Does Time Expand in All Directions in the Universe?

[Whitefire]

I recently had this idea (which perhaps is not a new one, but I have never heard of it), that on the scale of the entire universe, time expands in all directions at once. I believe it can be proven or disproven with more knowledge, so I am posting it here.

If we look around us, we generally understand time as 'direction of changes' and everything we see moves in this same direction at the same 'pace'. An hour for me is an hour for you etc. Thanks to Mr Einstein we know this is not a precise description, but from what I understand, if we ceased all movement (relatively of course), time would 'flow' the same for all non-moving objects.

Now, I was thinking, maybe that is wrong. At least, on the scale of all universe. For some reason I can't attach any image, so if you are interested, look at this crudely drawn picture:
http://www.mythai.info/images/various/time.jpg
It is simplified, but the circle represents the universe as it is 'now'. It could be slightly better to imagine it as a 'bubble', but much harder to draw. Please have look and place our Sun and us at point 'A'.

The range between 'D' and 'J' is the observable universe - what's on the other side 'didn't happen' - 'isn't happening' for us. The strange thing is, though, that if we were a piece of matter at point C, we could see, and even be influenced by, points D and E which is 'invisible' for us.

This idea also fits nicely with the expansion of universe and even with the dark energy.

If it is right, then a galaxy 6 billion l. years away is not only 6 billion years younger. Time for this galaxy, relatively as we see it, would actually pass slower because of the distance. I am sure that all of you experts in cosmology will swiftly disprove me and my idea will degenerate into yet another fruitless mental exercise, but still, I thought it may be interesting. And I believe we have so little data about objects billions years away that proving how does the time pass there may be challenging.

Regards and have fun :) Sorry if my English wasn't perfect.

 

[mfb]

To verify or disprove anything, you first have to define what "time expands in all directions at once" is supposed to mean. Does it give specific predictions for observations? Are they different from standard cosmology? If the first question can be answered with "no", it is pointless to discuss it. If the second answer is "no", it could be (but does not have to be) a nice model to consider.

 

[Chalnoth]

I recently had this idea (which perhaps is not a new one, but I have never heard of it), that on the scale of the entire universe, time expands in all directions at once.

The dimension of time is orthogonal to the dimensions of space. Yes, time has a direction, but that direction is not up or down, left or right, forward or backward. It's a fourth direction of motion: future/past. And it does have a direction given by changes in entropy. That is to say, the past is different from the future because entropy was lower in the past.

 

[timmdeeg]

I recently had this idea (which perhaps is not a new one, but I have never heard of it), that on the scale of the entire universe, time expands in all directions at once. I believe it can be proven or disproven with more knowledge, so I am posting it here.

Perhaps you have something in your mind, what people call cosmic time?

Cosmic time (also known as time since the big bang) is the time coordinate commonly used in the Big Bang models of physical cosmology. It is defined for homogeneous, expanding universes as follows: Choose a time coordinate so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). Measure the passage of time using clocks moving with the Hubble flow. Choose the big bang singularity as the origin of the time coordinate.

Cosmic time is the standard time coordinate for specifying the Friedmann–Lemaître–Robertson–Walker solutions of Einstein's equations.

At any specific instant of cosmic time the galaxies would measure the same scale factor, which represents the expansion of the universe.

 

[Whitefire]

Sorry for the delay. I like to think on my answers. I also have to use proxy to use this site, and it is discouraging. I swear it is not because I did anything to upset the administration of this forum. I have different IP with each connection, but it seems my entire provider is banned here (?).




By "direction" of time I meant, of course, 'from the past into future', but I also meant 'at a certain relative speed'. Perhaps a 'vector' (not 'scalar') would be a better word. I agree with what Chalnoth wrote, but nothing I posted above is in opposition to his description of time. (I understand this is important to define, that is why the topic title is formed as a question).

I see time as a vector, and I dare assign 'direction' to it, because it is not as universal as we thought before STR. If person A looks at B and sees his watch moving slower, it is as if person B is heading in a different time direction, moving along different vector. 'A' can only see that component of vector b which is parallel to his own movement. But for 'B', of course, time is not slowed down.

By time moving in 'all directions' I meant that on the scale of a whole universe, it can not only slow down, relatively, but even work 'backwords'--'towards the past'. And we are not capable of seeing it (obviously). But person B could just catch a glimpse of what is hidden from A because of the difference between his and A's direction.

Isn't it called a time frame, or am I mixing ideas? I am sorry if I am forging too many terms for the same thing :(

Mfb, as to your specific questions. Quite obviously, I do not want to try and prove something that is against established facts (here goes the second question). I hope that when you point a telescope at a galaxy 1 billion years away, you don't only see it as it was long time ago, but also you see time moving slower there (if you could see such details). Otherwise, my idea makes no sense, because it makes it sort of inherent property of space, that each point moves along slightly different direction in time.

Now, does it give any specific predictions?

The idea means that it doesn't even matter if two points are moving at different relative speeds--they are in different points of space and that is enough for them to have different vectors of time. At least that's what would happen if there was no other force at work (like gravity).

