Tom

Quantum Mechanics Question

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Hello, my last encounter with physics was last winter. I wrote a paper regarding Quantum Mechanics, and the professor I had wrote that QM is not "internally consistent."

Recently I have been trying to track down what he meant by QM not being "internally consistent." I know that in the context he wrote it, he meant that the theoretical structure of QM (perhaps with some of the concepts or the math) there were some problematic internal conflicts.

But anyway, I have been trying to get a hold of this professor to ask him about it, but he is gone for the summer. So I'm hoping someone here might know of any such internal inconsistencies within the theory of quantum mechanics--and if there are, what are they? Or better yet, have any decent papers been written on te subject?

Thank you,

Tom

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Hello, my last encounter with physics was last winter.  I wrote a paper regarding Quantum Mechanics, and the professor I had wrote that QM is not "internally consistent."

Recently I have been trying to track down what he meant by QM not being "internally consistent."  I know that in the context he wrote it, he meant that the theoretical structure of QM (perhaps with some of the concepts or the math) there were some problematic internal conflicts.

But anyway, I have been trying to get a hold of this professor to ask him about it, but he is gone for the summer.  So I'm hoping someone here might know of any such internal inconsistencies within the theory of quantum mechanics--and if there are, what are they?  Or better yet, have any decent papers been written on te subject?

There is not one theory labelled "quantum mechanics," but rather many competing theories which, for the most part, share the same or very similar mathematical formalism. Some of these theories are more bizarre than others, but most are ludicrous when looked at in a philosophical light. It is rare, however, for the more popular standard theories not to be self-consistent. Certainly the mathematics is self-consistent, and as I noted this is mostly commonly shared. There will be an occasional paper proclaiming some level of self-inconsistency for some particular theory; for instance, see B. Augenstein, "von Neumann standard quantum mechanics is logically inconsistent," Chaos, Solitons & Fractals, Vol. 13, No. 4, pp. 947-956, 2002. Also look to the work of David Hestenes, who developed an interesting approach called Geometric Algebra, a sort of Clifford Algebra that has been applied to both QM and relativity. Hestenes et al have written several papers claiming inconsistencies in the standard theories.

My own view is that the inconsistencies that most matter for the standard theories is their contradictory nature to fundamentally correct philosophical principles.

p.s. I am assuming you really mean "internally inconsistent" and not, as it is usually stated, the inconsistency of QM with certain classical elements and aspects of relativity.

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p.s. I am assuming you really mean "internally inconsistent" and not, as it is usually stated,  the inconsistency of QM with certain classical elements and aspects of relativity.

Yes I just meant "internally inconsistent" rather than conflicting with relativity. Thank you for the information!

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Yes I just meant "internally inconsistent" rather than conflicting with relativity. Thank you for the information!

You're welcome. There are other papers I can reference for you, but I strongly suspect that your professor had more of a philosophical inconsistency, rather than a technical inconsistency in mind. Perhaps something along the lines of measurement theory, about which much has been written for a long time. But the axioms of standard quantum field theory are well-grounded, and if they can be shown to be inconsistent then so too the underlying mathematical foundation, something which I am not wont to believe could be done.

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[Note: I originally wrote the following reply to a similar question asked on another forum.]

How does one (or, does one?) reach a 'that makes sense' level dealing

with Quantum Mechanics?

Unfortunately, many aspects of modern quantum mechanics are not readily reducible to the perceptually self-evident, primarily because many of its concepts are not grounded in reality by the physicists who practice it -- and I say this as a physics and philosophy major. In fact, many of the current quantum physicists actually take glee in the fact that "it just doesn't make sense," and you can hear them say this on popular science shows. I'm not against the idea of quantization, but the way it is represented in both physics class and popular science shows leaves understanding to be desired. Physics, more than any other actual science these days, needs a good philosophic washing.

However, some of the key concepts of quantization can be reduced to the perceptually self-evident, and some of this was actually done thousands of years ago by the Ancient Greeks. One of those philosopher-physicists was Democritus, who came up with the theory of atoms (yes, over two thousand years ago!).

While cutting up an apple one day, he realized that the apple could be cut up into smaller and smaller pieces, and he wondered just how small of a piece of apple one could get. Since the rational Ancient Greek philosophers knew that the universe was finite (something specific in *all* respects, existence is identity to quote Ayn Rand), they also knew that there was no such thing as the infinite or the infinitesimal. In other words, one would have to reach a point at which one had the smallest piece of apple that was possible -- it couldn't be made of an infinite number of pieces because the apple is something finite and specific.

Democritus called these smallest bits "atomos," which is where we get the modern word "atom." So, if one starts cutting up an apple, one can perceive that the bits get smaller and smaller, and applying further reasoning, conclude that at some point one will have the smallest bit of apple. Of course, we can't see atoms, because they are so small, but this is one way of grounding the idea of quantization of matter to the self-evident.

