The Foundational Problems of Quantum Mechanics

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Born and Heisenberg gave a joint paper in which they insisted that although quantum events could be described, finding reasons for the events was impossible.
"We maintain that QM is a complete theory; it's basic physical and mathematical hypotheses are not susceptible to further modifications."
This was Max Born's reply to Einsteins assertion that quantum mechanics was "not yet the real thing".
He said it was not only the real thing; it was the final thing.
Born and Heisenberg were now saying that the work was done. It was never going to be more intelligible or more fully connected to the rest of physics.
Starting with that Solvay Conference of 1927, Einstein ceased to be merely skeptical or dissatisfied with the state of quantum physics. He became definat , refusing to bow before the claim of completeness , finality , unmodifiability.
At the close of the formal session, Einstein had his first opportunity to show his new mood.
Bohr gave his summary of what physics was to be, now that mathematical probability had replaced physical causes.
This was the long-awaited new thinking promised at the end of Heisenberg's paper.
Bohr had presented these same ideas a month earlier at a conference in Italy, but many physicists, including Einstein had not attended that affair and did not know what Bohr said.
Bohr was never an articulate man, and any attempt to summarize his remarks inevitably makes them seem clearer and more focused than they appear to his audience.
Einstein tended to see wider and deeper than his colleagues and appears to have grapsed the nub of Bohr's point.
Einstein had imagined a solution in which relativity was a limiting case; Bohr presented something different.
The very nature of quantum theory , Bohr told his audience, forces us to take distinct concepts of classical physics and use them as complementary , exclusive features in a description of Quantum phenomena.
Physicists have been trying to understand light's waves and particle as a whole.
It cannot be done.
In some experiments light appears to be a particle; in others, it appears to be a wave.
The concepts are complementary. meaning that wer can understand light's nature only if we abandon the search for a coherent unit and think of it as sometimes being like a particle and sometimes like a wave.
We can think this way without becoming contradictory because these complementary concepts are also exclusive. That is , we can never perform an experiment an experiment in which light's wave and particle natures are both measurable.
This complimentary is the profound physical meaning of Heisenberg's principle. Whatever p symbolizes in Heisenberg's algebra is the compliment of whatever q symbolizes.
Thus, position and momentum or time and energy are complementary and exclusive notons in quantum physics.
Therefore, it is impossible to design an experiment that will simultaneously determine a photon's position and momentum or its time and energy.
Bohr was not given to mathematical reasoning of the sort that Max Born had used in arguing that a quantum wave was a mathematical fiction describing probabilties without underlying causes.
Nevertheless , Niels Bohr's theory of complementarity stood firmly in Max Born's camp, because it insisted that experimental outcomes could only be described, not explained in terms of real causes.
Bohr was replacing Einstein's theoretical arch in which facts and concepts supported one another with a new style in which rival facts and rival concepts tolerate each other.
Any observation of atomic phenomenon involves an interaction between the phenomenon and whatever tools the scientist uses to observe the event.
Thus Bohr told his audience
"an independent reality in the ordinary physical sense can neither be ascribed to the phenomenon nor to the agencies of observation."
The logic of Bohr's argument rested on one noval dogma: the language of classical physics could not be abandoned.
Quantum Mechanics had to be understood in classical terms and in order to avoid seeing classical terms such as wave and particle as contradictory, they had to be viewed as complimentary. Only when taken together did quantum mechanics "offer a natural generalization of the classical mode of description."
Bohr gave his reason for this axiom of complementarity that "every word in the language refers to our ordinary perception".
Classical physics does an excellent job of describing the events we can study with our senses. Our language , thus describes experience that are well suited to a classical understanding.
Quantum phenomenon, however cannot be tracked directly with our senses. We see hints of events - changes in the atomic spectra, for example - but when we try to talk about them we must think in classical terms , and in a quantum world such thinking makes sense only we we understand complementary notions rather than contradictory ones.
But surely some readers are bound to object, we can make up a new language that is more suited to this new world.
Physics had already done that by using the language of mathematics.
It coined a whole string of symbols applied to quantum events.
They work perfectly in equations , the sentences of mathematical language.
It is just when we try to understand these symbols - that is we try to imagine what is happening we fail.
Our perceptions have trapped our imaginations in a classical world where quantum events do not apply.
This argument aimed a secret assumption behind Einstein's talk of "accessibility." He often said that the world is lawful and the laws were accessible to us.
By that last point he meant that logic and fact were sufficient for us to discover and understand natural laws.
But Bohr was saying that accessibility rest on a third thing.
In addition to facts and logic there was language, and language can never dive down from the classical to the quantum level.
Einstien did not see Bohr as a true and faithful disciple, and he never had any patieence with Bohr's complementarity.
It seemed to him that it was simply giving up on the effort to understand the physics of quantum events.
