Can quantum theory be explained?

[Mike2]

Mike2
an imaginary number is something as "real" as number 2 is, having i for example in the schrodinger equation make a lot of sense and it is in that way that nature is
go to https://www.physicsforums.com/showthread.php?t=56771 when the "history" of complex number is presented

OK then... what physical thing is being described by the imaginary portion of Schrodinger's eq?

 

[cire]

for example that the probability of finding the particle at (x,y,z) doesnot goes to zero (or infinity) when time increase

 

[Kane O'Donnell]

OK then... what physical thing is being described by the imaginary portion of Schrodinger's eq?

This is actually a very subtle and interesting question!

Well, sort of.

When you separate time and space variables, the space equation is purely real (though it may have complex solutions of course). On the other hand, the time equation is of the form:

$$i\hbar\frac{\partial T}{\partial t} = E T(t)$$​

where E is the separation of variables constant and as we all know, turns out to be the energy of the solution. Before I go ranting on about the solutions, compare the above to the time equation derived from the electromagnetic wave equation:

$$\frac{\partial^2 T}{\partial t^2} = -\omega^2 T(t)$$​

It looks like the latter is just the second order form of the first. However, note that sin(wt) and cos(wt) can be solutions to the latter independently. That is, both:

$$T_{1}(t) = A_{1}\cos{\omega t}, T_{2}(t) = A_{2}\sin{\omega t}$$​

are solutions to the EM time equation. On the other hand, T1 and T2 are *not* solutions of the QM time equation. A particular linear combination is, though - if A2 = A1, then:

$$T_{3}(t) = T_{1}(t) - iT_{2}(t) = A_{1}(\cos{\omega t}-i\sin{\omega t})$$​

is a solution provided $$\omega = \frac{E}{\hbar}$$. But the solution above can be recognised as our old friend:

$$T_{3}(t) = A_{1} e^{-i\omega t}$$​

the complex exponential. Notice that physically, the electromagnetism solutions can be made to change phase forwards or backwards in time (for a given "forwards" direction) - they are symmetric in that respect, whereas the first-order QM equation only allows one direction of time evolution - to obtain time-reversed solutions one must change the sign of the i in the TDSE.

Now, why does this matter?

Well, let's examine the *observable* probability distribution. If a solution to the TISE is described by a space-solution multiplied by a time-varying sine (say), our probability distribution would look like: (* denotes complex conjugation)

$$\Psi^{*}\Psi = \psi(\vec{r})^{*}\psi(\vec{r})\sin^{2}{\omega t}$$​

That is, the probability distribution would *change* periodically in time. This would be fine, say, for linear combinations of stationary states, but certainly not for single stationary states. On the other hand, when the complex exponential is used, the time variance with the probability distribution is not present. This is one way of explaining what the 'stationary' in 'stationary state' means. Indeed, if we push degeneracy to one side, every stationary state is forced by the Schrodinger equation to have a time-independent probability distribution.

So both the EM and QM time equations allow us to assign a number called 'frequency' to the periodic phase changes that the wave functions go through. However, the fact that the TISE is first order in time forces us to use a particular kind of function to represent this periodic aspect of a quantum mechanical object.

Of course, the EM equation admits the complex exponentials (in both time directions) as solutions too, but I'm not sure whether that is interesting here.

As a side note, I should point out that the complex exponential here is one of a more general class of unitary operators that *implement* symmetries on the underlying state space. Every unitary operator has the form:

$$U = e^{iS}$$​

where S is the infinitessimal generator of the operator. What this exponential actually *means* is basically the subject of the functional calculus. Unitary operators have the property that they don't change the probability distribution. The simplest subclass of such operators are the constant phase factors $$e^{i\lambda}$$, where lambda is a real number.

This is sort of what I meant when I said the framework of Quantum Mechanics is strongly effected by the fact that the operators are complex. As has been mentioned, we could switch to a two-component formalism such as is used in electromagnetism, and we would then get real operators, but there isn't really much point.

