## Short tutorial on time

Discussions on classical and modern physics, quantum mechanics, particle physics, thermodynamics, general and special relativity, etc.

### Short tutorial on time

This is a good summary of current place of time in physics: section 1.2 of Rovelli's introductory chapter of a book collecting work of many authors on quantum gravity. You can get the chapter as a preprint by googling "rovelli unfinished revolution"

=quote from pages 3 and 4==
1.2 Time
Time is affected even more radically by the quantization of gravity. In conventional QM, time is treated as an external parameter and transition probabilities change in time. In GR there is no external time parameter. Coordinate time is a gauge variable which is not observable, and the physical variable measured by a clock is a nontrivial function of the gravitational field. Fundamental equations of quantum gravity might therefore not be written as evolution equations in an observable time variable. And in fact, in the quantum–gravity equation par excellence, the Wheeler-deWitt equation, there is no time variable t at all.
Much has been written on the fact that the equations of nonperturbative quantum gravity do not contain the time variable t. This presentation of the “problem of time in quantum gravity”, however, is a bit misleading, since it mixes a problem of classical GR with a specific quantum gravity issue. Indeed, classical GR as well can be entirely formulated in the Hamilton-Jacobi formalism, where no time variable appears either.

In classical GR, indeed, the notion of time differs strongly from the one used in the special- relativistic context. Before special relativity, one assumed that there is a universal physical variable t, measured by clocks, such that all physical phenomena can be described in terms of evolution equations in the independent variable t. In special relativity, this notion of time is weakened. Clocks do not measure a universal time variable, but only the proper time elapsed along inertial trajectories. If we fix a Lorentz frame, nevertheless, we can still describe all physical phenomena in terms of evolution equations in the independent variable x0, even though this description hides the covariance of the system.

In general relativity, when we describe the dynamics of the gravitational field (not to be confused with the dynamics of matter in a given gravitational field), there is no external time variable that can play the role of observable independent evolution variable. The field equations are written in terms of an evolution parameter, which is the time coordinate x0, but this coordinate, does not correspond to anything directly observable. The proper time τ along spacetime trajectories cannot be used as an independent variable either, as τ is a complicated non-local function of the gravitational field itself. Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable. This does not mean that GR lacks predictivity. Simply put, what GR predicts are relations between (partial) observables, which in general cannot be represented as the evolution of dependent variables on a preferred independent time variable.
This weakening of the notion of time in classical GR is rarely emphasized: After all, in classical GR we may disregard the full dynamical structure of the theory and consider only individual solutions of its equations of motion. A single solution of the GR equations of motion determines “a spacetime”, where a notion of proper time is associated to each timelike world line.

But in the quantum context a single solution of the dynamical equation is like a single “trajectory” of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues. Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory.

To make sense of the world at the Planck scale, and to find a consistent conceptual framework for GR and QM, we might have to give up the notion of time altogether, and learn ways to describe the world in atemporal terms. Time might be a useful concept only within an approximate description of the physical reality.
==endquote==

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

I liked the post above, but thought Rovelli was short-changing the concept of relative time (or relative motion) in GR as well glossing over the probable nature of the observables as if they didn't reveal well-defined results (patterns). In Marshall's earlier post he spoke of a particular "solution" to the equations, which seems to me to be required if one is talking about this universe, the one we take to be part of. And in introducing quantum theory, I'm a bit surprised to hear what might be a 'lament' in his 'only approximate' remark. It's as if because we aren't able to understand the formation and trajectory of trees we are unable to the say anything about the forests they yield. To conclude that time is a useful concept only within an approximate description seems to me to be saying quite a lot, if one takes 'approximate' to characterize an exact description at the "forest" level of examination.
owleye
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### Re: Short tutorial on time (to avoid senseless argument)

Help me out here - does the timeless formalism mean that approximate timelike description is something that works when you have a "now universe" that happens to have thermodynamics? There is no block, there is no time dimension, but if you have directional changes from thermodynamics, then you can address now-events on a large scale with an evolution variable?

Braininvat
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### Re: Short tutorial on time (to avoid senseless argument)

owleye » Fri Oct 10, 2014 6:54 am wrote:... To conclude that time is a useful concept only within an approximate description seems to me to be saying quite a lot, if one takes 'approximate' to characterize an exact description at the "forest" level of examination.

