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

TOPIC: The Nature of Time: from a Timeless Hamiltonian Framework to Clock Time of Metrology by Enrico Prati [refresh]

TOPIC: The Nature of Time: from a Timeless Hamiltonian Framework to Clock Time of Metrology by Enrico Prati [refresh]

The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental timelessness of Nature. However, the correct view that physics is described by relations between variables does not addresses the second problem of how time does emerge at the macroscopic scale on the ground of a timeless framework. In this work ordinary Hamiltonian dynamics is first recast in a timeless formalism capable to provide a definition of parameter time on the basis of the only generalized coordinates, together with the Hamiltonian invariance on trajectories, and a variational principle. Next, clock time emerges as a discrete macroscopic quantity by considering subsystems cyclic in the phase space, to which other subsystems refer. Suitable cyclic phenomena, under sufficiently restrictive assumptions on their stability (like atomic clocks) are indeed a good approximation of the canonical parameter time and describe time evolution of physical quantities by means of the same simple dynamical laws.

Enrico Prati is research scientist of Italian CNR at the Laboratorio Nazionale MDM. His main research interests are quantum transport, spin dynamics and decoherence in nanoscaled quantum devices, and the transition from quantum to classical physics. He is also involved in the broad field of emerging properties of metamaterials. He is particularly interested in the foundations of the physics of time. He has received the 2004 URSI-B Commission Young Scientist Award for his research in metamaterials.

Hello Enrico,

I enjoyed your paper!

However, some of your suppositions concern me, for instance: "The fact that time is not a measurable quantity can be clarified as follows [1, 2, 13–16]."

Time cannot be measured? Did you know that modern computers which power the internet rely on chips that have tiny clocks on them, which must be very, very accurate? Engineers had to measure this! Time can be measured and then some! My writing this, and your reading it, on a computer, testifies to this fact.

You write, "The problem of the Nature of Time consists of two parts: whether or not time is a fundamental quantity of Nature, and how clock time does emerge in the laboratory measurement in spite of a (timeless) theoretical and conceptual framework according to which parameter time is not observable."

But when you think about it, time is most fundamental to nature and physics, for no measurement can exist without change, and thus physics cannot exist without time.

Ergo, I propose that change be woven into the fundamental fabric of spacetime with dx4/dt=ic. From this simple postulate, that the fourth dimension is expanding relative to the three spatial dimensions, all of relativity may be derived, and too, a *physical* model is given for time and its arrows and assymetries across all realms, as well as entropy and quantum mechanics' entanglement and nonlocality.

All of this is elaborated on in my paper:

Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

http://fqxi.org/community/forum/topic/238

Enjoy!

Best,

Dr. E (The Real McCoy)

I enjoyed your paper!

However, some of your suppositions concern me, for instance: "The fact that time is not a measurable quantity can be clarified as follows [1, 2, 13–16]."

Time cannot be measured? Did you know that modern computers which power the internet rely on chips that have tiny clocks on them, which must be very, very accurate? Engineers had to measure this! Time can be measured and then some! My writing this, and your reading it, on a computer, testifies to this fact.

You write, "The problem of the Nature of Time consists of two parts: whether or not time is a fundamental quantity of Nature, and how clock time does emerge in the laboratory measurement in spite of a (timeless) theoretical and conceptual framework according to which parameter time is not observable."

But when you think about it, time is most fundamental to nature and physics, for no measurement can exist without change, and thus physics cannot exist without time.

Ergo, I propose that change be woven into the fundamental fabric of spacetime with dx4/dt=ic. From this simple postulate, that the fourth dimension is expanding relative to the three spatial dimensions, all of relativity may be derived, and too, a *physical* model is given for time and its arrows and assymetries across all realms, as well as entropy and quantum mechanics' entanglement and nonlocality.

All of this is elaborated on in my paper:

Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

http://fqxi.org/community/forum/topic/238

Enjoy!