Regards,

Kane O'Donnell

 

[Mike2]

Again, the argument from incredulity.

Imaginary numbers are only terms in mathematical statements, just like reals are. A priori, they are no more or less suitable for the task of describing physical phenomena than the reals are. Restricting yourself to the reals in quantitative physical descriptions makes no more sense than restricting yourself to 2-syllable words in qualitative physical descriptions.

Excuse me? You are introducing an entirely new dimension to solve an equation of one variable, and you find this perfectly understandable?

Thanks for the effort Kane O'Donnell.

 

[quantumdude]

Excuse me?

Excused. :rofl:

You are introducing an entirely new dimension to solve an equation of one variable, and you find this perfectly understandable?

What on Earth are you talking about?

Take a vector space of dimension n and basis {x_i}_n, such that an arbitrary vector v in the space is formed by taking linear combinations of the x_i with real coefficients a_i. Now extend the definition of the vector space to admit complex coefficients c_i.

Guess what? The dimension of the space is still n. Admitting complex numbers has nothing to do with dimension.

Now, if you have an argument that is based on something other than incredulity, I'll be happy to consider it.

edit to add:

You are introducing an entirely new dimension to solve an equation of one variable,

This reflects a deep misunderstanding of QM. Imaginary numbers aren't used to solve the Schrodinger equation. They are part and parcel of it. Note the difference.

and you find this perfectly understandable?

Yes. As any advanced undergraduate in physics knows, it is not possible to account for the quantum world without complex numbers, or something isomorphic to them. And when it comes to spin, it turns out that it is not possible to account for that without complex vector spaces.

 

[somy]

The theory says so! Go and ask from him or her!

 

[ohwilleke]

Can quantum theory be explained? Is it possible to look at quantum theory and say "this calculation works because in terms of physics..."? (even if the physics does not entirely correlate with classical ideas)

Eg - is it possible to explain in physics terms why electrons can only exist certain distances from nulcei in quantized energy level? Not just "cause the equations say so"!

Thanks.

The short and sincere answer is that no mechanism more fundamental than quantum theory is known to exist. (The question you have asked is basically one of mechanism), and physicists are business looking for mechanisms that would explain the version of quantum mechanics known as the standard model, because the see apparent inter-relationships between the elements of the standard model that seem to have some sort of deep connections, but can't quite figure it out.

People like string theorists, brane theorists, and the like make their livings trying to find mechanisms more fundamental than the standard model.

Most of the "mysterious" parts of QM, however, are likely to be equally mysterious in any more fundmental theory from which the standard model would emerge. They would simply have fewer moving parts (e.g. fundamental particles and constants).

 

[donjennix]

Golly - we need another 2 cents worth here for sure --- but I did not see anyone mention that without the complex solutions to Schroedinger you don't get "amplitudes" and you don't get the marvelous predictive power of QED. Adding amplitudes when indistinguishable outcomes are in the stew is the only way to predict the observable probabilities (I'm no expert in this and I am trying to quote Feynman vol 3 from memory). I'd think that would be enough to justify comlex numbers.

 

[reilly]

The concept of i = sqrt(-1) is as real as the concept of "the". That is to say, both are parts of a language use to describe Nature All mathematical science can be done without i -- often it's enough to replace complex exponentials by a sine cosine pair -- but why bother? (Check out any books on physics, differential equations.)

It's amazing what "i" can do -- the calculus of complex variables is many more times powerful than the calculus of real variables (itself a part of complex variable theory)


If "i" is too crazy, then think of it as a useful notational device.

Regards,
Reilly Atkinson

 

[jcsd]

Excuse me? You are introducing an entirely new dimension to solve an equation of one variable, and you find this perfectly understandable?

Thanks for the effort Kane O'Donnell.

I think what has you confused is that the complex numbers are themselves a two dimensional vector space over the reals and there is therefore a fairly obvious one-to-one corresponfdnace between the vectors in any N dimensional complex space and the vectors in any 2N dimensional real space. Though as Tom says this has nothing to do with the actual dimensions and what's more clearly an 2N dimensional vector space over R is not isomorphic to an N dimensional space over C as by definition the maximal set of linearly indepednt vectors in each space is different.

