Conservation Laws

[foodchain]

Could conservation laws possibly be a product of environment as a witness or constant monitoring by the environment? I am not asking for a direct yes or not as I don’t know if that exists just more or less why do universal conservation laws appear in any system that QM interacts with. Such as with the standard model, how could conservation laws come to exist universally within such? It would seem some mechanism has to exist that would define consistent relative "outcomes" such as angular momentum.

 

This question hinges on if say classical reality emerged from the quantum. Why would any particular direction or an arrow of time even emerge, or a point like particle for that matter or massive amounts of them like hydrogen. I don’t see how this could come to be universal without some mechanism as a constant, not a constant as in absolute such as a decay time that can always be predicted, but more or less why decay times even exist and seem to be somewhat random.

[swansont]

Some of the conservation laws stem from continuous symmetries.

[fredrik]

Could conservation laws possibly be a product of environment as a witness or constant monitoring by the environment? I am not asking for a direct yes or not as I don’t know if that exists just more or less why do universal conservation laws appear in any system that QM interacts with. Such as with the standard model, how could conservation laws come to exist universally within such? It would seem some mechanism has to exist that would define consistent relative "outcomes" such as angular momentum.

 

This question hinges on if say classical reality emerged from the quantum. Why would any particular direction or an arrow of time even emerge, or a point like particle for that matter or massive amounts of them like hydrogen. I don’t see how this could come to be universal without some mechanism as a constant, not a constant as in absolute such as a decay time that can always be predicted, but more or less why decay times even exist and seem to be somewhat random.

 

Foodchain, I think you often ask interesting questions!

 

Swansont mentions symmetries as a technical explanation for conservation laws. This is a standard view in the standard formalisms, it's in classical mechancis as well as QM. Look up Noether's theorem.

http://en.wikipedia.org/wiki/Noether's_theorem

 

But one may continue to ask where the symmetries come from, and what is the "physical basis" for them? I think your question aims to go further.

 

I think from your question you are probing the various concept of "emergent symmetries" which different people have been elaborating in different ways. Smolin has been reflecting over than in the context of quantum gravity for example.

 

I for one think this is a good type of reflection. From the information/observer point, you would certainly ask this: Symmetries or not, the pragmatic question is, how does the process of discovery of a symmetry look like? from a physical point of view? And does the ignorance of the symmetry affect the action of the observer? I think it does.

 

In the standard case of symmetries implying a conserved qty, one starts with some model. Some lagrangian or something. But how is this lagrangian form arrive at? I think that step must not be trivialized.

 

I don't think there is a simple answer to this, but philosophically speaking I personally see symmetries and conserved quantities are emergent form the observers microstructures during an evolutionary process. This would yield only something like a subjective symmetry. As for objective symmetries which all observers in a region would agree upon, the observers need to interact to "equilibrate" at this level. I think there is a selective pressure towards this. So symmetries represent equilibrium. Broken symmetries breaks the equilibrium.

 

Edit: The implicit association here from a game theory view is that there is a COST for beeing in disagreement with your environment. This is the basis for selection.

 

So, in a sense I agree with your association of environment. To get a deeper understanding of emergent symmetries the multidirectional interaction and feedback with the environment must be considered. But even here there are different ways. I think the standard decoherence view is not enough. One has to add ontop of this a further issue, of the limited information capacit of the observers. That's my *personal opinion*at least, I could be wrong.

 

As for mainstream answers, I'm not sure this is a mainstream question - unless of course you are content with noether's theorem. But I see a meaning in your question beyond that, to which there current'y is no standard answer to that I know of.

 

/Fredrik

[Klaynos]

I thought the symmetries came from the fact the laws of physics don't change in time?

[fredrik]

I thought the symmetries came from the fact the laws of physics don't change in time?

 

I agree that you can probably make several different perspectives on this, interesting in different ways.

 

What is a law, and what is time? And how can those things not then

be entangled up with what is a symmetry?

