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

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)

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

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

Dear Cristi,

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.

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

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 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? If that is the case then I see the strength in using sigma but understand if it is not physically measured. It would similarly be impractical to use temperature or pressure for coarse grained particles instead of their position and momentum which is dependent on uncertainties. Also the connection with entropy would be immediately apparent.

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. In the quantum Zeno experiment a radioactive element's decay can be prevented by collapsing the wavefunction, however, once measurement stops the wavefunction begins to spread out and then radiation is observed. How does this and similar phenomena fit into your big picture? I initially thought it would be the clock time because the measurement must be made "fast" enough. So if you are using the clock time argument it seems justified because it is always used and is able to accurately describe the results.

Truthfully, I have not studied GR in depth. If classical physics fails to describe the quantum world then how does GR stand a chance? When I see the result H|psi> = 0 I have a difficult time accepting it as timeless because I have never seen the justification for time's disappearance. My gut feeling is that a constant results from the derivation and the first order time derivative makes it zero. In the Schrodinger equation it is the complex conjugate but that is another problem too. GR involves non-euclidean space but QM uses a probability space how is it possible that the Hamiltonians and wavefunctions in the wdw equation represent those of the Schrodinger equation? If the Hilbert space disappears then would that mean the measurement problem is ignored? I could see the block universe as representing the finite number of possibilities of the evolving universe because taking the probability out of QM would be like declawing Schrodinger's cat. These questions may only show my lack of experience with GR, but I don't want to stay stupid.

I am only interested in the mathematics so do not worry because I know a proof containing a subjectivist operator for perceptions will never be found. I agree that, "change is to be different at different times" but I view that as a strength and think of the change in the flow of time as time dilation. I have taken an interest in your paper and read it many times. Each time I read it I seem to bounce between agreeing and disagreeing. Any more insight you can give me is appreciated.

Thanks,

B^2

"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.

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.Attachment #1: 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.

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 framework capable to account the Nature of Time, one can only start with a-temporal principles, wording and reasoning. In particular, one recognizes that the following concepts and words make direct or implicit use of the concept of time itself, so they must be avoided:

-propagation

-expansion

-time dimension, time arrow or direction

-before, after

-consecutive

-propagator

-evolution, Hamiltonian evolution

-motion

-period, periodicity, frequency

-Planck time

-speed of light, speed

-reversibility, irreversibility

-to increase/to decrease

-change

Any derivation of time which makes use of at least one of those concepts or definitions, cannot consistently explore the Nature of Time.

"Traveling back.." contains for sure a very interesting idea, but in my view the whole paper is affected by the critical use of the temporal concept of expansion and evolution, particularly attributed to the fourth dimension. It is not clear in terms of what such expansion is occurring, and consequently with respect to what, time is also expanding (it goes linearly with x4).

Dr. E (The Real McCoy) wrote on Nov. 23, 2008 @ 21:19 GMT

Thanks E Prati,

Your problem is actually with the tautological definition of time that Einstein noted--a seeming paradoxical, circular definition which MDT resolves by postulating that dx4/dt = ic is a fundamamental invariant--the fourth dimension is expanding relative to the three spatial dimensions, and t, or dt, is an emergent parameter that we measure on our watches and clocks, as timeless, ageless photons surf the fourth expanding dimension, giving rise to the oscillating change in our clock's cicuitry, which we tune to mark the propagation of time in seconds.

Please see MDT in the context of simple, tautological light clocks in the attached figure.

Our definititions of time are based on measurement, which is based on the propagatin of energy, which propagates at c, which is defined in units of m/s (distance/time)! So it is that the time measured on our quartz crystal watches and on our computers, which depends on the emission and propagation of photons, which propogate at c, which is measure in m/s or distance/time, is tautologically defined!

The great thing about MDT is that it also accounts for this tautology, with a deeper fundamental invariant--the fourth dimension is expanding at c--which sets the velocity of light to c, the maximum and minimum and only velocity through spacetime to c, while also weaving into the fabric of spacetime the fundamental rate of change--c. MDT postulates that the fourth dimension is expanding relative to the three spatial dimensions at c.

"My solution was really for the very concept of time, that is, that time is not absolutely defined but there is an inseparable connection between time and the signal [light] velocity." -Einstein

So it is that time rests upon the velocity of light, which of course is defined by units of m/s or distance/time, and this tautological definition and paradox is nothing new.

MDT takes the paradox head on and blows the tautological fog away, exposing a new fundamental universal invariant which weaves change into the fabric of spacetime for the first time in all of history, liberating us from frozen time and the block universe, while providing a physical mechanism for entropy and quantum entanglement and nonlocality--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c: dx4/dt=ic.

Best,

Dr. E (The Real McCoy)"

Furthermore, Einstein's general relativity is based upon dimensions curving, warping, and moving; which includes the fourth dimension. So to state that the fourth dimension is expanding relative to the three spatial dimensions is perfectly consistent with Einstein's relativity.

"My interest in science was always essentially limited to the study of principles.... That I have published so little is due to this same circumstance, as the great need to grasp principles has caused me to spend most of my time on fruitless pursuits." --Einstein

Einstein's Principle of Relativity, as well as his two postulates, derive from MDT's single postulate which is more concise and has the added benefits of providing for free will, liberating us from the block universe, weaving change into the fundamental fabric of spacetime for the first time in the history of relativity, and providing a *physical* model for time and all its arrows and assymetries, entropy, and quantum nonlocality and entanglement, as well as reality's probabilistic nature. The fourth dimension is inherently nonlocal via its invariant expansion.

MDT presents a new universal invariant--an elementary law from which Einstein's Principle of Relativity can be built by pure deduction. Begin with a universe with four dimensions x1, x2, x3, x4 where the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, dx4/dt=ic, and all of relativity naturally arises, as does quantum mechanics' nonlocality and entanglement, wave-particle duality, space-time duality, mass-energy duality, entropy, and time and all its arrows and assymmetries.

"Behind it all is surely an idea so simple, so beautiful, that when we grasp it - in a decade, a century, or a millennium - we will all say to each other, how could it have been otherwise? How could we have been so stupid?" --John A. Wheeler

MDT presents a physical principle more fundamental than Einstein's principle of relativity, as all of relativity naturally emerges from MDT's postulate.

Best,

Dr. E (The Real McCoy)

hi enrico

seems we have similar ideas, yours amritAttachment #1: 3_ETERNITY_IS_NOW_Sorli_2009.pdfAttachment #2: 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.