joigus

You forget mutation (slow) and recombination (fast). In a billion years almost nothing of your "bloodline" will be left because of mutation and recombination alone (half our bloodline genes on average is discarded every time one of our gametes is produced). One billion years up your (and my) family line all our ancestors were minute eukaryotes swimming around in aqueous solution.

Natural (man-made included) catastrophes and migrations are just another major factor of change, punctuating evolution, mainly acting as filters or local amplifiers, introducing a bottleneck effect. "Founder effect" it is called.

But you're right in your conclusion. (Grand)^N-children (N representing the number of generations in a billion years) will probably look nothing like us and won't look nearly as cute as we do in a family picture.

1 billion years is the domain of so-called deep time.

10 hours ago, swansont said:

Any notion that gravity can be replaced by electrostatics is trivially debunked, because there's no way to get an always-attractive force between more than two bodies.

Forget my suggestion. This is much better, and so simple. +1

47 minutes ago, Strange said:

The green ones are correct(ish) for the German and Swedish (the root is, presumably, something like and[e]r-) but that has no connection to the Romance/English words.

Yeah, you're right. Now that I think of it, not in French/Italian/Spanish. -ence, -enza, -encia are common morpheme endings, and loosely equivalent to "quality of". OTOH, änd sounds more lexical than functional, while -rung/-ring seem to be function marks, or morphemes. It's the sequence fer-enc fer-enz vër-änd för-änd (that sound so similar) that threw me off.

The -fer-/-vër/-ffer- I think you got totally right from Latin fero. As you say, "to carry".

I never thought that Romans took loan words from Latin. +1 When you think about it, it's quite natural.

Anyway, from what I gather, old Indoeuropean peoples don't seem to have been overly concerned about the difference between change in time and static differences. Or maybe some root has been lost or not identified as yet.

1 hour ago, MigL said:

So, we're all in agreement then ?
The problem is with our common definition of 'change' ?

I was right all along, again.
( I don't know, is that the right emoticon for a 'smug, smart-ass' ? )

 

Either that or we're all equally clueless. So don't be smug just yet.  

Don't think for a moment I'll forget you're the one who set me on a time travel.    I think that's because you think I trashed Fermi, which is not true.  Fermi is one of my heroes. Anyway...

Let's picture maths as an old grandma who never makes a processing mistake, but is totally neutral about the input. It just doesn't even cross her mind to doubt your premises. She only gives you information correlated to whatever mistakes are intrinsic to your language. Good input --> good output; bad input --> bad output.

I think we shouldn't hurry to dismiss bad or meaningless (or perhaps, conflicting) output as totally worthless. 

IOW, garbage in, garbage out, as they say. I think it was Fermat who said that maths is like a mill that gives you good or bad flour depending on the quality of the grain you put in. My suggestion is: Let's not throw away bad output (or input). Let's analyze it.

We all share the same fundamentally incurable disease: We live within a time. It is just not given to us to think outside of time. We need sequential thinking. We must do A, then B. Or perhaps B, then A. Grandma maths has no problem with that. She can handle A and B at the same time. We visit her and tell her that we've come up with something called "quantum mechanics", and she starts crunching numbers and operators. After a while she comes back with the answer. We take a look at it and it's full with "topological frustrations", and references to them, all of them around the funny "concepts",

\[\frac{1}{2}\left(AB-BA\right)\]

and,

\[\frac{1}{2}\left(AB+BA\right)\]

The commutator and the anti-commutator. Something very funny happens around these two concepts. They somehow represent the limits of our language in terms of "first A, then B". Those are the two references in trying to overcome the fundamental limitation that is inherent to our language and gives back singularities, limitations, or topological obstructions if you will, in terms of our alphabet of A and B. It is very telling to me that this fundamental splitting of the world comes in the alphabet of mathematical operations that can be understood as trying to make our operations simultaneous in the representation space of the world.

33 minutes ago, MigL said:

I was being facetious, Studiot.

I do admit that when I first brought up the subject ( Jul 28 ), I was possibly over emphasizing the 'observer', while I should have placed more emphasis on the fact that the ( spatial-temporal ) observer is the source of the word, and definition, of 'change'.
The fact that time has such a large and profound effect on our consciousness, and very existence, is the reason the concept of time is ingrained in our language.
It makes discussing the absence of time a little difficult.

+1. Maybe even impossible.

2 hours ago, studiot said:

Let us use the example "What is considered the ideal female form ?"

This varies from location to location and ethnic group to ethnic group.

It has also changed at one location / ethnic group over time. The models of Rubens were plumper than the models of today.

Now I think I can safely tell you that you're on a very slippery slope.

