Measuring Position: A Microscopic Being's Perspective

[newbee]

How would an imaginary microscopic being measure distance or more precisely measure its position in some spatial coordinate system?

 

[olgranpappy]

How would an imaginary microscopic being measure distance or more precisely measure its position in some spatial coordinate system?

An imaginary microscopic being would measure distance with an imaginary microscopic ruler. He would sleep in an imaginary microscopic bed and eat imaginary microscopic cheeseburgers.

 

[newbee]

But wouldn't this being need to know the simultaneous position and momentum of the microscopic ruler as a prerequisite to using it to measure his/her position?

 

[atyy]

An imaginary microscopic being is just an electron. It has to measure its distance to another electron correctly in order to know how to be repelled by that electron. It obviously does this much better than us, since it reacts exactly in real time, whereas we need quite a bit of supercomputer time to calculate how it does its measurement. Of course, there is this little problem that the electron may exist in all space, and at the moment of interaction may not have a well-defined separate existence.

 

[newbee]

So given the problems stated above how would this being map an electric potential.

 

[Fra]

How would an imaginary microscopic being measure distance or more precisely measure its position in some spatial coordinate system?

Although some may perceive the question as hypothetical, if I understnad you right I think it's an fundamentally excellent question, but not that easy to answer. I ask a similar question.

How to in an intrinsic way relationally, construct a measure complex given the constraints at hand. I think the possible benefits is that I think the laws of physics will look much simpler from this "inside view".

If you try to use the standard QM formalism to supply the answer, I personally find that it doesn't make sense. There is something lacking that concerns how possible intrinsic measures (of such a small observer) is constrained by the information capacity of the same. This is also closely conceptually related to inertial concepts and IMO possibly the link between gravity and particle physics.

I think the full answer to this question is not yet on the table. But to insist asking the question is a good first step.

/Fredrik

 

[newbee]

This is also closely conceptually related to inertial concepts and IMO possibly the link between gravity and particle physics. /Fredrik

That's a notion that I was entertaining as well but my QFT and gravity background isn't yet what I would like it to be. The notion of a potential or Lagragian as a function of a spatial coordinate to which there is no explicitly associated scale is bothering me. Anyhow, thanks for the thoughtful post. I hope this discussion continues and draws the interest of others.

 

[Fra]

I really can't provide clear answers, but I think it's important to agree on the general questions. The more of us that start to ask good question the better does the environment for research get! Without having the answer I support this question in the sense that I think it's good. Maybe someone else can provide more insight.

But wouldn't this being need to know the simultaneous position and momentum of the microscopic ruler as a prerequisite to using it to measure his/her position?

As I see it the abstraction of "stick" is simply an notion to define the measurement as such by defining the stick used to measure. A measurement RELATES to the stick.

In my abstraction, there are always two uncertainties, to determined the stick and to perform a measurement relative the stick. But again, how do you determine a stick? It's again a sort of measurement. So it seems we end up with a hierarchy of relations, and when does this stop? Here I envision that there is a fundamental scale where no pare distinguishable from others anymore, ie. we can not distinguish the "sticks".

Consider that we have many "sticks", perhaps some of space, some for electric charge, etc. At some poitns ALL the sticks simply blur from the point of view of a tiny observers. there is a limit to the number of intrinsically constructible "sticks". This sounds like unificaiton. So what about mass an inertia? I associate that to the information capacity, and thus "stability" of say any sticks.

But how to translate this into exact mathematics and also contain all the standard models seems like a massive task. But I think the road to success is in steps, if we can agree upon a direction to invest in that's a good start. As far as I am concerned I think a new framework may be needed to accomplish this. Standard QM or standard QFT can as far as I can see not implement this grand vision, and I think the problem is the arbitrary use of fix references. In an intrinsic observational view, such fixed references seem to lack physical basis IMO. To me physical basis = observational basis, meaning the observational method has to actually be constructed from the inside and out, not projected from an ad hoc external world.

Perhaps QM relates to this new formalism we are looking for, like old extrinsic diff geometry relates to intrinsic diff geometry. But the comparastion goes way beyond QM in curved spacetime, it touches the very notion of relational information.

/Fredrik

 

[newbee]

Fra

Thank you for the post.

