Is there a common moment of now throughout the Universe?

[1x0]

Time is different throughout the universe.

 

I think there is a common moment of now because something happening everywhere.

 

The question is what makes time different if there is a common moment of now since the beginning of the Universe?

 

Is it the combined effect of space and gravity?

 

Isnt´t time a firm information and space, speed, gravitational effects differes?

 

Share your thoughts.

Edited May 3, 2015 by 1x0

[ajb]

The FRW solutions are globally hyperbolic. So yes, you can define a notion of 'now' everywhere in the universe.

[1x0]

The FRW solutions are globally hyperbolic. So yes, you can define a notion of 'now' everywhere in the universe.

If there is a common moment of now and this common moment of now we share since the beginning of time what makes the difference in the measurement of time?

 

 

 

Time can differ throughout the universe but isn´t the differences in the circumstances gives the differences in the perception.

In other worlds the moment of now is the same but the circumstances of reality and perception is different.

 

Can time be a linear information about physical units/conceptions?

[ajb]

In general, a globally hyperbolic space-time is foliated by Cauchy surfaces, that is there is homomorphism

 

[math]\phi: \mathbb{R} \times \Sigma \rightarrow M[/math]

 

where [math]\Sigma[/math] is a 3 dimensional manifold and [math]M[/math] is 4 dimensional space-time. The Cauchy surfaces are the images of this homomorphism for each time in [math]\mathbb{R}[/math]. This result is from the 1970's but it is now known you can actually do this in a smooth way and not just topologically.

 

Anyway, this defines 'now'. However, such homomorphisms (diffeomorphisms) are not usually canonical. There is no absolutely defined space-time cut. Just think of Minkowski space-time which is an example of a globally hyperbolic space-time.

Edited May 3, 2015 by ajb

[md65536]

In general, a globally hyperbolic space-time is foliated by Cauchy surfaces, that is there is homomorphism

 

[math]\phi: \mathbb{R} \times \Sigma \rightarrow M[/math]

 

where [math]\Sigma[/math] is a 3 dimensional manifold and [math]M[/math] is 4 dimensional space-time. The Cauchy surfaces are the images of this homomorphism for each time in [math]\mathbb{R}[/math]. This result is from the 1970's but it is now known you can actually do this in a smooth way and not just topologically.

 

Anyway, this defines 'now'. However, such homomorphisms (diffeomorphisms) are not usually canonical. There is no absolutely defined space-time cut. Just think of Minkowski space-time which is an example of a globally hyperbolic space-time.

Dumbing it down to try to figure it out...

 

A foliation of spacetime is by analogy like a book of pages. Each page represents a Cauchy surface ie. one moment of time throughout the universe, in that particular foliation. The book can be twisted and curved, maybe stretched, I dunno, however none of the pages can intersect (the moments are well-ordered) and there are no "gaps" between pages anywhere (the foliation covers all of spacetime).

 

Edit: Note the pages/Cauchy surfaces are 3d and as big as the universe at that moment. The book analogy drops one spatial dimension to represent space as a 2d page.

 

However there is not a unique foliation. Different variations of books, distorted (and oriented?) in different ways, can cover the same spacetime (though not every foliation of spacetime would satisfy the homomorphism? Eg. rotate the book enough or twist it enough and a page can no longer represent a moment).

 

What this means is that you could choose a particular foliation and say that its Cauchy surfaces each represent a common "now" shared throughout the universe, however the choice would be arbitrary and it wouldn't be easy to get everyone to agree on it. In very different frames of references, the "common now" would not be experienced meaningfully as a single moment. This would be like arbitrarily choosing an inertial frame of reference and defining a universal time based on it (Lorentz ether theory?), which wouldn't describe local time very well in other frames, though everyone would agree with the arbitrary choice's ordering of events and their causes.

 

 

Is this explanation accurate?

Edited May 4, 2015 by md65536

[ajb]

Your description is okay.

 

What this means is that you could choose a particular foliation and say that its Cauchy surfaces each represent a common "now" shared throughout the universe, however the choice would be arbitrary and it wouldn't be easy to get everyone to agree on it.

This is exactly the point. Just look at Minkowski space-time. You can cut that up into space and time but not it any 'god given' way.

[michel123456]

Dumbing it down to try to figure it out...

 

A foliation of spacetime is by analogy like a book of pages. Each page represents a Cauchy surface ie. one moment of time throughout the universe, in that particular foliation. The book can be twisted and curved, maybe stretched, I dunno, however none of the pages can intersect (the moments are well-ordered) and there are no "gaps" between pages anywhere (the foliation covers all of spacetime).