The typical understanding is that 'space expands' and the galaxies 1 billion years away are speeding away so fast that when we look at them, we see time slow down.

Assuming the time vectors are not 'chaotic' but, throught the universe, they align into a concentric shape, it means that the farther things are, the more time needs to slow down (from our perspective). And I would see it as a reason, not the result, of expanding space. It expands, because time (on the scale of whole universe) is not moving in one 'direction'. So the space compensates by stretching.

All things said, I think this is not really anything new, but rather a nice new perspective on what is going on with the universe. you know, mfb, ideas don't have to immediately 'give specific predictions for observations'. When Copernicus said we move around the Sun, not Sun around us, it was only a shift in perspective. But it was huge...

For example, it might be easier to explain the existence of forces invisible to us, like dark energy. Space, especially distant parts of the universe, could be under influence of objects which we cannot percieve, because they are 'frozen' from *our* perspective. The same with the edge of observable universe. I like to compare it to a complex picture on a thin paper, seen from an angle that allows us to only see the edge. But as we jump several bilion l. years to another galaxy, this edge turns out to be several billion years farther, and and we suddenly are influenced by forces which we couldn't previously percieve.

And we wouldn't need to look for an answer to 'why is the space expanding'. We would only have to find out why time exists :)

@timmdeeg: I saw your reply only now. I will definitely look into the info you provided, thank you.

 

[mfb]

I hope that when you point a telescope at a galaxy 1 billion years away, you don't only see it as it was long time ago, but also you see time moving slower there (if you could see such details).

Due to the expansion of space, everything is redshifted (seems to be slowed down). This does not depend directly on the age, however, it is a property of the expansion speed. You can even reproduce a similar effect on Earth with the Doppler shift.

 

[Fredrik]

Sorry for the delay. I like to think on my answers. I also have to use proxy to use this site, and it is discouraging. I swear it is not because I did anything to upset the administration of this forum. I have different IP with each connection, but it seems my entire provider is banned here (?).

If you PM me your IP address, I can look into it. First make sure that you're currently unable to access Physics Forums without a proxy. Then go to the following site to find out what will be the source address of IP packets that are sent to our server when you don't use a proxy:

http://www.whatsmyip.org/

Copy the IP address at the top of the page and either PM it to me, or hit the report button next to this post, paste the IP address into the box that appears, and submit the report. This sends the report to a place where all the moderators (and no one else) can see it. It quotes this post automatically (if you specifically use the report button next to my post), so you don't have to type an explanation.

 

[Whitefire]

@ Fredrik: thanks, it seems the problem has been taken care of.

@mbf:

Due to the expansion of space, everything is redshifted (seems to be slowed down).

redshift and 'seems to be slowed' are only manifestations of a deeper problem, which is what I am trying to talk about, that time 'points' in different directions depending on where in space you are. During 100 years that passed for me, my alien friend in a galaxy far, far away seems to have aged only 50. The same is the other way around. You could say we are 'pointed' in different directions, different (shifted) futures.

Now, have you ever tried to imagine it the other way around: that it is the reason why galaxies drift apart?

@ timmdeeg: thank you for your contribution, the Wikipedia entry was too short really but I googled some details, It is generally the same concept (I also assumed 'homogeneousness' of the universe for the sake of simplicity). But I see very little about that in the Internet, except using it as a way to point to the origin of Big Bang. In my opinion it can lead to more interesting ideas.

 

[timmdeeg]

Whitefire, would you agree that the direction of time is given by the sequence of cause and effect?
If yes, then it seems a bit dubious to consider time as both, cause (you said reason) and direction.

Perhaps I misunderstood. Are you saying time is the cause that the galaxies are receding?

 

[Mordred]

lets take your analogy of times varying degrees of direction. This would imply that time has a preferred direction depending on the observer.

We measure the distance from one side of the sun, distance = x. We then measure that same distance from the other side of the sun. If time had a vector direction other than forwards and backwards. We should end up with a different value, based on current mathematics of time. If time had the vector like properties in your descriptive. We would need to factor time as a vector each and every instance we take a measurement. OK let's take measurements of the CMB. If we look in different directions according to your analogy, we should arrive at different time values for the time that the CMB formed.
Take this a step forward. Let's compare two readings of a distant object. Take one reading from Earth. the other reading from a space probe such as Voyager 1. If time were a multiple angle vector we would have two different values depending on the angles between the two measuring devices.

None of this occurs, why ? simply put time is not radiating outward from some central point. Its only two valid vectors is the vector representing forward and the vector representing its direct opposite.

 

[WannabeNewton]

redshift and 'seems to be slowed' are only manifestations of a deeper problem, which is what I am trying to talk about, that time 'points' in different directions depending on where in space you are.

What you have stated is a highly non-rigorous and ambiguous statement. If we are dealing with a FLRW universe $(M,g_{ab})$ then there exists a one-parameter family of space-like hypersurfaces $\Sigma_{t}$ that foliate $M$ and the global isotropy implies that the 4-velocity field of the family of isotropic observers $u^{a}$ is hypersurface orthogonal to $\Sigma_{t}$ meaning that at any given $t_{0}$ and any $p\in \Sigma_{t_{0}}$, $u^{a}$ is orthogonal to all $s^{a}\in T_{p}\Sigma_{t_{0}}$. You cannot just non-nonchalantly throw around the word "time" and "direction of time" in general relativity.