I think that's quite right. I agree with you of course. And I think CR would agree in general as well. What you say is in line with his recent (2012 to present) writings on time. A number of physicists seem to be intensely interested in time, wanting to understand the phenomenon of time (in a post-Block context) and its passage. Having found that time is NOT suitable to be spatialized or geometrized, they want to understand (the world and) the passage of time in a different way.

I can't speak as an authority (!!!) obviously :^)

But what you say about forest and trees bespeaks coarsegraining and THERMODYNAMICS. And it is rather much in line with the thermal time hypothesis. It is conjectured (so far in a small number of papers) that the passage of time arises from
(1) the state of the universe (in the world's algebraic hodgepodge of observables, the state is a function that determines their expected values and their correlations. Observations/interaction-events being all that is known of the world.
(2) which macroscopic variables or observables really matter to us, our "coarse-graining" of the world.

The word "only" does not, to me, have any tone of lament or disappointment, it is a logical qualifier. If you omit it the sentence does not have the same logical content.

Von Neumann was the one who proposed that the world according to quantum theory was an ALGEBRA OF OBSERVABLES. An algebra (in math) is a SET of things with certain operations to relate or combine them, like an algebra of square matrices that you can add, subtract, multiply.
That is, he wanted us to focus NOT on a set of POINTS (as if the world were a carved block of wood or molded plaster, a geometric figure) but on a set of interactions, readings, collisions, happenings, a set of OBSERVABLES in stead of points.
and instead of a shape that a geometric figure might have he wanted us to think of a state function defined on that set of observables.

It's pretty abstract isn't it? We are visual animals in love with shape. Von Neumann's idea came out around 1935 or so and it is still sinking in. Forcing its way in, I would say, as people finally get disappointed with the 1915 Block geometric figure of the world.

Let's not give too much importance to this! There are just a very few papers on the TTH and it is just an hypothesis. We have to be able to explore different alternatives. It is not part of the main work of quantizing gravity, or so I think. I have not seen a connection with for example Lqg, which has an active application to cosmology and over 100 papers coming out each year. TTH has I'd say less than 5 papers in the whole of its existence since around 1993 when the algebraist Connes and CR thought it up. Von Neumann algebra was in the title of the original paper.

Coarsegraining: Your "forest" image. The fact that what we care about is the PRESSURE AND TEMPERATURE of the air in the room, not the position and direction of motion of every molecule. There are the variables, the degrees of freedom that we INTERACT WITH, the variables through which we interact with the world, our doors and windows to reality. And there are all the rest that are lumped together, or coarse-grained.

Just reacting to your post. don't have anything definite to report at this point

I'll look at BiV's post. thanks to both for the reflections on this!

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

My response just now very off the cuff scattered and apparently disconnected. I don't think I can tighten and organize it right now.

I think the gist of the quoted section on time in the first post is the word "trajectory" and this short paragraph:

==quote==
But in the quantum context a single solution of the dynamical equation is like a single “trajectory” of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues. Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory.
==endquote==

Unless you put an observable at one of the two slits you don't know which it went thru. And in some fundamental way it went thru both..., or neither :^)

Trajectories are geometric, and conversely, geometries are trajectories. That is, space-time geometries (individual solutions of GR equation of motion) are trajectories of changing shape. Geometry, including time, must not be fundamental!!?? Maybe it arises from a kind of coarsegraining. Maybe it emerges from a welter of microscopic little fact-lets. The irritating gnats whose swarm is the world. Maybe. It's just a conjecture.

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

Braininvat » Fri Oct 10, 2014 8:03 am wrote:Help me out here - does the timeless formalism mean that approximate timelike description is something that works when you have a "now universe" that happens to have thermodynamics? There is no block, there is no time dimension, but if you have directional changes from thermodynamics, then you can address now-events on a large scale with an evolution variable?

You are helping me out by asking this kind of question. You may intuitively see certain parts of this more clearly than I do. In any case it's definitely helpful.

Part of the time I find LQG hard to understand and TTH just plain scary. Part of the time I find them both intriguing, but separate.

Ideally LQG should run autonomously, it's dynamics should be well defined and should run on its own. Like the myriad mechanics of the individual air molecules in the room. But what can dynamics MEAN without a large-scale evolution variable? These little triangles and tetrahedra of geometry crawling all over each other, messing and mingling with each other's angles and volumes. A seething mess. Maybe time is a large scale result whose local rate reflects that seething.

