Perhaps quantum physics is elegant, but we lack an understanding?

[Mike2]

I think you are curve fitting.

How do you figure?

Entropy can be calculated of any signal, physical or not. If entropy/information can be calculated of any geometric object, physical or not, and if some sort of conservation of information law is only logical, then since we describe physics in geometrical terms, it would seem that QM is perfectly logical in abstract terms as well as in physical terms.

Just to continue the thought process (whether anyone helps or not), I think that entropy would have to be invariant with respect to coordinate changes. It would have to be an intrinsic property of the geometry. Are there any studies or thoughts on how that would be calculated? I wonder if entropy would be connected to the curvature of a given geometry. Certainly straight lines and flat surfaces would have less entropy than wildly curved lines or surfaces, right? (actually, I'm not sure at this point whether the more wildly curved line would not have more information involved. It seems it would take more bits to describe a curve than a straight line, right?). Anyway, more or less, one might suspect that entropy is connected to how curved a geometry is and how often that curvature changes, etc. That would probably be how curved it is per length or per surface area. Are there any math procedures out there that I may wish to consider?

 

[ZapperZ]

How do you figure?

Entropy can be calculated of any signal, physical or not. If entropy/information can be calculated of any geometric object, physical or not, and if some sort of conservation of information law is only logical, then since we describe physics in geometrical terms, it would seem that QM is perfectly logical in abstract terms as well as in physical terms.

This is gooblygook! Entropy of a "geometric object"?! You can calculate the entropy of a cube? Please show this.

I take back what I said about you having only a superficial knowledge of QM. I think you have a superficial knowledge of physics. Period.

Zz.

 

[masudr]

Postulates as fundamental aspects of physical theories

In the 19th century, mechanics was based on "postulates" of varying kinds. For example, Newton used his (now) famous three laws and derived a complete mechanics based on those (and other expressions for force).

This was later reformulated by assuming the postulate that a trajectory that any particle takes is such that it's action is stationary with respect to extremal variations of the path (this is Lagrangian mechanics, look it up if you're interested). This postulate has been proven to be exactly the same as Newton's three laws. (There has also been a similar reformulation called Hamiltonian mechanics [this is related but indirectly to quantum mechanics, so just assume that it is a completely different thing; the argument is still the same]).

The point I am trying to make is that ALL physics is based on postulates of some kind. Even those that dream of a final theory which is self-evident still requires various postulates, one of them being the invariance of physical laws over spacetime. Or that reality is real and we are experiencing that through our senses; if not the theory wouldn't really describe reality and would be demoted into metaphysics.

Now onto quantum mechanics. QM was the result of about 26 years of research. The phrase "curve fitting" has now become slightly ambiguous since it has been used so many times. But of course there is curve fitting going on. And it always has been. Newton formulated his law of gravitation plus his three laws of motion by fitting his equations to the curves described by objects in gravitational attraction (his genius was to notice that all objects are falling).

Einstein fitted his special theory by noticing that no objects could discern motion when in an inertial frame and also on the invariance of light. There is no fundamental explanations for this. They have to be accepted.

So the same goes for QM, and Schrödinger's equation, and the canonical commutation relation and so on and on. These are based on thousands of experimental observations and hence we hold them to be "true". Based on the assumptions of QM we can build one of the most elegant theories so far, which has succeeded in describing the largest range of phenomena by any physical theory.

Some of the fruits of QM have been that based on these assumptions, theorists have been able to generate "new curves" and experimentalists have found that their experimental data fits these new curves (e.g. the existence of the positron etc.) This is a growing body of evidence that those initial assumptions are indeed correct or are the result of some other set of assumptions (this set could be of cardinality 1).

So, in conclusion, QM is a curve fitting process, but so are all physical theories. We cannot, however, discredit QM on the basis of its assumptions. The whole point of assumptions/postulates are that they are unquestionable and must be accepted on an ad hoc basis (or a priori as Einstein was fond of saying).

Even the greatest physical theory will be a curve fitting process. Any theory will have at least one degree of freedom. One constant to choose. A proportionality constant, for example. We then have to determine that constant (or whatever the variable may be) by adjusting it so the theory's curve fits the experimental curve.

As you can see from reading the above, the point of this discussion is highly non-physical and more philosophical. But I feel that without a true grasp of the ideas involved (e.g. Hilbert spaces, linear operators etc) one cannot truly appreciate quantum mechanics. Just to make things clear from the outset, I am an undergraduate in my first year of studying physics (i.e. I just started my "college" [as Americans would usually call it; I am from the UK] course); and most of my knowledge on these topics have come from extra reading beyond the scope of my course (at this stage anyway). So there may be errors in my understanding.