 

[godzilla7]

I think what confuses the issue is what we percieve if light appears as both a wave and a particle whichever way we look at it we have to take into account that we might not in fact be being objective, we are all just conditioned by DNA to see what isn't there? Or are we? I'm fed up of people asking this very question and being bombarded with so called proof? we must use philosophy to discuss physics; that why it's called a Doctorate of Philosophy, you are all just being sophists, sophistry is fine but don't say its prooven till the results are irrefutable, then question your own frame of reference and proove it wrong :tongue:

Think out of the envelope people.

QM is wrong? No just missing a few vital pieces, discussing our percetion is the key to understanding what if anything we're missing not discussing string theory as if it were prooven or QM for that matter, as Schrodinger once said his only regret was that he wouldn't be alive to see QM prooved wrong.

build a robot or computer which uses fuzzy logic to learn to think, have it do the same expereiment a million times and see what it comes up with, then trash it and start again:-)

or are we just monkeys with typewriters

Something to think about anyway?

Wake up with a hypothesis, proove it wrong over breakfast, then we are ready to work

me just then, plaguerising another scientist

Velly good chaps keep it up!

 

[alexepascual]

I think you guys have fallen into a very unfoccused conversation. Have you noticed that Cheman is not here anymore? He started the thread, but you got so involved in your discussion about the meaning of quantum theory that you didn't notice him leaving.
What we have here is someone who does not have a lot of mathematical knowledge but who is interested in understanding quantum mechanics.
I think that with the disclaimer that quantum mechanics is a highly mathematical theory and can only be properly understood after having mastered a good deal of math, it is possible to have an intuitive understanding of some of the features of this theory before having the required mathematical knowledge.
Probably some of you guys learned all the math and all the equations without trying to ask questions prematurely. You never interrupted your instructor and you did all your homework. Good for you. But not everybody comes form the same direction. Some people find it more fruitlul to have an understanding in terms of pictures before tackling the math. Some may not have the capacity, persevearence, or interest to tackle the math and are just happy to have a rough understanding. I don't think we should brush them off.
Going back to the original question,
Cheman,
(If you are still around)
Have you studied transverse waves on a rope? this would be very "physical". Don't you think so?
Well, it happens that electrons have wave properties and their motion and distribution can be understood in terms of these waves. Consider a circular orbit for an electron. Don't look at it as a planet circling the sun. In reality the electron does not have a definite position. So please replace the picture of a particle located some place in the orbit by some wave that wraps around the nucleus following the line of the orbit.
Now let's go back to the rope. (if you don't remember this stuff go back to your elementary physics book). You know that when you wiggle the rope, waves travel along it with certain speed. But you also know that if the rope has certain finite length, the waves are reflected at the other end and bounce back. When the rope has certain precise lenghts, the waves traveling in both directions form what is known as "standing" waves. This happens when the length of the rope is some multiple of half the length of the wave (wavelenght). The same would happen if you had a rope forming a circle. You would have standing waves forming when the waves fit a whole number of times in the circumference.
The same thing happens in the case of the electron circling the atom. Now, you know that the energy of the electron will depend on the distance from the nucleous and therefore from on the length of the orbit. But it also happens that the wavelength of the waves also depends on the energy of the orbit (deBroglie relationship). When you consider both relationships together, it will be only for certain distances from the nucleous that you will be able to fit a whole number of waves and form standing waves. I appears that only standing waves are possible. That rougly explains quantization of the orbits (and therefore of the energy levels).
Now, while the waves on a rope represent a sideways motion of its different segments, the waves in QM. are something different. They don't represent a motion of some "stuff" in space. They have a connection with probability distributuions, but if you have an electron moving in straight line in space, the probability of finding the electron at different points in the trajectory is the same (when you know the momentum precisely). This tells you that these are not really "probability waves" where the probability is more "compressed in certain regions". We could say that the "waving" corresponds to something that is going on in another dimmension, but we still don't know enough about that. But we do know very well the properties of these waves to the point of being able to make good predictions. We know that the frequency (how fast they wiggle) of the waves depends on the energy of the particle. And we also know that when we superpose two waves corresponding to the same particle then we do get probabilty waves with regions of space where is more likely to find the particle. Physicists have found that the best way to describe this oscillation is using imaginary numbers. For this and other reasons, it is important to understand a lot of math in order to gain a good understanding of quantum mechanics.
Another phenomenom that you may want to explore and which is simple and very important is the "double slit experiment".
I also recommend that you look for popularizations of quantum mechanics which are non-mathematical books that you can may be able to find in your local bookstore.
Titles that come to mind:
"Thirty years that shook physics" (Gamow)
"In search of schodringer's cat"
"Schodringer's Kitten"
"Quantum Reality"
Authors: Gribbin , Herbert
But remember that after reading these books you won't be able to say that you really "understand" quantum mechanics. In order to understand quantum mechanics you would have to study many years. And even then, there are many aspects of quantum mechanics that remain controversial, to the point that some would say that nobody really "understands" quantum mechanics.
With respect to may explanation of the quantized energy levels, I have to admit that it is very incomplete. But it would take a very long post to make it decently complete. So the best for you is to get that information from books. This forum is great for learning but you are only going to learn bits and pieces. It is best to read the books and come back here with questions about the things you don't understand from the books.
Godd luck.
Alex Pascual

