A little clarification on quantum theory

[Higgs Boson]

I would like a little clarification on the "Reason why quantum theory is accepted to be one of the foremost physical (metaphysical?) theory of nature". Currently have no knowledge about the intricacies of physics, having only skimmed over the basics of classical (newtonian) physics. I interpreted on an introduction to quantum theory, that the results that quantum theory predicts are in highly ideal conditions that can not be physically achieved by us or it considers possibilities which are beyond the feasible spectrum of environmental phenomena. How is the theory viable in this context ?

Another example if the heisenberg principle states that we can never measure the position and momentum of an electron with certainty relative to one another, then speculating on the position and path of the electron in Young's double slit experiment becomes null, doesn't it. I mean suppose even if we only calculating the probability of the electron falling at one place on the screen by doing the experiment with one slit and then repeat the procedure with two slits, the experiment becomes null because the heisenberg principle (assuming it is true) clearly does not allow us to predict the path of the electron. Why don't we assume that the results should be within the expanse of the postulates of classical mechanics and relativity rather than supposedly inventing an entirely new theory to justify an experiment, the results of which are uncommon ?

 

(Please ignore the factual inconsistencies if any and just look upon it as a meagre attempt to destabilise the oncoming quantum revolution.)

[ajb]

The simple answer is that to date there has been no consistent, repeatable experiment or observation that does not agree with quantum theory, within the defined domain of validity and within systematic experimental errors.

 

Even the strangest predictions are realised in nature.

[mississippichem]

Another example if the heisenberg principle states that we can never measure the position and momentum of an electron with certainty relative to one another, then speculating on the position and path of the electron in Young's double slit experiment becomes null, doesn't it.

 

[math] \sigma_x \sigma_p \ge \frac{\hbar}{2}. [/math]

 

The Heisenberg uncertainty principle doesn't state that one can't know anything about the position or momentum of an electron. It only means that the greater certainty one has in its momentum, the greater the uncertainty in it's position. One can be quite certain of an electron's position [to a point], but they will be quite uncertain of its momentum.

 

More mathematically [the best way to examine this], the product of the uncertainty in momentum and uncertainty in position can never exceed never be less than half of the that funny looking "h" depicted above, the reduced Planck's constant.

 

Quantum mechanics is more often than not counter-intuitive. There is rarely a clean classical analogy that "makes sense". Just know that, as ajb stated, quantum mechanics has endured the experimental test of fire and passed with flying colors.

 

EDIT: for accuracy

Edited February 28, 2011 by mississippichem

[IM Egdall]

The Uncertainty Principle is fully consistent with the results of the double-slit experiment. See link:

 

http://galileo.phys.virginia.edu/classes/252/uncertainty_principle.html

[swansont]

I interpreted on an introduction to quantum theory, that the results that quantum theory predicts are in highly ideal conditions that can not be physically achieved by us or it considers possibilities which are beyond the feasible spectrum of environmental phenomena. How is the theory viable in this context ?

 

I work on a project that relies on QM and routinely produce results that are consistent to a few parts in [imath]10^{16}[/imath]. One might say that a high-vacuum system, shielded from magnetic fields and temperature stabilized creates highly-idealized conditions. But they are achievable, highly-idealized conditions.

[DrRocket]

Quantum mechanics is more often than not counter-intuitive. There is rarely a clean classical analogy that "makes sense". Just know that, as ajb stated, quantum mechanics has endured the experimental test of fire and passed with flying colors.

 

 

 

"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper, a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I can safely say that nobody understands quantum mechanics." – Richard P. Feynman in The Character of Physical Law

[steevey]

The simple answer is that to date there has been no consistent, repeatable experiment or observation that does not agree with quantum theory, within the defined domain of validity and within systematic experimental errors.

 

Even the strangest predictions are realised in nature.

 

What about time dilation? If I'm standing near a black hole with an entangled particle while someone on Earth has one, and they become disentangled right...NOW!, then how could it appear at the same time to both observers if the time of the observer near the black hole would be slowed down?