 

And suppose we know what a law is and time is, then how do we know that this law will be wont need change in the future? I'd say we don't. We are just guessing. But the "physics of guessing" is sufficiently interesting IMO

 

/Fredrik

 

It's exactly this that Smolin has reflected over in various places: the nature of physical law, and how do you consistently distinguish the notion of physical law from initial condition? Or are they to be treated on the same level? IMO, the simple answer is yes, but the difference is that the confidence(inertia) in physical law is higher, so relatively speaking the initial condition is the low intertial part, seen from an information perspective.

 

I think you can make alot of ponderings about this, and I don't think it should be trivialized. Noethers theorem is nice, but it's a pretty simple thing and it lives in a context that is not explained.

 

/Fredrik

[abskebabs]

I thought the symmetries came from the fact the laws of physics don't change in time?

The symmetry "with respect to" time is just one kind of symmetry that can result from the lagrangian of a system, resulting a conserved quantity/first integral, aka the Hamiltonian. But many other conserved quantities can be derived, as has been mentioned already; angular momentum, when the angular coordinates have been made cyclic.

 

Anyway, I'm glad fredrik brought up Noether's theorem. I've done a course on Lagrangian and Hamiltonian mechanics this year, and even though Noether's theorem wasn't covered in detail, I think I get the gist of it. I just checked out the wikipedia article, and it said the extension in Quantum Mechanics was the Ward-Takahashi identity. Can anyone explain to me in as simple English as possible, how this extends Noether's theorem, the ways it differs and what it means?

 

P.S. It's great to finally be able to read some of these threads and understand them to a fair enough extent to make non-erroneous comments! Woohoo>!

 

Guess I won't be happy if someone corrects what I said above though:doh:.

[swansont]

I thought the symmetries came from the fact the laws of physics don't change in time?

 

That symmetry gives you conservation of energy. Rotational symmetry gives angular momentum and translational symmetry gives linear momentum.

[fredrik]

In standard QM the expectation value (denoted by the <>) of an operator A varies with time like

 

[math]\frac{d\langle A\rangle}{dt} = \langle \frac{\partial A}{\partial t}\rangle - \frac{i}{\hbar} \langle [A,H]\rangle[/math]

 

So for an operator without explicit time dependence we have

 

[math]\frac{d \langle A\rangle}{dt} =- \frac{i}{\hbar} \langle[A,H]\rangle[/math]

 

So if A commutes with the hamiltonian operator, then it's expectation value is conserved.

 

/Fredrik

[abskebabs]

That symmetry gives you conservation of energy. Rotational symmetry gives angular momentum and translational symmetry gives linear momentum.

I'm sure you implied this and I'm being pedantic, but the Hamiltonian, and the energy of the system are only equivalent; if the kinetic energy of the system can be expressed as a homogeneous quadratic of generalised velocities.

 

In standard QM the expectation value (denoted by the <>) of an operator A varies with time like

 

[math]\frac{d\langle A\rangle}{dt} = \langle \frac{\partial A}{\partial t}\rangle - \frac{i}{\hbar} \langle [A,H]\rangle[/math]

 

So for an operator without explicit time dependence we have

 

[math]\frac{d \langle A\rangle}{dt} =- \frac{i}{\hbar} \langle[A,H]\rangle[/math]

 

So if A commutes with the hamiltonian operator, then it's expectation value is conserved.

 

/Fredrik

I should probably know this, but; I know that this is the equivalent of the Poisson bracket for QM, but although I know the PB is made up of mixed partial derivatives, what is the quantum equivalent inside the bracketed commutation you have shown above.

 

I really need to start seriously revising QM... I have an exam in that too soon!

[fredrik]

It is interesting to compare the formalisms of QM and classical mechanics, and seemingly small formal adjustments and introducing an i and planck constants, replacing possion bracket with the commutator etc you can get to QM. But the physical meaning of the various quantisation procedures is IMO not as straightforward. The mathematically heuristic methods may be nice and is often used, but for the philosophical minded it isn't alwas satisfactory.

 

As you may know in QM, one is dealing with the state vector (wave function). This represents the observers information about the system. Measurement observables are special hermitian operators.