 

[Chalnoth]

@ Fredrik: thanks, it seems the problem has been taken care of.

@mbf:



redshift and 'seems to be slowed' are only manifestations of a deeper problem, which is what I am trying to talk about, that time 'points' in different directions depending on where in space you are. During 100 years that passed for me, my alien friend in a galaxy far, far away seems to have aged only 50. The same is the other way around. You could say we are 'pointed' in different directions, different (shifted) futures.

Now, have you ever tried to imagine it the other way around: that it is the reason why galaxies drift apart?

@ timmdeeg: thank you for your contribution, the Wikipedia entry was too short really but I googled some details, It is generally the same concept (I also assumed 'homogeneousness' of the universe for the sake of simplicity). But I see very little about that in the Internet, except using it as a way to point to the origin of Big Bang. In my opinion it can lead to more interesting ideas.

If time is to point in any direction at all, it points in the "time" direction, which is orthogonal to the three dimensions of space. It simply doesn't make sense to talk about time as pointing in a spatial dimension.

 

[Whitefire]

Are you saying time is the cause that the galaxies are receding?

More like 'the way time works on the scale of the whole universe is the cause that galaxies are receding'. Locally, meaning more or less within a single galaxy, it would be like trying to see the curvature of Earth by climbing a tree, with stars' gravity acting like mountains to obscure the view.

@Mordred: It occurs, the problem is probably with my poor choice of words. Just not really on the scale you write about (see paragraph above). Let's say you measure the distance from Milky Way to A--it is 5x10^25 meters away. Now to point B--it is 10x10^25
meters away, exactly twice the distance--looking from Milky Way. If (hypothetically) you
find the way to make a measurement while being in galaxy A *also now*, you will not get 5x10^25 to galaxy B. Because in the time it took the light to travel from B to A, and then from A to Milky Way... etc.

would you agree that the direction of time is given by the sequence of cause and
effect?

It's like saying you always move from behind and go forward. True, but not exactly about directions. When time passes, there's a change. You can say you move along it. If you add relativity and movement, what you get is very much like a direction, or vector, in 3D. If there is a better term for it though, just say it.

Here.

So maybe this is a problem. I made a visualization, flattened time and space into a 2 dimensional picture, and then I started to rely on it too much. I promise, when I learn a "less non-rigorous, less ambiguous and less non-nonchalant" way to say it, I will use it, unless it is so numerical it will obscure any real understanding. By all means, teach me.

But I don't know it yet, so I will stick to it for a while. From the past, into the future, at the speed of 1 second per second, strange as it sounds. That is what I mean by 'direction', and I am growing sure that it is something unique for each point in space.

If you prefer, and if you still have the patience, I can present what I drew on the pictures without using the word 'direction'.

1) If you look at a point halfway to the edge of the visible universe, 1 second for us is only 1/2 second there. Just this fact for a moment, forget about galaxies' movements and redshifts.

2) From 1) I conclude that a perfect 1 second per second is relatively ("if you look...") possible for only one the point in space. The observer.

3) Let's have 2 observers. They are in different points in space, so for each 10 seconds they measure for themselves, they only measure 9 seconds for the other one.

4) As the seconds pass, space between the observers has to stretch to provide the necessary relative movement. If the distance between them was the same at the beginning and the end of measurement, it would mean that time actually, non-relativistically passes at various speed at 2 points. It doesn't. So we're getting redshifts and movements.

5) I still think that presenting it as a picture with arrows and directions was a nice way :) For example, it is easy to see that the curvature from the picture can be nicely finished to form a circle.

@ WannabeNewton: ...translating...

If we are dealing with a FLRW universe (M,gab)

ok

then there exists a one-parameter family of space-like hypersurfaces Σt that foliate M and the global isotropy implies that the 4-velocity field of the family of isotropic observers ua is hypersurface orthogonal to Σt

wow, seems like a very fancy way of really saying NOW. I wouldn't be able to put it this way, which is a pity. Thinking about relativity really messes with what one can understand by 'now'. So precise is good. But what you write is what we really intuitively understand by 'now'. A caveman's wife would wait for him, tending to a little caveling, and think: 'what is my husband doing NOW'? And by 'now' she would just imagine the same time for him as it was for her. She wouldn't think that she can't really see him *immediately* even if he appeared. She just imagined this 'now'.

any p∈Σt0, ua is orthogonal to all sa∈TpΣt0

I translated 'orthogonal' (sorry for my language problems, I thought 'paralell' is the only term in English for that). Are you saying that for any observer in this imaginary 'now', time moves at the same rate? If I am right and that is what you are saying, than I agree. If you look at the picture in this post you will also see that for both A and B 10 seconds pass. I understand that. But A's 10 seconds aren't necessarily B's 10 seconds. What if your family of isotropic observers started to observe one another, not themselves? It is as if they move the same distance, but at different angles. In different directions...? Curse, that word again. Help. Replace it :) Different... what.