Best,

Dr. E (The Real McCoy)

Dear Elliot,

thank you for you comment. "The fact that time is not a measurable quantity can be clarified as follows [1, 2, 13–16]." means that the parameter time of Hamiltonian dynamics is not observable. Of course there is clock time which can be measured, and it is discussed in the section "Clock time". It consists of a macroscopic approximation of parameter time by means of other quantities related to the specific realization of the clock, at a wanted precision.

You report: >

The view well presented in the Contest also by some other authors is that physical quantities are mutually related and they can be parametrized very powerfully by a common parameter with respect to which they both evolve. There is no experimental evidence of a physical realization of that parameter as an observable quantity (remember that no time operator exists in quantum mechanics, according to a theorem for example), as I show in the Introduction by means of the two atomic clocks example. Time can be used in macroscopic systems interacting with microscopic or macroscopic ones, but if the interest is in time itself, at a fundamental level one as to avoid the implicit use of time in the reasoning and look only at what is effectively measured. In other words the fact that time is a fundamental quantity is the object of the investigation, not part of the assumption.

You state "Ergo, I propose that change be woven into the fundamental fabric of spacetime with dx4/dt=ic. From this simple postulate, that the fourth dimension is expanding relative to the three spatial dimensions, all of relativity may be derived, and too, a *physical* model is given for time and its arrows and assymetries across all realms, as well as entropy and quantum mechanics' entanglement and nonlocality."

I've read your paper very carefully, and I have to say that I cannot agree with all those sentences wich try to explain time with time-dependent words: the word "evolution" implies the assumption of an external absolute time. Also "expanding" implies that some external time is flowing. "Arrow of time" corresponds again to postulate that sime external time is assumed.

In order to explain time, one has to remove from the language and the definitions a series of "concept time-dependent" words, like "evolution", "before", "after", "to expand", "to evolve", "periodic".

As demonstrated in my work, one can define time only in a macroscopic framework, complex enough to contain a subsytesm which acts as a clock at the wanted precision.

Regards

Enrico

thank you for you comment. "The fact that time is not a measurable quantity can be clarified as follows [1, 2, 13–16]." means that the parameter time of Hamiltonian dynamics is not observable. Of course there is clock time which can be measured, and it is discussed in the section "Clock time". It consists of a macroscopic approximation of parameter time by means of other quantities related to the specific realization of the clock, at a wanted precision.

You report: >

The view well presented in the Contest also by some other authors is that physical quantities are mutually related and they can be parametrized very powerfully by a common parameter with respect to which they both evolve. There is no experimental evidence of a physical realization of that parameter as an observable quantity (remember that no time operator exists in quantum mechanics, according to a theorem for example), as I show in the Introduction by means of the two atomic clocks example. Time can be used in macroscopic systems interacting with microscopic or macroscopic ones, but if the interest is in time itself, at a fundamental level one as to avoid the implicit use of time in the reasoning and look only at what is effectively measured. In other words the fact that time is a fundamental quantity is the object of the investigation, not part of the assumption.

You state "Ergo, I propose that change be woven into the fundamental fabric of spacetime with dx4/dt=ic. From this simple postulate, that the fourth dimension is expanding relative to the three spatial dimensions, all of relativity may be derived, and too, a *physical* model is given for time and its arrows and assymetries across all realms, as well as entropy and quantum mechanics' entanglement and nonlocality."

I've read your paper very carefully, and I have to say that I cannot agree with all those sentences wich try to explain time with time-dependent words: the word "evolution" implies the assumption of an external absolute time. Also "expanding" implies that some external time is flowing. "Arrow of time" corresponds again to postulate that sime external time is assumed.

In order to explain time, one has to remove from the language and the definitions a series of "concept time-dependent" words, like "evolution", "before", "after", "to expand", "to evolve", "periodic".

As demonstrated in my work, one can define time only in a macroscopic framework, complex enough to contain a subsytesm which acts as a clock at the wanted precision.