 

Edit: Note the pages/Cauchy surfaces are 3d and as big as the universe at that moment. The book analogy drops one spatial dimension to represent space as a 2d page.

 

However there is not a unique foliation. Different variations of books, distorted (and oriented?) in different ways, can cover the same spacetime (though not every foliation of spacetime would satisfy the homomorphism? Eg. rotate the book enough or twist it enough and a page can no longer represent a moment).

 

What this means is that you could choose a particular foliation and say that its Cauchy surfaces each represent a common "now" shared throughout the universe, however the choice would be arbitrary and it wouldn't be easy to get everyone to agree on it. In very different frames of references, the "common now" would not be experienced meaningfully as a single moment. This would be like arbitrarily choosing an inertial frame of reference and defining a universal time based on it (Lorentz ether theory?), which wouldn't describe local time very well in other frames, though everyone would agree with the arbitrary choice's ordering of events and their causes.

 

 

Is this explanation accurate?

Your description is okay.

 

 

Does a foliation represent what one observes as being "now" ?

[Strange]

 

Does a foliation represent what one observes as being "now" ?

 

No, a "page" (a Cauchy surface) represents a "slice" through space-time at given time; one of those "pages" can be considered to be "now". A foliation represents the way you decide to slice it into pages.

 

(But there is no unique way of dividing space-time up in these slices and so so there is no single, unique "now" that everyone will agree on.)

 

[if I have understood it correctly!]

[iNow]

I'm reminded of a book I read years ago called The End of Time by Julian Barber. The concepts are strikingly similar.

 

http://en.m.wikipedia.org/wiki/The_End_of_Time_(book)

[michel123456]

 

No, a "page" (a Cauchy surface) represents a "slice" through space-time at given time; one of those "pages" can be considered to be "now". A foliation represents the way you decide to slice it into pages.

 

(But there is no unique way of dividing space-time up in these slices and so so there is no single, unique "now" that everyone will agree on.)

 

[if I have understood it correctly!]

Sorry I don't understand.

In a spacetime diagram, is the "slice" onto the horizontal (on the X axis) or on the diagonal?

[md65536]

Sorry I don't understand.

In a spacetime diagram, is the "slice" onto the horizontal (on the X axis) or on the diagonal?

Those are Minkowski diagrams, which represent one spatial dimension and time in flat spacetime.

Time is on the vertical axis, and a horizontal line represents one moment for the observer at rest in the diagram's reference frame.

A set of horizontal lines covering the diagram would be a foliation into Cauchy surfaces for that observer. If you allow an infinite number of instants of time, you could allow an infinite number of lines, completely filling the diagram.

 

A set of straight lines at an angle, up to approaching 45 degrees, would represent a foliation of that flat spacetime according to other inertial observers.

 

In curved spacetime the lines wouldn't be flat.

Add another spatial dimension and it would be a curved sheet instead of a line.

Consider all 3 spatial dimensions and you get a 3d surface in a 4d volume.

 

 

 

I feel like it would take pages to describe the details of the analogy, and all the ways that it is not like the math. And still it would not be as precise as the one line of maths that it represents. Also I think I have a terrible habit of trying to base conclusions off analyzing an analogy instead of the maths. Perhaps an analogy is a useful way of thinking about what the maths represent, but the details will only be found in the maths! Eg. in the definition of a foliation, etc.

[xyzt]

 

Does a foliation represent what one observes as being "now" ?

Yes, it does. You can ignore mdc's handwaving devoid of any math and look at the following:

 

The Minkowski diagram presents two frames of reference, in motion with speed V wrt each other. Frame F has the x and t axis orthogonal on each other, with the t axis in the vertical direction. Frame F' has the x' and t' axes inclined wrt to x and t respectively. The angle made by x' with x is [math] arccos \frac{1}{\gamma}[/math]. Proof:

 

[math]dx'=\gamma(dx-Vdt)[/math]

[math]dt'=\gamma(dt-Vdx/c^2)[/math]

 

The dx' axis represents the axis of "simultaneity" in F', i.e. [math]dt'=0[/math]

This means [math]dt=Vdx/c^2[/math]. Substituting dt in [math]dx'=\gamma(dx-Vdt)[/math] gives [math]dx'=\frac{1}{\gamma}dx[/math], so the angle between dx' and dx is [math] arccos \frac{1}{\gamma}[/math].

