What is time? (Again)

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On 7/14/2020 at 10:51 PM, jajrussel said:

I have always liked this question. The challenge seems to be in being as succinct as possible, and leaving no doubt that as defined it is not a Philosophy, so for the umpteenth and hopefully final time, I’ll try again. 🤔

Time is a physical dimension where all aspects defined by an observer reveal a rate of change.

Okay, what do you mean by "physical" and "dimension". For the first term are you making reference to our everyday intuitions about the permanent existence of matter around us (such as chairs, the floor, air) and what particle physics has to say on what exists or constitutes objects. By the latter term are you making use of a mathematical definition of the concept of "dimensions" or is this something other than that. "where all aspects", so is this the equivalent of taking in the greater environment of the universe and from that happening to find a consistent rate of change upon which other processes can be compared to?

On 7/15/2020 at 12:58 AM, Eise said:
On 7/14/2020 at 9:56 PM, The victorious truther said:

Physicists should care whether their exists time without change as this would seem to influence what sorts of quantum gravity/spacetime they are desiring to investigate (background independent vs. dependent).

I think every science has periods of reflection on their basic concepts. But the need for that should normally come from, in this case,  the physicists themselves. If they get stuck in the progress of understanding of nature, if they are confronted with anomalies or inconsistencies in (or better between) their theories, or get stuck in trying to encompass more phenomena in one single theory, it is time to reflect on what they are doing, which includes reflecting on fundamental concepts they use, like time. Some might feel the urge earlier than others (justified or not). Compare with two different 'cultures' in physics concerning QM: there is the camp of 'shut up and calculate', and look at what technology was developed on that basis! On the other side there is the camp that asks fundamental questions, e.g. the Bell theorem and experiments that are based on it. For the shut-up-and-calculators such experiments seem to be at most interesting, but of no use. But look what happened afterwards: from there we have now quantum cryptography, maybe one day we will have useful quantum computers.

So I would say: just give physicists time (pun intended).

I believe they are called instrumentalists or operationalists, those you would call the "shut up and calculate" crowd of physicists. Much of the literature i've read on the subject of the concept of "mass" in physics has also been seen with a large changes due to the fact that special relativity with it's rest mass/relativistic mass come into interpretational conflict with inertial mass in classical physics as you may wonder if either of those masses themselves are the same as the inertial concept newton initially gave.

On 7/15/2020 at 11:48 PM, Markus Hanke said:
On 7/11/2020 at 4:57 PM, The victorious truther said:

Those who were proponents of material/physical change being above time/space (perhaps even making it non-existent or its structures mere abstractions) go under the label of spacetime relationism. Those who are proponents of the distinction of change to time or the existence of time without change  (check out the original Sydney Shoemaker thought experiment) went under the label of substantivalists.

How about if space and time are simply methods of the mind to structure information? Essentially, the mind takes certain raw data and uses this to continuously construct a model of reality, which we then become aware of as an object of consciousness. It is difficult to imagine what such a mental model could look like without some method to introduce spatial relationships and causal structure between its constituent parts. In that view, spacetime is quite real, just not necessarily as an attribute of the ‘world an sich’ (to paraphrase Kant, not that I necessarily agree with all his ideas), but rather as a function of the mind - which, interestingly, is itself part of the created model.

Ahhh Kant, wonderful that somebody else has heard of his anti-realism strategy towards spacetime philosophy. Though, in reality it's intriguing to wonder how far you can strip reality of these properties of either space or time such that reality remains rather coherent. Perhaps at the base there is a sense of whether one object coincides with another or whether they overlap but that the metrical components of spacetime are more or less emergent. Think of an affine geometry in which there is no fundamental metrical notion aside from acknowledging that one thing is larger than another and the possibility of assigning metrical notions given a presumed base length being arbitrarily specified.

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23 hours ago, michel123456 said:

In this case, how do you explain space expansion & time dilation?