A similar solution could have followed the Lorentz equations if Einstein had tumbled over the edle of the Alps and never completed his work.
How could anyone then explain the electrivity - magnetism paradox that Einstein so worried over?
Surely no one would have settled for the "explanation" that the very nature of electrodynamics forced scientists into understandong electricity and magnetism as complementary concepts.
Einsteins argument was locked with a contradiction in Max Born's probabilistic understanding of QM and Niels Bohr's complementary interpretation.
Einsteins arguments were always grounded in experiments, usually imaginary ones.
In this case he pictured a photon passing through a slit in a photographic plate.
This thought experiment happens in reality every time a photographer snaps a shutter.
Light bends when it passes through the slit.
Schordingers equation shows that this bet light might land anywhere on film.
Max Born's probabilistic interpretation says the chances of the photon's stiking a point are spread over practically over every point on the film.
When the photon strikes the film, however the probability of its landing anywhere drops to zero.
We cannot know what will happen until it happens.
Bohr took a stronger view and insisted that during the underdetermined period the photon maintained a virtual reality as though it smeared like butter across every point where it might strike.
This idea however contradicts relativity because the collapse of the smeared photon into a single point would be instantaneous ( faster than the speed of light ) and like Newton's discredited accout of how gravity work, would constitute action at a distance.
Einstein proposed an alternate explanation.
The photon passes through the slit and follows a distinct trajectory to the point on the film where it strikes.
Quantum Mechanics cannot describe this trajectory and is therefore not the whole story.
Einstein had gotten, at a first hearing, to the central mystery of the revolution the Quantum Collapse.
What happens when a quantum particle that might appear in many possible places appear in one particular place?
Einstein didn't know nor did Bohr. Heisenberg, Pauli and Dirac however were more concerned with saving quantum mechanics than with complementarity and they insisted that Schrodinger's wave equation does not represent actual events in space time.
It expresses what observers can know about events.
We know that the photon entered the slit and that it hit the film at some point.
The wave equation tells us what changes were of it's hitting any point.
True , QM cannot descibe what happens between any two observations,
but incompleteness cannot be held againest the theory.
It is built into our own experimental limitations.
We can never perform experiments that give us part of the data.
We can never get the full objective data thus we cannot develop a full objective theory.
The dispute over the meaning of the quantum collaspe continues to this day.
Einstein had transformed Bohr's complimentarity from being an ambigous account of what happens in quantum events into being a way of talking about these events.
Over time would physicists feel the hurt from this sting.
Complementarity would become known as the "Copenhagen Interpretation" - rather than as theory and the worldwide shorthand for the paradoxes of quantum theory would not be Bohr's complementarity but Heisenberg's principle.
Not that Einstien wanted to prop us Heisenberg.
His thought experiment with photon and film had not challenged Heisenberg's principle but Einstein shifted his attention there.
He began looking for an experiment that would allow a more complete collection of data than the Heisenberg team thought possible.
If we could find a technique that allowed the simulataneous discovery of position and momentum or time and energy, he would provide that quantum mechanics had indeed not yet brought us to the secret of the Old One.
This effort led to the most famous set-pieces of debates with Einstien and Bohr over Quantum Mechanics.
Many of his arguments composed of concening photon's passing through slits.
A typical one used a shutter to guard the slit.
The shutter opens.
Light passes through and strikes the film plate.
As it passes through the slit , the light strikes the moving shutter's and then strikes the plate.
If we study both the plate's and the shutter's reaction to the photon collision, we can calculate the time, position and momentum of the photon to a greater accuracy than the uncertainity principle allows.
Einsteins mistake in his reasoning was to overlook the inherent uncertainity in the experiment.
Suppose the mass of the plate is infinite.
The photon's momenum will not know the plate ever so slightly.
Instead , according to the physics of momentum, the plates mass will increase slightly,except that changes in infinite things cannot be measured.
The experiment would give no data.
So we will assume the more realistic condition that the film plate's mass is not infinite.
Now the photon's momentum will jar the films plate ever so slightly, allowing in principle a technician to measure the photon's momentum; however jarring the photographic plate will slightly blur the point where the photon landed.
Working through the math in detail shows that Heisenberg principle survives intact.
The more momentum , the less certain the point of landing.
Similar considerations show that measuring the shutter action also includes enough uncertainty to make it impossible to calculate the exact times and energy of the photon's interaction with the shutter.
A certain kind of philosopher would have objected this reply "begs the question".
It assumes the point that it set out to test - that uncertainties in the photon's interaction prove the validity of Heisenbergs principle.
Einstein raised no such objection , however because scientific arguments are settled by experiment, not by logic.
Einstein used logic simply to look for contradictions.
In this case Heisenberg's principle was consistent even when Einstein didn't thin it was coherent.
So he moved on looking for other experiments.
Einstein was exhausted , as I am typing all of this from a book.
Einstien said he was getting old and that a younger man might do better.

