coordinate the same as time being a dimension?

Think about the different between a coordinate system of spacetime and spacetime itself. Two different things.

About the problem of two observers not being represented in a single graph is because each observer's coordinate system is shifted with respect to each other. For example, if my origin is not your origin but shifted on a certain way, then when i say this point of space, it won't be the same point of space in your coordinate system. That is why we need to do transformations.

So clearly you must realize you are dealing with charts of spacetime not spacetime itself.

Time is a path in spacetime not a dimension of spacetime. If time would be a dimension of spacetime all observers would agree on such time as is the case in Galilean spacetime.

 

[cshum00]

Think about the different between a coordinate system of spacetime and spacetime itself. Two different things.

Then to clear things up, i have been using them as the same thing. I don't get what you mean by coordinate. Can you explain further?

So clearly you must realize you are dealing with charts of spacetime not spacetime itself.

Time is a path in spacetime not a dimension of spacetime. If time would be a dimension of spacetime all observers would agree on such time as is the case in Galilean spacetime.

I am confused here. How can you see time dilation if you are on the Galilean spacetime? The reason why Galilean relativity could not do gave discrepancy errors was is because it did not have transformation of coordinates (which is what Special Relativity did). I think your problem lies that you don't understand that each observer is in their own coordinate system which needs to be transformed to that they could agree on what they are observing.

 

[Passionflower]

I think your problem lies that you don't understand that each observer is in their own coordinate system

I don't understand that each observer is in their own coordinate system?

So let me try to follow you, each observer is in their own coordinate system and all these unique coordinate systems relate how to spacetime and in particular the specific dimension you claim is time?

 

[cshum00]

So let me try to follow you, each observer is in their own coordinate system and all these unique coordinate systems relate how to spacetime and in particular the specific dimension you claim is time?

Not only time, but also for the 3-spacial dimensions too. There is also length contraction. I don't want to be rude but i am guessing that you didn't actually go through the mathematics of it but only read the conclusions instead. .Although the conclusions might be counter-intuitive, if you actually follow through the mathematics and the reason for such transformations; you should be able to have a better understanding of it

 

[Passionflower]

I don't want to be rude but i am guessing that you didn't actually go through the mathematics of it but only read the conclusions instead. .Although the conclusions might be counter-intuitive, if you actually follow through the mathematics and the reason for such transformations; you should be able to have a better understanding of it

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.

 

[cshum00]

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.

The word space-time refes to 3-spacial dimensions and one time dimension!

Let's modify your statement so that you see what are you saying mathematically.

x is a path in x-y dimension not a dimension of x-y.
Or mathematically, x = x(x, y)!

I think you missed my last post on page 5. You got mixed with my other earlier comments. Read my last post on page 5 which clarifies our earlier arguments then come back and explain to me what you mean by coordinates and how come time is not a dimension since I am unable to picture your problem.

 

[Passionflower]

The word space-time refes to 3-spacial dimensions and one time dimension!

Do you seriously think that such an argument would convince me?

Let's modify your statement so that you see what are you saying mathematically.

x is a path in x-y dimension not a dimension of x-y.
Or mathematically, x = x(x, y)!t

Surely you must be joking!

 

[cshum00]

Do you seriously think that such an argument would convince me?

No, i am not trying to convince you. It is the truth. Research the word spacetime. It is just like i said. It means 3-spacial dimensions and one time dimension.
http://en.wikipedia.org/wiki/Spacetime

Surely you must be joking!

No, i am not joking. Ask a mathematician to translate that statement to math for you and see what you get. I might be wrong but your statement is just as outrageous as it is.

 

[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?