What is time? (Again)

[Markus Hanke]

Great, thanks  It would appear that his thoughts were very roughly along the same lines as my own thinking on the subject. I shall definitely add this to my reading list

[joigus]

21 hours ago, studiot said:

That provides a good start to my thoughts.

The stated purpose of this thread is to examine the Physics of the question "What is Time ?"

One way to do this is to go through the properties of time and see where that leads.
Many entities are well describe by their properties in Physics.

We could also ask questions like

Is time a property of something ?

Is time a coordinate in a coordinate system?
If so, what if we do not have a coordinate system?

What processes does time allow that cannot occur without time?

Starting with coordinate systems.

Sketch 1 [...]

sketch 3 [...]

sketch 2.[...]

[...]

Sketch4 shows the result.

[...]

Thanks a lot for your drawings and explanations, @studiot. +1

The only reason why I would wait a little bit before totally endorsing your picture would be that, if anything, QFT has shown us that whatever it is that we perceive as space and time must be very deeply connected with the space of charge. After all, it's the composition of the 3 inversions (CPT) that produces a very robust discrete symmetry of Nature.

But I see no a priori reason why the "internal" dimension of charge could not be added to your picture.

Very interesting your rescuing Eddington's observation. It is so interesting that I will re-type it here:

Quote

It is evident from experience that a four-fold mesh-system must be used; and accordingly an event is located by four coordinates, generally taken as x, y, z, t. To understand the significance of this location, we first consider the simple case of two dimensions. If we describe the points of a plane figure by their rectangular coordinates x, y, the description of the figure is complete and would enable anyone to construct it; but it is also more than complete, because it specifies an arbitrary element, the orientation, which is irrelevant to the intrinsic properties of the figure and ought to be cast aside from a description of those properties. Alternatively we can describe the figure by stating the distances between the various pairs of points in it; this description is also complete, and it has the merit that it does not prescribe the orientation or contain anything else irrelevant to the intrinsic properties of the figure. The drawback is that it is usually too cumbersome to use in practice for any but the simplest figures.

(my emphasis). I couldn't agree more. But, in fact, it amounts to something both you and I (at least) have already (at least) implied:

On 7/28/2020 at 1:51 PM, studiot said:

What is also interesting is that there is more than one way to view these relationships, which is why we have several (slightly) different terms.

The condition I meant may be illustrated in the standard equation of an ellipse

This is the locus of a point which moves under the one condition

<implicit equation of the ellipse>

Alternatively we can introduce what is known as a parameter often denoted t, though sometimes a Greek letter is used.

<parametric equations of the ellipse>

Note the first form has two independent variables and one condition or equation, between them.

The second has one independent variable (the parameter) and two conditions or equations.

Both refer to the same ellipse.

IOW: describing relations between points in space as intrinsic, with no oriented parameter.

And, AAMOF, I have implied it too. Here it is:

On 7/23/2020 at 2:59 PM, joigus said:

If you define relations between variables (let's call them x, y) as some kind of implicit constraint,

\[f\left(x,y\right)=0\]

The natural (simplest, obvious, directly related to the pre-defined terms) parameter to describe the sequence of changing is the (class of) proper length parameter(s) given by,

\[ds^{2}=dx^{2}+dy^{2}\]

There's your time. Defined as a clear-cut* class of parametrizations, modulo (except for) its sign.

The only sticking point about time is its orientation (the arrow of time). That remaining bit of information cannot be given by implicit relations between the world variables. 

Maybe I didn't say it explicitly, but my point was that it is the first, the implicit picture, that is more objective. The oriented parameter t in this picture would be, let's say, just psychological, instrumental, etc., what have you, and have nothing to do** with what goes on in the physical world at large. That objective reality would be described by the intrinsic interdependence of states. The parameter would be just an artifact you need to introduce if you want to account for your experiencing the world as an ordered sequence of configurations. Nothing more. I wouldn't dare to call it emergent, but maybe immersive (more related to how the observer experiences the world).

Now, using the arc-length on the curve gives you a natural parametrization, defined except for its sign and a family of infinitely many re-parametrizations.