Regards

Enrico

Dear Enrico,

I enjoyed your essay, especially the solution you propose for recovering the time parameter from the Hamiltonian. I agree that this mechanism describes well the way we measure the time (and perhaps applies also to subjective time).

Best wishes,

Cristi Stoica,

Flowing with a Frozen River

I enjoyed your essay, especially the solution you propose for recovering the time parameter from the Hamiltonian. I agree that this mechanism describes well the way we measure the time (and perhaps applies also to subjective time).

Best wishes,

Cristi Stoica,

Flowing with a Frozen River

Dear Cristi,

thank you for your comment.

Enrico

thank you for your comment.

Enrico

Hi Enrico,

I enjoyed your essay. Thank you for being mathematically rigorous. If I'm not mistaken closed Hamiltonians are independent of time in QM and lead to the time-independent Schrodinger equation. The time-independence of the wavefunction give stationary states. However, when the wavefucntion collapses it begins to spread out again according to the time-dependent Schrodinger equation.

I have a couple of questions:

1) Is the above mention of time dependent/independent Schrodinger equations relevant to the discussion of your essay?

2) If I said time is change would you agree or disagree? I have noticed a few essays try to eliminate time. I am not sure if you are trying to eliminate time or only the variable. I imagine a universe without time as completely static and unchanging. I like many of your ideas and you show the nomenclature of time is lacking. No doubt this is a sign of the problem with time.

3) Have you replaced t with sigma? If I understood your essay the sigma is a conglomerate of all the systems parameters.

I enjoyed your essay. Thank you for being mathematically rigorous. If I'm not mistaken closed Hamiltonians are independent of time in QM and lead to the time-independent Schrodinger equation. The time-independence of the wavefunction give stationary states. However, when the wavefucntion collapses it begins to spread out again according to the time-dependent Schrodinger equation.

I have a couple of questions:

1) Is the above mention of time dependent/independent Schrodinger equations relevant to the discussion of your essay?

2) If I said time is change would you agree or disagree? I have noticed a few essays try to eliminate time. I am not sure if you are trying to eliminate time or only the variable. I imagine a universe without time as completely static and unchanging. I like many of your ideas and you show the nomenclature of time is lacking. No doubt this is a sign of the problem with time.

3) Have you replaced t with sigma? If I understood your essay the sigma is a conglomerate of all the systems parameters.

Dear Brian, thank you for giving me the opportunity of clarifying my contribution.

1) Time evolution is realizied in quantum mechanics by virtue of the Stone theorem and the fact the the unitary time evolution operator U(t,t0) is generated by a generic Hamilton operator, irrespectively from its dependence/independence from parameter time. Schroedinger equation is just an explicit consequence of unitary evolution. The fact that a system is stationary does not implies that the system is described in a time dependent framework. A different story for the Wheeler-DeWitt equation, which is truly timeless. My canonical approach is general enough to contain WdW, and flexible enough to return unitary evolution under coarse grained measurement when a clock is part of the system under investigation.

2) The concept of change is strictly related to time, unfortunately. This is a problem of wording. Change is "to be different at different times" by definition; so if you say that a system changes, it means that your framework is time-dependent. In my approach I eliminate time at a fundamental level; at the same time, the use of clocks allows to relate configurations in the phase space with a macroscopic variable T which is extremely useful because it consist of a physical measurable approximation of the pure mathematical parameter t (in my text: sigma), so laws of physics are described by the same simple laws!

3) This explains what is "sigma" in my notes: it is an unphysical parameter, which is generally written as "t" in textbooks; I used a different symbol to remember that t in canonical mechanics is assumed a priory to be "time", with respect to which the other variables change; in my derivation, which does not assume time in the framework, sigma is just a useful parameter to describe trajectories in the phase space: it is the clock time T in macroscopic systems which provides to the observer to describe himself and experiments as something evolving.

