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January 21, 2018

CATEGORY:
The Nature of Time Essay Contest (2008)
[back]

TOPIC: Time and Quantum - Musings about the Quantized Nature of Becoming by Chi Ming Hung [refresh]

TOPIC: Time and Quantum - Musings about the Quantized Nature of Becoming by Chi Ming Hung [refresh]

This is the story of an idea. An idea so deceptively simple and yet so potent that it ought to be investigated. The idea is to put the quantum back in Quantum Mechanics, i.e. to re-emphasize the discontinuity of Becoming that is suggested by Quantum Mechanics. By doing so, the physical nature of Becoming and Time may be better understood. We offer a simple toy model as illustration.

Chi Ming Hung is one of the many many descendants of Confucius. He studied Physics and Mathematics in the University of Hong Kong before migrating to the United States where he earned his Ph.D. in theoretical nuclear physics. He's currently a staff member in the C.N. Yang Institute for Theoretical Physics in Stony Brook, New York.

As pointed out in Prof.Hestenes' essay, there seems to be now first experimental evidence for some kind of fermionic process occurring at the Compton frequency inside the electron, as suggested also by our toy model. For details of the experiment, see the following reference:

M. Gouanère et. al. (2008), A Search for the de Broglie Particle Internal Clock by Means of

Electron Channeling, Foundations of Physics 38: 659-664.

M. Gouanère et. al. (2008), A Search for the de Broglie Particle Internal Clock by Means of

Electron Channeling, Foundations of Physics 38: 659-664.

Dear Chi Ming:

(A note to others: This conversation started in the forum of Julian Barbour's essay.)

We seem to agree, at least, that the concept of time is useful, which is the primary issue.

From your most recent comments and your essay, it also seems clear that what you are asserting is not a "paradox", but rather unscientific practice. Science is based on reproducible...

view entire post

(A note to others: This conversation started in the forum of Julian Barbour's essay.)

We seem to agree, at least, that the concept of time is useful, which is the primary issue.

From your most recent comments and your essay, it also seems clear that what you are asserting is not a "paradox", but rather unscientific practice. Science is based on reproducible...

view entire post

Dear Dr. Hung,

1. You posed very deep and important questions:

a. Frequency of what?

b. Becoming of what?

But your answer ``Energy is the Frequency of Becoming" seems to me a little bit extra-universal. Indeed: if you have some stable particle like electron (your example) then the frequency of ``mass process" nu= mc^2/h is rather ``frequency of being". What do you think? I absolutely sure that quantum particles are some processes.

I try to find answer on similar questions in the framework of model of N-level quantum system, see my essay ``Morphogenesis and dynamics of quantum state". Frequencies Omega^{alpha} take the place of non-Abelian gauge field shaping ``filed shell" of generalized coherent state.

2. You have postulated ``that all becoming (i.e. physical changes) of any system must be quantum in nature, ...". What it technically means? I assumed that there are some elementary quantum motions with quantized action (see, P. Leifer, Annales de la Fondation Louis de Broglie, {bf 32}, (1) 25 (2007)). However quantum dynamics of superposition state is assumed to be smooth in $CP(N-1)$.

3. Probabilistic transition from NOW_N to NOW_{N+1}? The state of world? Are these really theoretically accessible? I see that you agree that even ``realistic case of N-particle system is more complicated because...". Furthermore, even the notion of single relativistic particle is contradictable.

The end of questions. Good luck! Peter

P.S. The ``Lorentz-transformed snapshots of Becoming" I used for embedding quantum dynamics into dynamical space-time (P. Leifer, arXiv:0808.3172v1 [physics.gen-ph]). I called this process ``attachment of Lorentz frame" to quantum dynamics in $CP(N-1)$.

1. You posed very deep and important questions:

a. Frequency of what?

b. Becoming of what?

But your answer ``Energy is the Frequency of Becoming" seems to me a little bit extra-universal. Indeed: if you have some stable particle like electron (your example) then the frequency of ``mass process" nu= mc^2/h is rather ``frequency of being". What do you think? I absolutely sure that quantum particles are some processes.

I try to find answer on similar questions in the framework of model of N-level quantum system, see my essay ``Morphogenesis and dynamics of quantum state". Frequencies Omega^{alpha} take the place of non-Abelian gauge field shaping ``filed shell" of generalized coherent state.