I think most of us here would be closer to common ground for agreement if we made it as clear as possible what we mean.***

-------------------------------------------------------------

* I shouldn't have said "clear-cut" here. After all it's an infinite family.

** Well, not "nothing to do", but a lot more to do with what goes on in the observer's mind, measuring instruments, etc.

*** (Edit): This is rather meant as self-criticism, as I don't think I've been as clear as I could have, going back to my previous posts.

 

Edited August 2, 2020 by joigus
Addition

[studiot]

2 hours ago, joigus said:

And, AAMOF, I have implied it too. Here it is

etc................

Yes it is closely allied to those points.

If you look at Eddington's book pages and 11 he discusses why the 'four squares' metric is chosen over the full quadratic form.

He also considers why even more complicated expressions, eg a quartic, are not employed.

That is he justifies ds²  =  dx² + dy²

[MigL]

Interesting how we all perceive space-time differently.
Studiot in terms of intervals between events.
Markus in terms of metrics and tensors
I'm old fashioned. I see space-time diagrams in my head; and now I'm told that there is no actual need for my imaginary co-ordinate systems.

I'm crushed !

[michel123456]

On 8/2/2020 at 12:48 AM, studiot said:

So do we need an axis called time?

Very interesting.

I have missed the discussion this W.E., I will have to cope.

Before erasing something, you must be confident that it does not hide anything.

To the point: Time is the thing that is needed to transmit information from one point of the space to another.

Without time, space would be opaque: in no time no information can be transmitted at all (including light). Or the other way out: if time is not needed for information to go from one point to another (we know it is wrong) space would be fully transparent.

Since we know that the maximum speed for information is C (wathever its value really is), we (should) know that space is neither fully opaque, neither fully transparent. And if space is not fully transparent, it means that the 4th dimension is hiding something. The 4th dimension allows us to observe only a part of the B.U.

So IMHO if you work without the axis of time, you must be extremely cautious that your description of things includes everything.

 

Edited August 3, 2020 by michel123456

[studiot]

7 minutes ago, michel123456 said:

Very interesting.

I have missed the discussion this W.E., I will have to cope.

Before erasing something, you must be confident that it does not hide anything.

To the point: Time is the thing that is needed to transmit information from one point of the space to another.

Without time, space would be opaque: in no time no information can be transmitted at all (including light). Or the other way out: if time is not needed for information to go from one point to another (we know it is wrong) space would be fully transparent.

Since we know that the maximum speed for information is C (wathever its value really is), we (should) know that space is neither fully opaque, neither fully transparent. And if space is not fully transparent, it means that the 4th dimension is hiding something. The 4th dimension allows us to observe only a part of the B.U.

So IMHO if you work without the axis of time, you must be extremely cautious that your description of things includes everything.

 

 

5 hours ago, MigL said:

Interesting how we all perceive space-time differently.
Studiot in terms of intervals between events.
Markus in terms of metrics and tensors
I'm old fashioned. I see space-time diagrams in my head; and now I'm told that there is no actual need for my imaginary co-ordinate systems.

I'm crushed !

 

Michel in particular might like to note the anther point hidden in all this.

By imposing a coordinate system something has been added to the subject, not taken away.

That difference became clear to modern geometers as the important difference between classical Euclidian Geometry and the Geometry of that Frenchman.

Eddington points this out (he was not the first to realise this) towards the end of the second paragraph on page 9 of his book.

That which is added is inherent in the coordinate system, not the subject.

And the principle of relativity says that there are features of the subject that are independent of the coordinate system

(including even no coordinate system )
(How often do we forget zero when substituting values into some universal statement  : What is the direction of the zero vector ?)

 

[joigus]

8 hours ago, MigL said:

Interesting how we all perceive space-time differently.
Studiot in terms of intervals between events.
Markus in terms of metrics and tensors
I'm old fashioned. I see space-time diagrams in my head; and now I'm told that there is no actual need for my imaginary co-ordinate systems.

I'm crushed !

Don't be. If Plato was right and all knowledge is remembering, let me remind you of what you already know.

Try to picture your whole life as a chain of "congruences" of events, so to speak (relativity of simultaneity aside). Everything you live from birth to death is there placed in some database.