 

[Mordred]

There is an old expression " In order to change the rules, you must first understand the rules"

For one cosmology does measure the curvature of the cosmos. Its extremely close to flat, so close, that for all practicality it is flat.

Secondly we have what is called comoving distances as opposed to proper distances. What your describing doesn't even work in GR terms.

The current FLRW metric accounts for GR affects on large scales. (FLRW metric assumes homogeneous and isotropy on large scales.)

In order for your time direction analogy to work it would need to work at any scale even at the quantum level. Defining time is that critical.

here is a link on light cones. Might be a starting point to understand WannabeNewtons post

http://en.wikipedia.org/wiki/Light_cone
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/#spacetime

this article is technical but it covers the mathematics of light cones.

http://xxx.lanl.gov/abs/hep-th/0008096

by the way this is a cool link on light cones in different applications
http://web.mit.edu/redingtn/www/netadv/Xlightcone.html

that should cover light cones now let's look at time.

http://en.wikipedia.org/wiki/Time_in_physics
http://www.exactspent.com/time_in_physics.htm
http://philosophyfaculty.ucsd.edu/faculty/ccallender/index_files/time%20in%20physics.doc

now what's the difference between a scalar quantity and a vector quantity?

http://www.grc.nasa.gov/WWW/k-12/airplane/vectors.html
http://en.wikibooks.org/wiki/Physics_with_Calculus/Mechanics/Scalar_and_Vector_Quantities

time is a scalar not a vector property.

As stated at the beginning one needs to understand the rules before you change them

 

[Chronos]

Well, we already have a well defined direction for entropy, you cannot unbreak an egg, and you cannot unbreak the time line of the universe. Mathematically, we can run the universe backwards, but, our ability to predict the future is very limited and model dependent. I view that as insisting processes in the universe are irreversible and have an indeterminate future. To suggest otherwise suggests the universe is illogical [and filled with paradoxes] - and also suggests the scientific method is invalid. I fail to see how that would be meaningful.

 

[Whitefire]

Hey, no one's trying to unbreak the eggs :) For every egg there is, time moves 100% forward. Sounds like a nice slogan. Mordred, I looked up some of your links, only some so far, but I will get to it, promise.

Let's say we have a past light cone of a galaxy. Well, let's simplify it to a point. Is it possible for 1 galaxy to be in this light cone, while another (galaxy) is not (in the same 'hyperspace of present')?

 

[timmdeeg]

time is a scalar not a vector property.

As stated at the beginning one needs to understand the rules before you change them

Well said.
In my opinion this together with Chalnot's short and nevertheless sufficiently specific comment contains all neccesary for Whitefire to reconsider his point of view.

 

[timmdeeg]

Mathematically, we can run the universe backwards, but, our ability to predict the future is very limited and model dependent. I view that as insisting processes in the universe are irreversible and have an indeterminate future. To suggest otherwise suggests the universe is illogical [and filled with paradoxes] - and also suggests the scientific method is invalid. I fail to see how that would be meaningful.

Another approach - and still in the context of 'time is orthogonal to space' - would be to neglect the inhomogeneities and instead stay with the perfect fluid model, which expands adiabatically with constant entropy. With k = +1 cosmic time would run backwards in the recollapsing epoch.

 

[Whitefire]

Let's say we have a past light cone of a galaxy. Well, let's simplify it to a point. Is it possible for 1 galaxy to be in this light cone, while another (galaxy) is not (in the same 'hyperspace of present')?

If your answer to this is a definite no, preferably with some explanation, it will be one way for me to see the error of my ways :)

time is a scalar not a vector property.

Well this seems to be at the heart of this discussion.

 

[Mordred]

A light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.

so yes it is possible for a galaxy to be in one persons light cone as opposed to another observer.

1 example is the light cone from observer "a" sees a galaxy at the edge of the observable universe. However observer "B" on the opposite side of the universe would not see the same galaxy.

Yes scalar vs vector is the heart of the problem.

imagine this thought experiment.

LOL imagine teaching your 5 year old vector time?

I have a doctors apointment at 3:00_{coordinate x,y,z} by my watch its 2:30_{coordinate 1x,1y,1z} so I only have the vector half an hour to arrive.

sounds confusing, as well as impractical

lol imagine teaching your 5 year old vector time?

edit: here is another thought experiment. I'm driving down a windy road, I have 400 km to go and I'm going 100 km. how long does it take me?
as a scalar the answer is easy, as a vector I would have to factor in every vector angle along the path of travel.

 

[Whitefire]

I have a doctors apointment at 3:00coordinate x,y,z by my watch its 2:30coordinate 1x,1y,1z so I only have the vector half an hour to arrive.

I imagined explaining myself to my wife this way. That was funny enough. But seriously:

Your example:

1 example is the light cone from observer "a" sees a galaxy at the edge of the observable universe. However observer "B" on the opposite side of the universe would not see the same galaxy.

Mine from post 1:

The range between 'D' and 'J' is the observable universe - what's on the other side 'didn't happen' - 'isn't happening' for us. The strange thing is, though, that if we were a piece of matter at point C, we could see, and even be influenced by, points D and E which is 'invisible' for us.

