Can a causal or time-like structure emerge without assuming a metric?

[Dale]

Would you like it if I answered via the same info but in my less prfessional way of talking/speech?

100%. Without any doubt or hesitation.

 

[robphy]

@OmniThoughts Please don't post chatbot output here. If any of us wanted to have a conversation with a chatbot then we would just ask them directly.

Probably off-topic, how would one even type an em-dash in the forum software?

 

[renormalize]

I just asked the chatbot to refine my findings into a more professional and much less verbose way to answer the question. Would you like it if I answered via the same info but in my less prfessional way of talking/speech?

@OmniThoughts, by joining this forum you agreed to abide by all the rules stated here:

Thread 'Physics Forums Global Guidelines'

Sep 2, 2003

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Application and...

• Greg Bernhardt
• Replies: 2
• Forum: Feedback and Announcements

• 

In particular:
ChatGPT and AI-generated text

• Posting AI-generated text without attribution is categorically disallowed and will lead to a warning and an eventual permanent ban with continued use.
• Answering a science or math question with AI-generated text, even with attribution, is not allowed. AI-generated text apps like ChatGPT are not valid sources.

Simply put, AI generated answers are explicitly prohibited here. So yes, please formulate your posts using your own words.

 

[OmniThoughts]

Yes a causal or timelike structure can occur without assuming a metric because of the network of relations via cause and effect, since interactions cause propagations from a source at natural speed-limit speeds, and the leave traces that can be observed and measured which enables us to be able to figure parts of the related causal order, it happens/happened naturally no matter if measuring-capable existences exist/existed or never exist/existed.

Everything happening in space sends out energy that travels to us, which/that proves those events happened exactly "when and where" they did. It's proven due to because energy from exploding stars and spinning stars arrive at exact times matching the "however long" distances they traveled. And the energy from the start of the universe caused the galaxies to be where they are today.

Supernova 1987A is an example of the timing of our detectong neutrinos three hours before we saw the light and both the neurinos and the light traveled 168,000 years, without needing to be "observed in order to happen". Pulsars send out energy like clockwork and match general relativity’s predictions to the nanosecond, which proves non-local time is happening without needing to be "observed in order to happen". Galaxies' shapes and locations are the results of how they formed from energy left over from like the beginning of the universe, the galaxies already exist which implies that whatever events caused their shapes/locations/formations happened billions of years ago without needing to be "observed in order to happen".

 

[renormalize]

Yes a causal or timelike structure can occur without assuming a metric because of the network of relations via cause and effect ...

OK, this is a response to the OP's original question about the possible structure underlying classical spacetime. But you then write:

... the galaxies already exist which implies that whatever events caused their shapes/locations/formations happened billions of years ago without needing to be "observed in order to happen".

which reads like a version of the question "Does the moon exist when no one is looking at it?", sometimes raised in debates about the role of the observer in quantum mechanics. Can you be more explicit about how and why this is relevant to the OP's interest in pre-metric structure in classical relativity?

 

[PeterDonis]

the network of relations via cause and effect, since interactions cause propagations from a source at natural speed-limit speeds, and the leave traces that can be observed and measured which enables us to be able to figure parts of the related causal order

How is this different from a Lorentzian metric?

 

[OmniThoughts]

I answered the question with "Yes a causal or timelike structure can occur without assuming a metric because of the network of relations via cause and effect, since interactions cause propagations from a source at natural speed-limit speeds, and leave traces that can be observed and measured which enables us to be able to figure parts of the related causal order, it happens/happened naturally no matter if measuring-capable existences exist/existed or never exist/existed.”, but I got a little off-topic with the rest where I was going on about whether observation is necessary for stuff to be/occur.

 

[OmniThoughts]

How is this different from a Lorentzian metric?

I was simply saying that causal structure is via the universe's natural activity and such exists/occurs independent of any metric we try to impose.

 

[renormalize]

I was simply saying that causal structure is via the universe's natural activity and such exists/occurs independent of any metric we try to impose.

The natural activity you describe is indeed direct empirical evidence for the existence of a Lorentzian metric on spacetime, from which causality then logically follows. But that's not what the OP is asking about. Instead, they want to know if there is a theoretical way to derive that metric from some simpler, pre-existing causal structure. As far as I can see, your empirical observations in no way address that second question.