I understand that it is not trivial to understand how this relate to perceptions. In my view, an useful description of the world is like that: imagine that everything, the so called past, present and future, occur at the same time: every configuration of the phase space, in other words, is realized with the others. The sensation of being in a time-evolving world depends of being an internal part of such system, with a clock in the hand and memory in the brain.

The subjective feeling of time is not treated at the present level, so please keep this only as a useful tool to understand the mathematics and the experimental aspects.

Enrico

1) Time evolution is realizied in quantum mechanics by virtue of the Stone theorem and the fact the the unitary time evolution operator U(t,t0) is generated by a generic Hamilton operator, irrespectively from its dependence/independence from parameter time. Schroedinger equation is just an explicit consequence of unitary evolution. The fact that a system is stationary does not implies that the system is described in a time dependent framework. A different story for the Wheeler-DeWitt equation, which is truly timeless. My canonical approach is general enough to contain WdW, and flexible enough to return unitary evolution under coarse grained measurement when a clock is part of the system under investigation.

2) The concept of change is strictly related to time, unfortunately. This is a problem of wording. Change is "to be different at different times" by definition; so if you say that a system changes, it means that your framework is time-dependent. In my approach I eliminate time at a fundamental level; at the same time, the use of clocks allows to relate configurations in the phase space with a macroscopic variable T which is extremely useful because it consist of a physical measurable approximation of the pure mathematical parameter t (in my text: sigma), so laws of physics are described by the same simple laws!

3) This explains what is "sigma" in my notes: it is an unphysical parameter, which is generally written as "t" in textbooks; I used a different symbol to remember that t in canonical mechanics is assumed a priory to be "time", with respect to which the other variables change; in my derivation, which does not assume time in the framework, sigma is just a useful parameter to describe trajectories in the phase space: it is the clock time T in macroscopic systems which provides to the observer to describe himself and experiments as something evolving.

I understand that it is not trivial to understand how this relate to perceptions. In my view, an useful description of the world is like that: imagine that everything, the so called past, present and future, occur at the same time: every configuration of the phase space, in other words, is realized with the others. The sensation of being in a time-evolving world depends of being an internal part of such system, with a clock in the hand and memory in the brain.

The subjective feeling of time is not treated at the present level, so please keep this only as a useful tool to understand the mathematics and the experimental aspects.

Enrico

Enrico,

You're welcome and thank you for the reply I think I'm starting to get the big picture. If I may, I'd like to create an analogy to keep my bearings while working through your derivations. Please feel free to point out the problems with the analogy, also you can outright reject it or modify it.

The ideal gas can be described using the position and momentum space but the...

view entire post

You're welcome and thank you for the reply I think I'm starting to get the big picture. If I may, I'd like to create an analogy to keep my bearings while working through your derivations. Please feel free to point out the problems with the analogy, also you can outright reject it or modify it.

The ideal gas can be described using the position and momentum space but the...

view entire post

"The ideal gas can be described using the position and momentum space but the overall system is usually described with macroscopic properties like pressure and temperature. Is your idea of clock time similar to the concept of temperature or pressure?"

I think that your analogy has both a strong and a weak aspects. The strong aspect is that it clarifies in a familiar way why time, as well as temperature, has no meaning at the microscopic scale. This was already pointed out by Bohr, considering temperature and energy as complementary, as well described by Heisemberg. On the contrary, macroscopic time is built so that time-parametrized law of physics are preserved from the microscopic to the macroscopic domain; but there is no microscopic temperature-parameter governing microscopic laws of physics in my understanding. Maybe you could find some relationship with the order parameters of some critical phenomenon, but a formal analogy should be rigorously demonstrated.

"The root of my question involving the time dependent/independent Schrodinger equation was aimed at understanding how the measurement problem is addressed within your framework."

I agree that this problem is not treated explicitly. The reason is twofold: one is a principle issue, the second is very practical.