Well, even if space and time were organisational principles by the mind, that wouldn’t imply that those principles need to be Euclidean. What we already know about physics would of course remain valid, it’s just that they are no longer merely statements about an external world. In essence, it would mean that our physics are what they are not because of some deep physical reason, but because they reflect the structure of the observer’s mind, being a construct of and by it. The mind itself would be a constraint on what worlds are possible, and on how these options can differ.
Don’t get me wrong, I am not making any claims nor do I wish to introduce any alternative models. The comment was merely meant as something that is perhaps worth pondering. I am just not sure that the “me-world” duality really is as clear cut as might appear. What the details of this would - or could - look like, I don’t really know.

10 hours ago, The victorious truther said:

Ahhh Kant, wonderful that somebody else has heard of his anti-realism strategy towards spacetime philosophy.

Actually, I haven’t  I don’t know much about what philosophy as a discipline has to say on those things, though I do intend to rectify that in the near future. For the moment, I am just in the habit of pondering such questions myself, based on my own physics knowledge and the phenomenology of my own mind, which I am also in the habit of observing very carefully. So these are my own thoughts; if I am taking on a particular philosophical stance, be it Kantian or someone else’s, then that is not by design, but rather by accident.

10 hours ago, The victorious truther said:

Though, in reality it's intriguing to wonder how far you can strip reality of these properties of either space or time such that reality remains rather coherent.

Yes, that’s the question, isn’t it?
But I think specifically with time, it can be taken quite far. We initially started off with Newtonian time, which is an absolute background to everything that happens. People once thought this notion to be so fundamental that it requires no further consideration. Later the paradigm shift to relativistic physics happened, and suddenly time became purely local, and thus relative, albeit still an essential ingredient. Then quantum mechanics came along, and time lost its central status; it also turned out that on those scales physics are no longer fully local in the classical Einsteinian sense. This can be somewhat alleviated by combining the two latter models into quantum field theory, but of course the property of entanglement remains, not just between states (which are relative), but more importantly with the algebras of observables. Lastly then, going one step further into hypothetical models of quantum gravity, there are examples of models where both space and time completely loose their ontological status as fundamental entities. For example, in Loop Quantum Gravity, spacetime is not a fundamental entity, it emerges only on larger scales from the dynamics of the model (though it is yet to be shown that it reproduces the correct semi classical limit). So we have arrived at a situation where we describe the world without making any reference to space nor time, which are taken to be emergent quantities on larger scales only; the fundamental entities of the model are not themselves of a spatiotemporal nature, nor do they require - or indeed even permit - any a priori spacetime background.
I am just bringing up LQG as an example here, I am not saying it is a correct or physically useful model of quantum gravity. But it does demonstrate that it is possible in principle at least to write down a coherent description of the world without explicit reference to space and time as fundamental entities.

10 hours ago, The victorious truther said:

Think of an affine geometry in which there is no fundamental metrical notion aside from acknowledging that one thing is larger than another and the possibility of assigning metrical notions given a presumed base length being arbitrarily specified.

A manifold does not necessarily need to be endowed with a metric. It is indeed possible to meaningfully work with non-metric manifolds, which is what the discipline of differential topology does. Most relevant tensorial quantities and operations can be defined without any reference to a metric, all you need is a connection. It is in fact surprising just how much one can actually do without the presence of a metric! However, it is of course not possible to introduce any notion of measurement on such manifolds, as you rightly point out.

Edited by Markus Hanke
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On 7/17/2020 at 9:27 PM, The victorious truther said:

Ahhh Kant, wonderful that somebody else has heard of his anti-realism strategy towards spacetime philosophy.

'Anti-realism'? Not quite. Kant is a 'grand synthesis' of empiricism (all knowledge comes through the senses') and rationalism (the only way to understand reality is by reason).

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On 7/18/2020 at 12:54 AM, Markus Hanke said:

Actually, I haven’t  I don’t know much about what philosophy as a discipline has to say on those things, though I do intend to rectify that in the near future. For the moment, I am just in the habit of pondering such questions myself, based on my own physics knowledge and the phenomenology of my own mind, which I am also in the habit of observing very carefully. So these are my own thoughts; if I am taking on a particular philosophical stance, be it Kantian or someone else’s, then that is not by design, but rather by accident.

