[Halc]

But I thought that there can only be one time axis.

I guess for now I have to figure out how it is logically possible for one dimension to have multiple axis.

There can be only one time axis, just like there's just one x axis. But which way you decide to point it is arbitrary, again just like the x axis. The simple picture ES drew shows more than one way to orient it, but each frame defines only one time axis. There cannot be a second time axis in any given coordinate system.

I thought that we would not be able to do that because the time dimension t is indeed different than the spatial dimension x.  In that sense saying that something is only moving along the time axis or not would seem to actually make an objective difference.

The two are different since it is possible for a rock's worldline to correspond to the time axis if it is stationary in some coordinate system, and it is also at the origin of that coordinate system. The rock's worldline however cannot correspond to the x axis because that would require it to be at multiple locations simultaneously.

Newton is generally credited as the first to use the term "spacetime".

The term, yes, but 4D block universe (eternalism) is older than Galileo. The rotations back then were not Lorentzian (and not even Euclidean), but it was spacetime, if not by that name.

How long did you take to come up with that?

Quite some time ago, when first asked how to point in the 4th direction.

You have a reference for that?

I occasionally listen to Sean Carrol's Mindscape podcast, and he uses a line something like this in his monthly "Ask Me Anything" (AMA) episodes when people ask about the wave function of the universe, or whether the universe is infinite or finite. Such questions have popped up several times.
- As I understand it, in QM, the state space of wave functions exist in Hilbert Space
- Hilbert space may have an infinite or finite number of dimensions.
- Nobody knows whether the universe is infinite or finite, but Hilbert space can represent both
- The extremely large number that I vaguely recall for a finite dimensional Hilbert Space might represent the number of states in our observable universe (making no claims about the number of states in the non-observable universe).

Thanks for this. Funny that I came across a link for me on google news that mentions this, from physicist Sankar Das Sarma, who is speaking here of the landscape problem in string theory:
https://www.newscientist.com/article/2349359-why-the-laws-of-physics-dont-actually-exist/
It mentions the 10⁵⁰⁰ thing.

[String theory] also has a rather thorny stumbling block known as the landscape problem, where literally zillions of universes (around 10⁵⁰⁰, the number is so large that it seems obscene) are acceptable solutions of the theory. If string theory is correct one can declare victory as one of those zillions of universes must be our universe, and all one needs to do is to somehow find that particular solution to figure out what the laws of physics are for us. Of course, this is an impossible task because of the exceptionally large number of possible universes existing in the landscape, and all with their own distinct laws.

This scenario is often called the multiverse. All possible laws, conceivable and inconceivable, are allowed in some possible universe, and laws of physics are no longer meaningful or unique from a fundamental sense, since they depend entirely on where in the multiverse landscape one is looking. It is ironic that the theory of everything turned out to imply an everything which is exponentially larger than any everything anybody could have imagined before.

My comment here is about that multiverse reference in the 2nd paragraph. Under MWI , the other worlds all have the same laws of physics, just different outcomes of quantum measurements. This is talking of a different sort of multiverse (I can think of at least six kinds) where there's this huge number of possible sets of 'laws', which is more like the level II multiverse (Tegmark's classification) of eternal expansion bubbles and not the level III multiverse of MWI. Hence my balking at the seemingly low finite number, even if it looks kind of big.

The OP did not ask about entropy, either.

But he asked about the arrow of time (which way is positive along a given axis), and entropy is critical to that.

But I do know that those diagrams are not a proper geometric model of what is actually happening in the Minkowski space.

Those diagrams are an exact model actually, just as much as a map of Paris is a valid (not wrong) representation of actual Paris.

[Eternal Student]

Hi.

Some of the formating of quotes has gone wrong in your last post. So I'll just use something sensible here:

ES said:   How long did you take to come up with that?
Halc replied:  Quite some time ago, when first asked how to point in the 4th direction.
   The original comment was about the time axis and was sufficiently inspired it's worth repeating here:

The time dimension is like that. You pick two events (points in spacetime). You say 'this' event and clack two rocks together to define the event.  Then you wander off some arbitrary place and clack the same two rocks a 2nd time to define a second event. The one unique line through spacetime connecting those two events is now defined. You've chosen a totally arbitrary orientation for your time dimension since the two events you chose are completely arbitrary.