...and my example was in relation to the picture:

It IS the same, and I said also:

this idea (which perhaps is not a new one, but I have never heard of it)

So while I may have problems with proper names and terms, my understanding seems to be quite ok.

Mordred, do you realize that by saying, I will quote it again:

1 example is the light cone from observer "a" sees a galaxy at the edge of the observable universe. However observer "B" on the opposite side of the universe would not see the same galaxy.

you admit that other galaxies actually *must* be under influence which we cannot, and never will be able to see directly? A point I tried to make from post one? Something I have never read about, except when in context of things like unexplainable dark energy?

 

[Mordred]

you admit that other galaxies actually *must* be under influence which we cannot, and never will be able to see directly? A point I tried to make from post one? Something I have never read about, except when in context of things like unexplainable dark energy?

There is the observable portion of the universe. Beyond that obviously galaxies. However the amount of influence from outside the observable on our observable would be no different than what occurs inside the observable universe. So although we cannot directly measure the energy mass density of that region. We can calculate its influence in the same manner we do with the observable universe.
This fact has nothing to do with time being a scalar property.

 

[Mordred]

Lol I keep thinking about how one would go about making a vector time wrist watch. Vectors requiring a direction as well as the scalar value. Each watch would need a compass or GPS lol.
Then on top of it you would need reference points and location of your destination relative to you. As well as a good calculator lol

Makes one glad time is scalar and not a vector. Far Far easier.

 

[WannabeNewton]

Note that for a space-time with a space-llike foliation by a one-parameter family $\Sigma_{t}$ and an open subset of it covered by a coordinate chart adapted to the foliation (e.g. Schwarzschild coordinates for the associated space-time) we can interpret the coordinate vector field $(\frac{\partial }{\partial t})^{a}$ as the "time direction" or "flow of time" (you can interpret $\nabla^{a}t$ in the same way since the vector fields will be proportional). This is of course a very specialized situation since general space-times don't admit such coordinate charts / foliations.

 

[Whitefire]

Thank you for this attempt with gradients, WannabeNewton, I didn't think about it, but this still implies treating time as scalar. No, the idea as I see it gives time the quality of a vector (or some tensor) and if this is wrong, then go ahead, shoot it and sink it, and let me drown with it because I will still try to defend it (so I deserve going down for stubborness).

Mordred, I like your humour. I also hope we will never have to deal with vector time wrist watches. And as Wikipedia says:

A scalar is a quantity which can be described by a single number

meaning that '1 minute', '5 minutes', '10 minutes' is generally enough, and it is enough for all simple purposes of every day life-

-however, if you posted in Cosmology forum, and you wanted to be really really precise, you would actually need something to diffrentiate between "10 minutes time from where I am now to where I am now" and "10 minutes from here to the Sun". These would be two different things for any third observer. Similarly, there is a difference between 10 minutes in Milky Way and 10 minutes in Bullet Cluster way out there.

Imagine there is generally only one kind of movement on Earth: free fall; down. Someone suddenly lifted us up and now we are falling. Would you call this movement scalar, with one direction (to the center), or vector, as seen by an observer from the space? In this example, any distance between 2 falling objects will shorten over time. It is better to explain it by understanding the mechanics of gravity, rather than believe in shrinking space. Similarly, I would rather explain redshifts by understanding the mechanics of time, instead of simply believing in expanding of space.

If you come across a text specifically about time in context of scalar or vector (or something else), I would appreciate a link or a title. I did not find anything very specific, only a number of opinions here and there in the Net, most stating that 'time is scalar', but newer with any serious thought behind them.

For now, I gave up on the long articles about light cones, but thanks for the links to the shorter pages, they helped with terminology.

the amount of influence from outside the observable on our observable would be no different than what occurs inside the observable universe. So although we cannot directly measure the energy mass density of that region. We can calculate its influence in the same manner we do with the observable universe.

Now that is something I accept as a reasonable argument, even despite the fact that we would be talking about a homogeneous universe with equal mass distribution.
I didn't know (although I hoped) that such things are considered, and I didn't know (and I still don't) what is the scale of such influence. I imagine it would be greater near the edges of our observable universe, especially in directions where most energy/mass has been found, and smaller near the Milky Way, not only because of the distance, but also because of accleration that happened since there (a mental shortcut :).

Maybe it has nothing to do with time being scalar, but in my humble opinion, if time were truly scalar, the universe wouldn't need to expand, and we would end up facing the Newtonian gravity paradox.

 

[Chalnoth]

Similarly, I would rather explain redshifts by understanding the mechanics of time, instead of simply believing in expanding of space.

Okay. But you aren't making sense. Time points in the "time" direction, not in any of our three spatial directions.

We have a complete understanding of the expansion of our universe through General Relativity.

 

[WannabeNewton]

The key point, as made by Chalnoth, is that time points in the "time direction" whenever the notion of a "time direction" is definable so it doesn't make any sense to talk about the expansion of the space-like hypersurfaces by talking about the time-like components of vectors in the fibers of $T\Sigma_{t}$. In particular, note that $\nabla^{a}t$ will be hypersurface orthogonal to the $\Sigma_{t}$ so for any $s^{a}\in T_{p}\Sigma_{t}$ we have that $s^{a}\nabla_{a}t = 0$. In the coordinates adapted to the folitation, the hypersurface orthogonal vector field is just given by $\nabla_{\mu}t = \delta_{\mu}^{t}$ so $s^{\mu}\delta_{\mu}^{t} = s^{t} = 0$.