If I recall it was Kant who, through his transcendental idealism, attempted towards interpreting space/time as such by supposing that it was required for our cognitive understanding of the greater reality but that it did not exist separate from our cognitive faculties.

On 7/18/2020 at 12:54 AM, Markus Hanke said:

Yes, that’s the question, isn’t it?
But I think specifically with time, it can be taken quite far. We initially started off with Newtonian time, which is an absolute background to everything that happens. People once thought this notion to be so fundamental that it requires no further consideration. Later the paradigm shift to relativistic physics happened, and suddenly time became purely local, and thus relative, albeit still an essential ingredient. Then quantum mechanics came along, and time lost its central status; it also turned out that on those scales physics are no longer fully local in the classical Einsteinian sense. This can be somewhat alleviated by combining the two latter models into quantum field theory, but of course the property of entanglement remains, not just between states (which are relative), but more importantly with the algebras of observables. Lastly then, going one step further into hypothetical models of quantum gravity, there are examples of models where both space and time completely loose their ontological status as fundamental entities. For example, in Loop Quantum Gravity, spacetime is not a fundamental entity, it emerges only on larger scales from the dynamics of the model (though it is yet to be shown that it reproduces the correct semi classical limit). So we have arrived at a situation where we describe the world without making any reference to space nor time, which are taken to be emergent quantities on larger scales only; the fundamental entities of the model are not themselves of a spatiotemporal nature, nor do they require - or indeed even permit - any a priori spacetime background.
I am just bringing up LQG as an example here, I am not saying it is a correct or physically useful model of quantum gravity. But it does demonstrate that it is possible in principle at least to write down a coherent description of the world without explicit reference to space and time as fundamental entities.

Though, substantivalist time is similar in nature to a form of physical change that isn't entirely impeded by arbitrary physical relations. Think of the Sydney Shoemaker thought experiment of time without change in which despite the fact that no physical change is occurring there still seems to be an un-impeded (immaterial) external clock that ticks along at the same interval of years as measured by physical clocks in a non-frozen universe but not effected by this law-like freezing. The thing here is that in any of these situations we are not ignoring the fact that it's physical objects and the changes in their properties/relations which give rise to the rather abstract models of time or spacetime structure that were entertained by Einstein and Newton. I'd be more concerned with trying to strip the abstractions of time away but not loose site of the fundamental change inherent here.

On 7/18/2020 at 12:54 AM, Markus Hanke said:

A manifold does not necessarily need to be endowed with a metric. It is indeed possible to meaningfully work with non-metric manifolds, which is what the discipline of differential topology does. Most relevant tensorial quantities and operations can be defined without any reference to a metric, all you need is a connection. It is in fact surprising just how much one can actually do without the presence of a metric! However, it is of course not possible to introduce any notion of measurement on such manifolds, as you rightly point out.

What i'm concerned with then is a more general perspective on physical objects than special relativity itself gives. Special relativity goes in a relatively good direction with it, under certain interpretations, champing the fact that there is no known physical mechanism that allows for universal simultaneity let alone the specification of an immutable universal clock across the universe (ignore global time slices in GR here).  Not only that, there is a strong dependency of the change of objects relative to others perhaps making such a theory more amenable to those of a relationist guise. I've linked a Jstor paper on this which gets the gist of what my perspective is.

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6 hours ago, The victorious truther said:

If I recall it was Kant who, through his transcendental idealism, attempted towards interpreting space/time as such by supposing that it was required for our cognitive understanding of the greater reality but that it did not exist separate from our cognitive faculties.

Though, substantivalist time is similar in nature to a form of physical change that isn't entirely impeded by arbitrary physical relations. Think of the Sydney Shoemaker thought experiment of time without change in which despite the fact that no physical change is occurring there still seems to be an un-impeded (immaterial) external clock that ticks along at the same interval of years as measured by physical clocks in a non-frozen universe but not effected by this law-like freezing. The thing here is that in any of these situations we are not ignoring the fact that it's physical objects and the changes in their properties/relations which give rise to the rather abstract models of time or spacetime structure that were entertained by Einstein and Newton. I'd be more concerned with trying to strip the abstractions of time away but not loose site of the fundamental change inherent here.