Finally, as a message to Mike2; you seem to have some very interesting (although unoriginal) ideas regarding information as a fundamental part of mechanics, and attempting to base a theory on this and some other related principles. I would be very interested to see a full list of postulates that your mechanics requires, and how you would perform calculations on your new mechanics. At least von Neumann et. al showed us how their systems worked. Until you do that, your ideas are just incoherent jumble of English words, not precise mathematical statements. This isn't bad or wrong in itself, but it just doesn't allow others to subject it to careful scrutiny and thus support it or disprove it.

 

[keebs]

I suspect that the two cancel because the prior condition of extreme symmetry would seem to have no entropy associated with it.

You obviously don't understand path integrals: http://www.princeton.edu/~jhunt/qft_path.pdf

 

[Mike2]

This is gooblygook! Entropy of a "geometric object"?! You can calculate the entropy of a cube? Please show this.

Zz.

The entropy of continuous probability distributions is calculated all the time. Yet, this same probability distribution function is also a line on a graph of the distribution, a geometric object, as are all functions described by y=f(x). There are also probability distribution functions of many variables w=f(x,y,z), and these have the appearance of surfaces and volumes when plotted out. If the entropy of these distributions are the same when one rotates the coordinates so they are no longer single valued in the new coord system, then this will prove that entropy of such functions (whether viewed as distributions or geometric objects) is intrinsic. And if so, then entropy can be calculated of any geometric object. If the entropy of a probability distribution function (which appears as a geometric object when graphed) can be reformulated so that it is calculated along the line or along the surface, etc, then we could calculate the entropy of functions that loop-tee-loop (a technical term :-) all over the place so that they are not single valued functions. It could then apply to each path used in path integral formulations of QM.

My purpose is to stimulate study in this area in the hope that it has some intuitive appeal.

 

[masudr]

Geometry and reality

OK, so we use functions to map from one set of mathematical objects to another set (actually that's a mapping which is more general than a function). We can also use paper and computers for multi-dimensional mappings. But you must realize that the gemoetry of the function IS NOTHING TO DO WITH the actual function per se, except that it is just a description and nothing more.

For example, if y=f(x) represented how far objects went (y) after being thwacked with a force x, and it showed a parabola, then I couldn't continue to say that all parabola shapes have a "certain" force. Because this is what you are doing here - you are saying that entropy of continuous probability distributions is a shape, therefore we can calculate the entropy of that shape. That is simply incoherent and logically nonsensical.

What you say about physical quantities and their invariance with respect to different co-ordinate systems is another issue, not to be confused of geometric representation of functions. For example, non-relativistic physics would say that length, velocity, mass, momentum are all equal in inertial reference frames (this is a consequence of Newton's first law). But by saying that the speed of light is invariant in all inertial frames means we can no longer say momentum, energy etc. are invariant. Anyway, that is relativity and I won't go into that.

 

[ZapperZ]

The entropy of continuous probability distributions is calculated all the time. Yet, this same probability distribution function is also a line on a graph of the distribution, a geometric object, as are all functions described by y=f(x). There are also probability distribution functions of many variables w=f(x,y,z), and these have the appearance of surfaces and volumes when plotted out. If the entropy of these distributions are the same when one rotates the coordinates so they are no longer single valued in the new coord system, then this will prove that entropy of such functions (whether viewed as distributions or geometric objects) is intrinsic. And if so, then entropy can be calculated of any geometric object. If the entropy of a probability distribution function (which appears as a geometric object when graphed) can be reformulated so that it is calculated along the line or along the surface, etc, then we could calculate the entropy of functions that loop-tee-loop (a technical term :-) all over the place so that they are not single valued functions. It could then apply to each path used in path integral formulations of QM.

My purpose is to stimulate study in this area in the hope that it has some intuitive appeal.

Again, show me how you calculate the entropy of a cube.

What amuses me is that you see nothing wrong with making a statement such as

"...There are also probability distribution functions of many variables w=f(x,y,z), and these have the appearance of surfaces and volumes when plotted out"

You see the appearence of an elephant in the clouds. Using your logic, the clouds must be elephants. My avatar is a plot of the photoemission intensity of an overdopped high-Tc superconductor - it looks like a comet! Thus, I actually can find lifetimes and scattering rates of comets?

Your responses are continually making your understanding of what physics is more irrational.

Zz.

 

[Mike2]

Your responses are continually making your understanding of what physics is more irrational.

Zz.