 

[Cheman]

Yes, I am still hear. I'm glad somebody noticed what I was trying to get at - surely there must be a reason why all the maths works. It is not really "correct" to have a theory that say "everything happens in the universe because this 2nd order differential equation says so" or "the atoms works like this becase the integral of this derivative is...", etc. Fair enough, it makes the theory useful and we are able to work things out, but it doesn't really give us an understanding of the nature of things. There must be a reaon WHY things happen. After all, let's reflect on the flawed yet still quite ingenious concept of classical physics - when talking about, say, electricity we don't just say "Voltage = Current * Resistance; the end!" We say "this is because current is the number of electrons passing a point per second and this will double if we double the 'attractiveness' of the battery - this is voltage...etc".

So when I asked "can quantum theory be explained" I wasn't asking for you to show off how much hardcore maths you;ve learned or tell me "how can a theory which explains how things work be explained you silly boy" - I just wanted to know exactly what the maths meant. If nobody actually knows then that's fine - you just had to tell me.

Fair do's?

Thanks Alexepascual.

Cheman.

 

[|2eason]

I was of the understanding that theories such as the MWI were proposed as the physically descriptive underlaying mechanisms for QM.

 

[godzilla7]

Finally someone with some sense , just bating the maths heads, I am about to take a Degree in physics, but don't have great maths knowledge yet, I have however read extensively on the subject in preperation and have some learning in differentials and integrals pyhtagoras etc, so can discuss the maths; I read a report that the problem with physics is that the maths scares people off and that it would be better to introduce the theory before bombarding peoople with complex math, this way the widespread shortage of physisists would be somewhat assuaged, I'm tallking only about in England here. I don't know about the rest of the world.

Please maths heads, there are plenty of maths forums for you to mentally masturbate in, when someone asks you a question going into long complicated equations is not very apt, especially if there new to the subject!

Theres plenty of maths forums if you want to go over the symantics of a theory, anyway thanks dood.

If your not shocked by Quantum Mechanics then you have not really understood it properly

Plank

 

[Kane O'Donnell]

There must be a reaon WHY things happen

This is a *very* loaded statement, Cheman - can you prove this? Also, this creates an infinite chain - if there's a reason why things happen, then there must be a reason why there's a reason why things happen, etc etc...in which case, doesn't the idea of a 'reason' become a bit fuzzy?

it would be better to introduce the theory before bombarding peoople with complex math

They do, at least at most of the Australian universities. It's very painful for people who take a parallel maths stream, in my experience. On the other hand, this allows people who aren't going to actually *contribute* to quantum mechanical theory but need to have a good grasp of it in their field (photonicists, some electrical engineers, chemists) to keep up with the physics students. I would have preferred, during my 3rd year, to have had an advanced QM course taught at a higher level for students with a strong mathematical background.