What i'm concerned with then is a more general perspective on physical objects than special relativity itself gives. Special relativity goes in a relatively good direction with it, under certain interpretations, champing the fact that there is no known physical mechanism that allows for universal simultaneity let alone the specification of an immutable universal clock across the universe (ignore global time slices in GR here).  Not only that, there is a strong dependency of the change of objects relative to others perhaps making such a theory more amenable to those of a relationist guise. I've linked a Jstor paper on this which gets the gist of what my perspective is.

Thanks, I will need some time to read this paper, before I can formulate a meaningful reply.
But I don’t really understand where the argument is going, because the thought experiment implies the notion of time without change (which seems trivially true to me), and at the same time it is clear that you can have change without any notion of time. So the relationship between time and change is at best described as a correlation, but it is not causative nor an identity in the ontological sense.

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18 hours ago, Markus Hanke said:

Thanks, I will need some time to read this paper, before I can formulate a meaningful reply.
But I don’t really understand where the argument is going, because the thought experiment implies the notion of time without change (which seems trivially true to me), and at the same time it is clear that you can have change without any notion of time. So the relationship between time and change is at best described as a correlation, but it is not causative nor an identity in the ontological sense.

It's not that it's trivially true only that it conceptually possible whether it really is the case that all physical processes could halt and there still be a sense of time tick along without recourse to any physical thing thats a part of the universe. I wouldn't describe as correlation but rather as an abstract relation between two different but similar (perhaps the same) concepts of time which seems to be abstraction of imperfect physical change and the change of objects themselves which can be rather chaotic but also predictable. Change and time should be purely descriptions of what physical objects/relations/fields do but not what is (ontologically).

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5 hours ago, The victorious truther said:

Change and time should be purely descriptions of what physical objects/relations/fields do but not what is (ontologically).

I think this very much depends on how you define “time”. In the context of physics it is what clocks measure, and it is also a geometric property of the macroscopic universe. Mathematically speaking it is no problem to have empty vacuum spacetimes (they are valid solutions to the gravitational field equations), so you can have time without any process of change happening.

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2 hours ago, Markus Hanke said:

so you can have time without any process of change happening

But can you have change without time?

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9 hours ago, michel123456 said:

But can you have change without time?

Depends how you define change, but I would say yes.

Transformation is not the only type of change.

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21 hours ago, michel123456 said:

But can you have change without time?

Sure why not? Mathematically, instead of having quantities that change with respect to some time coordinate, you can always have quantities that change with respect to one another, without reference to any notion of time. ‘Change’ doesn’t imply time, and time doesn’t imply change. Derivatives (in the calculus sense) with respect to some quantity other than time are well defined and commonly used.

For example, imagine you have a purely 3D universe, without time, that contains a tea cup. The handle of the cup has a certain curvature; the interior surface of the cup also has curvature, which is probably numerically different. So the surface curvature changes with respect to spatial coordinates, rather than time. So you have a universe that encompasses changes, but no time. This is perfectly consistent and valid, at least in my mind

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9 minutes ago, Markus Hanke said:

Sure why not? Mathematically, instead of having quantities that change with respect to some time coordinate, you can always have quantities that change with respect to one another, without reference to any notion of time. ‘Change’ doesn’t imply time, and time doesn’t imply change. Derivatives (in the calculus sense) with respect to some quantity other than time are well defined and commonly used.

For example, imagine you have a purely 3D universe, without time, that contains a tea cup. The handle of the cup has a certain curvature; the interior surface of the cup also has curvature, which is probably numerically different. So the surface curvature changes with respect to spatial coordinates, rather than time. So you have a universe that encompasses changes, but no time. This is perfectly consistent and valid, at least in my mind

Nice example +1

A little milk but no sugar in my tea please.

Edited by studiot
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8 minutes ago, studiot said:

Nice example +1

A little milk but no sugar in my tea please.