   
   Now, I did mention in a post some time that it was "more or less" correct.   I'm just going to discuss the "less" part here because the "more" part speaks for itself, it's an amazing way of describing how you could choose a time axis.  So, there's genuinely no offence intended.  You've obviously spent some serious time replying to @Dimensional and might just want a little feedback or something to think about.

   Let's start by considering a person, we'll call her Roxanne ("Roxy") because she's the one who will be doing the rock clacking.   Now Roxy starts by clacking some rocks at  x=0, t=0 in whatever co-ordinate system she was originally using.   Supposedly, Roxy can clack more rocks at any arbitrarily chosen event in spacetime.  Let's say she clacks the rocks at the event   x=10, t=0   in her original co-ordinate system.   So that's just two events that were at the same co-ordinate time and just lay along the x-axis of her original co-ordinate system.....   do you see where I'm going with this?
    The spacetime interval between those two events =  +100   (in a suitable convention with  ΔS² =  Δx² - c²Δt²),  in particular they are most definitely spacelike separated.  Moreover, the spacetime interval is a conserved quantity under any Poincare transformation we apply.  So whatever new co-ordinates t'  and x' we try to generate,  we will still have    ΔS² = +100 = (Δx')² - c²(Δt')² .   It's the being positive thing which is the real sting in the tail.  The two events remain spacelike separated.   In particular there is no way those two events can lie along the new t'  time axis.
   More generally, the two events with the rock clacking can't be completely arbitrarily chosen,  the first one is arbitrary.  The second one must be timelike separated.
   **Also,  Roxy is only metaphorically allowed to "wander off" to the other rock clacking event.  Since that event must be timelike separated from the other one, she has to run faster than anything else in her world.  That's not too bad though, there doesn't need to be a Roxy and even if there was she was only metaphorically wandering off to the other event.**

Best Wishes.   

**LATE EDITING:  I've already spotted that the last paragraph was backwards,  Roxy can't get to spacelike separated events but timelike is no problem.   I've left the error in because we're all human.  **

[Halc]

Some of the formating of quotes has gone wrong in your last post.

Thanks. Fixed that now. The proof-read was too quick I guess.

Now, I did mention in a post some time that it was "more or less" correct.

Yes, was wondering about that, but didn't want to press.

   Let's start by considering a person, we'll call her Roxanne ("Roxy") because she's the one who will be doing the rock clacking.   Now Roxy starts by clacking some rocks at  x=0, t=0 in whatever co-ordinate system she was originally using.   Supposedly, Roxy can clack more rocks at any arbitrarily chosen event in spacetime.  Let's say she clacks the rocks at the event   x=10, t=0   in her original co-ordinate system.   So that's just two events that were at the same co-ordinate time and just lay along the x-axis of her original co-ordinate system.....   do you see where I'm going with this?[/quote]Sort of. I did say 'clack the same pair of rocks' which you're not doing because your two clacks are done simultaneously in different places, which defines two events with space-like separation, a nice choice for orientation of the x axis, but it cannot be a time axis, as you point out.

More generally, the two events with the rock clacking can't be completely arbitrarily chosen,  the first one is arbitrary.  The second one must be timelike separated.

Which it will be if you use the same pair of rocks.

Then you wander off some arbitrary place and clack the same two rocks a 2nd time to define a second event.

Also,  Roxy is only metaphorically allowed to "wander off" to the other rock clacking event.  Since that event must be timelike separated from the other one, she has to run faster than anything else in her world.

This comment I don't understand. Please clarify, because there seems to be no such restriction. Hence the choice of the verb 'wander'.

[Eternal Student]

made some editing to my post at almost the same time you posted.

[Dimensional (OP)]

But I thought that there can only be one time axis.

I guess for now I have to figure out how it is logically possible for one dimension to have multiple axis.