Rovelli seems to be letting the younger Loop people work out the dynamics and the continuum limit of LQG.
The person to watch most closely is Bianca Dittrich, I think. She just came out with a paper on continuum limit (to be a chapter of a GR centennial volume.)
I find her paper quite hard to understand. Eventually the construction must lead to a Hilbert space (which means to an algebra of observables, operators defined on that Hilbert space). That where quantization MUST lead. The intuitive nice visual geometry of GR gets swallowed up in the hard-to-imagine geometry of the set of all possible observations. Each with a matrix to embody its possible outcomes and uncertainties.
I'll give the link to her article not because it is understandable but because at the beginning and end she gives a kind of non-technical overview of the current situation and where she thinks the field has to go.
She has a GROUP of younger researchers working with her, so she has developed the ability to articulate an outlook and direction.
You can probably get Dittrich's September 2014 paper by googling "dittrich continuum framework". Don't be discouraged if the middle part, with all the equations, is illegible just skim the outlook in the introduction and in the conclusions. If you bother with it at all.

The point is it is all working at the microscopic "sub-geometry" level and doesn't need thermodynamics.

The TTH is at a different level. Or so I see it, anyway.

I googled "dittrich continuum framework" and it was the first hit http://arxiv.org/abs/1409.1450

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

??? A lengthy blog to due whut my Timex does?

Yes, I do like jocularity, how did you know?

Time = those events between 2 accepted/known events. © Timex Corp
CincyJim
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### Re: Short tutorial on time (to avoid senseless argument)

I suppose you would say it tells time. It's an informative device.

And it does this because it informs you about "those events between 2 accepted/known events."

Atomic clocks, however, are based on transitions, a specific count of which is deemed to be a second. However, it is unable to count these transitions unless they are observable and knowable. Thus, given "2 known events" (i.e., two consecutive transitions), I'm able to count the second of this pair in relation to the first as having a 'between' period. And it is your contention that between these transitions there are events that constitutes time. And as we don't know what these events are, it is difficult to understand that they represent time, and as such they are difficult to understand how a Timex can be said to inform us about them. But, perhaps your Timex doesn't do that and does something else.
owleye
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### Re: Short tutorial on time (to avoid senseless argument)

The point is it is all working at the microscopic "sub-geometry" level and doesn't need thermodynamics.

I can see the sense of this. I have to envision a nanoworld where time is something that, if you stepped back quite a distance and got a macro picture, you would perceive time as a trend, or to put it another way, a report delivered from your team of statisticians on the direction that things are taking.

Braininvat
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### Re: Short tutorial on time (to avoid senseless argument)

Delightful analogy. My team wears wears loafers, and have pencils perched behind their ears. They have come in to report and they say it is trending towards lunchtime. :^)

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

CincyJim » Fri Oct 17, 2014 10:10 pm wrote: whut my Timex does?

Maybe part of a liberal arts education, humanities breadth requirement is to know about the quartz crystal oscillator.

In this tutorial, look at the introduction if you want and then scroll down to section on PIERCE OSCILLATOR
http://www.electronics-tutorials.ws/osc ... ystal.html

It's a little wafer slice of quartz metalized on both faces. So like a capacitor with a thin crystal between the two plates.

Like an organ pipe resonates at a lower frequency the longer it is, and shorter pipes have higher pitch, or a pendulum swings at a higher frequency the shorter the string, the the thinner the crystal the higher frequency it vibrates.
And quartz has the special "piezo-electric" property that the voltage across the crystal varies with mechanical stress. So if one face of the crystal is pinned to ground, at a fixed zero voltage, the other face voltage will oscillate as the crystal itself trembles. Soundwaves bouncing back and forth between the two sides.
So you tap into the oscillating voltage and amplify it give it some momentum like the weight on the end of the pendulum.

And use that fixed frequency wave to drive something, like (in the case of a wrist watch or the battery powered alarm clock beside the bed) a COUNTER, that counts the number of cycles or humps in the signal that have gone by.

Time = cycle count.

You get some FREQUENCY STANDARD, like days, or years, or quartz vibration cycles, or pendulum swings.

and you count the cycles of whatever standard frequency.

The important thing physically speaking is the frequency

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

In the metric system time is the reciprocal of frequency.

Frequency is something we can produce reliably because it is in a fixed relation to ENERGY. If a certain orbital transition in a certain atom always involves emitting or absorbing a fixed energy E
then the emitted light or radio wave will have fixed (cycles) frequency E/h
where h is the most basic or one of two or three most basic proportions in Nature.

