Fundamental Physics: Difference between revisions
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File:Final state.png | The final state of the hypergraph after applying the rule many times | File:Final state.png | The final state of the hypergraph after applying the rule many times | ||
</gallery> | </gallery> | ||
[[File:Rewriting Events.png|thumb| | [[File:Rewriting Events.png|thumb|437x437px|The individual rewriting events in the application of <nowiki>{{x, y}, {x, z}}</nowiki> → <nowiki>{{x, z}, {x, w}, {y, w}, {z, w}}</nowiki>. Newly added connections are highlighted, and ones that are about to be removed are dashed).]] | ||
=== Multiway Systems === | === Multiway Systems === | ||
<nowiki>A rule may have multiple possible ways of applying it. For example, the rule {{</nowiki>''x'', ''y''}, {''x'', ''z''<nowiki>}} → {{</nowiki>''x'', ''z''}, {''x'', ''w''}, {''y'', ''w''}, {''z'', ''w''<nowiki>}} defines how to take take two connections in the hypergraph and transform them into four new connections. The rule just says to find two adjacent connections, and if there are several possible choices, it says nothing about which one. A crucial idea in the Wolfram Physics Project is in a sense just to do all of them.</nowiki><ref name=":0" /> | <nowiki>A rule may have multiple possible ways of applying it. For example, the rule {{</nowiki>''x'', ''y''}, {''x'', ''z''<nowiki>}} → {{</nowiki>''x'', ''z''}, {''x'', ''w''}, {''y'', ''w''}, {''z'', ''w''<nowiki>}} defines how to take take two connections in the hypergraph and transform them into four new connections. The rule just says to find two adjacent connections, and if there are several possible choices, it says nothing about which one. A crucial idea in the Wolfram Physics Project is in a sense just to do all of them.</nowiki><ref name=":0" />[[File:Multiway System.png|thumb|437x437px|<nowiki>The multiway graph showing all possible paths resulting from the application of the rule {{</nowiki>''x'', ''y''}, {''x'', ''z''<nowiki>}} → {{</nowiki>''x'', ''z''}, {''x'', ''w''}, {''y'', ''w''}, {''z'', ''w''<nowiki>}}. </nowiki>]] | ||
[[File:Multiway System.png | |||
All possible paths a system can take is represented by the [[Multiway Graph]].<ref>{{Cite journal |last=Wolfram |first=Stephen |date=2020 |title=A Class of Models with the Potential to Represent Fundamental Physics |url=https://www.complex-systems.com/abstracts/v29_i02_a01/ |journal=Complex Systems |chapter= |volume=29 |issue=2 |pages= |at=Multiway Systems for Our Models}}</ref> For the very first update, there are two possibilities. Then for each of the results of these, there are four additional possibilities. But at the next update, something important happens: two of the branches merge. In other words, even though we have done a different sequence of updates, the outcome is the same.<ref name=":0" /> | |||
So how does this relate to time? What it says is that in the basic statement of the model there is not just one path of time; there are many paths, and many “histories”. But the model—and the rule that is used—determines all of them. And we have seen a hint of something else: that even if we might think we are following an “independent” path of history, it may actually merge with another path<ref name=":0" />. | |||
== References == | == References == | ||
<references /> | <references /> | ||
Revision as of 03:47, 20 August 2025
Space & Time
Time as a Computational Process
In traditional physics, time is thought of as a coordinate similar to how we refer to a location in physical space. In the Wolfram Physics Project, time is thought of as the progressive application of computational rules, with each state of the system computed from the last. The implication of this new perspective is that time can no longer be set arbitrarily, as it is done often in traditional mathematical physics .[1] The reason for this is due to the phenomenon of Computational Irreducibility, which means that all prior states of the system must be computed if we want to learn about a system at a given time[2].
The Observer
By thinking of time as the progressive application of rules, this implies that it is theoretically possible for one to know all the possible states of a system. Stephen Wolfram's work in Observer Theory shows that the reason we do not experience such a phenomenon is because we are Computationally Bounded Observers. For us to be able to know the future would be to compute a computationally irreducible amount of work.
Space
In the Wolfram Model of physics, space consists of discrete, abstract relations between abstract points. [3]
-
A diagram showing the rule {{x, y, z}, {u, y, v}} → {{w, z, x}, {z, w, u}, {x, y, w}} -
The state of the hypergraph after each application of the rule -
The final state of the hypergraph after applying the rule many times
Multiway Systems
A rule may have multiple possible ways of applying it. For example, the rule {{x, y}, {x, z}} → {{x, z}, {x, w}, {y, w}, {z, w}} defines how to take take two connections in the hypergraph and transform them into four new connections. The rule just says to find two adjacent connections, and if there are several possible choices, it says nothing about which one. A crucial idea in the Wolfram Physics Project is in a sense just to do all of them.[3]
All possible paths a system can take is represented by the Multiway Graph.[4] For the very first update, there are two possibilities. Then for each of the results of these, there are four additional possibilities. But at the next update, something important happens: two of the branches merge. In other words, even though we have done a different sequence of updates, the outcome is the same.[3]
So how does this relate to time? What it says is that in the basic statement of the model there is not just one path of time; there are many paths, and many “histories”. But the model—and the rule that is used—determines all of them. And we have seen a hint of something else: that even if we might think we are following an “independent” path of history, it may actually merge with another path[3].
References
- ↑ Wolfram, Stephen (October 8, 2024). "On the Nature of Time".
- ↑ Wolfram, Stephen (2002). A New Kind of Science. Wolfram Media. p. 237. ISBN 1-57955-008-8.
- ↑ 3.0 3.1 3.2 3.3 Wolfram, Stephen (14 April 2020). "Finally We May Have a Path to the Fundamental Theory of Physics… and It's Beautiful". Stephen Wolfram Writings.
- ↑ Wolfram, Stephen (2020). "A Class of Models with the Potential to Represent Fundamental Physics". Complex Systems. 29 (2). Multiway Systems for Our Models.