 

[Whitefire]

We have a complete understanding of the expansion of our universe through General Relativity.

This means I am not making any discoveries and I will not be creating any new mathematics. I am merely trying connect relativity to cosmology in a way I haven't heard of before--which is again not necessarily a discovery.

Time points in the "time" direction, not in any of our three spatial directions.

An observer who is not observing the passage of time for himself, but in other points of space, *would* see movement in one of our 3 spatial direction - if he wanted to synchronize his own time and the time in a(very distant) place he is observing. In another words, he would have to look closer and closer to compensate for expanding universe.

Perhaps I am mixing the idea of 'time' as dimension and, well, the passage of time: 'what happens to things/everything/space/universe, when it moves in the dimension of time'. Would it be enough if I changed the topic title from 'can time have a direction?' to 'can the passage of time have a direction?'

If not, then please help me understand the correct terminology, by explaining this simple analogy:

We have a piece of paper, one side black, the other white. Let's assume this is a "2 dimensional world".

We pick it up and move it in 3D space, white side pointing up. Now we change the angle by 10 degrees and move it again. Now 25 degrees...

If you cannot say that the white side of 2D space is facing different directions in 3D space, as I would have it with space in 4D spacetime than what is the proper terminology for changing the angle and moving the paper?

Anotherwords, I would say that a lower-number dimension can have a 'direction' or 'orientation' in a higher-number dimension, while you are saying that this is incorrect, or perhaps has a different name.

(sorry if this turns out to be a topic for another forum)

 

[HeLiXe]

If not, then please help me understand the correct terminology, by explaining this simple analogy:

We have a piece of paper, one side black, the other white. Let's assume this is a "2 dimensional world".

We pick it up and move it in 3D space, white side pointing up. Now we change the angle by 10 degrees and move it again. Now 25 degrees...

If you cannot say that the white side of 2D space is facing different directions in 3D space, as I would have it with space in 4D spacetime than what is the proper terminology for changing the angle and moving the paper?

Anotherwords, I would say that a lower-number dimension can have a 'direction' or 'orientation' in a higher-number dimension, while you are saying that this is incorrect, or perhaps has a different name.

(sorry if this turns out to be a topic for another forum)

Are you talking about worldlines? I have studied a very limited amount of general relativity thus far, but it sounds like you are talking about worldlines and proper time. Have you looked at light cones yet? I think a lot of what you are talking about relates to light cones.

 

[petm1]

Lol I keep thinking about how one would go about making a vector time wrist watch. Vectors requiring a direction as well as the scalar value. Each watch would need a compass or GPS lol.
Then on top of it you would need reference points and location of your destination relative to you. As well as a good calculator lol

On my gps the tracking of my movement with vectors is called the scout program, I used it for backpacking.

Time points in the "time" direction, not in any of our three spatial directions.

I see all three elements of time which ever direction I look in the spatial dimensions. Space and time are always intertwined with the observer, in his own present, gazing outward toward the future but only receiving signals from the past. Just because I always see time as the same no matter which direction I am are facing in space does not mean that time is not in any of our spatial directions because all the spatial directions are the same direction in time.

 

[WannabeNewton]

petm1 I have already shown why your claim in the second paragraph is false when we have a way of slicing up spacetime into constant time slices which we can do for the FLRW universe.

 

[petm1]

petm1 I have already shown why your claim in the second paragraph is false when we have a way of slicing up spacetime into constant time slices which we can do for the FLRW universe.

Sorry I must admit that using the scale factor of the universe as a function of time looks like the best calendar man has to date but I fail to see why this proves my view false.

 

[Spourk]

I think the OP might be confusing the dimension of time as it pertains to math with imagery in their head of what things look like as time passes. Kind of like an animated movie where all the cells are overlapped so everything looks like a blob.

Whitefire: If you're sitting in a spaceship floating with a view point of the Earth above it's orbital plain and take a picture of the Earth every day for a year, then mash them all together, you'd get a picture of a blue ring around the sun. But all you've done is take a picture of matter moving over the course of a year, the direction the Earth is traveling isn't the "direction of time", just like the universe isn't expanding in the direction of time.

 

[Whitefire]

Spourk, in your image you are are cutting out the time direction entirely. You are also cutting out third space dimension, and leave only 2D image. This is not what I mean.

In pictures 1,2,3 the left and right always seem to point in 'one direction' for the line.
In pictures 4, 5 and 6 up and down always seems to point in 'one direction' for the paper.
in pictures 7, 8, 9 future and past would also always seem to point in 'one direction' for the space.

But any third observer would be wiser.

