Hi Henrik,

In quantum mechanics, there is the concept of Planck time, defined as the amount of time required for light to travel in a vaccum the distance of a unit of the Planck length. This time is approximately 5.39 × 10^-44 s, according to Wikipedia, and is described as the representation of "a rough time scale at which quantum gravitational effects are likely to become important". 

That's to say, we can't realistically model/simulate events seprated by a Plack time unit until we have a reliable and experimentaly verifiable theory of quantum gravity, which we don't have as of now.

The Planck lenght is roughly 1.616229×10^−35m and it is defined in Wikipedia as "the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart". It is also informed that it is 10^-20 times the diameter of a proton and that it is "theoretically considered to be the quantization of space".

So, if the granularity of the events you're trying to account for is very high, it seems that quantizing time and take it as a discrete parameter of the model is natural. Otherwise, if one is using continuous models (e.g. electromagnetic field theory) and is only concerned in tracking high-level measurable quantities, then the continuous time assumption might be a suitable approximation.

Carlos.

Dear Carlos,

Thank you for the very good and thorough response. Unfortunately, many years since I studied physics and even if I once wrote a short essay on Heisenberg's uncertainty principle I got lost when I discussed this question with a friend. The question was actually a bit more of philosophical nature; Does anything exists between 2 time quanta? :-)

Best Regards /Henrik

Interesting and some mind-blowing effects browsing trough, thanks Robert!

I have been looking into 'loop quantum gravity' a bit from a philosophical perspective. As I understand it on that account nothing would ’exists between 2 time quanta’. Below is a micro summery:

“Loop quantum gravity predicts that space comes in discrete lumps, the smallest of which is about a cubic Planck length, or 10–99 cubic centimeter. Time proceeds in discrete ticks of about a Planck time, or 10–43 second.” (Smolin, 2014, p. 96). On the loop quantum gravity account “space is an emergent description of relations between particles” (Smolin, 2008, p. 7) so a volume of a cubic Planck length is not just ‘space’ but is the smallest physical particle on the account.

 Smolin, Lee (2008), “The case for background independence,” [Preprint at arXiv.org] http://arxiv.org/pdf/hep-th/0507235v1.pdf

 Smolin, Lee (2014) Atoms of Space and Time. Scientific American (November 2014), 23, 94-103 

Published online: 23 October 2014 | doi:10.1038/scientificamericantime1114-94

Carlos R. B. Azevedo: “In quantum mechanics, there is the concept of Planck time, defined as the amount of time required for light to travel in a vacuum the distance of a unit of the Planck length.”

Henrik Almeida: “The question was actually a bit more of philosophical nature; Does anything exists between 2 time quanta?”

Johan Gamper: “As I understand it on that account nothing would ’exists between 2 time quanta’.”

 Allan: An EM-Wave has phase. Phase changes continuously as long as wave exists.

Therefore, as soon as wave changes its phase between any two given points there is the difference of phase between those points. Therefore, EM-Wave has eternal nature of propagation, and those changes do exist between any two given points regardless any small distance between them.

Before the derivation of the first examples of the solutions which were predict as hopefully existing, (see in paper "Cs. Ferencz: Electromagnetic wave propagation in general relativistic situation:: A general solution of the problem, Radio Science, Vol.47, RS1014, doi>10.1029/2011RS004905, 2012" in ch.4.) I can not say something more about the possible structure of the resulting space-time. This is an open question.

[UPDATE]: Adding missing link to Quanta magazine article: https://www.quantamagazine.org/20140416-times-arrow-traced-to-quantum-source/

[ORIGINAL]:

Hi Henrik, ok, I'm not a physicit (though I'd love to become one), but reading and thinking about physics and the nature of reality is one of my favorite hobbies! :-)

So, in the hope of elucidating what's at stake with your question, I'll shift the focus of your inquiry a little bit from "does time exist between 2 time quanta" to "why physical systems change/evolve toward equlibria states, i.e., why there is an arrow of time and where this comes from?"

You might be interested in reading this paper: "The Quantum Mechanical Arrows of Time", which states in the conclusion:

"No arrows of time need be built into a fundamental formulation of quantum mechanics of closed systems like the universe. Rather quantum mechanics can be formulated time-neutrally. The observed arrows of time are then emergent features of the asymmetries between conditions that specify our particular universe among the possibilities that the time-neutral theory allows."

There's also a nice article in Quanta Magazine that summarizes works that follow the same line. In that article, we can read:

"Popescu, Short and their colleagues Noah Linden and Andreas Winter reported the discovery in the journal Physical Review E in 2009, arguing that objects reach equilibrium, or a state of uniform energy distribution, within an infinite amount of time by becoming quantum mechanically entangled with their surroundings."

If this line is correct, then "quantum uncertainty gives rise to entanglement, the putative source of the arrow of time".