 

[OmniThoughts]

The natural activity you describe is indeed direct empirical evidence for the existence of a Lorentzian metric on spacetime, from which causality then logically follows. But that's not what the OP is asking about. Instead, they want to know if there is a theoretical way to derive that metric from some simpler, pre-existing causal structure. As far as I can see, your empirical observations in no way address that second question.

I would think that that would be like trying to figure out what circumstances (regarding circumstances captured in a still photo) are supposed to result (from the still photo's circumstances) from what's happening in a still photo. One wouldn't be able to know unless sufficient extent/parts of the universe's natural laws/rules are known beforehand and can be utilized to do such a prediction or figuring out, and even then it might only be able to be known that way if the universe actually does temporally progress deterministically.

The natural activity you describe is indeed direct empirical evidence for the existence of a Lorentzian metric on spacetime, from which causality then logically follows. But that's not what the OP is asking about. Instead, they want to know if there is a theoretical way to derive that metric from some simpler, pre-existing causal structure. As far as I can see, your empirical observations in no way address that second question.

The natural activity you describe is indeed direct empirical evidence for the existence of a Lorentzian metric on spacetime, from which causality then logically follows. But that's not what the OP is asking about. Instead, they want to know if there is a theoretical way to derive that metric from some simpler, pre-existing causal structure. As far as I can see, your empirical observations in no way address that second question.

I would think that that would be like trying to figure out what circumstances (regarding circumstances captured in a still photo) are supposed to result (from the still photo's circumstances) from what's happening in a still photo. One wouldn't be able to know unless sufficient extent/parts of the universe's natural laws/rules are known beforehand and can be utilized to do such a prediction or figuring out, and even then it might only be able to be known that way if the universe actually does temporally progress deterministically.

 

[PeterDonis]

I was simply saying that causal structure is via the universe's natural activity and such exists/occurs independent of any metric we try to impose.

We don't "impose" a metric. We figure out what it is by looking at "the universe's natural activity" and the causal structure it implies. So what you're basically saying is, we know the metric because we know the metric. Which doesn't address the question being discussed in this thread at all.

 

[PeterDonis]

I would think that that would be like trying to figure out what circumstances (regarding circumstances captured in a still photo) are supposed to result (from the still photo's circumstances) from what's happening in a still photo.

No, because we don't just have one "still photo" of observations. We observe things happening over the course of time. So time is part of what we observe.

 

[DavidMartin]

Could we come back to the sens of my question and ignore the emerging remaining ?

Let me restate the core question more concisely.

Suppose one starts with a directed relational structure 𝑅(𝑎,𝑏) that is not assumed to be transitive or acyclic.

Are there known mathematical results characterizing when such a structure can induce a genuine partial order (i.e. acyclic and transitive), without postulating that order from the outset?

In other words: is there a known mechanism by which a non-symmetric relation can become an order relation?

 

[renormalize]

Suppose one starts with a directed relational structure 𝑅(𝑎,𝑏) that is not assumed to be transitive or acyclic.

Are there known mathematical results characterizing when such a structure can induce a genuine partial order (i.e. acyclic and transitive), without postulating that order from the outset?

Yes, as I tried to point out to you back in post #8, namely the theory of causal sets.
Rafael Sorkin has authored a readable review of these so-called causets in his article: Causal Sets: Discrete Gravity. Let me quote a few excerpts from that paper to hopefully encourage you to read through it to see if and how it addresses your questions:

(Do note, however, that Sorkin's binary relation $\prec$ is postulated from the outset to be transitive, but not reflective.)

 

[DavidMartin]

Yes, as I tried to point out to you back in post #8, namely the theory of causal sets.
Rafael Sorkin has authored a readable review of these so-called causets in his article: Causal Sets: Discrete Gravity. Let me quote a few excerpts from that paper to hopefully encourage you to read through it to see if and how it addresses your questions:
View attachment 369573
View attachment 369574
(Do note, however, that Sorkin's binary relation $\prec$ is postulated from the outset to be transitive, but not reflective.)
View attachment 369576
View attachment 369577

I’m not asking whether partial orders can model spacetime (as in causal sets), but whether they can emerge from non-order relations ?