Where quantum mechanics seems to get weird is the idea that energy, as well as matter, is quantized. But using the same reasoning as Democritus, one can also conclude that there might be a smallest distance one can travel or a smallest energy one can exert. In fact, some of those same Ancient Greeks (possibly Aristotle) gave that as an answer to Xeno's paradox.

Xeno's paradox has to do with moving in a straight line from one position to another, always moving only half the distance remaining. In other words, let's say one wanted to move from point A to point B, which are twelve feet apart. The first move is six feet, the second move is three feet, the third move is one and a half feet, and so on. The question was: Would one ever reach point B?

Relying on the idea of there being no infinitesimal anything and no infinite amount of anything, one would have to conclude that at some point of moving there would be a smallest distance one could travel -- thus the last distance from point A to point B would be covered in one leap at the end, so to speak.

And if one translates moving into a conceptualization of energy (something acting or changing), then one can go from that idea to the idea that at some point there is a smallest energy that one could exert -- the universe cannot be comprised of either an infinite amount of matter nor an infinite amount of possible acting or changing (energy). In other words, at that next-to-the-last point before taking that last smallest movement, the energy required to move that smallest distance would require some finite small amount of energy imparted to the thing moving from point A to point B.

There are other aspects of quantum mechanics that I won't go into here, but basically some of the physicists conclusions do make sense, if one realizes that we live in a finite universe.

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I think one reason why some scientists want to fight against the idea that quantum particles jump from one position to another (at least under certain circumstances) is that they tend to think such particles as not being surrounded by anything (say in the absence of fields or in the absence of being directly influenced by other particles colliding with them).

But existence is a full plenum -- there is no nothing anywhere. And, again, the reason for this is that existence is identity. For there to be an actual bubble of nothing (or even a large amount of it) surrounding elementary particles would be to say that nothing is something, and that this existent-which-has-no-identity could influence particles in any way would also violate the law of causality. To be is to be something specific, which also means it would act or change according to its identity.

So, a further implication that the surrounded-by-nothing advocates are claiming is that nothing can become something -- i.e. a given point in the nothing can suddenly become transformed into a particle, as the particles moves from point A to point B, with nothing in between; say at points A1 and A2, those "points in space" go from having no quality to suddenly having the quality of the particle as the particles passes through them. And some physicists don't even mind saying that something can come from nothing! Now, I'll grant you that some of them don't mean it literally, but some of them do (as in the Big Bang theory). And some of these physicists claim that a particle that does jump does not pass through any point in between. I think it "passes through" the sub-points A1 and A2, but given the nature of that-which-is-inbetween, it just can't stop at those points.

Having a conception that there is something there can account for some of the wierd effects observed in quantum mechanics. Whoever discovers its properties would have the right to name it, but I like to call it the aether, and I've written a poem about it on my website in the aesthetics section here.

The aether, or whatever it gets named, would have certain specific properties and would act accordingly. So, instead of having the conception that particles "pass through empty space" the conception would be that such particles interact with that-which-is-inbetween and both the particle and the aether would act according to their own identities -- which would then be the answer to many of the wierd effects investigated in quantum mechanics (and probably Relativity as well).

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Hello, my last encounter with physics was last winter. I wrote a paper regarding Quantum Mechanics, and the professor I had wrote that QM is not "internally consistent."

Recently I have been trying to track down what he meant by QM not being "internally consistent." I know that in the context he wrote it, he meant that the theoretical structure of QM (perhaps with some of the concepts or the math) there were some problematic internal conflicts.

Tom

There was a problem within the Standard Model when it was detected that neutrino have non-zero rest mass. The SM assumed neutrinos are massless.

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Hello, my last encounter with physics was last winter. I wrote a paper regarding Quantum Mechanics, and the professor I had wrote that QM is not "internally consistent."

Recently I have been trying to track down what he meant by QM not being "internally consistent." I know that in the context he wrote it, he meant that the theoretical structure of QM (perhaps with some of the concepts or the math) there were some problematic internal conflicts.

There was a problem within the Standard Model when it was detected that neutrino have non-zero rest mass. The SM assumed neutrinos are massless.

Not that I care to defend the standard theory, but the neutrino mass was essentially just a parameter originally determined to be zero based on the data available at the time. This does not signify that "the theoretical structure of QM" is "not being 'internal consistent'." (Emphasis added.)

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With the term winding down I'm essentially finished the last of my undergraduate courses in physics. During my courses Ive tried to conceptualize how to the theory of elementary waves would avoid some of the bazare phenomenae. Successful for the most part, I find myself really stuck with the idea of tunnelling. If the elementary waves do not exert any forces how can a electron or any particle for that matter pass a classically forbidden barrier?

On an other note, it has been quite a while since I've visited the site and I must say the site is looking great.

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If the elementary waves do not exert any forces how can a electron or any particle for that matter pass a classically forbidden barrier?