Theres plenty of maths forums if you want to go over the symantics of a theory

I want to point out here that a lot of the thread wasn't about the semantics of the mathematical framework but with the idea of 'understanding' and 'explaining' and so on. This forum is an excellent place for such a discussion, since QM is almost (*almost*) unique in the number of headaches it gives to people seeking simple explanations (I'd whack SR/GR in this category too).

If your not shocked by Quantum Mechanics then you have not really understood it properly

This is an often-quoted saying, but a lot of us have grown up with quantum mechanics and are therefore a hell of a lot less shocked than some people think we should be. I believe the statement was made by Bohr around 80 years ago, maybe it's time it should be re-evaluated. QM has become somewhat stranger since Bohr made the remark - it's not immediate that Bohr would be in a position to make such a statement given the advances made over the last 80 years.


Regards,

Kane O'Donnell

 

[Cheman]

"who aren't going to actually *contribute* to quantum mechanical theory but need to have a good grasp of it in their field (photonicists, some electrical engineers, chemists) to keep up with the physics students."

Hmmm, surely its a different type of contribution?! Afterall, fine the "maths heads" can work stuff out which makes our ability to do things much easier but it gives us understanding of what things are really like - that is the contribution that eg chemists make. We can actually SEE and PICTURE what is going on. Eg - take an atom; what your saying is that it is ok to describe an atom as a load of maths. Fine - but what does that mean its actually like?! It seems that quantum mechnics has all the maths and knows what it does but doesn't know what it is referring to, etc. Correct me if I am wrong.

 

[Kea]

maths of QM

It seems that quantum mechnics has all the maths and knows what it does but doesn't know what it is referring to, etc. Correct me if I am wrong

In fact, the mathematics of QM is relatively simple by today's
standards. If one wants to REALLY understand QM one should
at least know the maths in which it was formulated in the early
20th century. Many physicists have a better idea of what QM is
referring to than they have the maths with which to formulate
it...but this just leads to MORE maths...

Kea

 

[Eye_in_the_Sky]

If your not shocked by Quantum Mechanics then you have not really understood it properly

This is an often-quoted saying, but a lot of us have grown up with quantum mechanics and are therefore a hell of a lot less shocked than some people think we should be. I believe the statement was made by Bohr around 80 years ago, maybe it's time it should be re-evaluated. QM has become somewhat stranger since Bohr made the remark - it's not immediate that Bohr would be in a position to make such a statement given the advances made over the last 80 years.

Yes, it was Bohr who made such a statement.

... For the record, here are three more (more recent) quotations:

Feynman (1964)

I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?" because you will go "down the drain" into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.

Gell-Mann (1981)

Quantum Mechanics, that mysterious, confusing discipline which none of us really understands but which we know how to use.

Feynman

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school ... . It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it ... . That is because I don't understand it. Nobody does.

--------

On another note, here are two more quotations of Feynman regarding the role of Mathematics:

One cannot understand ... the universality of the laws of nature, the relationship of things, without an understanding of mathematics. There is no other way to do it.

To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

 

[Kane O'Donnell]

Yep, I'd agree with the 'no one understands it' approach.

Cheerio,


Kane O'Donnell

 

[tavi_boada]

QM can be understood!(?)

I think it's somewhat arrogant to say we understand classical physics. First of all, what worries me less of QM is the discreteness of some magnitudes, e.g. energy of electrons in H atom. There are many examples of discrete energies in Classical Physics such as a rope oscilating with its endpoints fixed (many equations with suitable boundary conditions yield discrete values).