Edited March 1, 2011 by steevey

[ajb]

What about time dilation? If I'm standing near a black hole with an entangled particle while someone on Earth has one, and they become disentangled right...NOW!, then how could it appear at the same time to both observers if the time of the observer near the black hole would be slowed down?

 

 

No-one has done any experiment like that!

 

And I did place a caveat "domain of validity ". Non-relativistic quantum theory, which is what I think the OP is really talking about would not be expected to hold in such extreme relativistic situations.

 

Near a black hole one would have to use semi-classical gravity, that is the relativistic theory on a classical background.

 

In the more extreme one would expect quantum gravity to kick in, and we have no concrete model for that.

 

 

How would the observer on Earth know that you have detected that the particles are disentangled? It will take time for you to send a message back to him. And if you were right on the horizon this time delay would be infinite! I mean, I am not sure how you would decide what the "same time" means.

 

I will have to think a little more on this.

[lemur]

"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper, a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I can safely say that nobody understands quantum mechanics." – Richard P. Feynman in The Character of Physical Law

From a politics-of-science perspective, it seems like quantum physics is designed in a way that prevent people from understanding it. This is generally similar to statistical approaches to data that effectively prevent subjectivity from playing a role in scientific reasoning by encoding logic in mathematical procedures, which in turn generate encoded conclusions based on pre-defined parameters. The only reason I can think of that people would prefer this approach to science than a more comprehensible one like relativity or something else designed and desired to be understandable is that people are afraid of the consequence of physics being widely understood. So when Feynmans says he can "safely say that nobody understands QM," it seems to resonate with the fact that he witnessed first hand the conversion of atomic science into atomic weaponry/power. To me, once you let fear of the potential power of science exceed faith in its potential to facilitate good, you've lost the capacity to do real science at all because science emerged as a project of enlightenment not control.

Edited March 1, 2011 by lemur

[imatfaal]

Lemur - the fact is that with modern physics there is a choice between "something ... designed and desired to be understandable" which tallies with our innate preconceptions of the way the world works and theories that actually describe experimental reality and can claim to be consistent with the facts. If you can get hold of it, have a read of the introduction to Leonard Susskind's The Black Hole War which looks, briefly but nicely, at this matter. Whilst I can see the points of the argument that claims an almost deliberate obfuscation, it is incorrect; there are no easy, accessible, and everyday routes through QM and most of modern physics.

[lemur]

Lemur - the fact is that with modern physics there is a choice between "something ... designed and desired to be understandable" which tallies with our innate preconceptions of the way the world works and theories that actually describe experimental reality and can claim to be consistent with the facts. If you can get hold of it, have a read of the introduction to Leonard Susskind's The Black Hole War which looks, briefly but nicely, at this matter. Whilst I can see the points of the argument that claims an almost deliberate obfuscation, it is incorrect; there are no easy, accessible, and everyday routes through QM and most of modern physics.

It's not like I would ever expect someone to say that QM is a project to deliberately obfuscate theoretical physics and replace it with pure math; and I appreciate the logic that it doesn't make wrong predictions. I'm just more interested in understanding nature than translating it into math so I seek theories that explain things in ways that are comprehensible to my mind. I'm not insisting that nature has to make itself understandable in my terms, as people would accuse me of doing. I just don't think I should have to give up physics because a lot of the math is above me.

[imatfaal]

But at a point the translation into terms that are comprehensible to your mind removes the validity of the theory - it is then worthless. It is not just that QM doesn't make wrong predictions, it is the fact that no simple classical theory can make the correct predictions.

[lemur]

But at a point the translation into terms that are comprehensible to your mind removes the validity of the theory - it is then worthless. It is not just that QM doesn't make wrong predictions, it is the fact that no simple classical theory can make the correct predictions.