 

[math][A,H]\ := AH - HA[/math]

 

[math]\langle [A,H] \rangle := \langle \psi | AH - HA | \psi \rangle[/math]

 

The latters is to be interpreted as a scalar product in a complex vector space. The requirement for hermitian operators for observables guaratees that they have real observables (rather than complex).

http://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)

http://en.wikipedia.org/wiki/Bra-ket_notation

 

Not that since we are talking about operators here in general AB <> BA.

 

For example if we are talking about momentum in position representation.

 

Then P = [math]-i\hbar \frac{\partial}{\partial x}[/math]

 

[math]\langle [P,H] \rangle = \langle \psi | -i\hbar \frac{\partial}{\partial x}H + Hi\hbar \frac{\partial}{\partial x} | \psi \rangle = \langle \psi | -i\hbar \frac{\partial H}{\partial x}| \psi \rangle[/math]

 

Furthermore in position represetation the scalar product looks like

 

[math]\langle \psi | Q | \psi \rangle = \int \psi^{*}(x)Q\psi(x)d^3x[/math]

 

So the basics here is linear spaces, vectors and operators. More specifically one sees it as a vector space of functions, that's why you get into harmonics and fourier bases for many systems, as a basis for the space of state functions.

 

Note that above A and H are not real valued functions they are operators, acting on [math]\psi[/math]

 

/Fredrik

[foodchain]

I can understand certain aspects of the formalism behind QM such as what the Hamiltonian is but I am not capable of working with such yet. I have gone over various “interpretations” of QM which of course all use a little bit of variance in working with such. My question pertains basically to more modern applications of say decoherence and related topics such as einselection.

 

I still have a lot of confusion over issues pertaining to such, like if potential or kinetic energy is somewhat related to position or momentum or superposition even. The question I was more or less asking is on the basis of decoherence operating on a quantum environment that produces classical reality, such as conservation laws. The message that I am getting is that such laws are just static and immutable in time, I am just wondering if such are more or less a progression or reality of einselection or environment as a witness, in which symmetries, or conservation laws are arrived at or produced. For instance can you have a decoherence time less then the smallest unit of Planck time? Why not, is this related to other Planck scale variables such as the smallest unit of quanta? It would seem that you can set up a quantum experiment to get the same results over and over again, but in such “weirdness” how is such possible, more so when in reality you do indeed have to consider the apparatus and all measurement involved.

 

If classical reality did emerge from the quantum, then how did that “state of affairs” produce such a regular and predictable reality?

[abskebabs]

I can understand certain aspects of the formalism behind QM such as what the Hamiltonian is but I am not capable of working with such yet. I have gone over various “interpretations” of QM which of course all use a little bit of variance in working with such. My question pertains basically to more modern applications of say decoherence and related topics such as einselection.

 

I still have a lot of confusion over issues pertaining to such, like if potential or kinetic energy is somewhat related to position or momentum or superposition even. The question I was more or less asking is on the basis of decoherence operating on a quantum environment that produces classical reality, such as conservation laws. The message that I am getting is that such laws are just static and immutable in time, I am just wondering if such are more or less a progression or reality of einselection or environment as a witness, in which symmetries, or conservation laws are arrived at or produced. For instance can you have a decoherence time less then the smallest unit of Planck time? Why not, is this related to other Planck scale variables such as the smallest unit of quanta? It would seem that you can set up a quantum experiment to get the same results over and over again, but in such “weirdness” how is such possible, more so when in reality you do indeed have to consider the apparatus and all measurement involved.

 

If classical reality did emerge from the quantum, then how did that “state of affairs” produce such a regular and predictable reality?

 

The questions you're asking are fairly multifaceted, and I am finding them fairly interesting. I'm sorry if I didn't effectively reply to your OP, I think I was skim reading at that point. I will try and help you with what I consider the "easiest" 1st, to help further this discussion.

 

At least mathematically, it doesn't seem to me considering what I know, and especially after the reminder from fredrik's last post, that the conservation laws of CM, necessarily "emerge" from QM, though such laws are defined for both schemes independently(whether in the form of commutators in QM, or Poisson brackets for CM, though I think there are specific nuances to each). There may be convergences, but I suspect, that the way to get from one to the other, should not in prinicple be very much different, as with any other mechanical principles. I apologise if the last sentence sounded like gobbledy gook.