You are a detractor. Your comments are not useful or constructive.

My hypothesis is easily falsifiable. If the entropy of a probability distribution changes with a rotation, then it is not intrinsic and not applicable to arbitrary geometric shapes. Do that, and I will shut up.

 

[ZapperZ]

You are a detractor. Your comments are not useful or constructive.

My hypothesis is easily falsifiable. If the entropy of a probability distribution changes with a rotation, then it is not intrinsic and not applicable to arbitrary geometric shapes. Do that, and I will shut up.

How can I do that when I have no idea what you mean by "entropy" and what you mean by "entropy of a geometric shape". It is why I ASKED you to show how you would find the entropy of a cube! I didn't label you as a quack right away after you proposed your "hypothesis". I ASKED you to show it. You continually refused, the same way you avoid answering my question about your comprehension and understanding of QM.

Zz.

 

[quantumdude]

I don't know that I have a complete theory yet. I was simply trying to point out that in the process of the search for the basis of QM, it seems that it might be worth a try to see if some conservation of information law might be what we are looking for.

I wasn't asking if you have a complete theory, I was asking if you could cite an example of one. My point being that if QM is not complete, then I fail to see how any theory could be so considered.

And even if you do discover what is "behind" QM, why would that be considered complete? What's to stop anyone from asking what's behind that?

 

[Mike2]

How can I do that when I have no idea what you mean by "entropy" and what you mean by "entropy of a geometric shape". It is why I ASKED you to show how you would find the entropy of a cube! I didn't label you as a quack right away after you proposed your "hypothesis". I ASKED you to show it. You continually refused, the same way you avoid answering my question about your comprehension and understanding of QM.

Zz.

Well, I suppose there would be more "states" for a cube than for a sphere. That's all I know at this point. Are you suggesting that there is no difference in information between the sphere "symbol" and the cube symbol? Are you suggesting that there is no uncertainty in some very complicated shape as to what exactly it is?

 

[ZapperZ]

Well, I suppose there would be more "states" for a cube than for a sphere. That's all I know at this point. Are you suggesting that there is no difference in information between the sphere "symbol" and the cube symbol? Are you suggesting that there is no uncertainty in some very complicated shape as to what exactly it is?

I'm not suggesting anything! I asked you to show me how to find the entropy of a cube! You still haven't, or can't, or won't, or don't know how. This would make all your claims about entropy of "geometric shapes" to be very curious. Don't turn this around and pump me for information. YOU were the one who made such claims, which now appears to be unsubstantiated.

Zz.

 

[Mike2]

I'm not suggesting anything! I asked you to show me how to find the entropy of a cube! You still haven't, or can't, or won't, or don't know how. This would make all your claims about entropy of "geometric shapes" to be very curious. Don't turn this around and pump me for information. YOU were the one who made such claims, which now appears to be unsubstantiated.

Zz.

I did not make any actual claims; I only made suggestions about a possible research program.
At the moment, I don't know how to calculate the entropy of geometric shapes in general. Although, I suppose that the entropy of a line represented by a single valued function would be calculate in the same way that a distribution density function would be, except divided by the average. However, it seems (note the word "seems") quite obvious that some shapes are much more complex than a sphere. And as I understand it, complexity and entropy are mathematically related.

 

[ZapperZ]

I did not make any actual claims; I only made suggestions about a possible research program.
At the moment, I don't know how to calculate the entropy of geometric shapes in general. Although, I suppose that the entropy of a line represented by a single valued function would be calculate in the same way that a distribution density function would be, except divided by the average. However, it seems (note the word "seems") quite obvious that some shapes are much more complex than a sphere. And as I understand it, complexity and entropy are mathematically related.

1. So you don't know how to calculate the entropy of "geometric shapes". Fine. Show me an example of which you KNOW how to calculate the entropy of.

2. Show me the mathematics that you "understand" that relates "complexity" with "entropy". Hopefully, we can, once and for all, determine what you truly understand as "entropy".

Zz.

 

[jackle]

Mike, does it help to point out that geometric shapes have an entropy if they consist of something physical? eg. A real life cube of ice has an entropy and I believe you can calculate the entropy from thermodynamics by considering it's constituent molecules. If the ice melts, it changes shape and state and has a different entropy (if I recall). A cube of frozen oxygen has a different entropy again.

Therefore, it is not proper to calculate an entropy without specifying the material that forms the shape. The same shape has a different entropy depending on what it is made of. If it is made of nothing, it has no entropy at all - otherwise conceptual shapes would interfere with reality and they don't. Furthermore, I find a probability distribution meaningless in quantum mechanics unless it represents the probability of measuring real matter. Real matter does have an entropy.