 

[Mordred]

this article here may help you out a bit its on De-Sitter and anti-De-sitter. De-Sitter is a matter removed modelling system , anti De_Sitter is negative curvature.

http://www.bourbaphy.fr/moschella.pdf

the reason I feel the article may help is that it has a decent light cone coverage without unnecessary complexity. May help (keep in mind any gravitational effects is due to energy mass as opposed to matter mass)

 

[Spourk]

Spourk, in your image you are are cutting out the time direction entirely. You are also cutting out third space dimension, and leave only 2D image. This is not what I mean.

In pictures 1,2,3 the left and right always seem to point in 'one direction' for the line.
In pictures 4, 5 and 6 up and down always seems to point in 'one direction' for the paper.
in pictures 7, 8, 9 future and past would also always seem to point in 'one direction' for the space.

But any third observer would be wiser.

Hovering above a star to observe planet's orbital path is hardly a 2D image... and my point in the first place is that time doesn't move in a direction. What I tried to do was explain what I think is confusing you about the direction of time, which included all 3 spatial dimensions moving through a 4th time dimension, (which itself isn't moving in a direction).

 

[petm1]

Time dilates in every direction. I may be able to talk about the expansion rate of space between two or more objects with two or more directions between them but I would also be correct to speak of space as a single entity dilating in time. Space and time are two ways we use to describe the same thing with the motion within space being visible and the motion of time not so. Think of our visible universe as a affine space that is always dilating and every single thing has the same motion, outward. I do not see matter dilating but I do exist as a single part of a accelerated frame we call Earth also I do not see the motion of a photon I see it as a color yet to explain each I do need time. A clock may count its own simultaneous existence as a clock but the ticks measure the difference between simultaneous moments we see via photons. For this reason I think of time as all directions for they all exist in time with the same motion, keep in mind that all motion I see is twisted within a focal point from the three dimensions of space's outward motion into the pseudo time of inward motion i think of as my present.

 

[WannabeNewton]

What you have said is just word salad. If you can express your thoughts mathematically then please do so, otherwise you are just uttering nonsense.

 

[Whitefire]

WannabeNewton, I believe that even without mathematic symbols one can express ideas logically and meaningfully.

Spourk, I feel depressed by the way you interpret my words. "you'd get a picture of a blue ring around the sun" is a 2D picture and you cannot represent time/change in 2D without representing velocity. That is why all my representations of time have arrows and why I am talking about directions. Yes they are not merely directions of our '3D' space as we understand it from every day life. But there is just no other word for it. If you really want to make sense of your example, you would 1) need to consider something much larger than Earth and Sun; 2) notice that as you were observing your 'Earth's' movement, it would seem to move slower in the distant fragments of its orbit (relative to you), and faster when near you. You can delete the sun from the picture. In relation to sun, this effect has no meaning, because the sun is always generally the same distance from Earth. Plus 3) I am not sure if this would really happen, even if these were galaxies, not planet and star, because gravity seems to mess with the whole idea.

@Mordred: I thank you but I grasp the concept of light cones quite well. Believe or not but I have imagined light's progress in time as a (very flattened) "X" long before I saw the name 'light cone'. It is a very useful tool, but you are probably aware of the fact that light cones are also relative, meaning that in reality a light cone for point A is different than the light cone for point B. And what I am talking about here is simply (?) relativity, so light cones are only so much useful. You cannot take a single picture, a 'lightlike' image of the universe, and try to deduce how time works from that.

For relativity, you really, really need the third observer. Forget about how you percieve time. Forget about how time passes for other objects relative to you. You need to observe how objects relate to each other.

Perhaps the discussion is not as meaningful as I thought. I have a very specific understanding of spacetime and perhaps you are just used to picture it differently. I see time dilations as movements in specific direcitions, and it's that simple.

This kind of thinking can generate, however, some interesting thoughts. For example, I quite taken by an idea that as space expands, time contracts, and we are not going to have an infinite amount of it. If there was a Big Bang, then there perhaps will be a Big End ---perhaps a Big Freeze, but I would not really bet it is the same. In the Big End we would have the galaxies actually being torn apart by the same process which we now refer to as 'accelerated expansion of the universe', then matter itself being destroyed, and time coming to a stop... or a 'middle', if I am correct...

Good night :)

 

[Popper]

I recently had this idea (which perhaps is not a new one, but I have never heard of it), that on the scale of the entire universe, time expands in all directions at once.

That statement has no meaning since direction is a concept that pertains only to spatial relationships and not to temporal ones.

If we look around us, we generally understand time as 'direction of changes' ….

Who are “we”? Certainly not physicists who do not assign any kind of notion to time as having a “direction.”

And the only sense that one can give to time being orthogonal to space is a mathematical one, not a physical one. Take the spacetime physics that one works with in special relativity as an example. In spacetime physics one uses 4-vectors which reside in spacetime. The mathematical meaning to orthogonal uses the inner product between 4-vectors. When the inner product is zero then the vectors are said to be orthogonal. But the meaning of orthogonal in this context is different than in Euclidean geometry. For example; in spacetime physics the 4-momentum of a photon is orthogonal to itself because the inner product of the 4-momentum of a photon with itself is zero.

The dimension of time is orthogonal to the dimensions of space.