Lightwave cycles are too rapid to count. So to design a CLOCK you need to choose an ATOM that has a very low energy transition. Like Rubidium or Cesium atom has this lone outer electron far from the nucleus with the charge from the nucleus almost canceled by all the other sister electrons that are more inner than it.
And it can have its spin either aligned with the nucleus spin, contrary. And the difference in energy is sooooo slight!

So the frequency associated with that transition, from reasonably comfortable to just slightly more comfortable, is slow enough to count its cycles!

The metric system defines the SECOND as a definite number of those cycles in the case of Cesium.
The number is about NINE BILLION. The cesium clock is the standard, but the rubidium clock is used in a lot of applications like GPS navigation satellites etc because it is light and compact and less expensive.

So in the metric system time is the reciprocal of frequency (of the cesium outer electron transition signal).
Operationally, the way we actually work with it. A second is ONE OVER A HERTZ. And what you are really doing when you time something is you are COUNTING HOW MANY CYCLES of a certain standard signal IT TAKES TO HAPPEN.

The watch in your watch pocket is Planck's constant, actually.

This is epistemology. How we actually tell and define time.

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

Some details:

The basic metric unit Hz is defined by the equation

std. cesium frequency = 9,192,631,770 Hz

Which is the same as defining the Hertz to be cesium frequency DIVIDED by 9,192,631,770

By definition, 1 Hz = (1/9192631770) cesium standard or about one 9 billionth of cesium.

The rubidium frequency has been measured in terms of the standard cesium and found to be
6,834,682,610.904 Hz.

So to make a rough comparison, the rubidium clock frequency is about seven ninths of the standard cesium clock frequency. Or to be needlessly fussy, 683/919 of the standard frequency.

Rubidium clock is relatively cheap and compact and gets used in tons of applications including the GPS system that everybody is using when they drive places in the car these days.

So probably as part of the general humanities breadth requirement we should all have some idea how rubidium clock works. That is, how the rubidium frequency is produced in practical devices.

It's easy if you already know how the QUARTZ OSCILLATOR in your watch or household clocks works. You can TUNE piece of quartz resonant frequency by stressing it say by applying a electric field to it. So you have a little hot chamber full of rubidium vapor and you shine a microwave beam though it and have a sensor testing to see how much comes thru. You vary the frequency of the beam just slightly and suddenly when you hit exactly the right frequency about 1% of the beam energy will be ABSORBED!!!

So you hook the sensor to FEED BACK to the field that is stressing the quartz oscillator. So that it will hold the quartz in just the right stress level so that it makes the perfect frequency for the rubidium gas in the little hot chamber. It works automatically.

the key is to have a quartz oscillator that is tunable over a narrow range around the ideal rubidium frequency and have a sensor to see how much of the microwave beam energy is being absorbed, and feed back to the tuner. So that the right frequency is LOCKED IN.

The microwave signal (to be counted) is not made by Rubidium atoms, it is made by a tunable Quartz crystal that is PINNED by feedback to the frequency which Rubidium atoms love to absorb (and also re-emit in a scattering of directions but what counts here is that they absorb it.)

So the sensor across on the other side of the chamber from the microwave gun can TELL when the frequency is right.

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

Marshall...

I appreciated your explanation of atomic clocks but am concerned about one undoubtedly minor issue, which is the use of Hz as the dimension (of choice?) for such clocks. Though such a dimension is no doubt accurate (in that it refers to cycles per second), what it hides is that it doesn't differentiate analog from digital differences. As such, I think the term is too general. Atomic clocks, as far as I can understand them anyway, aren't analog clocks, which is to say they aren't linear within the time interval that constitutes the transition from one cycle to the next. When Hz is used, one gets the impression that there is some sort of wave form that an oscilloscope can capture. This may still be the case and I might be concerned over nothing, but in so far as we're at the the level where quantum theory is supposed to dominate, and the instability of the cesium atom, respecting the spin properties that apparently are such that when one spin is in play it eventually becomes weakened by its alternative and the atom transitions to it, I'm thinking the only way to capture it is digitally. (My guess would be that it has something to do with the orientation taken by the cesium nucleus as the transition occurs (or it's instead the reverse of this) but I don't really know what I'm talking about, so I should probably shut my mouth.) In any case, I'm thinking that it's best to think of atomic clocks as digital clocks where one cannot take the 'tick' of the clock at a point anywhere within the cycle, but instead it has to be at the time of the transition. And this is why it can only be represented as a tick count to get at the time interval duration.
owleye
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### Re: Short tutorial on time (to avoid senseless argument)

Hi Owl, good questions!