Your making a very broad assumption that because you observe a pattern of invalidity among comprehensible theories that this means that there's some essential incompatibility between comprehension and validity. In simpler terms, you like many other people are content to give up intuitive comprehension in exchange for effective math. Since math isn't as rewarding for me as it seems to be for many others, I'm stuck in a perpetual quest for intuitively comprehensible knowledge. Actually, it's not just about math. I don't like black boxes that process data in incomprehensible ways and spit out results that have to be accepted on the basis of faith in the machine. Even if the machine never makes mistakes, I dislike the fact that the processes are incomprehensible to me. If a shaman taught me a rain dance that ALWAYS worked, I would still consider it unscientific if I couldn't figure out the causal mechanics that linked the dance to the rain that fell afterward.

Edited March 1, 2011 by lemur

[imatfaal]

Not at all - the assumption is yours; to whit, that an explanation exists that is both valid and you can comprehend. Bell's inequality, whilst still argued over, goes a long way to confirming that classical theories cannot explain qm effects. The second reason for my contention is that, if a simple and true heuristic existed I wouldn't be trying to get my head around grassmann variables; ie the educators of the world would seize upon it with great sighs of relief.

[swansont]

From a politics-of-science perspective, it seems like quantum physics is designed in a way that prevent people from understanding it. This is generally similar to statistical approaches to data that effectively prevent subjectivity from playing a role in scientific reasoning by encoding logic in mathematical procedures, which in turn generate encoded conclusions based on pre-defined parameters. The only reason I can think of that people would prefer this approach to science than a more comprehensible one like relativity or something else designed and desired to be understandable is that people are afraid of the consequence of physics being widely understood. So when Feynmans says he can "safely say that nobody understands QM," it seems to resonate with the fact that he witnessed first hand the conversion of atomic science into atomic weaponry/power. To me, once you let fear of the potential power of science exceed faith in its potential to facilitate good, you've lost the capacity to do real science at all because science emerged as a project of enlightenment not control.

 

No, that's a bunch of baloney. There is no "politics of science" as you describe, which in any event runs contrary to Occam's law. I would love it if physics were more widely understood. The problem is the demand that it be easily understood, and that's not within anyone's power to grant. It is the job/goal of science to build models explain how nature behaves, but there is no guarantee that the behavior will be understandable. Statistical approaches to remove subjectivity are used because they have to be; you can't have laws of nature that are subjective.

 

So if you don't understand something and wish to place the blame somewhere other than the mirror, your complaint needs to be directed at mother nature rather than the scientists.

[Schrödinger's hat]

At the end of the day, creating a theory which is both functional and intuitively comprehensible is a much stricter requirement than something which is merely functional.

That being said, I don't think that an intuitive understanding of quantum physics is unattainable. At least to the degree that I intuitively understand anything.

 

I by no means claim to have such an understanding, but with further thought and improvements in pedagogical methods I do not see why it cannot be achieved.

 

I have a few textbooks on electromagnetism written early last century, and I think I am justified in saying that their authors' intuitive understanding of electromagnetism was far less well developed than that of the average first or second year undergraduate. The structure of the theory of EM has not really changed since then, but the ontology -- the analogies and the stories we tell ourselves -- involved has advanced.

In addition to this, people are exposed to concepts such as fields from an early age, toys have magnets in them. Concepts which were abstract and counter-intuitive -- accessible only through mechanics and mathematics -- then have become much easier to comprehend.

 

Of course I am glossing over the development and spread of relativity, and numerous other relevant points, but I do not feel this is important for what I am trying to communicate. There are as many people around with an intuitive understanding of EM that is based on a relativistic ontology as not.

 

Coming back to intuitive QM, there are some parts that are intuitively accessible.

Over time, I have learned to think of things as a probability distribution (I coopt the mathematical words as labels for intuitive objects because I have no other), an electron (or any other object) is an intuitive object which is neither wavelike, nor particle like. Letting go of thinking of the statement 'the electron is here' as having a definite truth value is important for this.

 

The thing I am having the most difficulty with is measurement theory (what exactly is an interaction and why?). One important point here is that there is no such thing as a passive measurement.

We think of observing or seeing as something which does not involve the system, but this is untrue.