Let's imagine that you can consult this database. Let's go to the day of my graduation. Bzzzz... There it is. You can also see the news of that day, the weather, everything! Someone yelling "taxi!!" 10 meters away, a fly landing on the window, your thoughts at a particular moment. Everything.

Because the equations of physics don't allow dynamical states of the whole system to repeat, except for very-long-time recurrences in closed systems, you could use your timeless concatenation of dynamical states to answer any question about what goes on in your life without ever having to use time. Your space of occurrences would have to include positions and momenta, of course. This database describes the whole physics, but time is out of the picture.

One last thing: You could use a parameter. You could re-wind the whole movie at any speed you want. Slow it down or speed it up. That would represent the re-parametrizations of an instrumental parameter that moves you back (rewind class of parameters) and forth (forward class of parameters). But that parameter would not be part of the physics.

If you think about it, when you solve the equations of motion you're kind of doing the same thing on a small scale. You get access to a small part of that database.

[michel123456]

42 minutes ago, joigus said:

Don't be. If Plato was right and all knowledge is remembering, let me remind you of what you already know.

Try to picture your whole life as a chain of "congruences" of events, so to speak (relativity of simultaneity aside). Everything you live from birth to death is there placed in some database.

Let's imagine that you can consult this database. Let's go to the day of my graduation. Bzzzz... There it is. You can also see the news of that day, the weather, everything! Someone yelling "taxi!!" 10 meters away, a fly landing on the window, your thoughts at a particular moment. Everything.

Because the equations of physics don't allow dynamical states of the whole system to repeat, except for very-long-time recurrences in closed systems, you could use your timeless concatenation of dynamical states to answer any question about what goes on in your life without ever having to use time. Your space of occurrences would have to include positions and momenta, of course. This database describes the whole physics, but time is out of the picture.

One last thing: You could use a parameter. You could re-wind the whole movie at any speed you want. Slow it down or speed it up. That would represent the re-parametrizations of an instrumental parameter that moves you back (rewind class of parameters) and forth (forward class of parameters). But that parameter would not be part of the physics.

If you think about it, when you solve the equations of motion you're kind of doing the same thing on a small scale. You get access to a small part of that database.

Have you ever asked yourself why you can see in the sky a star as it was thousand years ago, but you cannot directly observe yourself at your graduation? Why in the concatenation the one position is not able to directly observe the other one?

[studiot]

8 minutes ago, michel123456 said:

Have you ever asked yourself ............................., but you cannot directly observe yourself at your graduation?

Mirrors?

[joigus]

1 hour ago, michel123456 said:

Have you ever asked yourself why you can see in the sky a star as it was thousand years ago, but you cannot directly observe yourself at your graduation? Why in the concatenation the one position is not able to directly observe the other one?

If I could only tell you how many times. I have no answer for why is that. But the fact that once you solve the equations of evolution for one simple system, you can perform this miracle on a small scale, of seeing the whole histories, that's what's kept me wondering for decades. And still does.

I have this nagging feeling that most of us here share this intuition that what appears as time and slices (exterior of cones, rather) of present space is a characteristic of whatever makes some systems (us, conscious beings, other organisms, maybe some machines), and not something particularly intrinsic to the universe.

Saying that is one thing; trying to picture a mathematical structure that embeds this illusion, if you will; is quite another.

I remember that trend in the 70's[?] when the director showed you what was going on at different places by splitting the different courses of action in simultaneous squares. Airport (1970) was a good representative of that trend. Needless to say it didn't last. @MigL always has a metaphor for physics from movies. I wonder what he thinks of that.

4 hours ago, studiot said:

(How often do we forget zero when substituting values into some universal statement  : What is the direction of the zero vector ?)

That's a very slippery slope.  

Edit: On second thought...

4 hours ago, studiot said:

What is the direction of the zero vector ?

That's very interesting. +1. Silly me. If your coordinates in your self-reference are (0,0,0,0) at any moment, what direction is any direction? In particular, what direction is your time direction? The mathematics of vector spaces suggest, if anything, that that's just a choice.

Edited August 3, 2020 by joigus
minor correction/ correction exterior--> interior --> exterior of cones ("extended" simultaneity)

[michel123456]

2 hours ago, joigus said:

I have no answer for why is that.