2. You have postulated ``that all becoming (i.e. physical changes) of any system must be quantum in nature, ...". What it technically means? I assumed that there are some elementary quantum motions with quantized action (see, P. Leifer, Annales de la Fondation Louis de Broglie, {bf 32}, (1) 25 (2007)). However quantum dynamics of superposition state is assumed to be smooth in $CP(N-1)$.

3. Probabilistic transition from NOW_N to NOW_{N+1}? The state of world? Are these really theoretically accessible? I see that you agree that even ``realistic case of N-particle system is more complicated because...". Furthermore, even the notion of single relativistic particle is contradictable.

The end of questions. Good luck! Peter

P.S. The ``Lorentz-transformed snapshots of Becoming" I used for embedding quantum dynamics into dynamical space-time (P. Leifer, arXiv:0808.3172v1 [physics.gen-ph]). I called this process ``attachment of Lorentz frame" to quantum dynamics in $CP(N-1)$.

Ken,

Thanks for your comments about my essay.

You're correct that what I'm trying to achieve is no less than a new interpretation of QM, where the unobservable continuous temporal evolutions of wave functions and other things in an unobservable Time continuum are ultimately to be eliminated in favor of Physics at the observable discrete moments of Becoming/Being. It's an ambitious project, and I've barely started...

Your question about the existence of temporal moments between those postulated in my model is a very good question. The answer I believe lies in the fact that when we introduce another system into the one-particle system in my model, we must use a model for N-particle systems (N > 1). This is much more complicated but in the simplest case with negligible interaction between the systems, the combined system consists roughly of the sum of the processes for the separate systems. More generally the combined system will correspond to a new set of temporal moments, more dense than the original systems (because of the higher energy of the combined system), and with the particular measurement you have in mind located at some moment of the COMBINED system.

While I do not postulate a minimum time interval (such as the Planck time) between any two temporal moments in my model, in actuality there may very well be such a minimum time interval. e.g. if the total energy (E) of the universe is finite, then the time interval corresponding to h/E will effectively be the minimum time interval in our universe. The existence of such a minimum time interval or maximum energy will have significant implications for both quantum field theory and general relativity, because it'll mean an effective cut-off in both theories which will very possibly cure the infinities/singularities plaguing both theories...

I'll comment on the twin paradox and your ether theory a bit later in your essay's forum...

Thanks for your comments about my essay.

You're correct that what I'm trying to achieve is no less than a new interpretation of QM, where the unobservable continuous temporal evolutions of wave functions and other things in an unobservable Time continuum are ultimately to be eliminated in favor of Physics at the observable discrete moments of Becoming/Being. It's an ambitious project, and I've barely started...

Your question about the existence of temporal moments between those postulated in my model is a very good question. The answer I believe lies in the fact that when we introduce another system into the one-particle system in my model, we must use a model for N-particle systems (N > 1). This is much more complicated but in the simplest case with negligible interaction between the systems, the combined system consists roughly of the sum of the processes for the separate systems. More generally the combined system will correspond to a new set of temporal moments, more dense than the original systems (because of the higher energy of the combined system), and with the particular measurement you have in mind located at some moment of the COMBINED system.

While I do not postulate a minimum time interval (such as the Planck time) between any two temporal moments in my model, in actuality there may very well be such a minimum time interval. e.g. if the total energy (E) of the universe is finite, then the time interval corresponding to h/E will effectively be the minimum time interval in our universe. The existence of such a minimum time interval or maximum energy will have significant implications for both quantum field theory and general relativity, because it'll mean an effective cut-off in both theories which will very possibly cure the infinities/singularities plaguing both theories...

I'll comment on the twin paradox and your ether theory a bit later in your essay's forum...

Dear Chi Ming:

Upon further thought, I believe that your interpretation could contain two possible sub-interpretations. Perhaps you could call one Weak and the other Strong. The Weak could be agnostic about continuous time, while the Strong asserts its nonexistence.

For the Strong to be valid, you must have a minimum time interval/max energy; otherwise, you would have arbitrarily short time periods, making the idea of no time between moments vacuous (note that a minimum time interval is necessary, but not sufficient).

I look forward to your thoughts on my essay.

Take care,

Ken.

Upon further thought, I believe that your interpretation could contain two possible sub-interpretations. Perhaps you could call one Weak and the other Strong. The Weak could be agnostic about continuous time, while the Strong asserts its nonexistence.

For the Strong to be valid, you must have a minimum time interval/max energy; otherwise, you would have arbitrarily short time periods, making the idea of no time between moments vacuous (note that a minimum time interval is necessary, but not sufficient).

