iiinova — where your digital self keeps evolving

it also discretizes your modes. I think people just say 'whatever I'm interested in shouldn't depend on whether space wraps around very far away', maybe easier to swallow than small scales not mattering. At least as far as QFT goes, with gravity having a closed universe is tricky in other ways..

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Gregor @coexact.bsky.social · 5h

I think nowadays there's a lot of people who think IR regulation might not be so innocuous deep down (i.e. the mysterious 'UV-IR connection' of gravity). But one thing you can do in practice is put the theory on a torus

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Gregor @coexact.bsky.social · 5h

A lot of russian-published math has translations available, but this was published in german. The proof is only a few lines though, at the top of page 311

link.springer.com

Über die Summen durch den Zufall bestimmter unabhängiger Größen - Mathematische Annalen

Mathematische Annalen -

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Gregor @coexact.bsky.social · 6h

no see that's only the bad literary fiction, not the real Literary Fiction

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Gregor @coexact.bsky.social · 7h

you are preceded by the aptly-named Captain Sir Mansfield Smith-Cumming

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Gregor @coexact.bsky.social · 05/10/2026

I bet the Susskind lectures are a great way to start. I think having watched his QFT & particle physics lectures beforehand kept my head pointed in the right direction through some of the confusing bits of learning QFT properly later on

theoreticalminimum.com

Cosmology (Winter, 2013) | The Theoretical Minimum

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Gregor @coexact.bsky.social · 05/10/2026

as far as we know the maximal entropy state is pretty much entirely empty. De Sitter is weird like that, the horizon has most of the entropy so you want to make that as big as possible

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Gregor @coexact.bsky.social · 04/10/2026

with a finite regularization (in both UV and IR), the path integral is well-defined and Borel summation+instanton contributions ('thimble decomposition') together do recover it from a perturbation series.

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Gregor @coexact.bsky.social · 04/10/2026

one can always define a regularized (for example, discretized) path integral and maybe this is good enough. In neuro, I imagine the finite size and temporal resolution of neurons are a physical regulator.

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Gregor @coexact.bsky.social · 04/10/2026

otoh, I don't think it's clear that a path integral that's well-defined all the way down to the continuum limit is really a reasonable or necessary thing to ask for. It's mathematically interesting, but physically it seems more likely that there is a physical regularization at some scale

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Gregor @coexact.bsky.social · 04/10/2026

Zurek explains this at length, you can also see how it works in argument in the Carroll-Sebens paper on the Born rule

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Gregor @coexact.bsky.social · 04/10/2026

the reason I say so is bc the Born measure *is* a kind of counting measure in which unequal probabilities arise much as below by coarse-graining over the details of how a system entangles with the environment during decoherence.

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Gregor @coexact.bsky.social · 04/10/2026

I think it is legitimate to have a problem with assigning probabilities even there. But any time I try to lay out why a 'typical' (according to counting measure) observer should take their experience as evidence against a branching world, I do bottom out at a kind of 'why am I me' question

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Gregor @coexact.bsky.social · 04/10/2026

the same issue is there in a simplified model of a branching world with counting measure. imo there is no great difference to MWI philosophically and it is maybe simpler to think about. If one doesn't have a problem assigning equal probability there, I don't think one should have a problem with Born

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Gregor @coexact.bsky.social · 04/10/2026

I don't think it's the same: BBs are a problem if one convinces oneself that there are more of them than ordinary observers so that it becomes unlikely to not be one. You can't apply the same reasoning if you've on principle forbidden yourself from speaking abt probabilities when branching

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Gregor @coexact.bsky.social · 03/10/2026

I feel like your problem with MWI comes down to the same question though!

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Gregor @coexact.bsky.social · 02/10/2026

you should post sth so funny that Rochelle is willing to think about 'ordered pairs' over it

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Gregor @coexact.bsky.social · 01/10/2026

when the Prime Mover moves primes, composites necessarily go along for the ride

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Gregor @coexact.bsky.social · 01/10/2026

I don't know of anything in the world that I can point at and say it is a separate entity; the other kind of Existing has to be enough for me ^^

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Gregor @coexact.bsky.social · 01/10/2026

the example was supposed to illustrate this: even if there is only one step every 5s, if that step is exp(-iH*5s), the intermediate evolution is objectively defined and useful and I would consider it real

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Gregor @coexact.bsky.social · 01/10/2026

The wf then might not be a fundamental ingredient, but it is an objectively defined object which is useful (even necessary) in making sense of the future. We are used to this happening in physics. Lots of things aren't fundamental, including particles. the wf is just as real as particles are.

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Gregor @coexact.bsky.social · 01/10/2026

Just insisting that it isn't doesn't change what the theory is doing: In evolving the state, we don't just recall some simple fact abt the past, rather we do the whole thing of calculating the wavefunction;

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Gregor @coexact.bsky.social · 01/10/2026

rather I want to say that I don't think that calling the wavefunction a property of the past in a non-Markovian way makes it any less real: I would call a non-Markovian interpretation ψ-ontic (and maybe so would PBR)

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Gregor @coexact.bsky.social · 01/10/2026

I did see that you give trajectories, which I agree is at least well-defined. But the lack of an intermediate trajectory isn't what I was getting at here, though i guess my example might have been confusing there

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Gregor @coexact.bsky.social · 29/09/2026

So imo even if you consider QM to be non-Markovian stochastic, you still have to grapple with the fact that *the way in which* the past influences the present can be written via the evolution of several branches etc..