 

In a similar manner, one can determine the angle made by dt' with dt. Here is how:

dt' is the axis that represents all the points that have the same x', i.e. [math]dx'=0[/math]. This gives [math]dx=Vdt[/math]. Substituting into [math]dt'=\gamma(dt-Vdx/c^2)[/math] you get [math]dt'=\frac{1}{\gamma}dt[/math], The t',t axes make the same angle as the x',x axis in the Minkowski diagrams.

 

 

As you can see above, there are two types of what is pretentiously called "foliation": [math]dt=0[/math] and [math]dx=0[/math], i.e. lines of equal time and lines of equal position.

Edited May 6, 2015 by xyzt

[michel123456]

Yes, it does. You can ignore mdc's handwaving devoid of any math and look at the following:

 

The Minkowski diagram presents two frames of reference, in motion with speed V wrt each other. Frame F has the x and t axis orthogonal on each other, with the t axis in the vertical direction. Frame F' has the x' and t' axes inclined wrt to x and t respectively. The angle made by x' with x is [math] arccos \frac{1}{\gamma}[/math]. Proof:

 

[math]dx'=\gamma(dx-Vdt)[/math]

[math]dt'=\gamma(dt-Vdx/c^2)[/math]

 

The dx' axis represents the axis of "simultaneity" in F', i.e. [math]dt'=0[/math]

This means [math]dt=Vdx/c^2[/math]. Substituting dt in [math]dx'=\gamma(dx-Vdt)[/math] gives [math]dx'=\frac{1}{\gamma}dx[/math], so the angle between dx' and dx is [math] arccos \frac{1}{\gamma}[/math].

 

In a similar manner, one can determine the angle made by dt' with dt. Here is how:

dt' is the axis that represents all the points that have the same x', i.e. [math]dx'=0[/math]. This gives [math]dx=Vdt[/math]. Substituting into [math]dt'=\gamma(dt-Vdx/c^2)[/math] you get [math]dt'=\frac{1}{\gamma}dt[/math], The t',t axes make the same angle as the x',x axis in the Minkowski diagrams.

 

 

As you can see above, there are two types of what is pretentiously called "foliation": [math]dt=0[/math] and [math]dx=0[/math], i.e. lines of equal time and lines of equal position.

But the observer cannot observe anything at [math]dt'=0[/math], since information arrives at [math]t=d/c[/math].

The only information that arrives at [math]dt'=0[/math] comes from [math]d=0[/math], it arrives from the observer himself.

 

IOW the foliation along the x axis is not observable and even more, it has no physical substance, because no force can act in [math]t=0[/math].

[xyzt]

But the observer cannot observe anything at [math]dt'=0[/math], since information arrives at [math]t=d/c[/math].

The only information that arrives at [math]dt'=0[/math] comes from [math]d=0[/math], it arrives from the observer himself.

 

IOW the foliation along the x axis is not observable and even more, it has no physical substance, because no force can act in [math]t=0[/math].

I think you misunderstood, the AXIS [math]dt'=0[/math] represents all the simultaneous events in frame F'. I am not talking about [math]t'=0[/math]. I am talking about the set of events [math] (x'=arbitrary,t'=constant)[/math]. Do you understand the difference?

Edited May 6, 2015 by xyzt

[Alan McDougall]

No!!

Edited May 6, 2015 by Alan McDougall

[md65536]

Yes, it does. You can ignore mdc's handwaving devoid of any math and look at the following:

 

No it doesn't. The Cauchy surface is a representation of 'now'. The foliation is the decomposition of all of spacetime into a set of all moments, not just one 'now' but all of them. It's like mixing up what is a tree and what is a leaf.

 

The universe can't be fully represented by a Minkowski diagram because spacetime isn't flat. The thread is talking about a common moment throughout the universe, that includes in gravity wells etc. If you want to explain the maths, start with this:

 

In general, a globally hyperbolic space-time is foliated by Cauchy surfaces, that is there is homomorphism

 

[math]\phi: \mathbb{R} \times \Sigma \rightarrow M[/math]

 

where [math]\Sigma[/math] is a 3 dimensional manifold and [math]M[/math] is 4 dimensional space-time.

[xyzt]

 

No it doesn't. The Cauchy surface is a representation of 'now'.

 

I simply pointed out that you are posting prose without any mathematical backing.

 

 

 

The foliation is the decomposition of all of spacetime into a set of all moments, not just one 'now' but all of them. It's like mixing up what is a tree and what is a leaf.

 

If you could follow the math (you obviously, couldn't) you would have learned that this is exactly what the math I have posted expresses.