I look forward to your thoughts on my essay.

Take care,

Ken.

Peter,

Thanks for your comments, and sorry for the late reply. It's been a busy weekend...

As I mentioned in the essay, this is work in progress and my ideas are still at the infancy stage, and so I'm unable to give all the specifics, for now.

In particular I haven't quite pinned down the mathematical description best suited to my ideas. I guess my favored approach to...

view entire post

Thanks for your comments, and sorry for the late reply. It's been a busy weekend...

As I mentioned in the essay, this is work in progress and my ideas are still at the infancy stage, and so I'm unable to give all the specifics, for now.

In particular I haven't quite pinned down the mathematical description best suited to my ideas. I guess my favored approach to...

view entire post

Dear Dr. Hung,

I absolutely agree about priority of physics over mathematics. But you gave the interesting opposite example: the primitive and wrong physical idea of strings leads to very sophisticated mathematics.

What you really mean for ``underlying process"? Is it your ``mass process" with nu= mc^2/h? What is the ``cellular automata"?

I think that your approach to state changes ``happened abruptly" is dangerous. The argument that the transition is textbf{unobservable} is weak from the philosophical point of view (do you remember the discussion of Einstein and Heisenberg?). This agnostic point of view closes a way to understand dynamics of transition. What is ``observable"? Observable by whom? I assumed that discrete quantum states (like states of quantum oscillator with integer action or half-integer actions |n hbar>) may combine coherent superposition which smoothly evolve... Similar idea of discrete action is discussed by M. Stuckey and M. Silberstein (Time, Space and Matter in Relational Blockworld....). The measurement (or observation) in my version is replaced by invariant relations between local dynamical variables...see my essay.

It is correct that space-time localization of relativistic quantum particle is problematic

(Newton-Wigner + Hegerfeldt). This is the reason why state space has a priority (there the ``localization" is possible) but in any case, should be something like soliton-like solution describing particles as we see in cosmic rays. In may case it is realized in the dynamical space-time (DST).

Good luck! Peter

I absolutely agree about priority of physics over mathematics. But you gave the interesting opposite example: the primitive and wrong physical idea of strings leads to very sophisticated mathematics.

What you really mean for ``underlying process"? Is it your ``mass process" with nu= mc^2/h? What is the ``cellular automata"?

I think that your approach to state changes ``happened abruptly" is dangerous. The argument that the transition is textbf{unobservable} is weak from the philosophical point of view (do you remember the discussion of Einstein and Heisenberg?). This agnostic point of view closes a way to understand dynamics of transition. What is ``observable"? Observable by whom? I assumed that discrete quantum states (like states of quantum oscillator with integer action or half-integer actions |n hbar>) may combine coherent superposition which smoothly evolve... Similar idea of discrete action is discussed by M. Stuckey and M. Silberstein (Time, Space and Matter in Relational Blockworld....). The measurement (or observation) in my version is replaced by invariant relations between local dynamical variables...see my essay.

It is correct that space-time localization of relativistic quantum particle is problematic

(Newton-Wigner + Hegerfeldt). This is the reason why state space has a priority (there the ``localization" is possible) but in any case, should be something like soliton-like solution describing particles as we see in cosmic rays. In may case it is realized in the dynamical space-time (DST).

Good luck! Peter

Sorry, in the last sentence should be ``In my case...".

Dear Dr. Hung,

You wrote in your essay (p. 8): "So Time has the topology of a linearly ordered discrete set, isomorphic to the set of integers."

And in your posting from Dec. 3, 2008 @ 01:44 GMT, you expressed your belief that ".. we can define change as simply the discrete transition from the state at one instant to the state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN."

Do you know the nature of continuum, namely, how many points are there on a straight line in Euclidean space? (cf. Kurt Gödel, "What is Cantor's Continuum Problem?", American Mathematical Monthly, Vol. 54, No. 9, November 1947, pp. 515-525).

I believe the puzzle of these "points" can be explained with Thompson's lamp paradox: Imagine a lamp that is turned 'on' at some instant labeled with 0 , and is left 'on' for 1 min, then turned 'off' for 0.5 min, then 'on' for 0.25 min, etc., ad infinitum. Do we have a limit? Obviously yes: 2 min. Fine, but what is the state of the lamp in the instant/point labeled with '2 min'? UNdecidable?

Just some musings, prompted by your statement with capital letters.