Here's my situation:

This book is expensive , I'm only a Senior Highschool student with plans of heading to the University of Waterloo for my Bachelor of Mathematics degree but it still doesn't mean I don't understand what I'm reading.
And I'm pretty sure most users on this site , through Alexa.com Statistics are under 21 looking for support , this is obviously the wrong forum to post this but still Autistic's have deep perceptions into things.

Mathematicians are makers of patterns that start from vague pictures that are painted with symbols, I seek out those patterns through methods I call top-down learning and I end up with pictures , I hypothesize of what patterns they could be and I create my own name for them then I actually look for the formal pattern , this helps with divergent and lateral thinking as schools are mostly filled with narrow minded contemplation and rote memorization without much explanation of one's analysis -

I've already done this and it is working pretty well as I get completely absorbed in a topic for hours on end. I read reference books as they are more straight to the point and they include less jargon and dead language that mathematics education offers such as names like Quadrilateral instead of Four-sided or Sec X instead of the reciprocal of cosine.
I would say through this method , I've learned more mathematics and physics then I have in years.

Your probably thinking , well he can't do that , he's suppose to climb up the ladder like everyone else before he's entrusted with using Integrals and before the teacher knows he can learn differential calculus or matrix mechanics? Well that's a myth anyone can learn anything if they have a passion for it , regardless of intelligence. A gorilla had an IQ of 50 and learned sign-language , it boosted his IQ to 75.

Mathematics is suppose to be creative , it's not about memorization of formulas , signs , tables. Art is not a race. It's about using them to create your own mathematics or even discovering/inventing mathematics.
So please don't mention I can't learn this stuff , I've read through the preview of this book and if you can understand English you can understand the language of physics: Mathematics.

So my question is : if anyone finds a free version to download for this book , or at least a University Library that doesn't have expensive membership , as I come from a middle-class socioeconomic status , Please mention it.

Have you published any papers Ruveyn?

I am very interested in your thread but may I make a suggestion?

Personally I need for you to slow down and take one thing at a time. I know that that seems impossible because all of quantum theory runs into itself and is so exciting. It might be easier to understand where you are going if you leave behind the quotes of physicists of the past until you need to specifically reference them. Tell me in your own words what you think and believe then hopefully I can respond. It is just too much right now, I don't know where your going with this your being just too broad. I am very bad at organizing my thoughts and being coherent (as anyone who has read my posts soon finds out) so I am not the best coach on that but I would be very interested in talking about your topic.