Measurement in quantum physics is much more akin to reaching out and touching something.

You cannot know anything about a system without interacting with it. You have to hit it with a photon, or an electron or something else. This is what collapses the wave-function.

This only answers one of myriad question about what a measurement is, and I am simplifying an already incomplete understanding of the theory in order to communicate it in English.

 

I think another important question to ask ourselves is: what does it mean for a concept to be intuitive?

I think that as these concepts become more and more ingrained in the public mindset, and children grow up with stories, and toys (I've often pondered over making computer games where quantum concepts are important) which involve these concepts we will start to encounter people for whom Heisenberg's uncertainty principle is as obvious and elementary as the idea that a ball will fall when we drop it.

 

Look up Feynman's works. He was often interested in making concepts more intuitive.

[Higgs Boson]

But just consider something like the interpretations of the Schrodinger's Cat thought experiment, one of which prominently hypothesizes that until the time that we open the room and look at the cat to know, whether it is alive or dead, the cat is both alive and dead and "exists in something like simultaneous parts of the same universe." Now to a beginner like me this seems ridiculous.

 

Also, basing a theory only, on statically derived data and whose predictions we can only comprehend or speculate as seems to have been illustrated above-is rather imprecise to a beginner like me however much abstraction it may epitomize. I mean lets say that even if every phenomena in nature can be predicted to a high degree of accuracy and corresponds to the quantum theory, the predictions of quantum theory do not assert anything clearly. As far as I have read and to put it rather bluntly" Quantum theory is a collection of statistical data which nobody understands to quote Richard Feynman. Atleast the underlying sentiment seems to convey so."

 

I believe that not only does a good theory correspond to observations and make predictions but that it also makes sense (I don't know how can a theory make predictions, if it doesn't make sense.)

 

Also, i would like to state that the point i had made earlier of highly idealised conditions was in the context that if those highly idealised circumstances are never naturally or artificially generated, what is the relevance of talking about them ?

 

An example would be the above were the cat is either alive or dead. Speaking of that,(of course without using quantum mechanics in my case) how can we possibly confirm that whether the cat was alive or dead(or both!) without seeing the incident or recording the incident? In such a situation the highly idealised circumstance would be that no one records the incident and yet we come to know of the outcome, which is physically impossible. A similar kind of observation is also made in the Double Slit experiment.

 

Please reply.

 

 

 

 

 

[lemur]

No, that's a bunch of baloney. There is no "politics of science" as you describe, which in any event runs contrary to Occam's law. I would love it if physics were more widely understood. The problem is the demand that it be easily understood, and that's not within anyone's power to grant. It is the job/goal of science to build models explain how nature behaves, but there is no guarantee that the behavior will be understandable. Statistical approaches to remove subjectivity are used because they have to be; you can't have laws of nature that are subjective.

 

So if you don't understand something and wish to place the blame somewhere other than the mirror, your complaint needs to be directed at mother nature rather than the scientists.

I can't exclude the possibility that I'm too dumb to get it or that I think in a way that is different the the type of thinking that makes quantum theory seem logical to some people. I do know that statistics tend to obfuscate at the level of human-sciences. For example, when education is correlated statistically with income, it obfuscates any direct mechanical understanding of how education influences productivity and how productivity in turn influences the production and distribution of material and non-material forms of consumption and wealth. Similarly, when you say that a wave-function is a pure mathematical abstraction and spin has no relationship to any kind of classically mechanical angular momentum, it's as if you're saying that qualitative mechanical thought has to be traded in for correlations and predictive equations that don't actually describe anything except the process of getting Y by plugging in X and N values. If you can't reason predictively about possible relationships between different sub-atomic dynamics, what is the point of modeling?

