sethoflagos

12 minutes ago, Genady said:

In the Dirac equation, the evolving objects are spinors. They evolve in spacetime. They constitute states in a spinor space.

You seem to be saying that spacetime and a complex 4-D spinor space are the same thing.

To me, any object in a complex space does not have an energy content though its projection in real (non-complex) spacetime will. So they aren't the same thing,,, or are they?

13 minutes ago, Genady said:

I refer to eigenstates of any observable. We can expand any state in any basis.

This makes the notion of "states in a superposition" arbitrary.

Okay... so I've arbitrarily picked something.

1 hour ago, Genady said:

Yes, but I refer to a coordinate basis of the space of states rather than the geometric 3D space.

Could such a space be:

On 12/14/2023 at 9:20 PM, sethoflagos said:

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.

... or not.

33 minutes ago, Genady said:

Yes, but I refer to a coordinate basis of the space of states rather than the geometric 3D space.

If you're moving onto eigenstates of Hamiltonians again then you're losing me.

How does this invalidate my point 1), in easy steps.

6 minutes ago, Genady said:

1a) The evolution of any quantum state is described by an appropriate equation of motion, such as Schrödinger equation, Dirac equation, and Klein-Gordon equation. The equations of motion are not restricted to "the individual quantum states in a superposition."

This is consistent with what I posted I think, though you have made it more general in application.

8 minutes ago, Genady said:

1b) Any state is a superposition of some states. Being an "individual quantum state in a superposition" is not property of a state but property of a coordinate basis in which the state is expressed.

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?

33 minutes ago, Luc Turpin said:

also think that some sort of integrated system is at play, but nothing confirmed so far.

Nothing is a strong word. @iNow's comment is not to be dismissed lightly:

51 minutes ago, iNow said:

Have you already dismissed my recommendation of the cerebellum as the mostly likely answer if there is a center?

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. 

43 minutes ago, Luc Turpin said:

One more location that is added to the list of where mind could be in the brain. The RAS is located in the brainstem and I guess that this affects all of the brain.

Specifically, it links the midbrain and pons to the cerebral cortex.

43 minutes ago, Luc Turpin said:

We also lose consciousness when we are in a coma or when we are asleep. Different brain regions being dampepended or activated causing a temporary loss of consciousness.

These conditions are specifically linked to ARAS.

43 minutes ago, Luc Turpin said:

Where is the center of mind or consciousness in the brain remains uncertain.

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.

33 minutes ago, swansont said:

“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.”

I have no interest in this because my experience with superposition is with the expression of the eigenstates, and not the wave equation or how the wave function was determined. There’s no common ground for me, and so I have no comment.

 

 

IOW aψ1+bψ2 doesn’t really rely on the wave equation, so I’m not sure where you were going with your post

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.

2 hours ago, exchemist said:

At first glance it looks like no more than the expected exponential reduction in intensity with concentration of the absorber predicted by the Beer-Lambert law. Has anyone come across this being used as a counterargument to climate change science, is the implication true that further increases should have a proportionately lesser effect and what relevance does that  have to the models used to predict climate change?

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.

8 minutes ago, mar_mar said:

And science doesn't give an answer to a simple, but fundamental question, such as "who you are".

Neither does religion,

Though Sartre has a pretty good stab at it imho. "You are who you make yourself to be".

46 minutes ago, swansont said:

How does this happen?

How was the superposition created in the first place?

Does it even make sense to talk about the second law for such a system?

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

11 hours ago, DrmDoc said:

Consciousness is the efferently expressed behavior that suggests awareness and awareness is the basic progenitor of those processing in the brain that lead to the quality we perceive as having a mind.  To add emphasis, the entirety of this process requires energy and without that energy the system fails.  With brain function--and yes, this is about the brain--failure is not a option. Homeostasis is the process that drives brain function.

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. 