As far as looking for that book I can't help you there, but once you are in college there should not be any kind of membership fee to use the library, that is what you pay for in your tuition. I am only an undergrad and I am not in a physics or math program, I am studying for two degrees in biology, one in biotechnology and another in environmental biology and I am working in a research lab and we are discussing my research project which will begin next year, I am technically a freshman/everything else but senior depending on the program you want to look at. All that said, I love physics just as much but my college has a limited physics program so it is very nice to talk to others who have experience or an interest in this subject.

I am very interested in quantum mechanics and theory, specifically, but I do look at it from an intuitive perspective. I am very bad at math. (actually I am very good, never got anything less then an A, but I don't have the kind of mathematical background to speak in terms of quantum theory formulas.) I do, on the other hand have a natural sense of atomic behavior. As a child I could not understand people, but the periodic table was very clear, at six my favorite number was 6.022x10^23, I always understood the trends of the table (and why they are) and love bonding questions in chemistry, In other words I don't believe that it is impossible to have an intuitive feel for at least the very basics of quantum mechanics. So where do you stand on intuitive understanding of the basics? How did you become so interested? And what exactly would you like to discuss first?

_________________
preemptive apology, "Sorry for what I will say or do, I have A**#@%! syndrome."

True @ ruveyn (fond of your position on philosophy regarding this thread)
Agreed @jono & @ Fnord (nice list)

@OP: no offence but if you are still in high school and if you are not a prodigy (in which case you would probably be half-way through your Phd right now) I think you should get your feet wet at first. Then you would know why people look with an unfavourable eye to this thread.
Don't get me wrong - your enthusiasm is really admirable and I would encourage you to keep up with the good work. You are really well spoken and you should have no problem with your college interview, I would suggest aiming as high as you can.
However. Do you even have the slightiest idea what does a *foundation* of any scientific theory mean? You have a really long way to understanding that book you've just recommended. And if you do then I am in awe. Correct me if I am wrong, but it sounds like an arrogance of youth to me.
So...I suggest putting time and energy into your grades & university applications, do not go over your head right now, it is counter productive, imo. Then put some foundations for yourself. And maybe by the time you reach grad level you can enjoy The Foundations of Science. It goes something like this: http://hbpms.blogspot.com/
Studying science teaches one a whole lot of humility. What can I say - (advanced) quantum is no walk in a park. The question remains, though, what is your background on actual QM? Discard popular readings.
My post had no intentions of having a didactic tone but it apparently did. I just feel very strongly about people who are *talking science*. Philosophy is all good until it remains in a sandbox.

Quote mar00
True @ ruveyn (fond of your position on philosophy regarding this thread)
Agreed @jono & @ Fnord (nice list)

It goes something like this: http://hbpms.blogspot.com/
Studying science teaches one a whole lot of humility. What can I say - (advanced) quantum is no walk in a park.






I checked out that link and that is GREAT, I have been interested in expanding my understanding to the mathematical computations involved and was VERY excited about some of the links to free PDF books, it is hard to find anything as advanced in an undergrad school and I have looked online but never with much luck,

I'm at Stage 3 so far , but in no way do I consider myself a prodigy yet.

In response to the other user , I made a long reply

It'll be a long time before I create my own theory , and I will prove you wrong in the future , I'm already working on conceptual foundations that reject the concept of the atom. Something I do have is creativity , Neurotypicals usually don't that's why they end up doing drugs at parties with the math department.

Oh and I'm still going to continue posting , I still have to look for sources.

I'm not going to put down the kid. First of all I have so much to learn that I can only refer to a limited skill set myself. I think he is just young and when you are in high school you are limited to comparing yourself to the kids around you, whom are mostly more interested in who is sleeping with whom and what some housewives of someplace said on TV last night, so he may be in a lofty mind set because of that, when he (I know you can, and will, read this samarda, so don't take it like I am talking behind your back, I just think that what I'm saying might be true and might help you to express yourself better as you mature) does get to college and meets other students his age who are his equals intellectually he will have more of an actual peer group to base himself on and some of his (your) assumptions about others and yourself will become more realistic, not to say that you are wrong just that you may have a slightly skewed perception or at least a limited one based on the group you might interact with in high school.