I do.

[joigus]

Just now, michel123456 said:

I do.

I'm all ears.

[michel123456]

3 hours ago, studiot said:

Mirrors?

Try it. Put that in numbers & tell me if joigus can put a mirror anywhere in the universe to see himself graduating.

[dimreepr]

4 minutes ago, joigus said:

I'm all ears.

3 minutes ago, michel123456 said:

Try it. Put that in numbers & tell me if joigus can put a mirror anywhere in the universe to see himself graduating.

Sadly, a mirror is less effective with ears...

 

[joigus]

33 minutes ago, michel123456 said:

Try it. Put that in numbers & tell me if joigus can put a mirror anywhere in the universe to see himself graduating.

I don't even have a mirror to show me where I left my glasses 20 minutes ago. So...

24 minutes ago, dimreepr said:

Sadly, a mirror is less effective with ears...

 

LOL

[Markus Hanke]

18 hours ago, joigus said:

If I could only tell you how many times. I have no answer for why is that. But the fact that once you solve the equations of evolution for one simple system, you can perform this miracle on a small scale, of seeing the whole histories, that's what's kept me wondering for decades. And still does.

I have this nagging feeling that most of us here share this intuition that what appears as time and slices (exterior of cones, rather) of present space is a characteristic of whatever makes some systems (us, conscious beings, other organisms, maybe some machines), and not something particularly intrinsic to the universe.

Take that a step further - as thought experiment, imagine that you are carrying some kind of recording equipment 24/7 for the entirety of your life which records what you hear and see, and then save that data on some hypothetical large-capacity DVD-like disc. Now it is immediately obvious that information requires no specific spatiotemporal embedding - your direct experience of seeing and hearing took place in what appeared like (3+1) dimensions; the same information is stored in your brain in a very complex network that can probably be considered a Hausdorff space with some non-trivial number of Hausdorff dimensions; and also on the DVD, which is in itself (2+0)-dimensional. Interesting to note that there is no real distinction between spatial and temporal dimensions in a Hausdorff space, and no notion of time on the DVD at all...even in its real world embedding, all the information about your life exists on the DVD simultaneously (as it is small enough to be considered local). How we construct a play-back device for the DVD is an arbitrary choice.

In all cases, the exact same information (roughly at least) is referenced, so clearly information is quite independent from its spatiotemporal embedding. These embeddings are just arbitrary choices on how the same data set is represented - in the same way that a computer’s graphical user interface is an arbitrary choice of how to represented the information (which are just bits) in its memory banks. There’s nothing inside the memory banks that resembles a little “file” icon, or the letter “A”, or even any notion of a two-dimensional screen. None of this is intrinsic to the actual information contained in the computer’s memory; they are just arbitrary conventions imposed from the ‘outside’ in addition to the raw data. This is quite necessary for our mind though, because we would not be able to comprehend the data set in its raw form. 

So again - could the imposition of a particular spatiotemporal embedding (such as (3+1) of how we experience the world) be something the mind does to structure and order information, and assemble it into a linear and coherent model of the world?

[michel123456]

1 hour ago, Markus Hanke said:

Take that a step further - as thought experiment, imagine that you are carrying some kind of recording equipment 24/7 for the entirety of your life which records what you hear and see, and then save that data on some hypothetical large-capacity DVD-like disc. Now it is immediately obvious that information requires no specific spatiotemporal embedding - your direct experience of seeing and hearing took place in what appeared like (3+1) dimensions; the same information is stored in your brain in a very complex network that can probably be considered a Hausdorff space with some non-trivial number of Hausdorff dimensions; and also on the DVD, which is in itself (2+0)-dimensional. Interesting to note that there is no real distinction between spatial and temporal dimensions in a Hausdorff space, and no notion of time on the DVD at all...even in its real world embedding, all the information about your life exists on the DVD simultaneously (as it is small enough to be considered local). How we construct a play-back device for the DVD is an arbitrary choice.