Consider that we have many "sticks", perhaps some of space, some for electric charge, etc. At some poitns ALL the sticks simply blur from the point of view of a tiny observers. there is a limit to the number of intrinsically constructible "sticks". This sounds like unificaiton. So what about mass an inertia? I associate that to the information capacity, and thus "stability" of say any sticks.
/Fredrik

Have you written about mass and information capacity/stability or do you know of references to such work?

 

[Fra]

Actually the deeper idea of information capacity vs inertia mass connection i have in mind that should contain QM as emergent really belongs to open questions. I think one has to admitt that the questions are controversial.

So maybe the discussion here starts to diverge from the rules of the "QM" section. This sections is intended for questions regarding standard QM. If I understand your intention of the question right (but I could over-interpret your question!) then there is no answer to it within standard QM. So if you insist asking it anyway, it also implies looking for bigger theories. So perhaps the moderators would move this to some other section.

I am still working on these things and I have not yet published any papers on this. This progresses slowly for me since I don't work with this and thus I use my spare time for this. I'm working on assembling the ideas as I make progress but so far it's a long way to go.

But possible vague connections that touch current work are for example IMO, rovelli's "relational quantum mechanics" http://arxiv.org/abs/quant-ph/9609002. This certainly does not address the deepest issues in the above sense, but IMO it's a good conceptual start, and contains the idea that physical interactions are nothing but communication. I like this paper - it's a good read! although I don't agree with rovelli's reasoning all the way so to speak.

Other related ideas are ariel caticha's idea that the laws of physics are to be thought of as the laws of inductive inference, and he hopes to derive Einsteins field equations from general considerations of a Entropy dynamics principle. This is very interesting read, although neither this makes it all the way. He has written several papers. Look for "ariel catica" or arxiv. This are also a few other authors, workin in the similar spirit that has written various papers on this.

Other than this one can also associate this information/intertia idea to a yet unformulated version of the holographic principle in the sense that an intrinsically "knowable" theory of the world, should also be formulable as a theory of the observers image of the same. This takes the information to heart and thus locality gets a new meaning, because even information about "a remote" ojection is stored locally, and it's only the local information that determins the local action. And this imposes a sort of capacity constraint on the universe, as seen from any observer. I think this is something that is implicit in the original question - how does a small observer experience and see the world? For example, does this limit the possible interactions he can "see" (=participate in), I think that answer is yes. But as far as I know these are all floating ideas... I am still looking for the proper mathematical reconstruction for this.

I have a feeling that it's not that many professionals that are seriously working on this. Why that is so I don't know. I've always suspected that it's too difficult and borderline to philosophy that professionals doesn't want to risk their reputation by taking on such fuzzy and risky questions. But I think the undertone in the reasoning of many some visible physicists these days are somehow in my view at least sniffing in this direction but everybody is fightning with formulations.

I wish someonw wrote a paper which contained the full answer to these questions, but I haven't seen one yet.

/Fredrik

 

[atyy]

The notion of a potential or Lagragian as a function of a spatial coordinate to which there is no explicitly associated scale is bothering me.

Could you clarify the question, maybe with an example?

Actually the deeper idea of information capacity vs inertia mass connection i have in mind that should contain QM as emergent really belongs to open questions. I think one has to admitt that the questions are controversial.

So maybe the discussion here starts to diverge from the rules of the "QM" section.

This paper seems to bring some quantum gravity ideas into standard QM?

Area laws in quantum systems: mutual information and correlations
M.M. Wolf, F. Verstraete, M.B. Hastings, J.I. Cirac
http://arxiv.org/abs/0704.3906

 

[Fra]

This paper seems to bring some quantum gravity ideas into standard QM?

Area laws in quantum systems: mutual information and correlations
M.M. Wolf, F. Verstraete, M.B. Hastings, J.I. Cirac
http://arxiv.org/abs/0704.3906

Thanks for the link. I need to read it more later, I just saw the first paragraphs and..

IMHO intrinsic relational information is not the same thing as correlation. Correlation implies a third observer (OR a realist view of the degrees of freedom - which I do not have).

Correlation is how two systems seem to depend on each other - as described by a third observer. But then the same issues applies to the third observer. If this is continued the "observer" whose view the physicist takes here, gets larger and larger, and eventually encompasses the universe.

I think there is something to this, but things seem missing.

I think another aim is to explain not only the state of things, but also it's evolution. To guess the future us the ultimate in the best possible way is like the ultimate goal. It's like the human brain, research lately has shown that recalling old events and imagination of future events in the brain really activate the same parts. So it's like the brains "memory storage" is optimized not to remember, but to imagine the future. This is thought to part explain what memories are sometimes remodelled by the brain - for the benefit of predicting the future instead, which is clearly a much more important trait.