This part is also worth reading:

"The idea that entanglement might explain the arrow of time first occurred to Seth Lloyd about 30 years ago (...) Lloyd spent several years studying the evolution of particles in terms of shuffling 1s and 0s. He found that as the particles became increasingly entangled with one another, the information that originally described them (a “1” for clockwise spin and a “0” for counterclockwise, for example) would shift to describe the system of entangled particles as a whole. It was as though the particles gradually lost their individual autonomy and became pawns of the collective state. Eventually, the correlations contained all the information, and the individual particles contained none. At that point, Lloyd discovered, particles arrived at a state of equilibrium, and their states stopped changing, like coffee that has cooled to room temperature."

“What’s really going on is things are becoming more correlated with each other,” Lloyd recalls realizing “The arrow of time is an arrow of increasing correlations.”

The article then closes with this:

"(...) our ability to remember the past but not the future, another historically confounding manifestation of time’s arrow, can also be understood as a buildup of correlations between interacting particles. When you read a message on a piece of paper, your brain becomes correlated with it through the photons that reach your eyes. Only from that moment on will you be capable of remembering what the message says. As Lloyd put it: 'The present can be defined by the process of becoming correlated with our surroundings.'"

Now, if that does not give you enough food for thought, then you may want to read about a space-time crystal: "an open system in non-equilibrium with its environment that exhibits time translation symmetry breaking. The crystal's pattern repeats not in space, but in time, which remarkably allows for the crystal to be in perpetual motion".

Interesting. But how those crystals are related with the question of the nature of time? 

We can read some hints at Wikipedia:

"The basic idea of time-translation symmetry is that a translation in time has no effect on physical laws, that the laws of nature that apply today were the same in the past and will be the same in the future. (...) A violation in time-translation symmetry means that under certain conditions or select cases energy is not a conserved quantity and that laws of nature themselves are variable with time."

Which ends up increasing the weight of the physicists who claim time is absolute, such as Lee Smolin, cited in @Johan Gamper's answer above.Smolin and Roberto Mangabeira Unger, a Brazilian philosopher, put forward the idea that "not only is time real, but the laws of physics must themselves change over time". 

I have the intuition that this account may increase the likelihood of the answer "yes" to your original question of whether are there arrows of time between 2 time quanta.

I'll only mention the notion of delayed choice and retrocausality in QM :-)

I've attached some links to this answer so you can read more about those concepts and ideas.

All the best,

Carlos.

https://en.wikipedia.org/wiki/Space-time_crystal

https://phys.org/news/2017-03-crystals-envisioned-princeton-scientists.html

https://www.theguardian.com/books/2013/jun/10/time-reborn-farewell-reality-review

https://blogs.scientificamerican.com/cross-check/troublemaker-lee-smolin-says-physics-8211-and-its-laws-8211-must-evolve/

https://aeon.co/essays/can-retrocausality-solve-the-puzzle-of-action-at-a-distance

http://motls.blogspot.com.br/2016/10/no-retrocausality-in-qm-delayed-choice.html

https://www.quantamagazine.org/20140416-times-arrow-traced-to-quantum-source/

Article The Quantum Mechanical Arrows of Time

Article Pure state quantum statistical mechanics and black holes

No, there's no evidence for any ``shortest time''. Classically, time is continuous, and this is expressed by energy conservation, the expression of  global time translation invariance, that holds, also, when quantum effects are relevant, as long as gravitational effects can be considered as negligible. When gravitational effects can't be neglected, but are, still, classical, time is continuous, as an expression of general coordinate invariance. 

Stam Nicolis: “No, there's no evidence for any ``shortest time''.

 AZ: That is correct. As I mentioned above, EM-Wave has a phase that changes continuously. The best “clock” made by mankind uses EM-Waves to “determine the passage of Time.”

If QM gives another way of determination of “the shortest time” they should use that “basic oscillation” without any other physical process. That way is physically impossible.

As a result, they use only EM-Waves instead of “a signal of pure time coming from pure space detectable without any physical device.”

Hello and good day

The problem is : How can we define time for quantum states ?

Another question is : How quantum acceleration can be defined ?

But , as far as i know , there is no definition for time in quantum state.

Please guide me more.All ideas , opinions and aspects will be acknowledged.

Thank you so much in advance.Just we want to discuss to solve this problem.

Best regards

Hamed

Newton and Einstein's theory treats time as continuous flowing in one direction from past to present to future. In my theories I consider this as imaginary time. And since space time are not independent of each other, both are imaginary. The reality is based on wavelengths and periods of the particle waves. So time is periodic in nature. Definition of this periodic time quanta comes from de Broglie formalism as discussed in following article. The shortest time for anything to happen is Planck time 10^(-43) sec. When the period of the wave gets any smaller than this, it crosses the compton limit on wavelength 10^(-35) m. and this will make the particle wave to collapse leaving no mass gap. So energy of the particle will become perfectly motionless.

http://ptep-online.com/index_files/2015/PP-40-11.PDF

Article Periodic relativity: Basic framework of the theory

Hamed Daei Kasmaei: “The problem is : How can we define time for quantum states ? “

Allan: If you are talking about “time for quantum states” and some other “Time” for other processes you should explain the difference between those “different conditions of Time.”

