sethoflagos

If you're moving onto eigenstates of Hamiltonians again then you're losing me. How does this invalidate my point 1), in easy steps.

This is consistent with what I posted I think, though you have made it more general in application. In the sense that any arbitrary vector can be expressed as the sum of 3 vectors in your coordinate system of choice? Or are you making some deeper point that I'm missing?

Nothing is a strong word. @iNow's comment is not to be dismissed lightly: There is considerable evidence of the cerebrocerebellum playing an executive role in the planning of motor actions. It may be far from the whole picture, but it certainly appears to be apart of it.

Specifically, it links the midbrain and pons to the cerebral cortex. These conditions are specifically linked to ARAS. My money is on an emergence from the sum of all activity in the cerebral cortex with ARAS acting as a kind of switchboard/fusebox. The Fat Controller must have an office very nearby I think. As an engineer, that's where I'd put him.

That's fine. I have no difficulty in seeing the issues with my later inferences. Which is why I asked in the first place. So in a sense, you've been asking me to defend a position after I've announced that I've got my own problems with it. But I'd be quite interested to know where the train of thought actually went astray. If indeed it did.

Check the y-axis: it is radiant heat flux to space. Why would anyone not expect this to be a flat line close to the corresponding value of insolation and independent of CO2 concentration? There are reasons: eg temporary accumulation of heat in the system while it's temperature increased to a new equilibrium level, for instance? If so then the shape of the flux to space curve is dependent on some assumed temperature gradient that quantified that accumulation rate, otherwise the flux to space would be ill-defined. It is an issue of context framing. The graph, accurate or otherwise, provides an answer to a question that wasn't asked. We are not interested in the value of the nett flux to space - that is already known with some accuracy. Rather we are interested in the rate of temperature rise for the anticipated changes in CO2 concentration: a figure the presentation implicitly assumes, and in doing so, denies its sensitivity to the variable in question. Deliberately dishonest. So no surprise there.

Neither does religion, Though Sartre has a pretty good stab at it imho. "You are who you make yourself to be".

Not the foggiest. Hence points 1) to 5) of my earlier post that you seem to have no interest in.

By no means do I have any particular expertise in this area. However some years ago I went through a spell of being subject to occasional bouts of sudden neurally mediated syncope: temporary blackouts, a bit like someone hitting the reset button without warning. The way it was explained to me at the time was that I was experiencing (or rather, not experiencing) a temporary glitch in my ascending reticular activating system (ARAS), also known as the extrathalamic control modulatory system or simply the reticular activating system (RAS). Any partial loss of ARAS functionality tends to produce a corresponding reduction in degree of consciousness ranging from attentional dysregulation to sleep pattern issues through to deep coma. Brainstem features upstream of this structure were broadly sufficient to maintain life without consciousness. Therefore ARAS provided the gateway to all aspects of consciousness in areas of the brain downstream of it. I do hope I got this right, as it provides some sound constraints on the physical location of consciousness, and the degree of consciousness that may be experienced by other species. Lab experiments in this area seem to involve cats quite frequently.

We break the superposition by 'observing' and see a neutron?

Which entropy state is lower than that of the incoming (or more pertinently, the outgoing) neutron? There's clearly no issue with the decay path: it's the 'nearly decayed' back to 'as you were' path that's doing my head in.

I'm sure you'll be able to enlighten me why there isn't one. However, on the face of it, the superposition contains on average more particles; many more ways to distribute momentum and therefore, one might think, a higher total entropy.

But what about the 2nd Law? neutron => 1/2 neutron + 1/2 (proton + bits) => neutron ... might be a bit problematic. (though I'm sure I'm not the first to ask this question and somehow the problem must 'go away')

So science is of no assistance in assessing the potential benefits of reciprocity? Tough on those who were born with a low empathy level and are denied the means to work out that there may be some value in faking it now and then.

She doesn't. At no point does she state or even imply that: On the contrary, the entropy of a system may be defined absolutely by reference to the 3rd Law. And it is not 'all possible microstates of ðe system', it is 'all possible microstates of ðe applicable macrostate'. To understand this distinction, you need to understand the concept of microstate accessibility as referenced in the ergodic hypothesis. It's important. However, what she does say at ~9:40 is: This is true, but rather than follow this logic as I might to demonstate that there is no real conflict with the existence of domains of order within a closed system at thermodynamic equilibrium (for instance, the indefinite stability of an ice phase in an isolated system of water at its triple point) she continues with the following: Thermodynamic microstates are a snapshot of a system in a volume of space and have zero entropy; macrostates refer to the properties of that system observable in a volume of space-time. It is not 'still the same microstate': it is the ergodic progression through various microstates of different macrostates(!) Dr Hossenfelder seems to have confused the evolution of an out-of-equilibrium thermodynamic system stepwise through various macrostates towards a condition of thermodynamic equibrium (which is the process she describes) with the way in which a single quantum state may evolve. I suspect that she is encountering problems in attempting to square her curious views on determinism with the 2nd Law. Don't you mean “microstates wið respect to P"? No. All microstates have zero entropy. Entropy is an emergent property of all available microstates taken in combination. Hence a macrostate has a uniquely defined entropy even if some of the constituent microstates seem to exhibit spooky patterns.

Whatever that means. Forgive me but it comes over as avoiding the question.

First port of call would be a windscreen or headlight wiper mechanism from a car scrapyard. The cheap ones, not the ones with reversible motors. You might get the required sweep and cycle time by tinkering with the linkage, but incorporating a reducing gear might be more productive.