[Schrödinger's hat]

Your making a very broad assumption that because you observe a pattern of invalidity among comprehensible theories that this means that there's some essential incompatibility between comprehension and validity. In simpler terms, you like many other people are content to give up intuitive comprehension in exchange for effective math. Since math isn't as rewarding for me as it seems to be for many others, I'm stuck in a perpetual quest for intuitively comprehensible knowledge. Actually, it's not just about math. I don't like black boxes that process data in incomprehensible ways and spit out results that have to be accepted on the basis of faith in the machine. Even if the machine never makes mistakes, I dislike the fact that the processes are incomprehensible to me. If a shaman taught me a rain dance that ALWAYS worked, I would still consider it unscientific if I couldn't figure out the causal mechanics that linked the dance to the rain that fell afterward.

 

Anything which is sufficiently well defined and unambiguous is equivalent to mathematics.

We could take:

The total momentum of a system does not change.

or

[math]\frac{d}{dx}\sum_{n} p_i = 0[/math]

They contain the same information.

It just happens that the more complicated the thing we want to talk about, the more complicated and specific the words. There are plenty of concepts that are simple in one language, but describing them is a long and arduous task in another.

 

I believe that not only does a good theory correspond to observations and make predictions but that it also makes sense (I don't know how can a theory make predictions, if it doesn't make sense.)

You need to be clearer in what you mean. If 'makes sense' means you can understand it right now then this statement is absurd. Just because an individual cannot comprehend a given theory doesn't make it useless.

If 'makes sense' means that the theory is logically consistent, and consistent with experiment then QM already passes.

Also, i would like to state that the point i had made earlier of highly idealised conditions was in the context that if those highly idealised circumstances are never naturally or artificially generated, what is the relevance of talking about them ?

 

The circumstances in our models are never achieved. There's no such thing as flat space, a non-zero velocity where relativistic effects are not present or an ideal gas. That doesn't make newtonian mechanics or PV=nRT useless.

None of our models are correct, they're approximations. If any of our models were exact, we wouldn't need elaborate experiments, we could just predict, for example, the next thing you are going to post on this forum, to check them.

 

 

 

An example would be the above were the cat is either alive or dead. Speaking of that,(of course without using quantum mechanics in my case) how can we possibly confirm that whether the cat was alive or dead(or both!) without seeing the incident or recording the incident? In such a situation the highly idealised circumstance would be that no one records the incident and yet we come to know of the outcome, which is physically impossible. A similar kind of observation is also made in the Double Slit experiment.

I agree that the cat example is absurd, that would never happen. A cat would collapse into alive or dead because it would interact with things. It's too big.

Thinking about the cat too much is akin to thinking that 1000 years should have passed at home when I went to the shops because of relativistic effects. It's a parable.

 

 

Double slit we looked at the two classical possibilities:

The electron is a particle, a little ball-like object.

The electron is a wave, like a ripple.

 

We rejected these and came up with a third explanation

 

The electron is a wave function, an object a bit like a ripple and a ball

If parts of the wave function get out of phase, it interferes with itself producing patterns of high and low likelyhood of interaction.

If the wavefunction wasn't collapsed, the question 'did the electron pass through the left slit?' is nonsense, it doesn't have a truth value.

 

Sometimes we just have to accept concepts which were previously completely alien and unintuitive. This kind of thing can only be built through experience and interaction.

As it's pretty hard to have a meaningful interaction with objects where quantum properties are important, one way to experience it is through our models.

Sadly this is difficult without being able to do the mechanics and the mathematics.

 

 

I have some ideas involving the way integrals are done in QED, and letting go of the idea of free will (I see no evidence one way or another that it is needed. Our models work just as well if we decrease t as if we increase it) which may allow me to tell a story about measurement, like I have stories for gravity, or relativity or whatever. These ideas are not well formed, and I have a long way to go before I understand the theory properly, so I will not try to explain it.

 

One other thing to think about, is all your stories about the world are just that, stories. We make models and stories about the world to get a better grasp of reality, but none of them are all that likely to be true, many of them are already proved to be false. A crystal isn't a bunch of balls held together by sticks. Spacetime isn't a hyperbolic (3,1) vector space. You don't even touch things, it's just electromagnetic repulsion.

