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119 views
Could motives aid in the study of the Navier-Stokes equations?
Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
5
votes
2answers
252 views
Does the mathematics of physics require impure set theory?
Suppose for the sake of this question that all mathematics is ultimately reducible to set theory in such a way that the only mathematical objects there really are, are sets.
Now, there is a common ...
5
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1answer
61 views
Quantum causal structure
We take causal structure to be some relation defined over elements which are understood to be morphisms of some category. An example of such a relation is a domain, another is a directed acyclic ...
2
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1answer
125 views
The (co)algebra for the (co)monad of a light switch
If we take a light switch to embody an entire category, we could take the light switch to be a set with two elements and the morphisms are all endofunctions. Let's say, for fun, that we define the ...
2
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1answer
58 views
Causality and operationalism: from sets and functions to monads
When working in a laboratory, the most basic behaviour is to turn a knob or dial and then see a transformation of some data output. An example is increasing a magnetic field and seeing Zeeman ...
1
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2answers
126 views
Studying the logical structure of physics as a mathematical object per se? [closed]
I was wondering is there a branch of mathematical physics which studies the underlying logical structure of physics as a mathematical object per se?
Let me explain what I mean by that.
I'm ...
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0answers
19 views
Ontic state space from operational structures
Operationalism eschews a notion of system state in favour of the empirical behaviours of preparation and measurement. Abramsky has formalized operational structures as Chu spaces. It would be nice ...
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0answers
63 views
can we cast physics as an interface to underlying structure? [closed]
I have put down a few thoughts on how we can start to see physics as an interface to underlying "structure". "Structure" is posed without its normal qualifier "Causal" and it will become more clear ...
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0answers
86 views
Can quantum field theory be seen as an epistemic restriction on (quantum) causal structure
Suppose we take Vicary's quantum harmonic oscilator as a kind of "toy quantum field theory". Next, take the category of internal comonoids to not represent the background causal structure. We ...
