What is time? (Again)

[joigus]

I think @Markus Hanke has made an observation that is just pure genius. All of us, except @MigL have overlooked it.

I'll bring it up to your attention ASAP and come back and try to take up the gauntlet he's thrown.

Edit1: I'll bring it back to your attention. Maybe it was just me who wasn't paying attention.

Edit2: Maybe it was just I. Dammit!!

57 minutes ago, studiot said:

Granularity v continutity.

Very interesting. Now I understand much better, because you've brought this up before and I wasn't sure I completely understood.

Edited July 31, 2020 by joigus
Self-correction/self-explained

[studiot]

17 minutes ago, joigus said:

Very interesting. Now I understand much better, because you've brought this up before and I wasn't sure I completely understood.

You might find this book from Cambridge University very interesting

https://www.amazon.co.uk/Space-Time-Canto-Classics/dp/1107641683#reader_1107641683

This question (and others) is discussed in some detail by world famous experts.

 

So which of Markus' pearls have we missed?

Edited July 31, 2020 by studiot

[joigus]

1 hour ago, Strange said:

yes, I am thinking of the Time Cube guy

I was completely unaware of this. Thank you for opening that door into the weird for me. Sometimes I feel like I'm continually losing my innocence. I like to think that's a good thing.

47 minutes ago, studiot said:

So which of Markus' pearls have we missed?

Here it is:

21 hours ago, Markus Hanke said:

P.S. Very interesting discussion so far, fair play to everyone  But wait...the real fun starts when we raise the stakes a little - what happens when we have a universe that consists of only time dimensions, e.g. a (0+3)-dimensional universe? And would you believe it when I said that such a universe might be entirely indistinguishable from a (3+0)-dimensional one

I'm a little bit confused by the naught. But... Maybe Hanke was trying to make a further point that went over my head.

I would rather say. Would a (-1,+1,+1,+1) universe be in any sense distinguishable from a (+1,-1,-1,-1), or a (-1,+1.-1,-1), etc.? Or signature-changing: (-1,+1,+1,+1) What makes the sign so special? And the particular parameter/coordinate that represents it? You can actually continually re-parametrize it and nobody would be any the wiser.

This principle of indifference is whispering to our ear: Isn't there a fundamental decision about which coordinate in this continuum is the "selected" time for whatever characteristic determines what conscience is? And if so, which one is it?

It must be one of them.

And if not, if there is not a fundamental decision, what is it that makes the "special coordinate" so special in an inevitable way? A reshuffling of the basis entitles me in principle to decide that it's x that represents time in my mapping. x is x because I say so. x doesn't mean anything. It's just a mathematical tag. The mathematics speaks very clearly here. Invariance seems to suggest the opposite: There's nothing special about the time coordinate you pick, except it must be the only one with that sign in the metric.

47 minutes ago, studiot said:

You might find this book from Cambridge University very interesting

https://www.amazon.co.uk/Space-Time-Canto-Classics/dp/1107641683#reader_1107641683

This question (and others) is discussed in some detail by world famous experts.

Looks appetising. Thank you.

Edited July 31, 2020 by joigus
correct mistake in sign

[joigus]

1 hour ago, joigus said:

Or signature-changing: (-1,+1,+1,+1) 

Sorry. I meant, obviously: (+1,-1,-1,-1). I hope I wasn't too confusing.  

[Ghideon]

9 hours ago, joigus said:

<joke>

You can add your own. For example:

There's something spacial about being special

</joke>

I'm in group H:

H: The lazy group: not investing enough time to post anything of value, but having enough time to study and learn from the other members' interesting contributions.

 

Note regarding language:

9 hours ago, Eise said:

correct language

That points at one reason why I find it tricky to contribute to this interesting discussion. I checked translation of "change" and its actual meaning* in Swedish; it seems to (implicitly) include time; If I say "change" in Swedish the definition, AFAIK, means change as time passes. 