 

We may discover something soon that allows us to tell a much better story about QM, or make better predictions, or both. That doesn't mean current theory is any less right, or useful (and it's very, very good).

 

This brings me back to EM. The Lorentz Transforms were developed before Einstein's time, and your questions about QM mirror a lot of the questions about Maxwell's equations from the late 19th century.

There are other stories (warning: such things attract many crackpots and I have not examined this specific formulation in detail for flaws) we can tell about a universe which follows such mathematics, but they have their own problems, and require their own assumptions an counter-intuitive objects.

I'd suggest reading a bit about the history of EM and development of relativity.

 

Many physicist come to accept that: Whatever the real story is, it's probably not the one we are using. We know the mathematics is right and so we follow it where it leads, refining it where needed, and we tell ourselves whatever story is most useful at the time (be that particles, waves, balls on sticks, or clouds of probability).

 

Edit: combined posts to save space, this one is getting pretty epic

 

Similarly, when you say that a wave-function is a pure mathematical abstraction and spin has no relationship to any kind of classically mechanical angular momentum, it's as if you're saying that qualitative mechanical thought has to be traded in for correlations and predictive equations that don't actually describe anything except the process of getting Y by plugging in X and N values. If you can't reason predictively about possible relationships between different sub-atomic dynamics, what is the point of modeling?

 

 

We don't just have the maths, spin has a story too, it's just hard to tell the whole thing without the maths. It's a fundamental quantity, it provides some angular momentum, and interacts with charge.

Elaborating on one of my earlier points...somewhere. Sometimes we need to introduce a new character to our stories. Spin is a little bit like angular momentum. The same way a wave function is a bit like a wave and a particle. Trying to think about it in a way that relates to what I am familiar with in the macroscopic world doesn't work properly and hurts, but when it comes down to it, if you think about momentum, or mass, or position too hard they are no less abstract.

I am reminded of this: http://abstrusegoose.com/342

Edited March 1, 2011 by Schrödinger's hat

[DrRocket]

It's not like I would ever expect someone to say that QM is a project to deliberately obfuscate theoretical physics and replace it with pure math; and I appreciate the logic that it doesn't make wrong predictions. I'm just more interested in understanding nature than translating it into math so I seek theories that explain things in ways that are comprehensible to my mind. I'm not insisting that nature has to make itself understandable in my terms, as people would accuse me of doing. I just don't think I should have to give up physics because a lot of the math is above me.

 

 

"To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once." – Richard P. Feynman in The Character of Physical Law

 

 

[SMF]

I can't speak to the topic of this thread from which I hope to learn something, but I can't resist saying-- Lemur you apparently have no idea how science works and your statement regarding statistics in "human" or any science displays ignorance as well. Communications between scientists (e.g. research articles) are usually designed to be as accurate and clear as possible. When someone is unable, unwilling, or just doesn't have the time to learn an area of scientific specialization they should, perhaps in order to avoid embarrassment, consider not making strong assertions about the science. Just a thought. SM

[mississippichem]

I can't exclude the possibility that I'm too dumb to get it or that I think in a way that is different the the type of thinking that makes quantum theory seem logical to some people. I do know that statistics tend to obfuscate at the level of human-sciences. For example, when education is correlated statistically with income, it obfuscates any direct mechanical understanding of how education influences productivity and how productivity in turn influences the production and distribution of material and non-material forms of consumption and wealth. Similarly, when you say that a wave-function is a pure mathematical abstraction and spin has no relationship to any kind of classically mechanical angular momentum, it's as if you're saying that qualitative mechanical thought has to be traded in for correlations and predictive equations that don't actually describe anything except the process of getting Y by plugging in X and N values. If you can't reason predictively about possible relationships between different sub-atomic dynamics, what is the point of modeling?

 

What's the point of modeling at all in a non-quantitative manner? The math is there to ensure universal, homogeneous, and exact understanding between scientists. There is no other way to communicate that is not in some way subjective or imprecise.