There can be only one time axis, just like there's just one x axis. But which way you decide to point it is arbitrary, again just like the x axis. The simple picture ES drew shows more than one way to orient it, but each frame defines only one time axis. There cannot be a second time axis in any given coordinate system.

But there are two time axis in the diagram.   

I thought that we would not be able to do that because the time dimension t is indeed different than the spatial dimension x.  In that sense saying that something is only moving along the time axis or not would seem to actually make an objective difference.

The two are different since it is possible for a rock's worldline to correspond to the time axis if it is stationary in some coordinate system, and it is also at the origin of that coordinate system. The rock's worldline however cannot correspond to the x axis because that would require it to be at multiple locations simultaneously.

Okay, I understand that, but what I said there is the crux of my issue.  In my mind there is a special and absolute time axis because it is different than the spatial axis.

But I do know that those diagrams are not a proper geometric model of what is actually happening in the Minkowski space.

Those diagrams are an exact model actually, just as much as a map of Paris is a valid (not wrong) representation of actual Paris.

But the diagram is drawn from Euclidean geometry.  Even though the diagram is legitimate, we cannot actually draw timelike intervals. 

[Origin]

But there are two time axis in the diagram.

That is because the diagram is showing the time axis from 2 different frames.

In my mind there is a special and absolute time axis because it is different than the spatial axis

There is no absolute time.  In your frame 1 second is 1 second, in every other frame 1 second in their frame will be less than 1 second when compared to your frame.  That is why t' is tilted relative to t in the diagram.

Even though the diagram is legitimate, we cannot actually draw timelike intervals.

Why not? 

[Dimensional (OP)]

But there are two time axis in the diagram.

That is because the diagram is showing the time axis from 2 different frames.

Yes, but there are still two time axis in different locations.  Why should we have to illustrate the axis in two different locations if there weren't two different time axis.  Is it possible to show both frames using one time axis?

There is no absolute time.  In your frame 1 second is 1 second, in every other frame 1 second in their frame will be less than 1 second when compared to your frame.  That is why t' is tilted relative to t in the diagram.

Yes, I agree that there is no absolute time, but I am saying that I am confused as to how we can have two different time axis.   

Even though the diagram is legitimate, we cannot actually draw timelike intervals.

Why not?

Because it is a Minkowski metric.  We cannot illustrate worldlines with Euclidean geometry; they are an unimaginable geometry.

[Origin]

Yes, but there are still two time axis in different locations. 

Correct.

Why should we have to illustrate the axis in two different locations if there weren't two different time axis.

There are 2 different time axes because the single diagram is showing time for 2 different frames.

Is it possible to show both frames using one time axis?

Not that I am aware of.

Yes, I agree that there is no absolute time, but I am saying that I am confused as to how we can have two different time axis.

What confuses you?  Since there are 2 different inertial frames we know that time moves at a different rates for the different frames so they both couldn't possibly have the same time axis.

[Dimensional (OP)]

Yes, but there are still two time axis in different locations.

Correct.

Why should we have to illustrate the axis in two different locations if there weren't two different time axis.

There are 2 different time axes because the single diagram is showing time for 2 different frames.

Is it possible to show both frames using one time axis?

Not that I am aware of.

Yes, I agree that there is no absolute time, but I am saying that I am confused as to how we can have two different time axis.

What confuses you?  Since there are 2 different inertial frames we know that time moves at a different rates for the different frames so they both couldn't possibly have the same time axis.

I am confused as to how time can supposedly only have one direction but have multiple axis. 

To be totally honest, this extra dimension of time is so inconceivably strange that I question if there isn't a better explanation of space and time.  I mean maybe Minkowski space is just a mathematical description that sufficiently explains space and time for our purposes, be it practical and experimental, but just isn't the reality of our space and time. 

Then again, I am not sure either if there isn't something that I am misunderstanding about Minkowski space, or more specifically the mathematics of it.

[Eternal Student]

Hi.