In all cases, the exact same information (roughly at least) is referenced, so clearly information is quite independent from its spatiotemporal embedding. These embeddings are just arbitrary choices on how the same data set is represented - in the same way that a computer’s graphical user interface is an arbitrary choice of how to represented the information (which are just bits) in its memory banks. There’s nothing inside the memory banks that resembles a little “file” icon, or the letter “A”, or even any notion of a two-dimensional screen. None of this is intrinsic to the actual information contained in the computer’s memory; they are just arbitrary conventions imposed from the ‘outside’ in addition to the raw data. This is quite necessary for our mind though, because we would not be able to comprehend the data set in its raw form. 

So again - could the imposition of a particular spatiotemporal embedding (such as (3+1) of how we experience the world) be something the mind does to structure and order information, and assemble it into a linear and coherent model of the world?

That corresponds to the concept of the Block Universe, isn't it? Under this concept, everything is already "recorded" and static, and time is the very bizarre effect of reading the information that is already there.

Although I was very surprised that the wiki entry about the B.U. has changed (in English) into the "growing block universe", excluding the future, while the French page has not been updated.

https://en.wikipedia.org/wiki/Growing_block_universe

As if the recording process is the process of time.

 

Edited August 4, 2020 by michel123456

[Eise]

I think I must agree with Markus to disagree. The only last possibility I see is to replace the word 'change', when not applied to the flow of time, with another one: maybe 'to vary' will do? Y varies dependent on the variation of x. And the observation that in a few English dictionaries, I always see a reference to time in the 'change'-lemmas.

[joigus]

3 hours ago, Markus Hanke said:

Take that a step further - as thought experiment, imagine [...]

So again - could the imposition of a particular spatiotemporal embedding (such as (3+1) of how we experience the world) be something the mind does to structure and order information, and assemble it into a linear and coherent model of the world?

Baby steps, Hanke, pray you.  You're giving me a lot to digest here and in the other thread about CPT.

You introduce several very interesting ideas there.

Hausdorff dimension. I've sometimes toyed with the idea that fractality may play a part in what conscience, arbitrarily small scales, and in general some of the most intractable problems of science, could need as a framework to be formulated. I wouldn't know what to do with it for the very simple reason that I'm not cut for it. I haven't played much with fractals, or with loop quantum gravity. Somehow it's not me. But that doesn't mean I don't think it's an interesting idea. I will share an intimation here: The very fact that from the basis of mathematics you cannot prove whether there is a cardinality that makes "cardinal, or counting, sense" trapped between the discrete and the continuous, I think could signal to something very fundamental. I also think this connects with @studiot's "obsession" with continuity vs. granularity. It may be precisely because spaces with non-trivial Hausdorff dimension potentially have this kind of algorithmic inaccessibility that they could be very powerful stores of information in finite volumes. I don't know. Just giving you my thoughts here.

As to the embedding question, I do have a model only to be taken as a parametric setting of the problem, a framework to discuss these questions, rather than a theory, similar to what @studiot did with his pictographic mesh of events. And because we're starting to know each other somewhat better, maybe it could be shared here with no harm done, no nonsense, and no pressing any point on my part. But I do need to include an observation that @michel123456 made to me yesterday by PM, if he doesn't mind. I would have to adapt his idea a bit, because I think it's not applicable "as is". But that would require some discussion with him for authorship.  And, perhaps, with everybody else.

PD: Michel, I think your idea does not apply to elementary particles, and thus not in general, but it does apply to extended systems that need to sacrifice some of their own dynamical variables to represent what's going on outside.

 

Edited August 4, 2020 by joigus
emphasis added

[Duda Jarek]

2 minutes ago, joigus said:

Hausdorff dimension

I don't know what it has to do with time, but here is a great list: https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

Its two most complex formulas come from my https://demonstrations.wolfram.com/TheBoundaryOfPeriodicIteratedFunctionSystems/

[joigus]

2 minutes ago, Duda Jarek said:

I don't know what it has to do with time, but here is a great list: https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

Its two most complex formulas come from my https://demonstrations.wolfram.com/TheBoundaryOfPeriodicIteratedFunctionSystems/

Thanks a lot. +1

[joigus]

2 hours ago, Eise said:

I think I must agree with Markus to disagree. The only last possibility I see is to replace the word 'change', when not applied to the flow of time, with another one: maybe 'to vary' will do? Y varies dependent on the variation of x. And the observation that in a few English dictionaries, I always see a reference to time in the 'change'-lemmas.