You got it
That being said, our hypothetical tea cup system here is a stationary system, since nothing else is possible in a 3D universe. Meaning, if the cup is empty, it cannot ever be filled, since that would necessarily require a change with respect to some coordinate other than a spatial one. This would be a pretty boring universe

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14 minutes ago, Markus Hanke said:

You got it
That being said, our hypothetical tea cup system here is a stationary system, since nothing else is possible in a 3D universe. Meaning, if the cup is empty, it cannot ever be filled, since that would necessarily require a change with respect to some coordinate other than a spatial one. This would be a pretty boring universe

I thought it was one of those mythical cups of Old Ireland that are always full (though of wine).

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I my mind for change to appear you need a before/after relation.

In the spatial tea cup example,  how do you change spatial coordinates? Or how do you hover over the cup in order to notice the curve change?

On 7/22/2020 at 11:22 AM, Markus Hanke said:

You got it
That being said, our hypothetical tea cup system here is a stationary system, since nothing else is possible in a 3D universe. Meaning, if the cup is empty, it cannot ever be filled, since that would necessarily require a change with respect to some coordinate other than a spatial one. This would be a pretty boring universe

You can even say that the cup cannot have been created, it was always there. It is a mathematical cup-universe in which nothing can happen.

I have even the gut feeling that mathematics have inherently time inside it. How can you make any calculation without time?

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On 7/17/2020 at 3:27 PM, The victorious truther said:

Okay, what do you mean by "physical" and "dimension". For the first term are you making reference to our everyday intuitions about the permanent existence of matter around us (such as chairs, the floor, air) and what particle physics has to say on what exists or constitutes objects. By the latter term are you making use of a mathematical definition of the concept of "dimensions" or is this something other than that. "where all aspects", so is this the equivalent of taking in the greater environment of the universe and from that happening to find a consistent rate of change upon which other processes can be compared to?

😊 It appears you do want a  philosophical conversation. Why would you consider anything that is, or is not  corporeal, to be permanent, nothing stays the same. Why should it be any different for time? I suppose it could depend on the observers preference. It appears to me that original philosopher/scientist dealt with both.

I don’t see myself as an expert of either... I recently casually watched a video where the opinion seemed to be that  Minkowski threw a wrench into physics, that Einstein picked the wrench up, and time hasn’t been the same since.

I suppose that anyone can have as many different definitions of time as Einstein’s views of relativity seem to allow for. In a sense time went from a somewhat rigid  unit system dimensionally to one that exist for each individual on a sliding curve. As an individual time for me doesn’t change except that as an observer I can see that for you it does. We can now agree to disagree about observed differences.

As an individual I kinda like the sliding curve applied to time though some might not approve of my application. It is now time for me to take my meds...  technically, a little over an hour ago. 🙁

Edited by jajrussel
I thought about clarifying, but didn’t.
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On 7/22/2020 at 9:58 AM, Markus Hanke said:

Sure why not? Mathematically, instead of having quantities that change with respect to some time coordinate, you can always have quantities that change with respect to one another, without reference to any notion of time. ‘Change’ doesn’t imply time, and time doesn’t imply change. Derivatives (in the calculus sense) with respect to some quantity other than time are well defined and commonly used.

For example, imagine you have a purely 3D universe, without time, that contains a tea cup. The handle of the cup has a certain curvature; the interior surface of the cup also has curvature, which is probably numerically different. So the surface curvature changes with respect to spatial coordinates, rather than time. So you have a universe that encompasses changes, but no time. This is perfectly consistent and valid, at least in my mind

Fine point, very precise and illuminating. +1

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.

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57 minutes ago, michel123456 said:

I my mind for change to appear you need a before/after relation.

Hello michel123456:

As Studiot said, it depends on how you define change, and Markus is careful to initially put quotation marks around that word before he gives an example. And when you say "in your mind", you are offering nothing more than another definition.

57 minutes ago, michel123456 said:
1 hour ago, michel123456 said:

In the spatial tea cup example,  how do you change spatial coordinates? Or how do you hover over the cup in order to notice the curve change?