Interesting linguistic discussion. Here's a clumsy (and totally unreliable, mind you) attempt on my part at finding cognates for the concepts we're talking about.

change          difference (English)

changement différence (French)

cambio           differenza (Italian)

änderung       vëränderung (German)

cambio           diferencia (Spanish)

ändring           förändring (Swedish)

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

In Spanish there is "andar", which means "to walk". The green ones are probably just wrong. The red and blue ones I'm more confident that may betray semantic connections.

Not at all sure that this attempt at finding cognates means anything at all. I'm just pointing out that they all sound similar to a layman in linguistics like myself. I've been trying to find reliable cognates for "to change" and "to differ" in proto-indoeuropean, but haven't been successful so far. I'm totally out of my depth.

Puzzingly enough, in Latin there is a very clear word for change in time, which is mutatio, and has no lexeme in common with any of the above. I'd be very interested in the Greek version from @michel123456. Although this is spilling over into other fields very quickly.

I'm still suffering a bit of jet lag from the time travel you got me into. I'll try to react to that later.

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

7 hours ago, michel123456 said:

Maybe the most interesting thread of this Forum so far. It looks like the philosophy section is the most civil of all. Here we can disagree & continue the discussion, very nice.

+1. You just got one thing wrong: This is a physics forum. Although eventually it may be subject to change.

I agree that there's nothing you can do by arguing against. So here's an idea, although there is a risk that it might backfire.

You learn just enough about the mumbo jumbo of the supposed theory and get back to them with information that it has been confirmed. You must put on your best performance at this point. Once you get them all excited about how their beloved theory has been confirmed by a high-precision experiment, you reveal to them that you've made it all up and say something to the effect of: You see? You can believe anything!

It's not about proving or disproving the theory. When people think like that they couldn't care less. It's about making obvious how gullible they are, showing to them how fragile their belief system is.

Once a classmate attending an EM class came late and asked me if they had missed anything important in the class. I told them that the teacher had just reported that a new equation of electromagnetism had just been found: The fifth Maxwell equation. It worked!!

It should have been two more equations..., but never mind.

42 minutes ago, Duda Jarek said:

The difficulty comes with the continuous limit, but there are many hydrodynamical QM-like phenomena (like Casimir, Aharonov-Bohm, interference, tunneling, orbit quantization) - slides with links: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

There are at least two things connecting with this that I think are worth mentioning. There may be more, but there's only so much one can say.

1) Is the path to building a well-defined unitary S matrix the only sensible approach to quantum field theory? Aren't we leaving out important substance if we use the |in> and |out> unbounded Hilbert space as representation space for all phenomena? Actually I think many physicists are aware of this.

2) Grivov's ambiguity and a proper study/classification of topological sectors. What possible physical variables are (or may be) hidden behind the humongously big arbitrariness that gauge invariance doesn't let us see in the formalism because they don't appear in the gauge-invariant quantities? Are there missing variables to be described in what is normally described as "gauge junk"? Could there be that what we usually throw in the garbage bin has some meaningful invariants in it?

The more likely solution I see for the wave-particle duality of elementary particles is that what we see as quantum formalism is only dealing with the propagating factor of a more complete state that involves as a co-factor a topological Lagrangian that codifies in it the "only particle" aspect and, by suitable hypotheses, can be statistically correlated to the evolution of the linear wave in some kind of à la Bohm solution.

That's what I like to think when the lights go off.

There are other very interesting off-topic subjects in the link that you provided. Thank you.

3 hours ago, Duda Jarek said:

time ordering is required for performing calculations, but just to understand time/CPT symmetry it is sufficient to imagine e.g. history of the Universes as the result of ensemble of all possible Feynman diagrams throughout this history ... for unification with general relativity it should include ensemble of shapes of spacetime, what leads to infinity which is too large for standard renormalization techniques.

Assembling different space-times makes me much more uncomfortable, but that's just me. It's far over my head.

On 8/3/2020 at 9:38 AM, Duda Jarek said:

General relativity at least in theory allows to directly perform T symmetry by non-time-orientable spacetime.

For example imagine wormhole which glues like in Klein bottle - traveling through it should apply T or P symmetry.

<image>

 

Very nice point. +1. That's more or less what I had in mind when I said T, P (as Markus said, not C) as coming from some kind of homotopy or diff. transformation.

5 hours ago, joigus said:

with the ordering prescription given by,

<image>

Sorry, I didn't make it clear, although I'm sure you know. These diagrams represent the momentum space.

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.

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.

6 hours ago, Markus Hanke said:

So another technical question to you @joigus: when calculating the Dyson series in order to get to a S-matrix, how does one know the correct order of the terms?