 

[Mike2]

Mike, does it help to point out that geometric shapes have an entropy if they consist of something physical? eg. A real life cube of ice has an entropy and I believe you can calculate the entropy from thermodynamics by considering it's constituent molecules. If the ice melts, it changes shape and state and has a different entropy (if I recall). A cube of frozen oxygen has a different entropy again.

Therefore, it is not proper to calculate an entropy without specifying the material that forms the shape. The same shape has a different entropy depending on what it is made of. If it is made of nothing, it has no entropy at all - otherwise conceptual shapes would interfere with reality and they don't. Furthermore, I find a probability distribution meaningless in quantum mechanics unless it represents the probability of measuring real matter. Real matter does have an entropy.

The entropy that we are accustomed to using is measuring states of discrete points - the configuration of point particles - at least in statistical mechanics. However, even there we describe things in geometrical terms such as the distants between particles and their rates of change.

But now we are starting to describe particles in terms of strings, and loops, and branes, etc, which are in and of themselves geometric objects. We are beginning to describe physical properties in terms of geometric dynamics, how shapes change, or vibrate, or combine, etc. Though summing up the phase and amplitude of quantum mechanical alternatives does make things more complicated.

Why should we think that there is some conservation of information/entropy at the heart of QM? There is no alternative to nothing except something. There is no alternative but that our universe exist. The probability of our universe existing as a whole is 100%, and that is true always, no matter how the universe evolves. And the information content of something with a probability of 1 is zero. So the universe has information content of zero and will always remain zero since there is always a probability of 1 that the universe as a whole exists. The universe always conserves information.

This means that information is conserved (at zero) even when the universe was so small that the first quantum mechanical situation arose. This means that conservation of information is intimately involved with QM itself.

So I look to see how this might occur. I see the path integral offering alternative paths. I see a wave function whose square gives probabilities. And the only way I see (so far) that the information derived from these possible alternatives is if there is some entropy associated each of the paths.

I don't know how that all works together to produce the path integral. But I ask everyone to keep an open mind as they study these things.

As for the intrinsic nature of the information contained in a single valued function y=f(x) which graphs as a line. If the line is normalized by dividing it by the average, then the entropy of the line can be calculated in the same way as a probability density function. That being the case, it is easily seen that the entropy is the same even if the curve is shifted on the x-axis. However, I'm not so sure the entropy remains the same when the curve is shifted up or down, even though you would still divide by the average. Your thought are welcome.

 

[zeus_the_almighty]

Most people who are confused with the interpretation of quantum physics are asking the wrong questions. I think that a brief glance at the history of physics in general from the 16th century to 21th century could help them have another view of physics.

Physics has evolved over the centuries. There is no absolute, everlasting physics.
Physics looks like the way we work it out.

As long as planetary motions could be fully accounted for by Newton's laws, people thought that Physics was over. Then, people began to think of such things as light, magnetism, electricity, heat. To account for all such odd things in a coherent manner, it became necessary to work out other theories:classical thermodynamics and Maxwell's electromagnetic theory were born.
Still, as people knew more about these matters, a phenomenon, called the "blackbody radiation" came along and nobody could find a satisfactory explanation to it within the frame of the existing theories. The "blackbody radiation" problem came from the fact energy emitted by a blackbody would be infinite at high frequencies (short wavelengths) if one uses the classical electromagnetic theory. Namely, the intensity radiated by the blackbody would be 1/L^4 dependent, where L is the radiated wavelength. Planck solved the problem in a most elegant way with his famous "quanta" of energy which states that the energy of the molecules cannot occupy any arbitrary state: it must be a multiple of "hv" (h being Planck's Constant and v the frequency of the wave).
Then, still further on, Michelson and Morley's experiment gave the evidence that there is no such thing as "ether" in which electromagnetic waves would propagate and that the speed of light is a universal constant.
Then, Einstein built up his theory of Relativity (special and general) which was in very good agreement with experimental observations. For example, it allowed to account for the deviation of light coming from remote parts of the universe when it passes through a strong gravitational field
etc...etc...

Why did I bother ypu with all this stuff?
Just to say: May be quantum mechanics is not the ultimate theory. May be physics could be improved, and no one doubts such thing is going to happen sooner or later. But quantum mechanics is now THE theory which best explains what is going on when you have to deal with such tiny things as electrons. Moreover, till now, NO EXPERIMENT has allowed to challenge quantum mechanics. It has always been in agreement with observation.