34 minutes ago, swansont said:

There is no outgoing neutron

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

1 minute ago, swansont said:

Sure. But the superposition also includes the low-entropy state, so the average of the two (weighted by their amplitudes) is less than the entropy of the final state, so there’s no conflict with the 2nd law.

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.

35 minutes ago, swansont said:

What, precisely, is the problem?

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.  

34 minutes ago, swansont said:

Yes. There’s no violation of the law when you have a superposition.

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')

5 hours ago, dimreepr said:

My point is, science knowledge is not always relevant to one's life issue's; science isn't designed for empathy.

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.

6 hours ago, Tristan L said:

In her video I don't believe the 2nd law of thermodynamics. from about five monþs ago, Sabine Hossenfelder made ðe same key point 💡 I made more ðan þree-and-a-half years ago in my topic Will entropy be low much of the time?

She doesn't. At no point does she state or even imply that:

6 hours ago, Tristan L said:

Ðe entropy of a system can’t be defined absolutely. It has to be defined wið regard to a partition (mark ðat I use ðe linked-to set-þeoretic definition of “partition”) of ðe state space of ðe system, ðat is, of ðe set of all possible microstates of ðe system.

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:

Quote

What does entropy have to do with order? 

This has always confused me. I now think the brief answer is 'nothing', because 'order' does not have a well-defined meaning.

For instance, imagine you're pouring milk into tea. In the beginning they're neatly separated: 'ordered' you could say. At the end, they are evenly mixed. I'd also call this 'ordered', but in physics, this even distribution doesn't count as order.

This reference to order causes a lot of confusion.

                                                                                                                  S. Hossenfelder

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:

Quote

If we put air molecules in the corner of a box, we don't know where they're going, but at least we know where they are. 

If we now let the air spread into the entire box, it's still the same microstate. It's still the same microstate that one moment ago was in the corner of a box. But we can't tell. We used to have information about this state we no longer have. That's why entropy increases: because we lose access to information.

                                                                                                              S. Hossenfelder

 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.  

6 hours ago, Tristan L said:

Ðe elements of a partition P of ðe state space are pairwise disjoint subsets of state space whose union is state space. Ðey are called “macrostates wið respect to P”.

Don't you mean “microstates wið respect to P"?

6 hours ago, Tristan L said:

As I understand it (please set me right if I be wrong), ðe correct version of ðe Second Law of Þermodynamics says ðat for each partition P of ðe state space, ðe entropy wið respect to P is high more often ðan it is low.

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.

12 minutes ago, Genady said:

My position is that the component states are an expansion of the entire state in a specific basis.

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

2 hours ago, Externet said:

Thanks. 

No, stands alone.  10 to 270 degrees;  10 degrees/second; 30 seconds, no load (no torque).   20cm x 20cm x 20cm.   No.

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.

44 minutes ago, swansont said:

Do you have an example?

Quantum states I can think of will have an energy, and you need to add energy to put a system in the ground state into a superposition of energy eigenstates (unless they’re degenerate)

 

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.

1 hour ago, Genady said:

If a state is 'in a superposition' or not depends on basis in which it is expressed. The same state is 'individual' in one basis and 'in a superposition' in another.

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.

1 minute ago, studiot said:

Do you for instance mean an unoccupied state such as an anti bonding orbital ?

Wouldn't that be a physical state?

The mathematical description of it would be an abstraction without substance, 

On 11/30/2023 at 3:56 AM, swansont said:

Entanglement does not cause a wave function to collapse. The individual states in an entangled state are undetermined, and superposition does not require entanglement.

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. 

2 hours ago, Externet said:

Thanks.  Yes, a servo does work but strongly prefer something electronically simpler as geared motor with no circuitry as will have to work in corrosive hard-to-reach enclosure and no stepper motion but analog smooth.

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.

3 hours ago, Luc Turpin said:

Maybe I am mixing up non-linearity with chaos. Confusion still reins in my head. Need to think!

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.