Strictly speaking, Markus never said anything about changing the spatial coordinates; he said the curvature changes with respect to different spatial coordinates.

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1 hour ago, michel123456 said:

I have even the gut feeling that mathematics have inherently time inside it. How can you make any calculation without time?

Do you know I have this same gut feeling? I would love to discuss this point, whenever you have the time.  +1

I'm currently involved in a discussion with a mathematician friend of mine who says it doesn't. I, on the contrary, always have the feeling that in mathematics there's always a sequence of operations, if nothing else, which foreshadows time. Doesn't it?

He says no, and I'm not convinced.

Edit: That not to mention the concept of probability on a purely mathematical basis, which I think is heavily impregnated with a notion of time by construction.

Edited by joigus
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6 minutes ago, joigus said:

Do you know I have this same gut feeling? I would love to discuss this point, whenever you have the time.  +1

I'm currently involved in a discussion with a mathematician friend of mine who says it doesn't. I, on the contrary, always have the feeling that in mathematics there's always a sequence of operations, if nothing else, which foreshadows time. Doesn't it?

He says no, and I'm not convinced.

Edit: That not to mention the concept of probability on a purely mathematical basis, which I think is heavily impregnated with a notion of time by construction.

If it is true that aĺl concepts have time inherent in their  creation and out working then  can it be said that the time involved in making measurements ,such as that between moving frames of reference is a different , kind of time?

Time as it applies to spatial measurements....

The former kind of time is perhaps more elemental (or just unrelated to the latter)

Maybe it is subjective time?

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2 minutes ago, geordief said:

If it is true that aĺl concepts have time inherent in their  creation and out working then  can it be said that the time involved in making measurements ,such as that between moving frames of reference is a different , kind of time?

Time as it applies to spatial measurements....

The former kind of time is perhaps more elemental (or just unrelated to the latter)

Maybe it is subjective time?

Well, I may be wrong. Maybe this notion I have that time is inevitably present in anything we say, even in formal mathematics, is somehow misled. In some demonstrations, e.g., two different results of previous lemmas used in order to prove a theorem could be used in sequence but in interchangeable order. So there may be many flaws or grey areas to what I'm saying.

But, if that were verifiable in some sense; namely, that no matter what kind of logical/mathematical argument you make, you cannot help that your concept of time has some bearing on it, contaminates it, then it could well be that time itself is a formidable obstacle to formulate any system of ideas in complete (all encompassing) and completely consistent (free of contradictions) way.

IOW, it could be that you can "solve the world" except for this nagging presence of a sequencing parameter that we call time, because it's a constraint of conscience itself, not because it's an especially important (distinguished) variable of the universe. This connects roughly with some comments that @Markus Hanke has made before.

I wouldn't go as far as to distinguish a "logical time" and a "reference frame" time. That would be uneconomical to say the least.

As to "subjective time"... Well, we must agree that the perception that time goes the same way consistently (in orientation at least) for everybody involved is pretty persuasive.

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3 hours ago, vexspits said:

he said the curvature changes with respect to different spatial coordinates.

Nice point +1

On this subject it is more subtle than at first appears.

I think someone has already attributed to Wheeler the quotation

Quote

Time is what prevents everything happening at once.

although that quotation is actually older than Wheeler.

(There is an interesting coresponding quote on space in the linked article)

Now for there to be a cup, all the parts (handle, bowl, base etc) all have to happen all at once.

It is the archetypal 'block universe' where all parts of the universe happen or exist, even when the 'focus' is not upon them.

So the 'change' can be thought of as a comparison of the properties (eg curvature) from once place to another.

So we can compare the curvature of the handle to that of the bowl and draw the conclusion that it must exceed the curvature of the bowl since it goes round the outside of the bowl.

Time is not needed or involved in this comparison.

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18 hours ago, joigus said:

Do you know I have this same gut feeling? I would love to discuss this point, whenever you have the time.  +1

I'm currently involved in a discussion with a mathematician friend of mine who says it doesn't. I, on the contrary, always have the feeling that in mathematics there's always a sequence of operations, if nothing else, which foreshadows time. Doesn't it?