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Gregor @coexact.bsky.social · 29/09/2026

For me, not very much: even if I were convinced for some reason that this is true in some metaphysical sense, I still would consider all the events within a 5s stretch to be real.

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Gregor @coexact.bsky.social · 29/09/2026

Suppose I tell you that the world 'really' only exists in a discrete sequence of states, it's just that the update rule from one state to the next happens to be exp(-iHΔt), where Δt is say 5 seconds. What would this change for you?

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Gregor @coexact.bsky.social · 29/09/2026

There is one point which felt a bit murky to me at the time, so I was dancing around it rather than being able to state it clearly. Which is that I'm somewhat skeptical that claiming that intermediate representations are not real is even a coherent and meaningful thing to say.

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Gregor @coexact.bsky.social · 29/09/2026

I didn't know about this. He expresses himself infinitely better than I did in my blog about it but I'm glad that in content it has an overlap with my points of criticism (I even had the same example as in sec 7).

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Gregor @coexact.bsky.social · 29/09/2026

testable. try moving to the equator

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Gregor @coexact.bsky.social · 28/09/2026

no, it diminishes, as 1/x^2 I think? curvature radius in one direction is 1/x, in the other it's sth like x^3

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Gregor @coexact.bsky.social · 28/09/2026

mathematicians call that one "ignoring Tate twists"

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Gregor @coexact.bsky.social · 28/09/2026

my patented dip-coating technique for Gabriel's horns: just take a larger Gabriel's horn properly containing the first (scaled up by a factor) and fill it with paint. Clearly there's paint everywhere on the original one.

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Gregor @coexact.bsky.social · 27/09/2026

I guess Clockwork Orange

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Gregor @coexact.bsky.social · 26/09/2026

sure, just trivialize locally. In AG, the Chern class of the line bundle can tell you something about what kind of zeros/poles a meromorphic section will have for instance

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Gregor @coexact.bsky.social · 26/09/2026

"this is my story about nazis and my character who isn't one. He's called, uh, StormFront. yeah."

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Gregor @coexact.bsky.social · 25/09/2026

(oops, the 2πℏ should be in the numerator there)

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Gregor @coexact.bsky.social · 25/09/2026

g is the magnetic charge, yes! I don't know why I didn't write down C explicitly but it's 2πℏ. g and e can both be observed experimentally: So if we find a single monopole with charge g₀ say, it must be that every other particle has electric charge lying in the lattice ℤ/(2πℏg₀)

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Gregor @coexact.bsky.social · 24/09/2026

only if you want to go for all the a-states. acedia anhedonia alexithymia apathy abulia avolition and so forth

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Gregor @coexact.bsky.social · 24/09/2026

what might be confusing you is that QM is connected with probability theory in *two* ways: - the Born rule turns amplitudes into real probabilities - but separately(!) and esp. in relating SFT with QFT, one can view amplitudes, not their norm-squares, as directly generalizing probabilities

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Gregor @coexact.bsky.social · 22/09/2026

this is an opportunity. bonus quail egg in every carton

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Gregor @coexact.bsky.social · 22/09/2026

doesn't seem to be entirely ineffective

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Gregor @coexact.bsky.social · 22/09/2026

This other observer then sees multiple particles, despite us wanting to describe a single-particle theory. So rather than having a problem with causality as such we just don't have a relativistic {single-particle theory equipped with local position measurements}.

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Gregor @coexact.bsky.social · 22/09/2026

since the wavefunction spreads superluminally, I might an instant later find the particle somewhere else outside of the lightcone of the first location. But to some other observer in motion relative to me, these two events are simultaneous, or even in the opposite time-ordering.

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Gregor @coexact.bsky.social · 22/09/2026

we can't actually choose the measurement result (that the particle is found in the region) as our intervention, we can only choose to measure. What does happen is that while the single-particle sector is, when left to its own devices, stable under Lorentz transformations, the measurement kills this!

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Gregor @coexact.bsky.social · 22/09/2026

if a particle is localized like this, the wavefunction spreads outside the lightcone. Does this mean causality is violated? Not necessarily. Actually this basically still happens in QFT (eg the Reeh-Schlieder theorem). In that case causality is not violated, and the reason is down to the fact that

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Gregor @coexact.bsky.social · 22/09/2026

asking whether a theory is causal only makes sense if you specify some kind of allowed local intervention, so that you can then ask whether this allows the sending of a signal. In single-particle RQM, the obvious choice is measuring whether the particle is found in some region.

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Gregor @coexact.bsky.social · 21/09/2026

You're right that that's an invariant statement. But I'm also right to say that we can fix a gauge in which the vev is constant. In this gauge-fixed theory, the connection turns into the massive W & Z fields and a configuration like you describe into some collective excitation of these.

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Gregor @coexact.bsky.social · 21/09/2026

This is correct for breaking a global U(1) symmetry. For the SM: -The vacuum manifold isn't just connected but simply connected (even 2-connected) so there are no string or particle defects either -the symmetry is gauge: the gradual change of vev (which would be a Goldstone mode) can be gauged away

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