Do you know any analog (continuous) clocks? A pendulum clock has its tick-tock escapement. A classical Greek water drip clock (clepsydra ) has its drip-drop and even the flow of water breaks down into molecules :^).

I think that all real time-measuring devices are doomed to be discrete and the better they are the more apt they are to depend on some cyclic (periodic, oscillatory) physical process.

To ABSTRACT or IDEALIZE from actual time measuring with real clocks I think one has to appeal to the mathematical convention of passing to the limit
where we imagine technology advancing so that we can build faster and faster COUNTERS and use higher and higher frequency signals.

At each stage measuring remains a cycle counting process but we increase the resolution and imagine that instead of counting cycles of a 9 billion Hz signal we use a 9 trillion Hz signal. So then one cesium cycle is resolved into 1000 little timestep counts.

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

BTW we should have in mind the wavelength of that cesium signal. I estimate it is around 3 centimeters.

299792458/9192631770
3.26 cm.

blue light is about 80,000 times shorter wavelength, e.g. around 0.4 microns. You know the visible range is around 0.4 to 0.7 micron.

So if we could build a counter that was 80 thousand times faster we could count blue light! Visions of an improved clock. :^)

Just find some atom that emits or resonates to a particularly nice shade of blue light, and hook it up to our counter!

Keep improving clocks and then, like a mathematician, leap in your imagination to infinite resolution. Take the limit of all those steps of improvement, in your mind. There's a continuous or analog clock!

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

Perhaps a sundial. However, I see your point, I think. What I think I had in mind was more like the ordinary distinction between an analog clock and a digital one, where in the case of an analog watch, the hands appear to be moving continuously, whereas in the digital case, it would appear to jump.

In any case, I gather atomic clocks are no different than pendulum-based clocks, the difference being solely in the forces that act on them to produce their periodicity. I'd been thinking of it wrongly when I spoke about quantum-level transitions, even though it takes a state transition to move from one spin state to another spin state and that this is best understood within quantum theory, not classical theory. It doesn't really matter that we don't know what goes on within that transition.

With respect to your "taking to the limit" idea of an analog clock, what I assumed was that you can't do that, because "quantum theory" prevents it. What I neglected is in the hbar*nu formula where nu is not restricted by quantum theory.
owleye
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### Re: Short tutorial on time (to avoid senseless argument)

Marshall quoted Rovelli's introductory chapter of a book collecting work of many authors on quantum gravity. “Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory.
To make sense of the world at the Planck scale, and to find a consistent conceptual framework for GR and QM, we might have to give up the notion of time altogether, and learn ways to describe the world in atemporal terms. Time might be a useful concept only within an approximate description of the physical reality.”

I personally like the message in the last sentence because I’ve always had trouble getting my mind around the notion of ‘spacetime’ (and the way in which quantum theory is being extrapolated to explain almost everything from ingrown toenails to multiverses). I agree entirely with his last sentence that “Time might be a useful concept only within an approximate description of the physical reality”.

I believe Rovelli is ‘on the money’ in this last sentence. In my mature life I’ve always looked for the origins of any concept in order to understand that concept. In the 1940s, my family did not have an alarm clock - with the result that my brother and I used to wake up in the dark and go down to the local newspaper shop to deliver morning newspapers without having any idea of what time it was. We seemed to be waiting around for hours on some mornings until the newspaper-delivery truck turned up with the goods.

I can only assume that thousands of years ago, our remote ancestors must have been in similar situations in which they would have liked to synchronise with others the notion of the ‘time’ they could meet for any of numbers of reasons.

At one stage I felt that our early Australian Aborigines may have provided a clue for the need for a notion of ‘time’. I’d imagined that the nomadic Australian Aborigines had no need for a sense of time because they existed as separate language groups each consisting of about 200 individuals occupying an area of about 10000 square miles. John Mathew’s 1860s record of the Gubbi Gubbi group of the east coast Fraser Island area (http://www.gubbigubbi.com/ ) shows that in 1860 at least they had words for ‘when’ and ‘at what time’ - wen'yo (when) and wen'yobola {when (at what time)}.