 

Secondly, at least classically, as long as we choose to carry out analysis in an inertial frame, Kinetic energy is only dependent on canonical momenta, and Potential energy only on coordinates(for nonconservative force fields, potential however becomes time dependent). If not inertial, then for the purposes of classification, we may adopt "effective potentials", and these potentials adopt cyclic terms(usually) from the Kinetic energy, and therefore, would include momenta. With regards to your confusion, I'm not sure how the situation could change in QM for this, the question of superposition, and how it plays a part in such a scheme is especially intriguing for me, and I guess suspect that, perhaps some relation is shared with the "cross terms" resulting from the "KE" expression in the Hamiltonian, when we have several particles.

 

As to whether these laws are changing, whether as a result of some form of decoherence, or "einselection", I guess I'm stumped for answering yes or no to that question I'm afraid, though I'm intriugued as to why you think this may be the case. I think it would be useful if someone else tried filling in the rest maybe...

[foodchain]

As to whether these laws are changing, whether as a result of some form of decoherence, or "einselection", I guess I'm stumped for answering yes or no to that question I'm afraid, though I'm intriugued as to why you think this may be the case. I think it would be useful if someone else tried filling in the rest maybe...

 

I mostly study biology. I know more about QM then anything else in physics which is close to zero percent actually.

 

Here is a link on wiki for einselection, you can also find various papers on the subject at arvix.

 

http://en.wikipedia.org/wiki/Einselection

 

I got intersted in QM because I am intersted in molecular biology/natural selection.

[fredrik]

I got intersted in QM because I am intersted in molecular biology/natural selection.

 

I think this is a good association, but I think it will be more difficult to appreciate the association without knowing the basics of standard QM first. With the basics I mean the basic structure, the supposed physical contents of the axioms and idealisations QM rests on and how this applies to real world problems.

 

I think the interesting associations on this is beyond standard QM in the sense to understnad how theories and laws themselves are selected.

 

What I don't find satisfactory about decoherence alone is that it uses a very complex picture(alot of information), to explain a constrained picture - by information reduction. That I think is easier. But a more interesting problem would be howto grow a complex picture from true ignorance, without relying on a background structure that has no inside-justification. Ie. without a "map" of our ignorance. I think that this map itself contains information, and the realistic scenario is that there is no such map. And then the question becomes, what actions would one expect from such an observer? I think the observer is gambling. And what kind of gamblers would be suspect to survive and be likely to be observed? Somewhat rational decision makers I'd say. That doesn't mean that one wouldn't expect variation. Variation would also be expected.

 

Foodchain, I would think that you might be interested in some of the QM + gravity things, and information physics, but that is even harder to read without the basics. And I also have hard to find interesting papers on this because it's open questions. And there are different lines of speculation out there. And some are more fundamental than others.

 

I think standard QM isn't the best place to look for evolutionary ideas in physics. It's probalbly deeper. Some cosmological thinkers are reflecting over different universes where different laws apply, and ponder which are "viable" and which are not. I take another view, I think you can make the same ponderings by instead of considering a cosmological universe and it's birth, one can consider the birth of an observer in an unknown environment, I think may in many respects be two different views of the same thing. Which abstraction you prefer probably depends on personal history.

 

/Fredrik

[foodchain]

I think this is a good association, but I think it will be more difficult to appreciate the association without knowing the basics of standard QM first. With the basics I mean the basic structure, the supposed physical contents of the axioms and idealisations QM rests on and how this applies to real world problems.

 

I think the interesting associations on this is beyond standard QM in the sense to understnad how theories and laws themselves are selected.

 

What I don't find satisfactory about decoherence alone is that it uses a very complex picture(alot of information), to explain a constrained picture - by information reduction. That I think is easier. But a more interesting problem would be howto grow a complex picture from true ignorance, without relying on a background structure that has no inside-justification. Ie. without a "map" of our ignorance. I think that this map itself contains information, and the realistic scenario is that there is no such map. And then the question becomes, what actions would one expect from such an observer? I think the observer is gambling. And what kind of gamblers would be suspect to survive and be likely to be observed? Somewhat rational decision makers I'd say. That doesn't mean that one wouldn't expect variation. Variation would also be expected.