Using the example from @studiot I get the point and I can follow the arguments but I can't express my views using the word "change" as a translation from Swedish.

Maybe I could say that without time the colour still "switch", "shift", "alternate", "fluctuate" or "vary" in the circle? I'm not sure which word, if any, that is best.

By the way, this is a version of the drawing where the colour "changes" (hopefully the animation works):

This is not an attempt at finding flaws in studiots example. I just use it to highlight my view: the original question "What is time" is really hard for me to discuss due to the way various languages and words "works"; I end up trying to analyse the meaning of the words instead of thinking about an answer. Maybe others have the same experience? 

 

*)  SAOB – a comprehensive historical dictionary published by the Swedish Academy, covering the entire modern Swedish period from 1521 onwards https://www.saob.se/in-english/

 

 

Edited July 31, 2020 by Ghideon
grammar

[geordief]

42 minutes ago, Ghideon said:

I'm in group H:

H: The lazy group: not investing enough time to post anything of value, but having enough time to study and learn from the other members' interesting contributions.

 

Note regarding language:

That points at one reason why I find it tricky to contribute to this interesting discussion. I checked translation of "change" and its actual meaning* in Swedish; it seems to (implicitly) include time; If I say "change" in Swedish the definition, AFAIK, means change as time passes. 

Using the example from @studiot I get the point and I can follow the arguments but I can't express my views using the word "change" as a translation from Swedish.

Maybe I could say that without time the colour still "switch", "shift", "alternate", "fluctuate" or "vary" in the circle? I'm not sure which word, if any, that is best.

By the way, this is a version of the drawing where the colour "changes" (hopefully the animation works):

This is not an attempt at finding flaws in studiots example. I just use it to highlight my view: the original question "What is time" is really hard for me to discuss due to the way various languages and words "works"; I end up trying to analyse the meaning of the words instead of thinking about an answer. Maybe others have the same experience? 

 

*)  SAOB – a comprehensive historical dictionary published by the Swedish Academy, covering the entire modern Swedish period from 1521 onwards https://www.saob.se/in-english/

 

 

From memory (perhaps flawed) the first words in the Bible are "first was the word " (logos in Greek)

Whilst disapproving of the Bible in general I have been fascinatied by this mise en scene..(if correct)

It may be relevant to your apparent trouble with language and the idea it attempts to express.

Maybe we are all more prisoner than we imagine of the languages we have learned and by expanding our vocabulary we can unearth meanings we did not imagine we there to be discovered. 

 

Even so some meanings may just not be available  to express and they may just "fall through the cracks"

Time may be one of those concepts that is just too fundamental  (and wears too many "disguises")  for all its characteristics to be able to be expressed in words

One of its disguises  is the scientific usage most of us are familiar with (I am not familiar  with its usage in quantum mechanics,which may be good for my sanity)

[studiot]

10 hours ago, Ghideon said:

Using the example from @studiot I get the point and I can follow the arguments but I can't express my views using the word "change" as a translation from Swedish.

Maybe I could say that without time the colour still "switch", "shift", "alternate", "fluctuate" or "vary" in the circle? I'm not sure which word, if any, that is best.

By the way, this is a version of the drawing where the colour "changes" (hopefully the animation works):

Absolutely works. Smart. +1

 

I have never suggested that change and time are not connected in some cases.

All that I have been saying is that time is not necessary for change.

Equally Change is not necessary for time.

Sometimes (pun intended) we monitor our gauges over time and wish to record 'no change' or 'zero change' .

[Markus Hanke]

21 hours ago, Strange said:

Isn't that like saying you have to imagine reading all the digits of pi to know what its value is?

Nice point  I never thought of this.

20 hours ago, joigus said:

I would rather say. Would a (-1,+1,+1,+1) universe be in any sense distinguishable from a (+1,-1,-1,-1), or a (-1,+1.-1,-1), etc.? Or signature-changing: (-1,+1,+1,+1) What makes the sign so special? And the particular parameter/coordinate that represents it? You can actually continually re-parametrize it and nobody would be any the wiser.