 

You simply don't understand that understanding the mathematical workings of a system is knowing the system, and is a model even more prefect than a prosaic description. Even if you could understand the workings of quantum mechanics or an physical science at all without math what good would it do? Well how fast is the baseball moving?...fast...how fast?...really fast!

 

This problem gets exponentially worse when dealing with complicated systems that are beyond the scale of human experience. It is very anthropocentric of you to expect the universe to work in a way that you can easily understand. I could explain some of this stuff to you, but first you need to know about gradients, matricies, eigenfunctions and so on. The system we are dealing with just requires that level of technical understanding.

 

I couldn't build a rocket. I don't know the first thing about engineering, other than mathematics. It would be quite silly of me to demand that an engineer explain to me how to build a rocket. I would first have to go learn some basic principles of engineering.

 

Same scenario here. It is silly to even hint at the notion that physical science is purposefully designed to be cryptic or hard to understand. Once you understand it, then you are in a position to propose changes and point out grievances. I'm not positing an appeal to or from authority here either. I'm just saying that you don't understand, and will not understand until you understand more. Note that my use of "understand" three times in a sentence is intentional.

[swansont]

I can't exclude the possibility that I'm too dumb to get it or that I think in a way that is different the the type of thinking that makes quantum theory seem logical to some people. I do know that statistics tend to obfuscate at the level of human-sciences. For example, when education is correlated statistically with income, it obfuscates any direct mechanical understanding of how education influences productivity and how productivity in turn influences the production and distribution of material and non-material forms of consumption and wealth. Similarly, when you say that a wave-function is a pure mathematical abstraction and spin has no relationship to any kind of classically mechanical angular momentum, it's as if you're saying that qualitative mechanical thought has to be traded in for correlations and predictive equations that don't actually describe anything except the process of getting Y by plugging in X and N values. If you can't reason predictively about possible relationships between different sub-atomic dynamics, what is the point of modeling?

 

Modeling allows you to be able to predict what happens under different circumstances. Reasoning predictively is not limited to knowing a mechanism by which something works. If I have a black box with holes in it, and when I drop a marble in one hole, it comes out another, I can build a model of how the system behaves. The model may or may not accurately portray what's inside the box, but that's not necessary as long as the model works.

[Schrödinger's hat]

You simply don't understand that understanding the mathematical workings of a system is knowing the system, and is a model even more prefect than a prosaic description.

 

I would disagree. The mathematics is simply one representation. I don't think anyone really knows the universe. The mathematical representation is certainly a very descriptive and beautiful one, and it is the closest to the true workings of the universe.

Also, one can perform the mathematics without understanding it the way you do (or sometimes at all).

 

I think about things slightly differently depending on whether describe the situation with multivectors, or tensors.

Very differently if I am using a relativistic formulation rather than non.

You could argue that the relativistic model is the correct one, but in many situations the Newtonian one is more descriptive.

I could also use the same argument about any theory, all present theories diverge somewhere and I think the likelyhood that we will never find any holes in whatever the next iteration is is vanishing. As someone mentioned earlier. QM breaks down in strongly curved space, and we don't have anything really ready to replace it.

 

Sometimes a mathematical model will translate into a story in English in more than one way. (see neo-Lorentzian aether theories, I think they break pretty hard as soon as you mention gravity, but the point remains that it's another story that can be told about a flat universe with the same maths as SR)

 

but first you need to know about gradients, matricies, eigenfunctions and so on.

Again, I don't think these are absolutely necessary.

Some understanding of the quantum world can be achieved without a formal mathematical understanding of these, but the process of learning (and teaching) would be incredibly laborious and far less efficient than the mathematical route. There would have to be some representation of these concepts. Much as anyone who has ridden a bicycle over hills has some representation of the concepts of gradient, and potential well.

Edited March 1, 2011 by Schrödinger's hat

[lemur]

Anything which is sufficiently well defined and unambiguous is equivalent to mathematics.

We could take:

The total momentum of a system does not change.

or

[math]\frac{d}{dx}\sum_{n} p_i = 0[/math]

They contain the same information.