Why, then, do people claim QM is not understandable? Or why do people say its indeterministic? Amplitudes are completely determined by the theory. Can you explain further why you say QM is not understandable?

I'm sorry if I've said things already posted, I haven't had time to read all the posts.

 

[Kane O'Donnell]

Why, then, do people claim QM is not understandable?

What I'm referring to is that we can't, in QM, say *why* the mathematical framework is the way it is (with probability amplitudes, wavefunctions, operators, etc). We've made a lot of progress, in fact, in explaining the 'why', but unfortunately for those who crave an explanation in simple pictorial form or something like "balls travel in a wind-bent parabola because of gravity", the (partial) explanations of the 'why' in QM are mathematically quite sophisticated.

For a simple (ish) example, why do we want self-adjoint operators? Well, from linear algebra we know that in finite dimensions SA operators have real eigenvalues. We know that this can be generalised to bounded operators on an infinite dimensional space too. Real numbers are the only kind we can measure, so no wonder we want real eigenvalues if we're interpreting eigenvalues as the measurable values of an observable. Problem is, there are *lots* of unbounded operators, including the momentum operator, the kinetic energy operator and hence the Hamiltonian.

We already know that the TISE works magnificently well for some systems. As such, we really, really want to have some reason why this unbounded operator (the Hamiltonian) has a real spectrum for a wide variety of potentials. If we can do this, we will be able to write down a more general QM axiom that tells us the class of operators we are allowed to use as observables in QM. (obviously, since non-relativistic QM has been studied in depth for years, we would guess that the answer is already known, and it is).

It turns out that the notion of self-adjoint generalises in the unbounded case, although in order to generalise we have to restrict the class of wavefunctions upon which the operators can act. This is excellent, because the restriction, usually, is to require that the wavefunctions be continuous and differentiable to some degree, hence explaining the requirement for a continuous/differentiable wavefunction without referring to infinite energy gradients and so on (the latter explanation is sort of a circular argument, I would guess).

Ok that got a little technical at some points, but I hope it's a reasonable example as to what explanation might mean when we try to 'understand' quantum mechanics. In this sense, we don't understand QM, because it's mathematical framework is not fully understood as being a requirement of some underlying conditions.

Regards,

Kane O'Donnell

 

[tavi_boada]

Are you saying that people say they don't understand QM because of the problematics of unbound operators being self adjoint?

 

[dextercioby]

Are you saying that people say they don't understand QM because of the problematics of unbound operators being self adjoint?

No,that part of QM is perfectly understood.I'll post again the famous quote from Feynman:
"I think it is safe to say that no one understands quantum mechanics".
My guess is that the key word from phrase is not "understand",but "safe".Feynman must have meant:Okay,let's assume the situation in which some individual claims he masters QM,he understood it.But then,another guy comes to him and says:"Hey,use your QM knowledge to explain this..."(and gives him an example).And so our "QM expert" makes a fools outta himself,as he cannot explain some awkward phenomenon.

So all of us theoretical physicists should "play it safe" and say that we don't really know every aspect of this theory and moreover we cannot give answers to the fundamental question "why?".

Daniel.

 

[Kane O'Donnell]

Are you saying that people say they don't understand QM because of the problematics of unbound operators being self adjoint?

No, it was just a simple example that hopefully illustrated the kind of things theoretical physicists *do* when they're investigating a theory in order to try to 'understand' it.

Kane O'Donnell

 

[Louis Cypher]

Yes, it was Bohr who made such a statement.

... For the record, here are three more (more recent) quotations:

--------

On another note, here are two more quotations of Feynman regarding the role of Mathematics:

Thanks for putting me straight on the ins and outs; yes precisely my point although rather cryptically made do not try to understand what we cannot yet understand is perhaps a dangerous way of looking at things, with the current understanding it beehoves us to find ways to understand the mysteries whether we are able to really see what's going on after all that's what science is about; maths is usefull in giving us an appreciation of a theory if we are mathematically inclined and experiment is taking said maths and then seeing if its congruent with reality both are to be applauded; though one should be carefull in making predictions based on predictions; the house of cards thing; because say qm is wrong then surely string theory is wrong by an order of magnitude and m theory well now were possibly in the realms of the absurd; much as I like the simplicity of string theory it's tenuous existence rests solely in the hands of mathemeticains who in my opinion are being driven slowly insane by there incomprehension of the infinite and the infinitesimal.