Exactly, you got it  What distinguishes time from space in the metric signature is only the fact that they have opposite sign - whether the sign itself is plus or minus is arbitrary. My original (3+0)-dimensional tea cup universe had metric signature {+,+,+} OR {-,-,-}...a purely time-like (0+3)-dimensional universe would have a metric signature of {-,-,-} OR {+,+,+). Hence, their metric would be precisely identical. In theory at least, unless I am overlooking something, these universes should be indistinguishable, at least geometrically. Crucially, in both cases they are static and stationary - so not only is change<>time (IMHO), but also time<>change.

13 hours ago, Ghideon said:

If I say "change" in Swedish the definition, AFAIK, means change as time passes.

Interesting...this isn’t really true in German though, at least not directly. There are, in fact, two nouns for ‘change’ - Änderung, which is the concept of non-homogeneity, of something having different attributes as a comparative relationship; and then there is Veränderung or Abänderung, which is the process of making something different. Only the latter has a connotation of implying time, at least in my opinion.

 

[joigus]

14 hours ago, Ghideon said:

(hopefully the animation works):

It does. I'm getting dizzy.  

14 hours ago, Ghideon said:

I'm in group H:

H: The lazy group: not investing enough time to post anything of value, but having enough time to study and learn from the other members' interesting contributions.

We all want to have one foot on that group, I think. But, as Newton once said (or so they say he said), you become a prisoner of what you've said.  

[geordief]

21 minutes ago, joigus said:

 

But, as Newton once said (or so they say he said), you become a prisoner of what you've said.  

That is how Churchill quit smoking ,the story goes.

Once he said he was quitting he had little choice.

[joigus]

5 minutes ago, geordief said:

That is how Churchill quit smoking ,the story goes.

Once he said he was quitting he had little choice.

Maybe it's a British thing.  

[geordief]

9 minutes ago, joigus said:

Maybe it's a British thing.  

There was Titus Oates  as well 

""I am just going outside and may be some time"

https://en.m.wikipedia.org/wiki/Lawrence_Oates

Edited August 1, 2020 by geordief

[joigus]

8 minutes ago, geordief said:

""I am just going outside and may be some time"

I'm glad you mentioned time. We're still on-topic.

[geordief]

6 minutes ago, joigus said:

I'm glad you mentioned time. We're still on-topic.

I didn't notice that.

[studiot]

2 hours ago, Markus Hanke said:

Exactly, you got it  What distinguishes time from space in the metric signature is only the fact that they have opposite sign - whether the sign itself is plus or minus is arbitrary. My original (3+0)-dimensional tea cup universe had metric signature {+,+,+} OR {-,-,-}...a purely time-like (0+3)-dimensional universe would have a metric signature of {-,-,-} OR {+,+,+). Hence, their metric would be precisely identical. In theory at least, unless I am overlooking something, these universes should be indistinguishable, at least geometrically. Crucially, in both cases they are static and stationary - so not only is change<>time (IMHO), but also time<>change.

Actually one would be real and one would be imaginary.

Mixed signs (as in our universe) are even more interesting because here the Physicists break the Mathematicians' rule of positive definiteness.

I have prepared some sketches I will put up later with some new thoughts.

 

 

[joigus]

1 hour ago, studiot said:

Actually one would be real and one would be imaginary.

OK. Point taken. But that's just another fiduciary or referential choice. I'm not convinced it's that essential, although it could have consequences.

What I think Hanke is trying to say (maybe clumsily re-phrased by me) is illustrated with this parable:

A very advanced ultra-dimensional civilization makes contact with us. They know we're inquisitive organisms and are very interested in our opinion on foundational questions about physical reality. They somehow develop a code to communicate with us (I'm leaving to them all the hard work). And they ask us: Hi, lot, what does the universe look like for you? Starting with: What dimensions do you see?"

