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

Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
56 replies · 8K views
OmniThoughts said:
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.
 
Physics news on Phys.org
Dale said:
@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?
 
OmniThoughts said:
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:
Greg Bernhardt

Thread 'Physics Forums Global Guidelines'

Welcome to Physics Forums!

In an effort to maintain the integrity of this site and to provide a comfortable environment for people to communicate, we ask that you please follow these Guidelines when posting on this site. These guidelines are global and apply to every area of this site. Mentors may choose to enact specific guidelines for individual forums, which are to be taken as an extension to the global guidelines when posting and visiting that specific forum. These specific guidelines are usually sticky topics placed at the top of the specific forum.

Application and...
  • Like
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.
 
Reply
  • Like
  • Informative
Likes   Reactions: Motore, Dale and PeroK
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".
 
Last edited by a moderator:
OmniThoughts said:
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:
OmniThoughts said:
... 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?
 
Reply
  • Like
Likes   Reactions: PeroK and Motore
OmniThoughts said:
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?
 
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.
 
PeterDonis said:
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.
 
OmniThoughts said:
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.
 
renormalize said:
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.
renormalize said:
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.
renormalize said:
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.
 
OmniThoughts said:
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.
 
OmniThoughts said:
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.
 
Could we come back to the sens of my question and ignore the emerging remaining ? :smile:

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?
 
DavidMartin said:
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:
1770969763421.webp

1770969835086.webp

(Do note, however, that Sorkin's binary relation ##\prec## is postulated from the outset to be transitive, but not reflective.)
1770969982423.webp

1770970037843.webp
 
renormalize said:
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 said:
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

DavidMartin said:
robphy said:
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?
 
Last edited:
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.
 
DavidMartin said:
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.
 
robphy said:
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.
 
DavidMartin said:
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?
 
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?
 
robphy said:
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.

1771085668232.webp
 
DavidMartin said:
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.
 
Reply
  • Like
Likes   Reactions: PeroK and Dale
DavidMartin said:
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?
 
DavidMartin said:
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.)
 
robphy said:
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.
 
Last edited:
robphy said:
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.