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I'm a post-doctoral researcher with a wide range of interests. My career is in complex systems science (or maybe cybernetics) and the origins of life, but I also have research interests in

  • the foundations of statistical mechanics and its relationship to information theory
  • Earth systems science
  • non-equilibrium thermodynamics in general

I'm also generally interested in the foundations of quantum mechanics and in black holes, though I wouldn't say I'm an expert on those things.

It's probably worth noting that despite the fact that my research is in physics-related areas, all my degrees are in other subjects. If I occasionally seem to start talking in an alien language, this is probably why.


Apr
13
comment Are the Hamiltonian and Lagrangian always convex functions?
@Qmechanic note that one of the answers on that related question is by me. A non-convex Lagrangian would imply a multiple-valued Hamiltonian, and vice versa, so I'm still slightly confused by this. (In the classical context.)
Apr
8
comment Aside from experimental evidence, is there any reason to model space as Euclidean?
Evidently I completely missed the "aside from experimental evidence" in the title. OP, if this was remotely useful to you then let me know, otherwise I'll delete it.
Apr
8
comment Is the sun's solar radiance spectrum matching up with water's absorption spectrum just coincidence?
It's 100% just coincidence - there's no plausible way in which these two facts could possibly be causally related.
Apr
8
comment Is the sun's solar radiance spectrum matching up with water's absorption spectrum just coincidence?
(1) What evidence do you have that nobody intelligent evolved on such stars? (2) It's not as if red or blue stars don't give off any light in the visible spectrum. You can see them in the night sky after all, so eyes would hardly be impossible on worlds orbiting such stars. Conclusion: it's not anthropic bias, it's just coincidence.
Apr
4
comment Why are bricks typically constructed to have six faces at, or near right-angles to each the other?
@qarma there may be some truth in that. The bases of traditional Japanese castles are built from irregularly shaped stones and are remarkably earthquake-resistant; conversely, living in Japan, I rarely if ever see a wall built of rectangular bricks (though they are sometimes used as cladding over concrete structures), and I think earthquakes are part of the reason. (But I think the design I drew above would not be particularly good, as it would collapse just as easily as a brick wall. The irregular blocks need to lean against one another for it to work as an earthquake resistant structure.)
Apr
3
comment Natural refrigeration
You could increase the rate of evaporation by heating the system, but that would be rather counterproductive. You could try pointing a fan at it.
Apr
3
comment The Lagrangian as a metric
The metric as you write it seems to be defined on configuration space rather than generalised space-time. I'm wondering whether including time as a coordinate (and parameterising the curve with some other variable) would allow potentials to be considered.
Apr
3
comment The Lagrangian as a metric
Thanks for the answer - I somehow managed to miss it until today. Having defined Synge's world function, what does one then do with it? (The Wikipedia page doesn't say either.)
Apr
2
comment Does space have a “radiation pressure” caused by subatomic particles?
@EnjoysMath please don't accept this answer, it doesn't really address your question properly at all. There is a right answer to your question, but nobody has posted it yet. (I'd give it a go myself, only I don't know enough about quantum field theory, which is what you need to answer your question properly.)
Apr
1
comment How stupid is this theory of gravity?
Yes, that can happen. It can also not happen, in which case the bodies continue moving apart forever, or orbit one another. I guess I don't really see your point...
Apr
1
comment How stupid is this theory of gravity?
"What you would perceive would be 2 circles of fixed size accelerating towards each other." - I think this is where you went wrong. They're not accelerating towards each other, they're just moving towards each other. You make the opposite mistake when you say "We perceive gravity as a force that causes the distance between masses to decrease over time". No we don't - we perceive it as a force that causes masses to accelerate towards each other over time, but they might initially be moving away from one another.
Apr
1
comment A real gas with gravitation-like interaction
I believe this is a major unsolved problem in cosmology, although I haven't looked into it in any depth.
Mar
31
comment The Lagrangian as a metric
When calculating distance from a metric tensor, the integrand depends upon not only the position of each point along a curve, but also upon the direction of the curve at that point. The Lagrangian has the same property -- if you plot $\mathbf{q}$ against $t$ it's easy to see that $\mathbf{\dot q}$ tells you the direction of the curve. It's because of this similarity that I think $L$ might formally be a metric in $\mathbf{r}$ space, if expressed in the right way.
Mar
31
comment The Lagrangian as a metric
That should be $\mathbb{R}\times\mathbb{R}^n$, or $\mathbb{R}\times\mathbb{R}^{3m}$ for an $m$-particle system. I think the other person who answered was confused by that as well, so I've edited it.
Mar
31
comment Equivalence between Hamiltonian and Lagrangian Mechanics
I see, thanks. (I would write it $\left.\frac{\partial L(q,\dot q, t)}{\partial \dot q}\right|_{\dot Q(p,q,t)}$, but then I often find myself notating things differently from the conventions physicists use.)
Mar
31
comment Equivalence between Hamiltonian and Lagrangian Mechanics
What does your notation $\frac{\partial L}{\partial \dot q} (q, \dot Q(p,q,t), t)$ mean? The way it's written it looks like $L$ doesn't depend on $\dot q$, so that partial derivative should be zero.
Mar
31
comment The Lagrangian as a metric
By the way, I don't get notified when you update your answer, so if you make any changes you'd like me to see, it's a good idea to leave a comment to let me know.
Mar
31
comment The Lagrangian as a metric
Thanks for your second example, but it seems to be showing something different. The metric you describe is only for the spatial coordinates, and doesn't include time. Still, it's again suggestive of a "deep" relationship between Lagrangian mechanics and geodesics (at least in the case where there are no forces besides the constraints), and so I appreciate it.
Mar
31
comment The Lagrangian as a metric
The vector space I'm talking about is not space-time. For a single-particle system it has the same dimensionality but a different metric. (The Lagrangian not only has dimensions if energy but also depends on the particle's mass.) For an $n$-particle system it has $3n+1$ dimensions.
Mar
30
comment The Lagrangian as a metric
I suppose another way to put the question is, can we always write the Lagrangian in this form, even if $x$ refers to the "generalised space-time coordinates" for many particles (as defined in the question), and $\mu$ and $\nu$ range over a different number of dimensions than the dimensionality of space-time?