That is incorrect. In the first place it’s mathematically incorrect to speak of a dimension as being orthogonal to something. It’s only meaningful for a 4-vector, or a spatial/temporal axis to be orthogonal to each other. And only then does it have a mathematical meaning, not a physical one.

Yes, time has a direction, but that direction is not up or down, left or right, forward or backward.

That is incorrect. Time does not have a direction. Direction is only something that pertains to spatial relations, not temporal ones. Only when one draws these things on a piece of paper do they actually have physical direction.

Direction quite literally only pertains to spatial directions, not temporal ones. However one does speak of them as having such thing but that’s merely for purpose of visualizing objects in spacetime is that done. There is no physical meaning to it.

 

[WannabeNewton]

That is incorrect. Time does not have a direction.

This is a very broad statement that is incorrect in and of itself. See here:

Note that for a space-time with a space-llike foliation by a one-parameter family $\Sigma_{t}$ and an open subset of it covered by a coordinate chart adapted to the foliation (e.g. Schwarzschild coordinates for the associated space-time) we can interpret the coordinate vector field $(\frac{\partial }{\partial t})^{a}$ as the "time direction" or "flow of time" (you can interpret $\nabla^{a}t$ in the same way since the vector fields will be proportional). This is of course a very specialized situation since general space-times don't admit such coordinate charts / foliations.

 

[WannabeNewton]

I don't get why people treat integral curves of $\nabla^{a}t$ so differently from integral curves of space-like vector fields, apart from the trivial differences. When space-like foliations exist, the hypersurface orthogonal vector field $\nabla^{a}t$ can geometrically be interpreted as the "flow of time". Anyone who has seen the Hamiltonian formalism of general relativity will not find anything alien in this as they will have seen even more general vector fields $t^{a}$ representing the "flow of time" chosen along with a time function $t$ such that the surfaces $\Sigma_{t}$ are space-like Cauchy surfaces and such that $t^{a}\nabla_{a}t = 1$.

 

[Whitefire]

Direction quite literally only pertains to spatial directions, not temporal ones.

I don't think we can resolve this without a really good definition of 'direction'. A one that we all would agree upon.

 

[Fredrik]

I don't think we can resolve this without a really good definition of 'direction'. A one that we all would agree upon.

There is a really good one that's agreed upon by everyone who understands it: A unit vector in the tangent space at the event where you want to assign time a direction.

Edit: A unit vector defines a direction in spacetime. But it can't by itself give us a reason to think of that direction as the direction of time.

The only thing that can define a direction of time is the kind of stuff that WannabeNewton is talking about. First you slice up spacetime into 3-dimensional hypersurfaces labeled by a real parameter t, so that each event belongs to exactly one of these hypersurfaces. Now if we want to find the direction of time at an event p, we would look at the hypersurface that p belongs to. There are two directions that are orthogonal to this hypersurface at p. In one of these directions, t is increasing, and in the other direction, t is decreasing. The direction that's orthogonal to the hypersurface and such that t is increasing, can then be considered the direction of time at p.

Note that this direction depends on our choice of how to do the "slicing".

 

[WannabeNewton]

Indeed so for the FLRW metric $ds^2 = -d\tau^{2} + a^{2}(\tau)dS^{2}$ just take $n^{a} = (\frac{\partial }{\partial \tau})^{a}$ which, in the coordinate basis, is just $n^{\mu} = \delta^{\mu}_\tau$ or put more suggestively $\mathbf{n} = (1,0,0,0)$. You can consider this as the time direction given the spatial slices $\Sigma_{\tau}$, which are of course orthogonal to $n^{a}$. Recall that $\tau$ is the proper time as measured by a clock carried along a chosen congruence of isotropic observers in the FLRW universe so the time direction is just pointing along the unit normal to this congruence i.e. $n^{a} = u^{a}$ where $u^{a}$ is the 4-velocity field of the congruence.

 

[Whitefire]

First you slice up spacetime into 3-dimensional hypersurfaces labeled by a real parameter t, so that each event belongs to exactly one of these hypersurfaces.

And why do you need to do the slicing? Why can't we consider a single point?

 

[Fredrik]

And why do you need to do the slicing? Why can't we consider a single point?

Because a point doesn't determine a direction. You need something like a point and a timelike curve through that point, or a point and a spacelike hypersurface through that point.

 

[Chalnoth]

And why do you need to do the slicing? Why can't we consider a single point?

Another way to look at it, in addition to Fredrik's point, is that time exists at every location, so while we're at it, why not define what we mean by time everywhere? Then we have a space-like surface which we can define as "now" everywhere, and the time direction points perpendicular to that surface (no, you can't visualize it, because it requires four-dimensional thinking to visualize, and we can only think in three dimensions).

Incidentally, one of the better discussions of extra dimensions is this one by Carl Sagan from Cosmos:

 

[write4u]

I don't think we can resolve this without a really good definition of 'direction'. A one that we all would agree upon.

Is "forward" sufficient? It does not rule out any precise direction except backward and sideways.

 

[Fredrik]

Is "forward" sufficient? It does not rule out any precise direction except backward and sideways.

"Forward" is the direction we're talking about how to define. Edit: I meant forward in time, not forward in space.