Every particle can be conceived in terms of propagator of a Feynman graph; the point is how much it is close to being at the mass shell. In some sense, real particles can be considered as virtual particles close to the mass shell (Griffith). The point is that an observer can trace only real particles because the interact in a causal way. It is for an antropic reason that our habit leads us to consider particles stable, expect those which terminate their life at a certain moment. If you believe that all the particle exist as propagator (which has one termination in the event of the measurement) in a virtual sense, there is no reason to justify a decay; it just occurs because it dependes on how well its mass was tuned to be at the mass shell.

So you can conceive a stationary relationship between all the propagators as a huge network, which is the arena of mass shell compatible subsystems which is the so called real world, where random events appear to occur if you count macroscopic time. I understand that this is a reasoning still based on a shaky ground but I believe that it is impossible to ignore that the energy conservation (and being at the mass shell) defines a subsystem of the vast world of virtual particles, and probably the apparent randomness of quantum measurements has to do with such underlying arena. A recent paper reproduces and improves the Harari Shupe model of preons only starting from the x and p coordinates, and this is a strong indication that time and energy conservation are not necessary at the fundamental level.

I think that your analogy has both a strong and a weak aspects. The strong aspect is that it clarifies in a familiar way why time, as well as temperature, has no meaning at the microscopic scale. This was already pointed out by Bohr, considering temperature and energy as complementary, as well described by Heisemberg. On the contrary, macroscopic time is built so that time-parametrized law of physics are preserved from the microscopic to the macroscopic domain; but there is no microscopic temperature-parameter governing microscopic laws of physics in my understanding. Maybe you could find some relationship with the order parameters of some critical phenomenon, but a formal analogy should be rigorously demonstrated.

"The root of my question involving the time dependent/independent Schrodinger equation was aimed at understanding how the measurement problem is addressed within your framework."

I agree that this problem is not treated explicitly. The reason is twofold: one is a principle issue, the second is very practical.

Every particle can be conceived in terms of propagator of a Feynman graph; the point is how much it is close to being at the mass shell. In some sense, real particles can be considered as virtual particles close to the mass shell (Griffith). The point is that an observer can trace only real particles because the interact in a causal way. It is for an antropic reason that our habit leads us to consider particles stable, expect those which terminate their life at a certain moment. If you believe that all the particle exist as propagator (which has one termination in the event of the measurement) in a virtual sense, there is no reason to justify a decay; it just occurs because it dependes on how well its mass was tuned to be at the mass shell.

So you can conceive a stationary relationship between all the propagators as a huge network, which is the arena of mass shell compatible subsystems which is the so called real world, where random events appear to occur if you count macroscopic time. I understand that this is a reasoning still based on a shaky ground but I believe that it is impossible to ignore that the energy conservation (and being at the mass shell) defines a subsystem of the vast world of virtual particles, and probably the apparent randomness of quantum measurements has to do with such underlying arena. A recent paper reproduces and improves the Harari Shupe model of preons only starting from the x and p coordinates, and this is a strong indication that time and energy conservation are not necessary at the fundamental level.

hi enrico

Eleven steps to right understanding of time

1. Motion of objects and particles do not happen in time, it happens in space only.

2. Time is what we measure with clocks: with clocks we measure duration and numerical order of massive objects and elementary particles motion into space.

3. As a “fourth” coordinate of space-time time is a “coordinate of motion”, it describes motion of massive bodies and particles into space.

4. Space-time is a math model only; space-time does not exist as a physical reality.

5. In a model of space-time we describe motion of objects and particles into space.

6. Space itself is atemporal.

7. Humans experience atemporal space as a present moment.

8. Past and future exists only in the mind; physical past and future do not exist.

9. Time as a coordinate of motion in atemporal space exists only when we measure it.

10. Time as a “coordinate of motion” is not elementary physical quantity as energy matter, space and motion are.

11. Universe is an atemporal phenomenon.

attachments: 1_In_The_Theory_of_Relativity__Time_is_a_Coordinate_of_Motion__Sorli__FOUNDATIONS_OF_PHYSICS_2009.pdf

Eleven steps to right understanding of time

1. Motion of objects and particles do not happen in time, it happens in space only.

2. Time is what we measure with clocks: with clocks we measure duration and numerical order of massive objects and elementary particles motion into space.