He says no, and I'm not convinced.

Edit: That not to mention the concept of probability on a purely mathematical basis, which I think is heavily impregnated with a notion of time by construction.

You're welcome.

I have to admit that I am quite surprised because the last time I suggested that time could  inherently be inside mathematics I was hit by Zeus thunderbolt.

14 hours ago, studiot said:

Now for there to be a cup, all the parts (handle, bowl, base etc) all have to happen all at once.

It is the archetypal 'block universe' where all parts of the universe happen or exist, even when the 'focus' is not upon them.

So the 'change' can be thought of as a comparison of the properties (eg curvature) from once place to another.

So we can compare the curvature of the handle to that of the bowl and draw the conclusion that it must exceed the curvature of the bowl since it goes round the outside of the bowl.

Time is not needed or involved in this comparison.

IMHO what is described as a "change" is in fact a "difference".

Another example: you walk in the desert an then enter the savanna, then the jungle. You can eventually say that the land changes (like the cup curvature) but what you are describing is not a "change in the environment", what you are describing is yourself traveling.

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34 minutes ago, michel123456 said:

IMHO what is described as a "change" is in fact a "difference".

Yes indeed, that is why I aksed for your definition of 'change'.

Although that merely substitutes defining 'difference' for defining change.

35 minutes ago, michel123456 said:

Another example: you walk in the desert an then enter the savanna, then the jungle. You can eventually say that the land changes (like the cup curvature) but what you are describing is not a "change in the environment", what you are describing is yourself traveling.

Your example suggests to me that you have not picked up my point.

Sorry that point is very important but also very difficult to describe/define.

Since I have not succeeded in providing enough clarity I will try again.

The desert, savannah etc could have separate existance, each in their own right.

As you move, they could also be changed (wink into and out of existence) like a Hollywood set.

So they are different from a cup which is only  a cup when all the parts are present together.

A handle is not a cup, a base is not a cup, a bowl is not a cup etc.

But thank you for the continued discussion.

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19 hours ago, joigus said:

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

Well, what you have defined here is an interval between two points on a differentiable manifold. Of course you can interpret this quantity as ‘time’ in some sense (ref the usual maths of GR), but I don’t think that is a necessary, sufficient, or even obvious conclusion. In the physics sense, time is what clocks measure, and unfortunately in a 3D universe no physical clock can ever measure $$ds^2$$, because all physical clocks are stationary and extended objects, just like the tea cup; ie. their world lines are equal to their spatial embedding. This quantity is thus simply a spatial distance in 3D.

Also, in our own normal universe (but not in 3D of course), you have physically realisable world lines for which $$ds^2=0$$; does this imply that no time exists? Obviously not - a photon still propagates at a well defined speed and momentum - so there is a notion of change - even though no proper time elapses for it. So I wouldn’t equate this quantity with time in a general sense (even though it can sometimes be useful to do so), and definitely wouldn’t draw conclusions from it as to the existence of time.

19 hours ago, vexspits said:

Markus never said anything about changing the spatial coordinates; he said the curvature changes with respect to different spatial coordinates.

Indeed - for precisely the reasons pointed out

19 hours ago, joigus said:

I, on the contrary, always have the feeling that in mathematics there's always a sequence of operations, if nothing else, which foreshadows time. Doesn't it?

You mean there is a sequence of operations in doing maths? That is of course true, but that sequence isn’t inherent in the structure of maths, at least not in my opinion.
Consider for example the two statements

$y(x)’=y(x)$

and

$y(x)=ae^x +C$

Of course one can - and frequently will - construct a sequence of statements in between these, i.e. solve the equation analytically. However, in structural terms, these two statements about y(x) are exactly equivalent. It’s simply two formally different ways to make the same statement about y(x). So there is no notion of ‘sequence’ or ‘time’ inherent in the maths themselves - only in the process of formally showing the equivalence with pen and paper, which is a different thing altogether. Both of the above statements are true simultaneously, and are simultaneously equivalent.