I was hoping to keep this general and not get sidetracked into the details of specific cases. Maybe the superposition of free neutron and its decay products. Obviously both states have a particular defined and equal total energy as isolated states in our physical universe. However, in superposition, these states do not exist as the simple sum which amongst other things would double the total energy content. Does the superposition actually have a concrete form within our universe or does it imply some degree of real existence in a space outside of it as does its abstract complex mathematical description? It's that abstract form of existence that I'm asking about. Not massless neutrons. As in my above response. It's the unmeasurable nature of the superposition - the coexistence of multiple versions of a single system - that's of interest to me here. @studiot, @Genady & @swansont I can understand the attraction of dogpiling onto point 6) Please confirm your position on points 3) & 4) to help me understand where we have parted in the logical progression.

Wouldn't that be a physical state? The mathematical description of it would be an abstraction without substance,

Went back to the start of the thread to see how far I could follow it before I got lost. The following list a a sequence of what appear to be logical inferences that spring to me from the above post. At which step does the logic break down? 1) The evolution of the individual quantum states in a superposition are accurately described by an appropriate wave equation such as (eg for Dirac fermions) the Dirac equation. 2) Although the Dirac equation maps onto our R3+1 spacetime, it is expressed in terms of a 4 dimensional complex vector space that is not defined within our R3+1 spacetime. 3) It is unclear whether or not quantum states in superposition have an individual material presence, but either way, they appear to be unmeasurable while they remain in superposition. 4) If indeed these individual quantum states have no concrete, physical existence within R3+1, then they appear to be only abstract objects existing outside of R3+1. 5) Side note: Point 4) is consistent with the possible emergence of our R3+1 universe from an initial quantum state that was not a part of our R3+1 universe. 6) As an abstract form, a quantum state need have no energy content, and therefore may coexist with an infinite multiplicity of alternate quantum states without conflict with the 1st Law of Thermodynamics. 7) As a uniquely defined state, it has a single permutation and therefore zero entropy. It may therefore coexist with an infinite multiplicity of (independent, non-interacting) alternate quantum states without conflict with the 2nd Law of Thermodynamics. 😎 Side note: if a quantum state in superposition did have a concrete physical presence in R3+1, then points 6) & 7) become difficult to explain away. 9) As any specific solution to the Dirac equation is bidirectional in time (explicitly includes an advanced wave acting on the state in the time reversed direction), using point 7), no information is exchanged in this process and properties apparently exhibiting computation of eg Feynmann's 'sum over histories' concept may evolve without conflict with the principle of Causality. 10) It appears that an unambiguous measurement within our R3+1 universe requires an action originating from somewhere external to it. 11) It is really difficult to refer to a point 😎 on this site.

Are you looking to operate another mechanism with it? What's the desired amplitude, cycle period and torque? How much space is avaiable? Can you be more specific about 'corrosive'?

Cave troglodytam. ... or was that Diogenes.

Chaos is imho an unhelpful word. As mentioned above I find that replacing it with 'diversity' a great help. We then see complex systems featuring diverse inhomogenies of structure, energy and mass density, chemistry etc., each of which are quantifiable in terms of entropy. And a little mathematical experimenting with the 2nd Law inequality shows that entropy scales with the logarithm of each of its system state variables (volume, temperature etc) Boltzmann's (actually Planck's) famous formula for entropy S= k ln W where W is the number of microstates (possible permutations of location, momentum, particle type etc) encapsulate this non-linear logarithmic characteristic to all measures of diversity in a complex system. It's really rather fundamental and built in to macroscopic systems. Of course a single isolated particle (a normal helium atom to keep things simple) taken in its own frame of reference is completely and uniquely identified. There is only one permutation. W = 1, ln W = 0 therefore S = 0. Entropy does not exist at the level of an isolated particle. It is purely a property of a multiplicity of particles. It is an emergent property that does not exist at the level of its constituent parts. This is really the basis of most non-linear behaviour in complex physical systems such as weather. Another time we can extend the discussion to information content and see that this reasoning governs much of our lives.

So causal influences are simply a dichotomy of the determined and the random? Are these the only possibilities? Why do you omit those arising from the infintely larger sphere of the abstract? Under conditions of physical duress, I might turn my mind to imagining a full-blooded chorus of Ritt der Walküren to summon power and fortitude from its driving ferocity. Where does all this magnificent sound come from? Do I have a high fidelity recording somehow etched into my brain? What if I change the tempo a little - or a lot? What if I decide to try out Kirsten Flagstad as Brünnhilde in place of Birgit Nilsson. I've only heard snippets of Flagstad's Brünnhilde and that was in Götterdämmerung but I can imagine her in Die Walküre, her subtly different timbre and undeniable glamour bringing an altogether different feel to the staging? What if I imagine the all-important bass trombone is thundering a little on the flat side... or god forbid! sharp!? Each change will impact my mood and my actions on my surroundings (or at least my long-suffering wife). Nothing of this is 'random' according to my understanding of the word. Nor can it be written into the entropy of any historical arrangement of material particles and be thus determined. And yet the sight, sound, scent, taste and touch of that conscious experience have existed since at least the dawn of time as a distinct potential in the abstract. Every bit as real as the number seven. So when I decide seven is greater than six and act accordingly, it's not a random decision; it isn't determined (though it may be expressed) by my environment; it just is. So I affirm that fact with my will. If and when I'm in the mood to do so.

Indifferent to a stationary human though comforted by a stationary car. Cautious of a nearby moving human yet terrified of a distant moving car (in a 20 mph zone) Non-linear responses. Have we got around to tipping points yet? I've spent quite a lot of time on my birdwatching treks watching the reactions of various wild beasts to my presence and your summary is a good generalisation. Except when an elephant waves its ears and its me who has to do the running. On second thoughts, it's the same deal.