That question leads to another groundbreaking question. What is Time? As soon as there is not any well-known answer on that question in modern science, you cannot define quantum time.  

In other words, you should answer the central question about Time to make the derivation of that category in other branches of science (including QM).

Would you like to know more? You can read my paper ‘Human’s delusion of Time.'

Simple answers are the best.

Planck time is the smallest quantum of time ~ 10^-42 sec.

In my actual derivations the space-time is continuous, no sign of discrete space-time appeared. 

Konrad Turzyński: “IN FACT adequate for the physical time, now it is still not possible, because human's knowledge about the nature of physical time seems to be not complete.

Allan Zade: Tell us please what do you mean with a notion of physical time? What does make you think that time is a significant part of physical reality? For example, have you any physical instrument that makes direct physical interaction with physical time?  Can you explain such interaction?

“Should time be considered continous or are there definitions for a time quantum (e.g. shortest time for anything to happen)?”

the answer see SS post in https://www.researchgate.net/post/Is_the_constancy_of_light_speed_in_vacuum_a_physical_reality_or_merely_a_convention#58d798e9cbd5c2a1f22e8326

22 page; in other pages possibly useful also, though.

Cheers

Hello Henrik,

Anyone interested in time might be interested in a paper that reports the identification of the basis of time in the universe. The paper provides the answers to the questions, What is time?, Why does time occur?, and Why does time have the specific qualities that it has?

The paper reports that the basis of time in the universe is intrinsically continuous.

People have been wondering about the nature of time for thousands of years. Nevertheless, no one has ever been able to find the basis of time in the universe. There is a specific reason for this—it is not possible to discover what time is by examining the observable qualities of time.

Trying to find the basis of time by way of the qualities of time is a top-down process. The problem is that those qualities do not reveal what time is or why it occurs. They do not carry understanding deep enough into the foundations of the universe to reveal the basis of time.

The discovery of the basis of time was serendipitous. I was not then working on the question of time. Rather I was studying space, specifically the continuing-existence of space. (This is the continuing-existence of space as measured by a clock, not the extension of three-dimensional space as measured by a ruler.)

While looking at space, I came upon the basis of time unexpectedly—by way of a bottom-up approach.

My work involves developing methodology for multi-discipline-spanning transdisciplinary understanding that enhances communication between the disciplines. To develop the methodology it is necessary to examine and compare the real-world subject matters of the various disciplines. Every component of the transdisciplinary understanding must be true in every discipline in which the component occurs.

When listing the intrinsic qualities of the continuing-existence of space, for transdisciplinary purposes, it became evident that these qualities of an aspect of space were the same as the qualities that can realistically be attributed to time.

In the universe, spatial-continuing-existence plays all the roles of time, and is thereby the basis of time in the universe

Spatial-continuing-existence is time due to the general role of spatial-continuing-existence in the universe. This role is a consequence of the role in the universe of space itself.

In the real-world, space can be observed to exist as extensional three-dimensional immaterial place. Spatial-place provides an existential-context, a place-to-be, for all that exists. For example, matter occupies, exists in, spatial-place. The three-dimensional extensional qualities of matter occupy the three-dimensional extension of spatial-place.

Continuing-existence is a form of change. The general role of spatial-continuing-existence is that it provides an existential-context, a place-to-occur, for all forms of change. All forms of ongoing change occur in concert, simultaneously, with the continuously ongoing change-existential-context provided by the continuing-existence of the spatial-place in which those changes are occurring.

The reason I keep referring to the universe, and to roles in the universe, is because the discussion here, and in the paper, is not about concepts. It is about the reality-referents of concepts. It is not about the concept of time. It is about time itself. Concepts are recognized to be mental tools that are used by the mind to achieve understanding of the world outside the mind, outside the brain.

Regards,

Vincent Vesterby

[email protected]

Vesterby, Vincent. 2014. The Identification of the Intrinsic Nature of Time.

https://philpapers.org/rec/VESTIO-4

https://www.researchgate.net/publication/299437469_The_Identification_of_the_Intrinsic_Nature_of_Time

https://www.academia.edu/21710898/The_Identification_of_the_Intrinsic_Nature_of_Time

There are two more papers that help explain the intrinsic nature of time.

Paul Davies and Why Time Is Not a Flow.

Vesterby, Vincent. 2016. Paul Davies and Why Time Is Not a Flow.

https://www.researchgate.net/publication/309619974_Paul_Davies_and_Why_Time_Is_Not_a_Flow

Temporal Naturalism—Analysis of the Paper by Lee Smolin.

Vesterby, Vincent. 2017. Temporal Naturalism—Analysis of the Paper by Lee Smolin.

https://www.researchgate.net/publication/313604997_TEMPORAL_NATURALISM_ANALYSIS_OF_THE_PAPER_BY_LEE_SMOLIN

Research The Identification of the Intrinsic Nature of Time

Article Paul Davies and Why Time Is Not a Flow

Article TEMPORAL NATURALISM—ANALYSIS OF THE PAPER BY LEE SMOLIN