Edited by Markus Hanke
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1 hour ago, Markus Hanke said:

Well, what you have defined here is an interval between two points on a differentiable manifold. Of course you can interpret this quantity as ‘time’ in some sense (ref the usual maths of GR), but I don’t think that is a necessary, sufficient, or even obvious conclusion. In the physics sense, time is what clocks measure, and unfortunately in a 3D universe no physical clock can ever measure ds2 , because all physical clocks are stationary and extended objects, just like the tea cup; ie. their world lines are equal to their spatial embedding. This quantity is thus simply a spatial distance in 3D.

Well, I was going for minimal conditions for a time to be possible to define (from a purely mathematical POV, so no operationalism, no clocks at this stage). Another example to add to the ones you provide in which this technique wouldn't quite work are chaotic systems, because for chaotic systems there aren't nearly enough integrals of motion to reduce the dynamics to a clear trajectory that can be pictured as an implicit relation between your dynamical variables of which a one-parameter could be deduced. To me, once you have defined (in clear-enough cases) this one parameter that suggests to you a sequencing of events, you still have the enormous freedom to choose which particular parametrization corresponds to your clocks, how different sets of clocks relate to one another, etc.

1 hour ago, Markus Hanke said:

Also, in our own normal universe (but not in 3D of course), you have physically realisable world lines for which ds2=0; does this imply that no time exists? Obviously not - a photon still propagates at a well defined speed and momentum - so there is a notion of change - even though no proper time elapses for it. So I wouldn’t equate this quantity with time in a general sense (even though it can sometimes be useful to do so), and definitely wouldn’t draw conclusions from it as to the existence of time.

That would be problematic if one photon were the only thing that exists in the universe (you could always define an affine parametrization for a photon which is what people do to describe the geodesic equation for photons, but the interpretation of such parameter as a time is another matter). In the scenario that I'm talking about, there are more things, and the coordinates of the photon could in principle be included in the aforementioned implicit equations fi(xmatter,pmatter,xphoton,kphoton)=0, so a one-parameter sequencing for the whole system would be possible to define.

Now, on the proviso that this sequencing can serve as the minimal condition for a time to be definable, and taking into consideration your caveats about clocks (the question would be pending of what re-parametrization of this emergent parameter to use so that it corresponds to our physical clocks), there's still the subtle matter that it's defined from a metric or pseudo-metric. And these are always based in physics on quadratic forms, and thereby you must chose an orientation for the sequencing parameter to run along.

1 hour ago, Markus Hanke said:

You mean there is a sequence of operations in doing maths? [...]

Here I think you took me a little bit too seriously. Mind you, I said:

20 hours ago, joigus said:

Well, I may be wrong. Maybe this notion I have that time is inevitably present in anything we say, even in formal mathematics, is somehow misled.

So I was more cautious than you seem to suggest, and just expressing a feeling. This feeling has been seeded through many moments when studying physics, but the strongest one by far is QFT. In QFT you start from very neatly defined state operators in terms of a given coordinate time, write down the Heisenberg evolution equation, and formally solve it in terms of creation and annihilation operators in momentum space. Because Dyson's formula imposes on you a time ordering, you get a sequence of products. For one of these terms, e.g.:

$a\left(a^{+}\right)^{2}aa^{+}a^{3}a^{+}a$

What's the next thing you do before you engage in any calculation at all? Well, you re-define your exact solution to be "better represented" by the normal ordering:

$:a\left(a^{+}\right)^{2}aa^{+}a^{3}a^{+}a:\overset{{\scriptstyle \textrm{def}}}{=}\left(a^{+}\right)^{4}a^{6}$

If nothing else, to me, that very strongly suggests that there's something deeply problematic about time. It may be possible that sequencing of concepts might have consequences, logical consequences, that we simply cannot get rid of within our present system.

I'm not saying that every mathematical statement we make has time impregnated in it, but I'm saying that it may well be that we are quite incapable of totally escaping the non-trivial consequences of having a sequential language.

Don't pay too much attention to what I'm saying. Maybe I'm just sounding people out about my deepest intellectual insecurities, that's all.

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