I'm a bit hazy about this, because it's been a while. There's a lot that has to do with prescriptions you adopt just because you want your fields to propagate causally. After some investigation, you find out that your Fourier expansion of the fields must contain both,

\[e^{-ip_{\mu}x^{\mu}}\]

and,

\[e^{ip_{\mu}x^{\mu}}\]

with the ordering prescription given by,

which amounts to prescribing the "positive energies" to propagate forwards in time, and the "negative ones" to propagate backwards. I don't think this is a big deal: After all, you're interpreting what you energy-dimensional parameter E is doing in your physics.

So far you're kind of forcing your amplitudes to behave causally (microcausality). If you do all that, you get amplitudes that commute outside of their causal cones (anti-commute, if they're fermions):

\[\left[\varphi\left(x\right),\varphi\left(x'\right)\right]=i\delta^{\left(3\right)}\left(\boldsymbol{x}-\boldsymbol{x}'\right)\]

provided that,

\[\left(x-x'\right)^{2}<0\]

(depending on signature criterion). Then you proceed to solve Heisenberg's evolution eq. in the Dirac or interaction picture.

\[\varphi_{\textrm{int}}=e^{-iH_{\textrm{int}}t}\varphi e^{iH_{\textrm{int}}t}\]

Then you substitute this expression into the Heisenberg evolution equation in the Dirac picture and discover that the solution must include the time ordering given by Dyson's formula:

\[\varphi_{\textrm{int}}\left(t\right)=\left[T\exp\int_{0}^{t}dt'H\left(t'\right)\right]\varphi_{\textrm{int}}\left(0\right)\]

So far, so good. It's complicated, you have implemented what you know about the world, as well as used the room that the quantum formalism gives you to represent the states (change picture to a unitarily equiv. one). The really weird step, IMO, comes now. If you try to expand this as a Fourier series in harmonic oscillators, you have an infinite sequence of differently-ordered powers of creation and annihilation operators, so you (again, IMO) kind of pull a rabbit out of a hat by re-defining your formal series as,

\[:\varphi_{\textrm{int}}\left(t\right):=:\left[T\exp\int_{0}^{t'}dt'H\left(t'\right)\right]\varphi_{\textrm{int}}\left(0\right):\]

The colon-bracketing means that everything that has differently-ordered power of creators and annihilators, is re-ordered so that all the creators are to the left (and conv. for the annihilators). When you do that, you don't end up with the same operator. It's a different one!

Then comes the use of Wick's theorem, by using the vacuum state. The re-ordering that you've imposed proves now very useful, because the annihilators to the right kill the vacuum, so that you remove a lot of junk. I think, or vaguely remember, that the steps are justified.

This is not the way most people learn QFT. In the old days people invested a lot of time in understanding the gradual steps. Today, everything is considered justified and people tend to jump as swiftly as possible to Feynman diagrams, so they can do calculations.

I just want to add (and sorry for a lengthy and perhaps obscure explanation) that in order to rigourously get to Feynman graphs, there are quite many (mainly combinatoric) steps farther ahead. Basically you must remove over-counting due to your re-ordering, because, obviously, when you identify expressions like,

\[a^{\dagger}aa^{\dagger}\]

and,

\[aa^{\dagger}a^{\dagger}\]

with,

\[:a^{\dagger}aa^{\dagger}:=:aa^{\dagger}a^{\dagger}:=a^{\dagger}a^{\dagger}a\]

you must keep track of how many times this last term appears by re-ordering operators.

Sorry for such a lengthy attempt at an answer, I may not have been very helpful. Take it just as an appetiser, and feel free to ignore it. Sorry if you know many of these things.

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

I suppose my succinct answer to your question would be: Dyson's time ordering appears to me as quite natural, because it's a step for you to make your solution formally satisfy the evolution eq. But steps come later that, although immensely useful and allegedly "rigorous" by many people, do present fuzzy areas, at least to me. I'd love to understand them better.

For me it's a work in progress, maybe a lifetime-long project, to get to understand the fundamentals satisfactorily enough.

PD: Both @Duda Jarek and you have made comments about topology that I think are very interesting and point in the direction that I would like the theory to go. AAMOF, it was Gerard 'tHooft, Polyakov, among others, one of the first pioneers to try to develop a more geometric language for QFT. I can't say that's the ticket, but it sounds to me like a much more promising scope.

Other things are going on in QFT. Have you guys heard of MHV amplitude calculations? It's a very quickly-developing subject.

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

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.

3 minutes ago, Eise said:

Yes. And I think compatibilism accounts for both views. Your talents, chances you have in your life, cultures in which you grow up determine who you are. But that has no impact on the compatibilist conception of free will: because that is about what you want (determined by all kind of external and internal factors), and the possibility to act according it.