Regards,

Dimi Chakalov

You wrote in your essay (p. 8): "So Time has the topology of a linearly ordered discrete set, isomorphic to the set of integers."

And in your posting from Dec. 3, 2008 @ 01:44 GMT, you expressed your belief that ".. we can define change as simply the discrete transition from the state at one instant to the state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN."

Do you know the nature of continuum, namely, how many points are there on a straight line in Euclidean space? (cf. Kurt Gödel, "What is Cantor's Continuum Problem?", American Mathematical Monthly, Vol. 54, No. 9, November 1947, pp. 515-525).

I believe the puzzle of these "points" can be explained with Thompson's lamp paradox: Imagine a lamp that is turned 'on' at some instant labeled with 0 , and is left 'on' for 1 min, then turned 'off' for 0.5 min, then 'on' for 0.25 min, etc., ad infinitum. Do we have a limit? Obviously yes: 2 min. Fine, but what is the state of the lamp in the instant/point labeled with '2 min'? UNdecidable?

Just some musings, prompted by your statement with capital letters.

Regards,

Dimi Chakalov

Peter,

I think you mistook my meaning when I used string theory as a prime example of how the "math over physics" approach can go terribly wrong. I think we're in agreement here :)

As for the processes underlying the generalized E=hnu law I mentioned in the essay, I honestly don't know what they might turn out to be. All I'm postulating is that e.g. for a "particle" of mass m, the process corresponding to it should occur at a temporal frequency equal to that of the Compton frequency for the particle, as measured in the rest frame of the particle. For a fermion, this underlying process may be something like zitterbewegung or the Feynman zig-zag that I mentioned in my essay, but I don't believe it'll be anything like what David Hestenes is postulating because his model uses continuous classical trajectories for the electron, which is not compatible with the discrete moments of Becoming/Being I'm advocating.

The processes I'm thinking of are akin to cellular automata in the sense that both involve discete evolution of states in time, but that's where the similarity ends.

Whatever the underlying process may be, I'm glad that the first experimental evidence may have been found for it (see my comment above).

I agree with you that what should be called "observable" and "unobservable" in physics is a rather tricky question with no universally accepted answers. But in the case of Quantum Mechanics at least, it seems natural to call what's being observed during quantum measurements (quantum jumps) as being observable, while anything in between as being unobservable. The whole point of my thesis is that QM can and should be re-formulated so that emphasis is given to what actually occurs during measurements, and not to what is supposed to happen in the supposed time continuum in between measurements.

While I agree that the time continuum is of significant practical value as a mathematical device for correlating the states of a quantum system at different stages of its evolution, we should not treat the time continuum as something physical simply because it's mathematically convenient, especially when this convenient mathematical assumption has been shown to be paradoxical when describing quantum measurements...

As for the arena in which the state of a system should be defined at each moment of Becoming/Being, I haven't pinned it down yet, but in general it'll probably be something like the usual Fock space in QFT, which is probably similar to the "state space" you referred to, so it seems we're not in disagreement here...

I think you mistook my meaning when I used string theory as a prime example of how the "math over physics" approach can go terribly wrong. I think we're in agreement here :)

As for the processes underlying the generalized E=hnu law I mentioned in the essay, I honestly don't know what they might turn out to be. All I'm postulating is that e.g. for a "particle" of mass m, the process corresponding to it should occur at a temporal frequency equal to that of the Compton frequency for the particle, as measured in the rest frame of the particle. For a fermion, this underlying process may be something like zitterbewegung or the Feynman zig-zag that I mentioned in my essay, but I don't believe it'll be anything like what David Hestenes is postulating because his model uses continuous classical trajectories for the electron, which is not compatible with the discrete moments of Becoming/Being I'm advocating.

The processes I'm thinking of are akin to cellular automata in the sense that both involve discete evolution of states in time, but that's where the similarity ends.

Whatever the underlying process may be, I'm glad that the first experimental evidence may have been found for it (see my comment above).

I agree with you that what should be called "observable" and "unobservable" in physics is a rather tricky question with no universally accepted answers. But in the case of Quantum Mechanics at least, it seems natural to call what's being observed during quantum measurements (quantum jumps) as being observable, while anything in between as being unobservable. The whole point of my thesis is that QM can and should be re-formulated so that emphasis is given to what actually occurs during measurements, and not to what is supposed to happen in the supposed time continuum in between measurements.

While I agree that the time continuum is of significant practical value as a mathematical device for correlating the states of a quantum system at different stages of its evolution, we should not treat the time continuum as something physical simply because it's mathematically convenient, especially when this convenient mathematical assumption has been shown to be paradoxical when describing quantum measurements...