Physics are built from observation and the will to account for still unexplained facts.

 

[zeus_the_almighty]

[completion of the above post]
I think that the highly formal aspect of 20th and 21th centuries physics must convince us to give up any attempt to reach any underlying philosophical or "who knows what" interpretation of physics.
Quantum mechanics are effective in giving satisfactory agreement with experimetal observations. That is all what matters. Any other "meta-discussion" on the "real" nature or QM has no usefullness. Such physicists as R. Feynmann, when asked regarding what he was thinking of the interpretation of Quantum Electrodynamics simply replied that there was no point trying to bother oneself with such things.

QM itself can be formulated in various ways : Schrödinger's equation, Feynman's path integrals, Heisenberg's matrices. So, which one is the RIGHT one? They are all right and shed light on a specific aspect of the "physical world".

Personnaly, I think that trying to embrace the whole real world with one theory which could account for everything is, AT BEST, a task no human being can achieve and, AT WORST, a waste of time.

 

[dextercioby]

Moreover, till now, NO EXPERIMENT has allowed to challenge quantum mechanics. It has always been in agreement with observation.

Yep,that's right.Not in the next 100 years experimentalists (is this the word corresponding to "theorists"?) could not prove right/wrong the predictions of the string theory.At least i think they won't.

Physics are built from observation and the will to account for still unexplained facts.

Tell that to the string theorists who work all day in some equations whose veridicity ca be proved only by mathematical means...

 

[Mike2]

Why did I bother ypu with all this stuff?
Just to say: May be quantum mechanics is not the ultimate theory. May be physics could be improved, and no one doubts such thing is going to happen sooner or later. But quantum mechanics is now THE theory which best explains what is going on when you have to deal with such tiny things as electrons. Moreover, till now, NO EXPERIMENT has allowed to challenge quantum mechanics. It has always been in agreement with observation.

Physics are built from observation and the will to account for still unexplained facts.

yes, well... my argument to this has been, if we are not able to derive physics from principle alone, then we cannot say that it won't all of a sudden change and act unexpectantly at some point. Just like with the observation that the universe is now accelerating its expansion, we may discover something in the future is changing at the fundamental level as well. This is not to say that observation is not important. Whatever principle is proposed to derive physics, it will have to predict observations.

 

[ZapperZ]

yes, well... my argument to this has been, if we are not able to derive physics from principle alone, then we cannot say that it won't all of a sudden change and act unexpectantly at some point.

Show me a specific example where this has happened... oh wait, I forget. You do not and are not capable of giving specific examples. I'm still waiting for you to show me something of which you know how to find the entropy of...

Zz.

 

[zeus_the_almighty]

Mike2, your issue is epistemological.

In general, the lifetime of a theory in physics is built in the following path:

1/-You make a few observations in the physical world. These observations may not be clearly related to each other in a straightforward way.

2/-You think of a theory (equations and so on...) to explain them all. This step is among the hardest.

3/-Your theory successfully accounts for phenomena observed in 1/ (here is what you called "the curve fitting process")

4/-Skyrocketed by such a success, you, or another physicist, predict NEW ODD THINGS from your theory, things that nobody has ever thought of nor seen before.

5/-Experimentalists, willingly or by chance (rarely now), find out that these NEW ODD THINGS actually exist and are in total agreement with what your theory predicted.

6/-Unfortunately, some people, working night and day, later find out a new phenomenon that can't definitely be embraced by your theory. You are stunned but this is life.

7/- A young talented physicist publishes an outstanding article in which he brilliantly demonstrates that your theory was a special occurrence of HIS new theory when, say, velocity is low compared to "c".

Right now, quantum mechanics is at stage 5/. It seems likely that we won't reach stage 7/ before a few decades. Newton's physics were overthrown by Einstein in 1905.

The point is: building a theory in physics is a long process which is the result of interactions between theory and observation. You cannot just throw observations into the garbage and expect to build quite a new theory throughout a thought process only. Such a way is of doing physics is not fertile and the history of science has proven it.

 

[Mike2]

The point is: building a theory in physics is a long process which is the result of interactions between theory and observation. You cannot just throw observations into the garbage and expect to build quite a new theory throughout a thought process only. Such a way is of doing physics is not fertile and the history of science has proven it.

You might keep in mind that the methods of logical deduction and induction are already generalizations of observations. The ancients observed a relationship between so many physical phenomena that eventually they generalized physical phenomena to propositions and the relationship between them to logical deduction. Only later was it realized that the same principles of logic also apply to abstract notions like mathematics. So we should not at this stage think that logic has no relationship to physics.