I think we should take a long ahard look at that which we hold true and try and proove that b4 flying off into a philosophical debate about strings,I'll leave that to the Doctors of Philosophy. PhD fellows after all there eminently more qualified to explore it than I.

Facinating though theories are at the end of the day there just theories, like the Theory of Gravity, one day someone will find the flaws in QM and it will come crashing to the ground replaced by a new mechanics simillar but closer to the truth; God help us if we ever reach a point where we find the truth, I'd have to give up my degree because there'd be no future in physics

Nice quotes like it.

 

[lawtonfogle]

If we found the truth would we want to know it.

The truth might be better off never being found.

The government keeps secrets from the public for its safety. If the public ever found out about a (lets just say, nuclear threat from terrorist) there would be a panic.

Who says this 'truth' is not the same.

 

[Louis Cypher]

I think your missing the point here, natures truths are beautiful and we would benefit greatly from knowing them, I don't necessarily need to know if a major terrorist threat has been averted at the time, because the panic caused by said threat would be counter productive to intelligence gathering.

To catch a glimpse at how the universe would be great, nature cannot keep secrets from us forever just like governments can't keep secrets indefinitely, people have a way of hearing the truth all be it an objective truth - or an obfuscated and fudged truth in the case of governments - sooner or later, but is it truth?

Anyway enough philosophy

 

[kristobal hunta]

time has not come yet

Right now QM is more describing than explaining. Actually its authors never put the goal to explain why it happens, instead they just tried to make predictions what would happen in the experiment. And this is normal. Newton first make mathematical model for gravity, but only after Einstein we know that it is explained by curvature of space-time...well now we have to wait until somebody would explain to us what the space-time is and so forth...

I mean don't try to make mechanical models of QM or trying to understand it. First you need to feel it mathematical sense and later maybe you would feel like you "underdstand" it.

Maybe in another hundred years there will be an answer to your question. And the rules of QM would be just a simple consequence of space-time properties or whatever...

 

[Louis Cypher]

Maths

Personally I think the problem with QM is divide between the mathemticians and the experimentalists.

A good pysisist is both, getting tanlged up in mathematical somantics is fine and worthy work but if that's all you do then your wasting your time; pure maths is pointless for a physisist after all aren't we really asking a simple quiestion abput everything, and if so don't we need to put our elgeant theories to some practical use? Einstein was relatively poor at maths compared to his colleagues so he got them to do the maths for him and then when he learned to be more fluent in maths he invented mathematics to explain his theories, his outlook as a Scientist was to theorise and then experiment and then invent formulae it bemuses me that people now do the reverse ? both is fine but both need to be done by all surely, It's no longer science mathematics its philosophical sophistry it seems. Fine if your doing a PhD but innapropraite for most

 

[trosten]

In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.
Douglas Adams

I just want to say its great that someone quotes D. Adams if u really want to know what's going on I think his books can help you.

In the beginning I started studying QM to learn why the world behaves they way it does, is there a god etc. Now I find myself studying it because I am stunned by the way the world behaves, its just simply amazing.

I aslo feel that Bell with the Bell inequality made it clear that there is no answer to the question why things behave the way they do.

 

[godzilla7]

I meant no offence about the maths heads, just a little more explanation than maths would have been nice or some sort of description of the concepts. Anyway, I used the shocked quote to convey the way I felt when I first had to get to grips with the weird world of QM, I didn't mean it to be taken in its original context, perhaps I should have made that clear. And unfortunately in England there isn't the choice to avoid some of the more theoretical maths, the first year is always spent going through the complex anture of classical and quantum maths, sa shame I think it would be better to run through the maths after exploring the concepts, so as not to scare people off and to tweak there imagination, show I'm learning and it helps to have a grip of the aplication of maths before you fully understand it I find the reverse way more stimulating and infinitely more interesting than the rather dry pure maths ythat are the precursors to the course.