And we say, "well, it'll be difficult to explain what we see, but just for a start, we can see three spacial dimensions and one time dimension for describing change in this four-dimensional universe".

Reply: "Mmmm. That's funny. We see one spacial dimension and three of what you call time dimensions"

They exchange documentation in the form of theories, equations, experimental data, etc. And everything checks. It's only that what we call time, they call radius of a 3-dimensional time around the individual that's perceiving that time; and vice-versa.

Who would be any the wiser about what they are calling time or space? The words "time" and "space" would just be arbitrary tags, mathematical dummies.

I'm leaving the next idea for later.

[studiot]

1 hour ago, joigus said:

I'm leaving the next idea for later.

I'm coming to that.

[MigL]

Who would have thought these advanced beings have the same difficulties defining time as we do.

But seriously, and metric signatures aside, you can't change the rules and imagine the three time dimension (0+3) universe having time behave differently than it behaves in our universe. It still needs to be one way only, and allow interaction with only the local now, as opposed to our spatial dimensions, which allow more degrees of freedom and interaction at a distance.

If we consider no spatial dimensions and one of time, the space-time diagram would consist of one axis, the event would be a point on that axis. and its world line would describe a line segment along that axis.
Similarly, no spatial and three time dimensions would allow that event, still just a point as it has no spatial extent, to move along three separate time axis, and so describe a curved, or three dimensional, line segment. Still moving only forward ( one way ) along each axis, but the requirement for interaction at a distance is gone as there are no interactions ( or distance ).
I really don't know what a curved timeline as opposed to a straight timeline implies in those particular universes

 

[joigus]

 

 

6 hours ago, studiot said:

I have prepared some sketches I will put up later with some new thoughts.

Looking forward to it.

2 hours ago, MigL said:

But seriously, and metric signatures aside, you can't change the rules and imagine the three time dimension (0+3) universe having time behave differently than it behaves in our universe. It still needs to be one way only, and allow interaction with only the local now, as opposed to our spatial dimensions, which allow more degrees of freedom and interaction at a distance.

You're probably right. You just can't change the rules. But you can change the names. So, what tells you which one of the four directions is time if you know nothing else? Let us remove any sequential notation that suggests an ordering, like t, x, y, z or a, b, c, d, etc., and make the argument clearer. Let's say your event coordinates are:

\[\otimes,\boxplus,\oplus,\boxtimes\]

Which one is time? If some "angel" told you the metric is:

\[\otimes^{2}-\boxplus^{2}-\oplus^{2}-\boxtimes^{2}\]

It would be clear your time must be \[\otimes\]

But if you were allowed to continuously change to,

\[\otimes^{2}+\boxplus^{2}-\oplus^{2}+\boxtimes^{2}\]

now time would be \[\oplus\]

...

After thinking about it for a while longer, I think you're right, @MigL. I think the mathematical reason has to do with the fact that the Lorentz group splits into 4 disconnected parts,

\[L_{+}^{\uparrow},L_{+}^{\downarrow},L_{-}^{\uparrow},L_{-}^{\downarrow}\]

Only one of them is a group, because it contains the identity transformation.

The up-arrow ones are called orthochronous, and the + and - have to do with space orientation. The only one that can be continuously connected with the identity is the proper orthochronous. So I guess it can't be done. You can't reshuffle time and space, even if you preserve the metric signature.

But it was fun.

Edit: Although GR is different. You can move more freely with coordinate changes. I'd like to know what @Markus Hanke, @Mordred or other experts think about that.

Edited August 1, 2020 by joigus
Addition

[studiot]

3 hours ago, MigL said:

But seriously, and metric signatures aside, you can't change the rules and imagine the three time dimension (0+3) universe having time behave differently than it behaves in our universe. It still needs to be one way only, and allow interaction with only the local now, as opposed to our spatial dimensions, which allow more degrees of freedom and interaction at a distance.