Tunneling falls out of the Schroedinger wave equation, and, simply put, it is seen as the leaking of amplitude across the potential step region. It is considered a wave phenomena, and it only seems strange or weird for a theory in which wave-particle duality exists. In the TEW, where the elementary waves and the particles are considered to be separate existents (with the particle dynamics carried by the waves), the elementary waves behave just as described by the Schroedinger equation. The quantum laws affecting tunneling are obeyed by the wave-particle of the standard theory, but are obeyed solely by the elementary waves in the TEW. The actual particles just follow the already established path of the elementary waves, with their dynamics already determined. It is the waves that "tunnel," and there is no force necessary to push or pull the particle through a potential step region.

On an other note, it has been quite a while since I've visited the site and I must say the site is looking great.

Glad you like THE FORUM, Alex. We have a great group of members.

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Tunneling falls out of the Schroedinger wave equation, and, simply put, it is seen as the leaking of amplitude across the potential step region. It is considered a wave phenomena, and it only seems strange or weird for a theory in which wave-particle duality exists. In the TEW, where the elementary waves and the particles are considered to be separate existents (with the particle dynamics carried by the waves), the elementary waves behave just as described by the Schroedinger equation. The quantum laws affecting tunneling are obeyed by the wave-particle of the standard theory, but are obeyed solely by the elementary waves in the TEW. The actual particles just follow the already established path of the elementary waves, with their dynamics already determined. It is the waves that "tunnel," and there is no force necessary to push or pull the particle through a potential step region.

Wow, that was awesome! Thanks! I have always been at least somewhat confused by tunneling every time it's been brought up in one of my classes; this made it conceptually so much more clear.

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The actual particles just follow the already established path of the elementary waves, with their dynamics already determined. It is the waves that "tunnel," and there is no force necessary to push or pull the particle through a potential step region.

The part that really confuses me is where the particle(s) penetrate the barrier. With the standard theory the idea of a wave penetrating a barrier and have a transmission through to the other side seems conceptually simple to accept, but adopts the wave particle duality for the transmitted particle, which seems to make no sense. If the incident particle is strictly a particle, it requires a certain energy to overcome a potential step. Since the elementary waves do not exert any forces but merely dictate the path, how can a particle be transmitted past the barrier?

Does the particle source not produce particles with a discrete energy, but rather produces particles with an energy that fits a distrubtion, say a gaussian? Thus the transmitted particles are the exceptionally rare particles with enough energy to overcome the barrier, and follow the corresponding wave to the transmitted side?

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The part that really confuses me is where the particle(s) penetrate the barrier. With the standard theory the idea of a wave penetrating a barrier and have a transmission through to the other side seems conceptually simple to accept, but adopts the wave particle duality for the transmitted particle, which seems to make no sense. If the incident particle is strictly a particle, it requires a certain energy to overcome a potential step. Since the elementary waves do not exert any forces but merely dictate the path, how can a particle be transmitted past the barrier?

Previously I tried to get across that the whole way of looking at "tunneling" is mysterious only because of how the standard theory sets up the situation with their reliance on the uncertainty relations and such. In the standard account, if the region was a potential step, say V, and the particle had an energy E < V, there would be a contradiction if the particle's energy was measured to be less than V as it passes through this step region. However, because of the Heisenberg uncertainty relation, the measurement accuracy is limited to <delta>E * <delta>t > h. If the particle had extended duration in the step region, <delta>E could be measured quite accurately. However, the time spent in crossing the step region (which is the time between an incident wave packet arriving at the step and the wave packet emerging from the step region) is less than h/(V-E). So, <delta>E > V - E and the standard theory concludes that it cannot be certain that the E was less than V, and that the particle was in the step region.

As I mentioned previously, amplitude leakage is part and parcel of the Schroedinger equation. Psi is established as a probability amplitude, and when one derives the equation the amplitude spreads out across the neighboring intervals along the infinite intervals associated with the infinite components of the state vector. The TEW maintains the mathematical characteristics of psi, but probability is replaced by stimulated emission of real particles by real waves. It might be helpful to study the qualitative interpretation and the quantitative correspondence of Feynman diagrams in section 8 and section 9, respectively, of Little's 1996 paper.

Does the particle source not produce particles with a discrete energy, but rather produces particles with an energy that fits a distrubtion, say a gaussian? Thus the transmitted particles are the exceptionally rare particles with enough energy to overcome the barrier, and follow the corresponding wave to the transmitted side?

A Gaussian wave packet is exactly what was assumed even long ago when the standard theory had to address the situation I discussed above, but now for a large V with a long potential barrier. For a large transition time the standard theory needs to distort the wave packet, which of course is absent in the TEW. See "Tunneling of a Wave Packet," T. E. Hartman, Journal of Applied Physics, Vol. 33, No. 12, pp. 3427-3433, Dec. 1962.

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Thank you Stephen. You explain things with such clarity, it's a great gift you have.

More likely: A skill gained through life-long focus and decades of practice in communicating.

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