As for the arena in which the state of a system should be defined at each moment of Becoming/Being, I haven't pinned it down yet, but in general it'll probably be something like the usual Fock space in QFT, which is probably similar to the "state space" you referred to, so it seems we're not in disagreement here...

Dimi,

Thank you for your comments.

I'm not sure whether you're objecting to my use of the word "continuum" (which has the usual mathematical meaning of a set isomorphic to the set of real numbers), or whether you're objecting to my postulate that the set of physical moments of Becoming/Being of any system is isomorphic to the set of integers, not the continuum as defined above.

Assuming you're objecting to the latter, I think I understand your argument which is similar to Zeno's. But in order for your argument to hold, you actually need to assume a physical time continuum (or at least a dense set) from the start! The property of denseness for a linearly-ordered set (i.e. between any two elements we can find another element in between the two) does not apply to the set of integers, and thus not to the set of physical moments of Becoming/Being I'm postulating.

One can argue that physically one can always make an additional observation in between any other two observations in time, but as I mentioned in my answer to Ken (Dec. 6, 2008 @ 02:40 GMT), we then need to consider the combined system and the physical moments of Becoming/Being that belongs to the combined system, which together should contain all the measurements in question.

Thank you for your comments.

I'm not sure whether you're objecting to my use of the word "continuum" (which has the usual mathematical meaning of a set isomorphic to the set of real numbers), or whether you're objecting to my postulate that the set of physical moments of Becoming/Being of any system is isomorphic to the set of integers, not the continuum as defined above.

Assuming you're objecting to the latter, I think I understand your argument which is similar to Zeno's. But in order for your argument to hold, you actually need to assume a physical time continuum (or at least a dense set) from the start! The property of denseness for a linearly-ordered set (i.e. between any two elements we can find another element in between the two) does not apply to the set of integers, and thus not to the set of physical moments of Becoming/Being I'm postulating.

One can argue that physically one can always make an additional observation in between any other two observations in time, but as I mentioned in my answer to Ken (Dec. 6, 2008 @ 02:40 GMT), we then need to consider the combined system and the physical moments of Becoming/Being that belongs to the combined system, which together should contain all the measurements in question.

Dear Chi,

Thank you for your prompt reply from Dec. 11, 2008 @ 01:07 GMT.

You wrote: "But in order for your argument to hold, you actually need to assume a physical time continuum (or at least a dense set) from the start!"

I don't need to assume any additional properties of the continuum, apart from those identified by Kurt Gödel -- please read his 1947 article. I only object to your belief that ".. we can define change as simply the discrete transition from the state at one instant to the state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN."

Nothing can go "in between" two adjacent points, and nothing can verify the state of the Thompson lamp at the point labeled with '2'. Perhaps you may wish to think of it as superposition of |on> + |off> , which of course will produce even more musings.

Regards,

Dimi

Thank you for your prompt reply from Dec. 11, 2008 @ 01:07 GMT.

You wrote: "But in order for your argument to hold, you actually need to assume a physical time continuum (or at least a dense set) from the start!"

I don't need to assume any additional properties of the continuum, apart from those identified by Kurt Gödel -- please read his 1947 article. I only object to your belief that ".. we can define change as simply the discrete transition from the state at one instant to the state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN."

Nothing can go "in between" two adjacent points, and nothing can verify the state of the Thompson lamp at the point labeled with '2'. Perhaps you may wish to think of it as superposition of |on> + |off> , which of course will produce even more musings.

Regards,

Dimi

Dimi,

I checked the Gödel paper you mentioned, but it's about Cantor's Continuum Hypothesis (CH), which is a fascinating topic to me, but has nothing to do with my essay, because I rejected physical Time as a continuum from the beginning!

In fact, the mathematical complexity of the continuum (as exemplified by the CH) is one of the reasons I rejected it as a model of physical Time...

I checked the Gödel paper you mentioned, but it's about Cantor's Continuum Hypothesis (CH), which is a fascinating topic to me, but has nothing to do with my essay, because I rejected physical Time as a continuum from the beginning!

In fact, the mathematical complexity of the continuum (as exemplified by the CH) is one of the reasons I rejected it as a model of physical Time...

Chi,

You confessed that "... the mathematical complexity of the continuum (as exemplified by the CH) is one of the reasons I rejected it as a model of physical Time..."