It just happens that the more complicated the thing we want to talk about, the more complicated and specific the words. There are plenty of concepts that are simple in one language, but describing them is a long and arduous task in another.

"System" is far from ambiguous, isn't it? If the math equation version of your statement expresses the same thing, I wonder if it lends itself as easily to questioning what exactly is meant by "system." In my experience, using math instead of descriptive language makes it more difficult to elaborate using concrete examples. If you say that the total momentum of a system never changes, I can come up with numerous examples of "systems" and contemplate what "total momentum" would refer to and whether all the possible momentum-transfers and transformations would always add up to the same amount. OR I could just think in terms of conservation of energy and ask where additional energy would come from or go to if the system was closed.

 

We don't just have the maths, spin has a story too, it's just hard to tell the whole thing without the maths. It's a fundamental quantity, it provides some angular momentum, and interacts with charge.

Again, where's the unambiguity? In what sense is it a "fundamental quantity?" What does that mean exactly? What does "some angular momentum" refer to? Interacting with charge is clearer language, but also vague. How does it interact with charge? In what sense does it interact? Purely in the sense that two variables "interact" by influencing each other's outcomes by some unknown mechanism?

 

As I noted in another post, statistics has a bad habit of using empirically-oriented words to describe mathematical relationships. Statisticians will say that education and age "interact" as variables to determine income, but "interact" doesn't mean anything except that when one variable changes, it doesn't directly change the dependent variable except as mitigated in some way by the other variable it interacts with. This tells you nothing about what is really going on when someone decides to pay someone else a certain amount of income based on their education and age. So the actual empirical "interaction" is obfuscated by using the term to refer to relations between variables in an abstract mathematical model. It's fine. They may be able to predict people's incomes with some accuracy using such a model, but it is misleading to say that there aren't actual material "interactions" occurring that aren't even considered by the model because the model relies on statistical samping/populations to make generalized predictions instead of concerning itself with what is or could be happening in actual interactions. I don't if this approximates what quantum equations are doing with data or if they are actually attempting to describe and explain concrete physical mechanics. The language is too ambiguous to tell.

 

Elaborating on one of my earlier points...somewhere. Sometimes we need to introduce a new character to our stories. Spin is a little bit like angular momentum. The same way a wave function is a bit like a wave and a particle.

My understanding of a wave function is that it operates as a wave though it consists of numerous repellant fields (electrons) that "dance around" variously disappearing and appearing with a certain probability within the wave. What I don't understand is does a hydrogen molecule, for example, only have two such "dancing points/fields" and do those two move around the nucleus randomly according to the probability-gradiations of the wave-pattern? Have I completely misinterpreted what wave-function refers to?

 

if you think about momentum, or mass, or position too hard they are no less abstract.

I am reminded of this: http://abstrusegoose.com/342

In bowling, momentum, mass, and position are experienced intuitively whether they are abstract in some philosophical context or not.

 

 

 

I can't speak to the topic of this thread from which I hope to learn something, but I can't resist saying-- Lemur you apparently have no idea how science works and your statement regarding statistics in "human" or any science displays ignorance as well. Communications between scientists (e.g. research articles) are usually designed to be as accurate and clear as possible. When someone is unable, unwilling, or just doesn't have the time to learn an area of scientific specialization they should, perhaps in order to avoid embarrassment, consider not making strong assertions about the science. Just a thought. SM

Embarassment? What should anyone's ego have to do with any of this? The fact is that research communications are subject to reasonable criticism from any angle. It is easier to do with social science because social interactions are concretely observable without instrumentation, etc. So when you suggest that the problem with criticizing statistical language is that one hasn't learned statistics well enough, you're ignoring the fact that they do in fact understand it well enough to criticize it. That makes it a dodging tactic to avoid responding to that criticism by shifting the blame to the critic's comprehension of the science. In this manner, you could endlessly suppress any reasonable claim to knowledge by saying that anyone who disagrees with you has yet to meet your standards of educational status.