 

[robphy]

This might be of interest:

E. H. Kronheimer & R. Penrose (1967) "On the structure of causal spaces"
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 481 - 501
DOI: https://doi.org/10.1017/S030500410004144X

Peter Szekeres (1991) "Signal spaces—an axiomatic approach to space-time"
https://www.semanticscholar.org/paper/Signal-spaces—an-axiomatic-approach-to-space-time-Szekeres/2e5912578d6f4d56aeff34d567e7257f4d02f73f
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 355 - 363
DOI: https://doi.org/10.1017/S0004972700029191

Did you look at the Szekeres "Signal Space" reference?
His S relation is reflexive, but not symmetric.

That seems close in spirit to what I’m asking about — although in that framework the S relation itself is still taken as primitive.

My question is whether there are approaches where even that non-symmetric signal/causal relation arises from something more primitive, rather than being postulated axiomatically.

So, can you specify by what you mean by "something more primitive" than Szekeres' signal relation S which "is reflexive, but not symmetric"?

What specific mathematical structures
are you looking for that are more primitive than one [reflexive, non-symmetric] relation?

 

[DavidMartin]

I don’t mean metaphysically fundamental — I mean structurally weaker.

Szekeres’ signal relation is already assumed to satisfy certain axioms (e.g. reflexivity and other order-like properties). What I’m wondering about is whether one can start with a weaker structure — for example:


• a directed graph (i.e. a binary relation with no assumed transitivity or acyclicity),
• or even a weighted directed relation,


and ask under what conditions such a structure could give rise to a genuine partial order.


I’m looking for results where order-theoretic properties (transitivity, acyclicity) are derived rather than assumed.

 

[robphy]

I don’t mean metaphysically fundamental — I mean structurally weaker.

By the way, how you do type that dash ? I can't find it on my keyboard.

 

[DavidMartin]

By the way, how you do type that dash ? I can't find it on my keyboard.

Type two hyphens (--) it generaly convert to em dash. I use that format in Visual Studio editor and .md files.

 

[robphy]

Type two hyphens (--) it generaly convert to em dash. I use that format in Visual Studio editor and .md files.

I use -- in Microsoft Word and it converts to the em-dash there.
But how do you do it with this website's interface in Chrome or Edge?
Or do you use another browser?

 

[DavidMartin]

I usually draft in Markdown as well and paste it in.

Back to origin :

Suppose we have a directed weighted relation and define a stability condition that suppresses cycles.
Under what conditions would transitivity appear as a stable configuration?

 

[DrGreg]

I use -- in Microsoft Word and it converts to the em-dash there.
But how do you do it with this website's interface in Chrome or Edge?
Or do you use another browser?

If you are using Windows, place your text cursor where you want to type, then summon the Emoji Keyboard by pressing Windows+period, then scroll down to find the Symbols section.

 

[renormalize]

Suppose we have a directed weighted relation and define a stability condition that suppresses cycles.
Under what conditions would transitivity appear as a stable configuration?

This would happen whenever your stability condition (acyclicity?) forces the transitive closure of your general binary relation $R\,$, i.e., $R\rightarrow R^{+}$. See: https://en.wikipedia.org/wiki/Transitive_closure.

 

[martinbn]

Back to origin :

Suppose we have a directed weighted relation and define a stability condition that suppresses cycles.
Under what conditions would transitivity appear as a stable configuration?

What is the motivation for all these questions?

 

[robphy]

Back to origin :

Suppose we have a directed weighted relation and define a stability condition that suppresses cycles.
Under what conditions would transitivity appear as a stable configuration?

Although this has some overlap with causal structure and relativity,
your specific questions are more about the mathematics rather than physics.
So, I think a continued discussion on these specific questions is better suited for a mathematics forum,
not here on this relativity forum.

(The references that I provided earlier are from my literature search on
some attempts at the foundations of causal structure. But I am no longer active in that aspect.)

 

[DavidMartin]

Although this has some overlap with causal structure and relativity,
your specific questions are more about the mathematics rather than physics.
So, I think a continued discussion on these specific questions is better suited for a mathematics forum,
not here on this relativity forum.

(The references that I provided earlier are from my literature search on
some attempts at the foundations of causal structure. But I am no longer active in that aspect.)

Thanks robphy makes sense. Thank you for the clarification and the references.
I may follow up on the mathematical side elsewhere.

 

[Dale]

I think a continued discussion on these specific questions is better suited for a mathematics forum

That sounds likely. I know enough to understand and articulate the problem. But I haven’t a clue about actually determining the answer.