OK, Eise. I must tell you I don't find in the least diminishing to use some time to get to understand Dennett's thinking better. There are many gradients of meaning here that are taking me some time to understand. I don't have good ears, but I'm restless.

If, after all, it takes me about three months to get a consistent picture of it, it will be time well spent. A good investment of my time, I would say. And I will have mostly you to thank for that. Some people find disagreement spiteful. I don't. It's a fertile ground, when your interlocutor makes sense. And you do.

Panta rhei

That's in the nature of things.

Changes require adaptations, which bring about further changes, which require further adaptations.

Were it football, I would be worried, if I cared about football at all.

Education is different. It was there millenia before football, and it will be there long after football becomes a hazy memory.

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

Just now, michel123456 said:

I do.

I'm all ears.

19 hours ago, andsm said:

Really, misread it, sorry. So you not expressed your belief here, not towards realism or towards idealism.

That was very honest. +1

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.

I'd go with option 2 as the most demographically significant. But I agree with Strange that 1 would probably be very popular among conspiracy nuts. If I were allowed, I'd pick something like a 40 % 60 %, fifty-fifty or the other way.

The reason is that people tend to look at the past with the strangest mixture of incredulity and gullibility. Example: It is impossible that an ancient society like the Egyptians 5000 y.a. were able to build the pyramids (incredulity), therefore some alien civilization must have made it (weird, weird gullibility).

When things are happening before your eyes, so to speak, I think it's more difficult to be gullible against the facts.

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.

2 hours ago, Markus Hanke said:

Question to you, [...] - is there some version of the CPT theorem that holds in curved spacetime QFTs as well? I don’t see how it could be possible, since in general curved spacetimes there won’t be any time-translation symmetry.

Very good question. +1 A quick scan of,

https://books.google.es/books/about/The_Global_Approach_to_Quantum_Field_The.html?id=-LtutgAACAAJ&redir_esc=y

(The Global Approach to Quantum Field Theory, Volume 1

By Bryce Seligman DeWitt)

Allows you to find only a couple of paragraphs where space and time inversions are introduced on a coordinate-patch basis. Nothing like the predictive power and generality of CPT in flat space-time is suggested. For all I can remember, the context where CPT is really powerful is the S-matrix approach. And defining assymptotic states in a curved space time is problematic, to say the least.

Searches on other more modern books, or on Quantum Field Theory in Curved Space-Times, also by Brice DeWitt, haven't produced anything that remotely resembles "CPT". Not even mentioned AFAIK.

I do not think there is anything like CPT valid for curved ST that is remotely as robust as it is in flat ST. But I would be very thankful if anybody knows.

This is very interesting, because it connects with my question following up on a suggestion by you on the thread about "What is time?"

Would you have some licence to consider signature-preserving continuous transformations that re-shuffled the space-time coordinates, of which our T, P transformations were a discrete version?

Just now, andsm said:

Really, misread it, sorry. So you not expressed your belief here, not towards realism or towards idealism.

OK. Not that it's interesting to anybody, but I was raised in a Catholic country, and had to do away with a lot of cultural/religious/mythical/ceremonial baggage. I tend to mistrust my own opinions very often; let alone other's. I did that at a very high price. The brain can be a crook. It likes to show to you pleasing landscapes. It likes to prove you right. It also tends to have you accept propositions just because they will make you fit in socially, or stand out. I don't trust the brain's inertial forces.

I suppose I'm just a runaway from belief towards degrees of certainty.

Just now, andsm said:

I may not know your beliefs, but I can see that you wrote. And you wrote that Unverse existed long before observers. And here you expressed your beliefs. Such vision, that Universe exists independent of observers, have name realism. It is not scientifically proved, so it is not knowledge, it is belief. If you disagree that realism is belief, I would be interested to know when realsim was proved.

That's not what I said.

Here's what I said:

46 minutes ago, joigus said:

Universe did a pretty nifty job of looking as if it had existed long before any intelligent observers were around.

Can you read it now? Take some time. Read it twice, three times, if necessary.

1 minute ago, andsm said:

These is your philosophical beleif. You believe in realism, and believe that Universe exists independent of observers.

If my theory wrong, we live in Universe based on subjective idealism, and realism is wrong. My theory even can be, in principle, tested for predictions. So, question of that is true, realism or idealism, can be verified. 

Note - the subjective idealism can be directly derived from my theory. So, while you express your beliefs,  the question can be considered based on scientific method.

You believe too much with too little evidence. AAMOF, you believe I believe something. Not only that; you go on to assert it, as if you were privy to my mental states. You couldn't be farther from knowing how I form my opinions. Which goes to prove that you give too much value to your beliefs.

I don't to mine. Neither I do to yours.

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.***

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* 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.