To understand how things evolve, I personally want to understnad how things grow from inside and out, not how the outside self-organises relative some fixed lattice. This includes to understand the dynamics of the lattice itself.

The shannon inspired relative information is not an intrinsically relative one IMO, it's a strict external-reference "correlation" in the ordinary sense. IE. it's not what I would call an intrinsic measure.

/Fredrik

 

[newbee]

atyy asked:

"Could you clarify the question, maybe with an example?" in regards to my post that read "The notion of a potential or Lagragian as a function of a spatial coordinate to which there is no explicitly associated scale is bothering me.".

I don't know what type of example you may be looking for. It just appears to me that the notion of position would make little sense to my imaginary microscopic observer. So he/she would never write down a potential or Lagrangian (at least not as a function of position) in any model intended to predict his/her observations. To us macroscopic beings the notion of position makes some sense but possibly only for macroscopic systems. So what would our microfriend write down?

 

[newbee]

atyy

Oh and thanks for the link. I will try to read the paper later in the week.

 

[atyy]

I don't know what type of example you may be looking for. It just appears to me that the notion of position would make little sense to my imaginary microscopic observer. So he/she would never write down a potential or Lagrangian (at least not as a function of position) in any model intended to predict his/her observations. To us macroscopic beings the notion of position makes some sense but possibly only for macroscopic systems. So what would our microfriend write down?

What theory is this? Just standard non-relativstic QM? There's a wave equation, and it makes sense just like the wave equation for an electromagnetic wave ... no?

 

[Fra]

I think it's clear that particles don't "write equations" etc, but I see what newbee is asking, he is asking how a very simple observer can relate to it's environment, and things like spacetime. I think "what would our microfriend write down" is a metaphor for how a simple observer can relate to a complex environment.

If there is a limit to the exten it can (which I think; and which is also I think the intuitive idea) then the question becomes how does spacetime EMERGE from the inside point of view, as say that observer grows larger. And how does the "laws of physics" scale, along with this?

The unification that we espect from the current law of physics, we expect some kind of "unification" at "high energy", but in practice high energy just means that we smash all the parts into the smallest possible. And these smallest parts then can be thought of as minimal observers, and perhaps the point of view of these "minimal observers" is the point of view that makes unification intuitive. Then as these minimal observes start to condense together, and thus "grow", we start to distinguish the usual forces.

So I think the question asked here is closely related also to unification. This is why I think the high energy scale relative to one observer, required to break the parts up into unification, is dual to the "low complexity scale" of the inside view, if you take on the view of one of the minimal players. As per the current expectations gravity and perhaps thus spacetime might be expected to be the first thing that condensates.

Then perhaps the original question one should not think of electrons but perhaps even smaller things, something that touches the quantum of spacetime, the minimal observer that exists not only at some GUT energy scale but even at some TOE or Planck energy scale.

/Fredrik

 

[newbee]

What theory is this? Just standard non-relativstic QM? There's a wave equation, and it makes sense just like the wave equation for an electromagnetic wave ... no?

Well both, in a some sense.

Obviously NRQM and RQM as models of our universe work well with respect to predicting many phenomena not predicted by classical mechanics. The question I am ultimately asking is whether we have fallen into a trap set by our notion of what position is and that this trap may be hindering the creation of better models of our universe.

I used the micro-observer in the OP as a means of trying to get people to think about the shortcomings of our notion of position. I am pointing out that IMO an operational definition ( a process for identification of a thing by distinguishing it from its background of empirical experience) of position would be impossible for the imaginary micro-observer.

Furthermore I am pointing out that the seed of the "problem" with position might be contained in NRQM. In a manner similar to how the seed of the "problem" with time was contained in the classical notion of relativism. In that case it could be demonstrated that the laws of physics would not be expected to be invariant under classical relativistic transformations. Some were bothered by this lack of invariance although there was nothing within the theory of classical mechanics that told us we should be bothered.

 

[newbee]

I probably should have written: I am pointing out that IMO an operational definition of position would be impossible for the imaginary micro-observer or it would be, at the least, very different from ours.

 

[my_wan]

What Fredrik said. Unfortunately I can't articulate any better at this point.

 

[newbee]

Would a mentor or administrator please move this thread to the general physics-> independent research area. Thank you from the OPer.