 

Foodchain, I would think that you might be interested in some of the QM + gravity things, and information physics, but that is even harder to read without the basics. And I also have hard to find interesting papers on this because it's open questions. And there are different lines of speculation out there. And some are more fundamental than others.

 

I think standard QM isn't the best place to look for evolutionary ideas in physics. It's probalbly deeper. Some cosmological thinkers are reflecting over different universes where different laws apply, and ponder which are "viable" and which are not. I take another view, I think you can make the same ponderings by instead of considering a cosmological universe and it's birth, one can consider the birth of an observer in an unknown environment, I think may in many respects be two different views of the same thing. Which abstraction you prefer probably depends on personal history.

 

/Fredrik

 

Well that’s the thing. I have about two years of college or university done and really am perplexed severely about where to go. I do a lot of outside study on my own as I obviously have not taken any in depth college level courses on QM.

 

That being said its just a question of course, one that keeps me up at night.

 

----------------------

 

Speaking of gravity you can make the speculative jump that constant monitoring is pretty constant like gravity, but what if the reality of whatever everything is happens to be so counterintuitive that the mere idea of thinking in some odd direction is just to much crack pottery for anyone including modern day crackpots. I mean when QM first appeared on the scene the modern day giants such as Einstein in particular just would not have any of it at all, to weird I think is what he keep insisting. Even then we still have modern day ideas that border on the line of such, like branes and strings or whatever. I think the point that gets missed is like you say it all takes some sort of formalism to be expressed in human thought, be it math or some other form of thinking.

 

My interest in the subject though does not really take me into the rest of physics. I am interested in the cosmos of course but we really cant do much with it save record what hits earth or some observational device we post or a telescope of some kind. I mean to make it to the moon is incredibly complex to undertake even today, not to mention the bottoms of our oceans.

 

The reason I like QM is because maybe physics did discover the elementary or basic level of reality, such as it does not go any farther down in a reductionist sense. My big questions hinge on that, and if the current form of anything via QM is the only possible form. Decoherence seems to imply in my eyes a hint that it might not always be just that. The more urging questions I have for QM and of course issues like einselection and decoherence is the possible role it could play in explaining the origin of life. Being I think a standard view is that chemical species/behavior can be explained in such or originate from such it would be of direct consequence on explaining the origin of life then. I also think that understanding that would allow for a base in which to be able to grasp the molecular basis of life up to the uncertainty principal in detail, which would answer so many questions.

[fredrik]

It sure can be difficuly to choose, and perhaps sometimes a sidetrack is necessary to gain perspective.

 

I did the other way around, I studied only physics and math, but I have studied alot of biochemistry and molecular biology on my own. It was very enriching to be added ontop of a very "dry" physics education.

 

Perhaps you should just keep what you are doing, and maybe you can find your own angles to all this. Hard problems probably begs for unexpected solutions Beeing broad in your interest and education is I think a very good thing these days because it's hard to guess your future endeavours.

 

/Fredrik

[Ti]

Could conservation laws possibly be a product of environment as a witness or constant monitoring by the environment? I am not asking for a direct yes or not as I don’t know if that exists just more or less why do universal conservation laws appear in any system that QM interacts with. Such as with the standard model, how could conservation laws come to exist universally within such? It would seem some mechanism has to exist that would define consistent relative "outcomes" such as angular momentum.

 

This question hinges on if say classical reality emerged from the quantum. Why would any particular direction or an arrow of time even emerge, or a point like particle for that matter or massive amounts of them like hydrogen. I don’t see how this could come to be universal without some mechanism as a constant, not a constant as in absolute such as a decay time that can always be predicted, but more or less why decay times even exist and seem to be somewhat random.

 

I think laws are based on experiments.

So I think your question is:

Cons. Law = f(environment?)

or

Environment = f(Cons. law?)