   I'm at risk of just repeating something that was already mentioned but I think it's important to do so:

You ( @Dimensional ) seem to be thinking that there is an extra dimension of time,   so there's  5 dimensions,  3 of space plus 2 of time.     This is NOT at all what has been said so far.

In any reference frame there are only 4 dimensions,  3 of space and 1 of time.

However it is possible to draw the time axis of a completely different reference frame on the same  spacetime diagram if you want to.    That  extra time axis   (e.g. the blue one on my diagram) is NOT used as a time axis in the black frame.   In the black frame the only time axis that is used is the black one.
   We can just draw the other time axis for the other reference frame on that same diagram because it's often helpful to do so.

Does that make sense?

Best Wishes.

[Dimensional (OP)]

Hi.

   I'm at risk of just repeating something that was already mentioned but I think it's important to do so:

You ( @Dimensional ) seem to be thinking that there is an extra dimension of time,   so there's  5 dimensions,  3 of space plus 2 of time.

   

Not exactly.  Right now I am stuck thinking that there has to be more than one direction of time as multiple axis would seem to suggest this.   

However it is possible to draw the time axis of a completely different reference frame on the same  spacetime diagram if you want to.    That  extra time axis   (e.g. the blue one on my diagram) is NOT used as a time axis in the black frame.   In the black frame the only time axis that is used is the black one.
   We can just draw the other time axis for the other reference frame on that same diagram because it's often helpful to do so.

Does that make sense?

I understand what you are saying, but I do not understand how it explains only one direction of time.  With the information given so far about the graph, I don't seem to have a choice but to think that both objects are both running along two different time axis.  And then I take this to imply that there must be more that one time axis. 

[alancalverd]

Not sure whether this adds clarity or confusoin, but it's an idea forming in my addled brain:

Time is what separates sequential events, or as Einstein said, it is what prevents everything from happening at once. Space is what separates objects, or to paraphrase Einstein, it is what prevents everything being in one place. 

We find it convenient to assign three orthogonal vectors to the spatial separation of objects, and we need one additional vector to distinguish between events. So if A is not identical to B they must be separated by at least one of x,y, z and t.

The problem of being alive, is that all our perceptions, and thus all the information we possess, inevitably progress in one direction with t increasing so whilst we can move things in x,y,z, we can't undo the entropy of the universe or unremember what happened so we can't move events in t. 

This is beginning to sound horribly like the anthropic "observer effect" that I despise as a product of philosophy, so I'll stop and go to bed.

 

[Eternal Student]

Hi.

Right now I am stuck thinking that there has to be more than one direction of time as multiple axis would seem to suggest this.   

     I expect most of us would prefer to say "orientation" of the time axis instead of direction - but overall this is right.   You have stated something that is true and really is a very important consequence of special relativity, well done.
    Special relativity does suggest that the time axis can have all sorts of orientations.   It depends on the motion of the reference frame you have chosen to use.   So there honestly isn't one universal time axis for everything, everyone and every valid reference frame.
    Since there is no "absolute" or most truthful reference frame, they are all as good and as valid as any other,  I can't tell you how your time axis is orientated right now.  It is some way.   We might just as well call that  "straight up" and start drawing our spacetime diagram on an ordinary flat Euclidean space (a piece of paper) like we did in an earlier post.  Just to make this clear:   The black axis was shown in the usual way, with the black time axis straight up and the black x-axis running horizontally across the page but we would have an equally valid diagram if we had decided the blue axis was arranged that way (the blue time axis went straight up and the blue x-axis - which I never really put on the diagram anyway - running across the page).

    The only thing I can tell you is how the time axis that someone else is using will compare to your time axis.   Specifically, if you tell me the offset velocity (how their frame is moving relative to yours) then I can tell you how their time axis is orientated compared to yours.   That is all we can do.   
     There is no objective way that I can determine the absolute orientation of your time axis right now.   Intuitively, you will probably understand what I'm trying to say with terms like an "absolute orientation".... this is because we are human and our ideas are manifestly those of Euclidean geometry anyway.    To phrase it more mathematically we have something like this:    If an ordinary Euclidean (and not Minkowski) metric was applied to spacetime, then the chances of your time axis being Euclidean-orthogonal to the x-axis (i.e. really running straight up) is low.  It will be sloping somehow.    There should be only one inertial reference frame (up to translations and spatial rotations) where the time axis would really be Euclidean-orthogonal to the x-axis but we have no way of finding or identifying that reference frame.   In any valid inertial reference frame, the laws of physics do hold,  there is nothing special or obvious that would happen if, by chance, the time axis really was Euclidean-orthogonal to the x-axis.