It is quite unusual for a descendant of Confucius and a staff member in the C.N. Yang Institute for Theoretical Physics in Stony Brook, New York, to treat theoretical physics like a supermarket from which one can choose to purchase only the food needed for a particular meal, and ignore everything else.

Please correct your attitude, and convey my best regards to Albert Einstein Professor Chen Ning Yang.

Sincerely,

D. Chakalov

You confessed that "... the mathematical complexity of the continuum (as exemplified by the CH) is one of the reasons I rejected it as a model of physical Time..."

It is quite unusual for a descendant of Confucius and a staff member in the C.N. Yang Institute for Theoretical Physics in Stony Brook, New York, to treat theoretical physics like a supermarket from which one can choose to purchase only the food needed for a particular meal, and ignore everything else.

Please correct your attitude, and convey my best regards to Albert Einstein Professor Chen Ning Yang.

Sincerely,

D. Chakalov

Dimi,

My opinions are my own, and they don't represent the views of the YITP or anybody else.

As for your criticism of me choosing concepts based on my personal tastes, I suggest this is more the norm than the exception in theoretical physics. When approaching a subject as speculative as the one we're discussing here, I chose concepts and ideas based on my own educated guesses just like any other physicist would. After all, there's no empirical evidence to suggest whether physical Time is a continuum or not, so we're all free to propose our own models, which is what I'm doing here. All I'm suggesting is my own toy model of Time and Becoming, nothing more.

The ones who try to impose their views on others are the ones who need to have their attitudes corrected.

My opinions are my own, and they don't represent the views of the YITP or anybody else.

As for your criticism of me choosing concepts based on my personal tastes, I suggest this is more the norm than the exception in theoretical physics. When approaching a subject as speculative as the one we're discussing here, I chose concepts and ideas based on my own educated guesses just like any other physicist would. After all, there's no empirical evidence to suggest whether physical Time is a continuum or not, so we're all free to propose our own models, which is what I'm doing here. All I'm suggesting is my own toy model of Time and Becoming, nothing more.

The ones who try to impose their views on others are the ones who need to have their attitudes corrected.

Chi,

You wrote: "As for your criticism of me choosing concepts based on my personal tastes, ... "

Correction: I cannot agree with your systematic neglect of particular facts which run against your ideas. If you treat physics as a hobby, you should at least acknowledge that your hobby may be easily spoiled by some well-known facts, such as those explained in my previous postings.

If you respect theoretical physics, please correct your attitude.

If you treat it as a hobby, don't bother to even reply.

You wrote: "As for your criticism of me choosing concepts based on my personal tastes, ... "

Correction: I cannot agree with your systematic neglect of particular facts which run against your ideas. If you treat physics as a hobby, you should at least acknowledge that your hobby may be easily spoiled by some well-known facts, such as those explained in my previous postings.

If you respect theoretical physics, please correct your attitude.

If you treat it as a hobby, don't bother to even reply.

Dimi,

You have your opinions, and I respect that (even though you don't seem to want to reciprocate), I just happen not to agree with you. If that offends you, too bad...

You have your opinions, and I respect that (even though you don't seem to want to reciprocate), I just happen not to agree with you. If that offends you, too bad...

Dear Dr. Chi Ming Hung,

I like the idea of frequency being more fundamental that energy. Although my approach of QM is complementary, being based rather on smoothness than discontinuity, I find your explorations into discreteness very interesting (I don’t see them incompatible at all since, as perhaps your work in progress will show, there may be an equivalence). Again, although I feel comfortable in the block world, I consider nice your idea of using indeterminism as an “escape” to a presentist view. If you will succeed in eliminating the GR singularities and the QFT infinities by using the discrete approach, this will be a big leap forward.

Best wishes,

Cristi Stoica

Flowing with a Frozen River

I like the idea of frequency being more fundamental that energy. Although my approach of QM is complementary, being based rather on smoothness than discontinuity, I find your explorations into discreteness very interesting (I don’t see them incompatible at all since, as perhaps your work in progress will show, there may be an equivalence). Again, although I feel comfortable in the block world, I consider nice your idea of using indeterminism as an “escape” to a presentist view. If you will succeed in eliminating the GR singularities and the QFT infinities by using the discrete approach, this will be a big leap forward.

Best wishes,

Cristi Stoica

Flowing with a Frozen River

Cristi,

Thank you for your comments about my essay.

Good Luck to you too!

Thank you for your comments about my essay.

Good Luck to you too!

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