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 shows a block universe, including time. I have only included 2 spactial dimensions (height and breadth) to be able to easily draw it.
 

Since I have 2 spatial dimensions they permit areas so I can think about such concepts as pressure, magnetic flux density etc, and in conjunction with time processes such as magnetic induction.

But there is a twist, depending upon how we regard the times, past present and future.
In a block universe is 'time' Omar Khyam's moving finger that moves through the block universe as a temporal plane called the present ?
If so it is like the focusing device of a scanner.

Yet this temporal plane occupies zero duration (length) in time and its coordinate axes are purely spatial (height and breadth)
So what happens if we are the past and future are inaccessible and throw them away ? We are left with plane that has no time.

I have shown this idea in sketch 3 and a similar one operating on one of the spatial dimensions (height) in sketch 2.

 

What else do we do with coordinate systems ?

Well we look for invariants so we can transform them. So how about the ultimate transformation, doing away with the coordinate system alltogether ?

In Minkowski space the invariant is the interval, symbol S, treating each axes as equivalent, but using Markus sign system.

Each point in a Minkowski space is called an event and I have picked 4 of them and labelled them A, B C and D.

Again for ease of drawing I have reduced the space this time to one temporal and one spatial axis.

Sketch4 shows the result.

Each event has an invariant interval to every other event in the space.
The network formed by all these invariants will be the same in all coordinate systems, by definition.

So we can throw away the coordinate system  -  We don't need it, all the information is contained in the table of S values, presented conveniently in matrix format at the bottom.

So do we need an axis called time?

[The victorious truther]

19 hours ago, studiot said:

I have never suggested that change and time are not connected in some cases.

All that I have been saying is that time is not necessary for change.

Equally Change is not necessary for time.

Sometimes (pun intended) we monitor our gauges over time and wish to record 'no change' or 'zero change' .

It's entirely undeniable that certain physical processes occur (in relation to set unit clocks) and what was investigated in Sydney Shoemakers thought experiment was whether time progressed without their being physical processes. What if every object remained spatially the same distance from each other and retained the same properties would we say that it still makes sense to say that some temporal change occurs despite no physical process alerting us to it? Distinct universal slices both previous and future oriented that look physically exactly the same being distinguished in some unknown manner (by what ever is defined ontologically as time substantially here)? 

I should note again that the thought experiment doesn't rule out nor come into complications with spatial or other change. 

[Markus Hanke]

10 hours ago, studiot said:

So do we need an axis called time?

Very nicely presented, thank you for the time and effort spent on that post! +1 (I’d give more if I could)

The answer is of course no, you don’t need time. Neither do you need space. All you need in order to capture all relevant information/dynamics of the system is a suitable network of relationships, as represented by your S-matrix (which should transform as a tensor). This is intuitively obvious for spacetime and gravity, which is explicitly about relationships between events, entirely independent of how we embed these into a spatiotemporal coordinate system (given some basic conditions). The big question, however, is this - can this be generalised for any physical system or model? In other words, is it conceivably possible to formulate all of physics entirely independently from spatiotemporal embeddings, using a suitable ‘language’ such as (e.g.) tensor networks, algebraic topology, etc?

I have a feeling it just might be. If it is, then we must seriously ask ourselves in what sense space and time can possibly be ontologically fundamental properties of the world.

It is probably obvious by now that I am personally of the opinion that space and time are not fundamental in the sense we usually take them to be; I think they are artefacts of our perception of reality, rather than fundamental properties of reality itself. I think what is fundamental to the ontology of reality are only networks of relationships, which is why I kept going on about that during the discussion on ‘change’. I think it is actually much like functions in mathematics - the fundamental ontology of a function is a relationship between two or more sets; you can then choose to embed these relationships in a spatiotemporal coordinate system of a suitable kind, and draw them as a plot. But the plot is in no way fundamental to the function - only the domain(s) and codomain(s) and their relationships are. The plot is simply a more or less arbitrary way to visualise that information, to embed it spatially, similar to how a computer monitor spatially embeds the non-spatiotemporal information in a computer’s memory banks. Note that such embeddings are not entirely arbitrary though, since the structure of the underlying network constraints (but perhaps not uniquely determines) how it can be represented; so there will be privileged embeddings for specific underlying structures, in terms of how many axis are needed, how they are arranged etc. 