   I hope that's helping a bit.   The orientation of the time axis is not pre-ordained or taken as some fact.  We have no idea if we are using the one where it would be Euclidean-orthogonal to the x-axis.   We are just using a time axis which is Minkowski-orthogonal to the x-axis.   Any reference frame where the space and time axis are Minkowsi-orthogonal is just as good as any other.

Best Wishes.

[Dimensional (OP)]

Hi.

Right now I am stuck thinking that there has to be more than one direction of time as multiple axis would seem to suggest this.   

     I expect most of us would prefer to say "orientation" of the time axis instead of direction - but overall this is right.   You have stated something that is true and really is a very important consequence of special relativity, well done.
    Special relativity does suggest that the time axis can have all sorts of orientations.   It depends on the motion of the reference frame you have chosen to use.   So there honestly isn't one universal time axis for everything, everyone and every valid reference frame.
    Since there is no "absolute" or most truthful reference frame, they are all as good and as valid as any other,  I can't tell you how your time axis is orientated right now.  It is some way.   We might just as well call that  "straight up" and start drawing our spacetime diagram on an ordinary flat Euclidean space (a piece of paper) like we did in an earlier post.  Just to make this clear:   The black axis was shown in the usual way, with the black time axis straight up and the black x-axis running horizontally across the page but we would have an equally valid diagram if we had decided the blue axis was arranged that way (the blue time axis went straight up and the blue x-axis - which I never really put on the diagram anyway - running across the page).

    The only thing I can tell you is how the time axis that someone else is using will compare to your time axis.   Specifically, if you tell me the offset velocity (how their frame is moving relative to yours) then I can tell you how their time axis is orientated compared to yours.   That is all we can do.   
     There is no objective way that I can determine the absolute orientation of your time axis right now.   Intuitively, you will probably understand what I'm trying to say with terms like an "absolute orientation".... this is because we are human and our ideas are manifestly those of Euclidean geometry anyway.    To phrase it more mathematically we have something like this:    If an ordinary Euclidean (and not Minkowski) metric was applied to spacetime, then the chances of your time axis being Euclidean-orthogonal to the x-axis (i.e. really running straight up) is low.  It will be sloping somehow.    There should be only one inertial reference frame (up to translations and spatial rotations) where the time axis would really be Euclidean-orthogonal to the x-axis but we have no way of finding or identifying that reference frame.   In any valid inertial reference frame, the laws of physics do hold,  there is nothing special or obvious that would happen if, by chance, the time axis really was Euclidean-orthogonal to the x-axis.

   I hope that's helping a bit.   The orientation of the time axis is not pre-ordained or taken as some fact.  We have no idea if we are using the one where it would be Euclidean-orthogonal to the x-axis.   We are just using a time axis which is Minkowski-orthogonal to the x-axis.   Any reference frame where the space and time axis are Minkowsi-orthogonal is just as good as any other.

Best Wishes.

Ok, you mention "Minkowski-orthogonal".  This is probably where my problem lies.  I was reading that the orthogonality can be "Euclidean-othogonal" because it uses the Minkowski metric.  I forgot to think about that.  So I guess that is how the world lines would intersect to the x axis orthogonally which would be impossible in only the Euclidean metric.

[evan_au]

I heard about this preprint on the somewhat quirky Astronomy Daily podcast (about 10 minutes per weekday): "'Quantum time flip' makes light move simultaneously forward and backward in time"
https://www.livescience.com/quantum-time-flipped-photon-first-time

Is this the story that triggered this thread?
- And the confusion about whether it was light or time moving backwards in time?