I'm all in favour of enriching the vocabulary to reflect nuances in what we say. I find no reason for strong disagreement here, as I see it.

But the very fact that you (or I, or anybody) feel the need to use a substitute for "change" into a timeless (but isomorphically related one) "variation", suggests to me that neither of us can escape time, in the representation space of ideas that constitutes language, if we want to convey meaning, even though our thoughts do not appear sometimes as an ordered sequence, but as a tangled web of ideas.

Very interesting (and I think related to what we're talking about here). Listen to Steven Pinker at,

26' 44'':

https://www.youtube.com/watch?v=OV5J6BfToSw

Quote

But what happens when you have to translate your web of ideas into a sentence? Well, now you've got to convert that tangled web into a linear string of words.

There's the rub.

Edited August 4, 2020 by joigus
choice of word

[MigL]

On ‎8‎/‎3‎/‎2020 at 11:31 AM, michel123456 said:

Try it. Put that in numbers & tell me if joigus can put a mirror anywhere in the universe to see himself graduating.

He certainly can't place the mirror...
But if he were to look at a pre-existing mirror 20 light years away, he could ( with suitable technology ), see himself graduating 40 years ago.

Hope I'm not being offensive at estimating your age to be in the 60s, joigus.

[joigus]

1 hour ago, MigL said:

He certainly can't place the mirror...
But if he were to look at a pre-existing mirror 20 light years away, he could ( with suitable technology ), see himself graduating 40 years ago.

Hope I'm not being offensive at estimating your age to be in the 60s, joigus.

I'm 55 actually, actually. But not even at your most polemical, or personal,  are you offensive to me, MigL.

[Markus Hanke]

19 hours ago, michel123456 said:

That corresponds to the concept of the Block Universe, isn't it? Under this concept, everything is already "recorded" and static, and time is the very bizarre effect of reading the information that is already there

The BU concept is kind of related to this, but I am going a step further by saying that information itself requires neither space nor time - these concepts arise only at the point where one attributes context to that information, which requires the imposition of a structure, which generally will be a spatiotemporal embedding. But I say this is an extraneous thing, and not inherent in the information itself.

16 hours ago, joigus said:

Hausdorff dimension. I've sometimes toyed with the idea that fractality may play a part in what conscience, arbitrarily small scales, and in general some of the most intractable problems of science, could need as a framework to be formulated. I wouldn't know what to do with it for the very simple reason that I'm not cut for it. I haven't played much with fractals, or with loop quantum gravity. Somehow it's not me. But that doesn't mean I don't think it's an interesting idea. I will share an intimation here: The very fact that from the basis of mathematics you cannot prove whether there is a cardinality that makes "cardinal, or counting, sense" trapped between the discrete and the continuous, I think could signal to something very fundamental. I also think this connects with @studiot's "obsession" with continuity vs. granularity. It may be precisely because spaces with non-trivial Hausdorff dimension potentially have this kind of algorithmic inaccessibility that they could be very powerful stores of information in finite volumes. I don't know. Just giving you my thoughts here.

Ok, I haven't actually taken it that far  For me, a Hausdorff space simply seems a natural way to think of a complex network such as the brain. Another option would be to think of it as a tensor network that maps inputs (sense data) into outputs (brain states? specific behaviours?). Whether or not spacetime itself can be modelled as some kind of Hausdorff space is another matter, albeit an interesting one. It reminds me of a model called Causal Dynamical Triangulations - one result of this model is that, while spacetime has the usual (3+1) dimensions on large scales, it reduces to just 2D with a fractal geometry on small scales. I don't know too much about this model, but it's an interesting concept.

17 hours ago, Eise said:

I think I must agree with Markus to disagree. The only last possibility I see is to replace the word 'change', when not applied to the flow of time, with another one: maybe 'to vary' will do? Y varies dependent on the variation of x

Fair enough, but I'd put it the other way around - 'to vary' inevitably implies a process (and thus time) to me, whereas 'change' does not. But that's just convention

15 hours ago, joigus said:

There's the rub.

Exactly - information vs the embedding of it.