 

[misogynisticfeminist]

I meant no offence about the maths heads, just a little more explanation than maths would have been nice or some sort of description of the concepts. Anyway, I used the shocked quote to convey the way I felt when I first had to get to grips with the weird world of QM, I didn't mean it to be taken in its original context, perhaps I should have made that clear. And unfortunately in England there isn't the choice to avoid some of the more theoretical maths, the first year is always spent going through the complex anture of classical and quantum maths, sa shame I think it would be better to run through the maths after exploring the concepts, so as not to scare people off and to tweak there imagination, show I'm learning and it helps to have a grip of the aplication of maths before you fully understand it I find the reverse way more stimulating and infinitely more interesting than the rather dry pure maths ythat are the precursors to the course.

agreed, i strongly believe that the conceptual foundations of QM should be presented non-mathematically before the math comes in. I believe that this helps students appreciate the theory better and realize that there's much beauty undelying quantum mechanics other than elegant mathematics or excellent predicting power.

 

[ZapperZ]

agreed, i strongly believe that the conceptual foundations of QM should be presented non-mathematically before the math comes in. I believe that this helps students appreciate the theory better and realize that there's much beauty undelying quantum mechanics other than elegant mathematics or excellent predicting power.

In the Malay/Indonesian language, there is a word to refer to a singular third person without referring to his or her gender. The word is "dia". However, this word does not exist in the English language. I cannot refer to a singular third person easily without knowing that person's gender, or making either tedious, or awkward, or impersonal-sounding statement, such as using "he/she", "that person", etc.

Now, what does THAT have to do with what you just said? I'm trying to illustrate the fact that it is a distinct possibility that QM is describing something in which our currrent "language" or understanding has no ability to accurately convey! Our understanding, concepts, and qualities are inherently tied to the classical world that we already understand, such as the meaning of "position", "momentum", "energy", etc... Yet, such concepts may have vague, or even faulty meanings when we try to apply that in the QM realm. I am convinced that it is why when we measure these things, they give us "weird" answers. You are forcing a square block through a round hole, and you get an outcome that has the appearence of a square block, but with chopped corners. Yet, we complain about the round hole, never the fact that we had square blocks in the first place that wasn't MEANT to be passed through a round hole.

QM isn't supposed to make classical sense. That's the whole point! Therefore, how does one convey the "conceptual foundation" of QM without having the mathematical rigor first? If you have paid any attention to the quackeries on here, you will have noticed that most of them have the impression that they understand the concepts of QM, and yet, lacking severely the mathematical understanding of what it is. This usually results in outright bastardization of what QM is and often leads to hysterical conclusions.

So no. I disagree with the assertion that one must first teach and establish "conceptual understanding" of QM before any mathematical description. For most of us who have gone through the process, our "conceptual understanding" of QM is still evolving and hopefully, progressing. To think that one can simply describe in words the conceptual foundation of QM is to trivialize the complexities of QM, and to "dumb down" the intricate details of its description. I do not see anything good coming out of that for students about to learn the subject.

Zz.

 

[misogynisticfeminist]

I do understand what you mean Zapperz and i myself have come across "quackeries" where QM is concerned. But actually, establishing the context of what I said, I meant that non-mathematical descriptions of "conceptual foundations" be introduced first to incite curiosity and excitement amongst those who learn them.

In fact, it was the counter-intuitive nature of QM that first attracted me to physics. But of course this does not undermine the importance of mathematical rigour in really understanding QM but I think that before you learn something, you got to get excited about it first.

I do not see non-mathematical descriptions of QM as a suitable substitute for a mathematical course and the education of someone studying QM is FAR from complete without the math. But like i said, the purpose of non-mathematical descriptions is to incite curiosity.