Please ask question in simpler form and write it properly. Thanks.

[foodchain]

I think laws are based on experiments.

So I think your question is:

Cons. Law = f(environment?)

or

Environment = f(Cons. law?)

Please ask question in simpler form and write it properly. Thanks.

 

That’s sort of the problem. See you have all kinds of interpretations of QM floating around. I am particularly interested in decoherence because the rest of them I don’t find as interesting.

 

IN the experiments you cant separate anything. Such as simply looking at the experiments or the apparatus involved changes the experiment, this to me of course implies the idea that quantum systems are not isolated, and even in the presence of a bec you have to have a highly controlled environment, or typically its always some kind of an environmental function, or subsystem of the environment.

 

I was reading on some nanotech based methods of wave function engineering that dealt with the super periodic. I can only think what is the complete wave function over time of my keyboard via all the strokes made on keys through the day and why my keyboard even keeps a resemblance of itself over time:D;)

 

To me the environmental idea of decoherence over subsystems makes sense in reaction to the idea of superposition and why anything in reality is ever not in complete and constant superposition, which implies a particle-wave thing being anywhere at anytime physically possible.

 

So any type of a constant that has evolved from any kind of a physical system ultimately deals with the quantum, so how could a arrow of time or classical reality or anything normal or routine come from such, like planets or solar systems or hydrogen or matter or mass or light or anything really. It all hinges of course on the question that classical reality and its laws emerged from a quantum one, if not the question is sort of pointless, but if indeed the visible universe is a product of quantum reality then some mechanism has to exist in the quantum world that would lead to anything regular I would think out of superposition.

 

I mean what if some person accidentally does put the right chemical formula for life together but fails to get the spark because the wave function does not happen to come across as is needed, so many many questions for something like that, I mean what if its decoherence of subsystems in the current form that allows for the Planck constant? Then of course you deal with the reality that to escape this might require that apparatus that is the universe to change. I mean QM is functioning in everything constantly, its what describes atoms for example.

[Ti]

Yeah, what happened if it is all of a dream? your senses are being play into duping you into reality, like the "Matrix". Senses like smell, sight, hearing, touch are all stimulate. While you thought you were doing physics experiment handling data and coming up with laws and theories, it was just a dream.

"But we're all saw it." "It is on data, we videotape the whole experiment." "I did it myself." "You were there, weren't you."

 

That's what happened to some guy that did the cold fusion experiment.

[foodchain]

Yeah, what happened if it is all of a dream? your senses are being play into duping you into reality, like the "Matrix". Senses like smell, sight, hearing, touch are all stimulate. While you thought you were doing physics experiment handling data and coming up with laws and theories, it was just a dream.

"But we're all saw it." "It is on data, we videotape the whole experiment." "I did it myself." "You were there, weren't you."

 

That's what happened to some guy that did the cold fusion experiment.

 

I try to avoid that whole line of thinking. I think quantum mechanics is surely physical. I don’t think however of course that our senses see everything obviously, but that has to do with evolution, and of course being we can react to photons, evolution, biologically speaking then of course also deals with quantum reality as an aspect or variable in natural selection then, like 1,2,3 really.

 

QM is used to explain chemical reality and bonding behavior, or it can be, its also experimentally verified up the ying yang so I could hardly care to get into some aspect of conscious thought changing reality, that whole aspect of QM is pure garbage in my opinion. If you detect a photon obviously you have interacted with it thus changing it. I attribute measurement to simply being any kind of physical interaction really, which again leads to my interest in decoherence and really more specifically einselection as I am looking for a basis in QM in which the environment is made paramount simply because of intuition about reality.

 

 

 

"Received 10 September 1996

 

A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time with a few photon coherent field trapped in a high Q microwave cavity. The mesoscopic superposition was the equivalent of an “ atom+measuring apparatus ” system in which the “meter” was pointing simultaneously towards two different directions—a “Schrödinger cat.” The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement."

 

http://prola.aps.org/abstract/PRL/v77/i24/p4887_1

 

You can find this link from the wiki article, its among so many anymore its hard to try and read a small fraction of them really.