On the actual subject, I do think that there is some truth to the idea that we as humans, in general, do limit our understanding of the universe by trying to make it fit what we consider to be law or theory. By this I am trying to say that we try to simplify, categorize, and place laws on everything. For instance the thought process that goes along with wave/particles. Most (not all) people can only think of something in one way or the other but in reality these things are what they are regardless of how we see them and would exist just as they do whether we existed or not. It is a waveparticle not a wave or particle, It appears that way to us because we are trying to stop something or interfere with its normal activity in an attempt to study it, (this is a bad analogy but the only one I could come up with) like if you wanted to know if a tree makes a noise while it falls in a forest if no one is there to hear it, of course it does, the vibrations will be made no matter what, the question becomes does a sound count if it is not registered by anything or do the sound waves count if they never interact with anything and just go into infinity. I think about these things in this way, everything we perceive is a wavelength and frequency of and interaction on the subatomic scale; light, solidity, gravity, sound, even (of course) my own brain activity. We can put a name to these things, we can place them in categories, we can build instruments to measure and compare these things but when it all comes down to it it is all a perception of mankind and nature does not care whether we are able to understand it or not. That being said I sure would like to understand it, categorize it, and know the laws governing it I am sure that some day, in the future, quantum physics will be all figured out and be common knowledge taught in school but by then there will be some great new mystery. Till then all we can do is theorize, formulate, discuss, and test new hypothesis.

_________________
preemptive apology, "Sorry for what I will say or do, I have A**#@%! syndrome."

If this doesn't sound absurd , that's a bad thing since this took alot more imagination then knowledge. I'm thinking thoughts that aren't grounded in wisdom that is a repetitive cycle of stereotypical knowledge about phenomenon passed on to younger "kids". I do admit you people are wise at avoiding this problem.

I'm glad it's flying in the face of decades of research that's a healthy process , my perseverance will finish it as I'm working on something I love. Everything in science is a set of assumptions. It is true that no one knows for sure, and we just accept that for now to be the proof that something is what it is and something is how it is.

I do have a healthy self-concept , I socialize once and while with only a few of my peers on topics that are far beyond are reach for amusement. I think were off to a pretty good start considering our ages and marks (86+) in Formal and Natural Sciences. I usually talk to me teacher about questions about the universe. But in my view , they are just speaking about what they learn in school and never even heard of K/M theory.

Thanks for the concern , I will focus on school more but it's better if interest is intrinsic and overriding.

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The main potential of this hypothesis is to try to uncover the form in the formless , to explain random unpredictable behavior in predictability , and to never assert that it is final. This hypothesis will only be a development , I'm still incubating this baby.

I'm working on conceptual independent-backgrounds for non-linear dynamics , what I'm doing is trying to explain my hypothesis in terms of continuum mechanics without convection - that is without the assumption of atoms/molecules.

I'm already finished learning intermediate calculus but even calculus nor continuum is sufficient in describing this anomaly. So I'll have to create new mathematics from this conceptual picture in the future , when I'm a graduate.

It is not similar to the Navier-Stoke Equations since it tries to discover why certain turbulent positions in gas/fluid amorphations in 3-dimensions are in a certain way and why the function behind smooth manifolds is such , thus it is trying to discover the form in the formless.

It is a contender for the Navier-Stokes Existance and Smoothness problems as it hints turbulence, through many failures in this invention that are studied will lead to discoveries.

I'm also looking for the behaviour of subatomic particles and their chemical and physical properties in forming new compounds in bonding , I've turned to interdisciplinarity - Biophysical Chemistry.

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What were you doing at 17? I've already reached Stage 3.

Perseverance is the ultimate ingredient. Your ideas can gain the momentum required to become established as the works , only if you are strong willed in the face of opposition and misfortune.