I am hoping that this perhaps translates into physics - for example, it might eventually be possible to show that we perceive the world as (3+1)-dimensional simply because that is the privileged (or perhaps even only possible?) scheme to consistently embed the underlying network of relationships for gravity and electromagnetism, being the two interactions that are directly relevant on our length scale. So the big question then is - is there a single underlying network that is fundamental to reality? What are its nodes, and how can it be described and represented? 

15 hours ago, MigL said:

It still needs to be one way only

There actually seems to be an issue with this. None of the fundamental laws of our universe determine a unique time orientation, except the second law of thermodynamics (the Standard Model is CPT invariant, and GR is T-symmetric). However, because in our (0,3) toy universe there are no spatial degrees of freedom, so there is no consistent notion of entropy in the thermodynamics sense, and hence the second law simply does not exist in this universe (obviously, since there are no ensembles of particles). So even though there is plenty of time here, there is nothing that could pick out a unique ‘future’ direction on any of the axes. There is nothing to even stop ‘future’ and ‘past’ being oppositely oriented on different time axes. Also, the differential equations describing the physics in this universe would contain multiple derivatives with respect to the three time axis, and no spatial derivatives; that makes them elliptical, so what little dynamics there are in this universe would be deterministic, but nonetheless entirely unpredictable. I don’t even see how there could be a consistent notion of causality.

Note also that this universe as a whole, even though it consists of only time, is an entirely static block universe  

[studiot]

27 minutes ago, Markus Hanke said:

The answer is of course no, you don’t need time. Neither do you need space. All you need in order to capture all relevant information/dynamics of the system is a suitable network of relationships, as represented by your S-matrix (which should transform as a tensor).

Thank you for the reply, I considered mentioning an alternative tensor reprentation, but as you may have gathered I don't like tensors or E's notation, preferring the matrix version.
This shows you explicitly many thingsthat the tensor version hides. And these hidden things are just those things people actually using the equations to calculate with or put into a computer want to compute.

 

31 minutes ago, Markus Hanke said:

I have a feeling it just might be. If it is, then we must seriously ask ourselves in what sense space and time can possibly be ontologically fundamental properties of the world.

Have you read Eddington's discussion of the subject and of the consequences of different numbers of dimensions of different types?

[Markus Hanke]

12 minutes ago, studiot said:

Have you read Eddington's discussion of the subject and of the consequences of different numbers of dimensions of different types?

No I haven’t, but it sounds very interesting. Have you got a link or a reference to this?

14 minutes ago, studiot said:

I don't like tensors or E's notation, preferring the matrix version

Really? But what do you do if the object in question is of higher rank or dimension, such as e.g. the rank-4 Riemann tensor? It’d be a bit awkward to write that out as a matrix  

[studiot]

38 minutes ago, Markus Hanke said:

No I haven’t, but it sounds very interesting. Have you got a link or a reference to this?

Eddington wrote two books in the subject, both from Cambridge Univesity Press.
Both are excellent reading. Eddington was a thoughtful man and he shares his thoughts and reasoning.
There were several editions (and revisions) of both books

Get the latest you can.

Mine were 1966 for the first and 1954 for the second (mathematical) one.

First was a smaller more populist volume

Space, Time and Gravitation

An outline of the General Theory of Relativity.

Second was a full blooded mathematical volume

The Mathematical Theory of Relativity.

It is interesting that Einstein published several populist books but kept his mathematics for papers.

I have attached four pages from Eddington's Mathematical Theory.

The place where he introduces the locked interval (your relationships) idea is marked on book page 10