 

 

 

The universe can't be fully represented by a Minkowski diagram because spacetime isn't flat.

 

True. Except I am talking about flat spacetime. So, your post is a non-sequitur.

 

 

 

The thread is talking about a common moment throughout the universe, that includes in gravity wells etc.

 

There is no such thing. In GR , the notion of simultaneity is strictly local, there is no such thing as a global simultaneity, as in flat spacetime. You can stop posturing now.

Edited May 6, 2015 by xyzt

[md65536]

True. Except I am talking about flat spacetime. So, your post is a non-sequitur.

The thread is talking about the universe, not a flat spacetime. Your post is off-topic. Why not start a new thread? It's misleading to post maths that relate to a new topic without mentioning it. Some people might think you're talking about the question that everyone else is discussing.

[xyzt]

Those are Minkowski diagrams, which represent one spatial dimension and time in flat spacetime.

Time is on the vertical axis, and a horizontal line represents one moment for the observer at rest in the diagram's reference frame.

A set of horizontal lines covering the diagram would be a foliation into Cauchy surfaces for that observer. If you allow an infinite number of instants of time, you could allow an infinite number of lines, completely filling the diagram.

 

Yes, the thread is talking about the universe but you were babbling about "Minkowski diagrams" and "foliations", so I commented on your babbling <shrug>

Edited May 6, 2015 by xyzt

[md65536]

Yes, the thread is talking about the universe but you were babbling about "Minkowski diagrams" and "foliations", so I commented on your babbling <shrug>

Fair enough. To get back on track, I'll stress what I didn't say clearly enough: Spacetime diagrams aka Minkowski diagrams only represent flat spacetime and can't fully represent the foliations or Cauchy surfaces being talked about, except in a simplified way (with straight parallel lines, instead of curved surfaces).

 

You can use the diagrams and your maths to examine the topic with a simpler subset of spacetime, but you can't generalize the simplified case into an answer for the thread.

[xyzt]

Fair enough. To get back on track, I'll stress what I didn't say clearly enough: Spacetime diagrams aka Minkowski diagrams only represent flat spacetime and can't fully represent the foliations or Cauchy surfaces being talked about, except in a simplified way (with straight parallel lines, instead of curved surfaces).

 

You can use the diagrams and your maths to examine the topic with a simpler subset of spacetime, but you can't generalize the simplified case into an answer for the thread.

The flat spacetime formalism (Minkowski-Lorentz) applies only in a infinitesimal domain of the curved spacetime.

There is no global notion of simultaneity in curved spacetime.

[1x0]

Time can differe throughout the universe but the differences in the circumstances gives the differences in the perception.

In other worlds the moment of now is the same but the circumstances of reality and perception is different.

 

For example: My body is existing in a 4D spacetime. In our current understanding of relativity at my head there is a different time than at my toe. My concern is that the differences what the measurments of time presents depends on the differences in the measured circumstances. (gravity is weaker at my head than at my toe)

 

So time is a relative information and everything actually happens at the same time. Doesn´t matter that space are curved or time pass slower or faster because every physical entity shares a moment (a fragment of time in the individual circumstances they exist in) with the rest of the system.

 

There is just one present moment which is cut in the physical reality.

 

My thought is that this present moment happens throughout the Universe at the same moment indipendent from the physical circumstances. In other worlds every physical entity can have its own time relative to it´s circumstances it is existing in and relative the rest of the system but time will pass everywhere in the universe so no matter which circumstences they exist in they share a moment of now with everything else.

Edited May 7, 2015 by 1x0

[michel123456]

I think you misunderstood, the AXIS [math]dt'=0[/math] represents all the simultaneous events in frame F'. I am not talking about [math]t'=0[/math]. I am talking about the set of events [math] (x'=arbitrary,t'=constant)[/math]. Do you understand the difference?

Most probably I have misunderstood.

the set of events [math] (x'=arbitrary,t'=constant)[/math], in a simplified flat universe, is represented by the x axis for t'=constant. No?

[xyzt]

Most probably I have misunderstood.

the set of events [math] (x'=arbitrary,t'=constant)[/math], in a simplified flat universe, is represented by the x axis for t'=constant. No?

Close: it is the line parallel with the axis x'=0 for t'=constant.

Edited May 7, 2015 by xyzt

[michel123456]

Close: it is the line parallel with the axis x'=0 for t'=constant.

OK.

What I say is that the points that this line is made of are connected by simultaneity, which is unphysical. Because all forces need time. IOW this line is unphysical.

Edited May 7, 2015 by michel123456