3. As a “fourth” coordinate of space-time time is a “coordinate of motion”, it describes motion of massive bodies and particles into space.

4. Space-time is a math model only; space-time does not exist as a physical reality.

5. In a model of space-time we describe motion of objects and particles into space.

6. Space itself is atemporal.

7. Humans experience atemporal space as a present moment.

8. Past and future exists only in the mind; physical past and future do not exist.

9. Time as a coordinate of motion in atemporal space exists only when we measure it.

10. Time as a “coordinate of motion” is not elementary physical quantity as energy matter, space and motion are.

11. Universe is an atemporal phenomenon.

attachments: 1_In_The_Theory_of_Relativity__Time_is_a_Coordinate_of_Motion__Sorli__FOUNDATIONS_OF_PHYSICS_2009.pdf

Enrico,

Sorry, for the delay in my reply. Thank you for working through my questions I appreciate it and I enjoy your paper even more now. I've printed it out and I'm going through the derivations myself. I'll be sure to ask more questions if I have them.

Sorry, for the delay in my reply. Thank you for working through my questions I appreciate it and I enjoy your paper even more now. I've printed it out and I'm going through the derivations myself. I'll be sure to ask more questions if I have them.

Hello Enrico,

I answered your question in my own forum, but thought that I would add the answers here too, so as to answer your question from "E. Prati wrote on Nov. 18, 2008 @ 10:45 GMT" above!

In my forum http://fqxi.org/community/forum/topic/238

, you write, and I answer: "E Prati wrote on Nov. 23, 2008 @ 20:48 GMT

In order to develop a theoretical...

view entire post

I answered your question in my own forum, but thought that I would add the answers here too, so as to answer your question from "E. Prati wrote on Nov. 18, 2008 @ 10:45 GMT" above!

In my forum http://fqxi.org/community/forum/topic/238

, you write, and I answer: "E Prati wrote on Nov. 23, 2008 @ 20:48 GMT

In order to develop a theoretical...

view entire post

hi enrico

seems we have similar ideas, yours amrit

attachments: 3_ETERNITY_IS_NOW_Sorli_2009.pdf, 2_ITT_phenomena__sorli_2009.pdf

seems we have similar ideas, yours amrit

attachments: 3_ETERNITY_IS_NOW_Sorli_2009.pdf, 2_ITT_phenomena__sorli_2009.pdf

Words are problematic. I would like to add, past ,present and future to the list of words to be avoided. However change is an interesting one, as are increase and decrease.

I have taken to saying motion when I really mean change of position, as it is quicker (but not as accurate.)That is probably a mistake on my part as I will be misunderstood.

According to my own model, change of position along the 4th dimension can lead to instantaneous change of position in 3D space. Subjectively the particle would seem to be time travelling so that it can disappear and reappear instantaneously in 3D space. So the change would appear to be independent of time from a 3D vector space perspective.

Likewise increase or decrease in value of (universal)potential energy i.e. promotional energy would appear to be instantaneous for the same reason.

So within the context of this model i feel that change, increase and decrease can be used since subjective observation is not considered as the same as objective reality.

I have taken to saying motion when I really mean change of position, as it is quicker (but not as accurate.)That is probably a mistake on my part as I will be misunderstood.

According to my own model, change of position along the 4th dimension can lead to instantaneous change of position in 3D space. Subjectively the particle would seem to be time travelling so that it can disappear and reappear instantaneously in 3D space. So the change would appear to be independent of time from a 3D vector space perspective.

Likewise increase or decrease in value of (universal)potential energy i.e. promotional energy would appear to be instantaneous for the same reason.

So within the context of this model i feel that change, increase and decrease can be used since subjective observation is not considered as the same as objective reality.

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