Wikipedia (http://en.wikipedia.org/wiki/Sundial , viewed 23.10.2014) presents a plausible summary of the history of timepieces used by our species – “The earliest sundials known from the archaeological record are the obelisks (3500 BC) and shadow clocks (1500 BC) from ancient Egyptian astronomy and Babylonian astronomy. Presumably, humans were telling time from shadow-lengths at an even earlier date, but this is hard to verify. In roughly 700 BC, the Old Testament describes a sundial — the "dial of Ahaz" mentioned in Isaiah 38:8 and II Kings. The Roman writer Vitruvius lists dials and shadow clocks known at that time. Italian astronomer Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Giuseppe Biancani's Constructio instrumenti ad horologia solaria (ca. 1620) discusses how to make a perfect sundial.[citation needed] They have been commonly used since the 16th century.

Mechanical timepieces did not appear till the 17th century.

Essentially sundials gave our ancestors a rough idea of the interval between midday to midday (when the shadow was at the middle point) on consecutive days. So, in those days apparently, our ancestors made appointments to meet before midday (ante meridiem in Latin or post meridiem). The reasons for dividing day and night into 12 hour sessions are open to working theories because no written records appear to exist for the decision. One is that a decimal division was in vogue because we have 10 fingers etc and an extra period was added for the change of light in the dawn and the sunset. Who knows? Another was that 12 was a good division of the times of midday to midnight because 12 is a number that can be a multiple of 1,2,3 and 4. The same type of logic has been used to explain the further subdivision of the hour into minutes and seconds - in that 60 can be a multiple of 1, 2, 3, 4, 5, (and 6, 10 and 12). Who knows, in the absence of records? But we do now have some more refined methods.

We all now know that our notion of 24 hours as a measure of the Earth’s rotation with reference to the sun or any fixed point in space is no longer accurate, and that corrections have to be made to fit in with seasonal regularities. Corrections were made for this anomaly in the times of Julius Caesar and Pope Gregory. The latter correction from memory was something in the order of months. People apparently went to bed one night and then had to set their calendars ahead some months when they woke up the next morning. The Leap Years are an automatic gross correction that we make every four years, but there are others planned for the odd day or so over the next few millennia.

As Marshall pointed out, we now have an official definition of a standard second as described once again by Wikipedia on http://physics.nist.gov/cuu/Units/second.html - “The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.”

But reasonably accurate mechanical timepieces have been in existence only since the 17th century. One of the reasons given for Captain Cook (who proclaimed Australia as a colony of England) being an exceptionally good navigator was that he was the first to use the best Swiss timepieces ever made at the time he sailed extensively over the southern Pacific area in the late 18th century.

Sure, we have extended our knowledge of time for the successful landings on the moon, for interplanetary satellite exploration of the solar system, and for the development of working theories on the age of the universe and the distance of the various galaxies etc. The official definition of a metre is now also given in terms of the wavelength of the caesium atom - Wikipedia cites a definition of a Standard Metre thus – “The metre (BIPM spelling), or meter (American spelling), (SI unit symbol: m), is the fundamental unit of length (SI dimension symbol: L) in the International System of Units (SI).[1] Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level), its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it has been defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."

Time and distance appear to be interrelated by definition.

This research by Wikipedia also mentions that, as Marshall pointed out, the caesium wavelength clock has a high degree of accuracy. “This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain atomic clock (U = 5×10−16). “

I personally have problems comprehending the ‘time’ aspects of the universe about me outside of these limits and therefore can identify with Rovelli’s final statements “To make sense of the world at the Planck scale, and to find a consistent conceptual framework for GR and QM, we might have to give up the notion of time altogether, and learn ways to describe the world in atemporal terms. Time might be a useful concept only within an approximate description of the physical reality.”

doogles
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### Re: Short tutorial on time (to avoid senseless argument)

Thanks Owleye and Doogles for the comments. Interesting reflections and historical detail!

All I originally wanted to do with this "short tutorial" thread was post that paragraph or so from Rovelli's 2006 essay.
It's fairly general and simple and gives an overview of the problem. There have been some interesting developments since then. If we try to discuss some of them it won't be a tutorial any more. It'll be more like me floundering around in confusion, but why not? Let's give it a try.

The three windows on current research and thinking that I'd suggest we look at are articles that appeared in 2014 by Fay Dowker, by Cortês and Smolin, and by Wolfgang Wieland. Wieland's is hard, maybe we can make do with just the first two. Dowker's is very easy to read but it does not go quite far enough.

For Dowker's piece, google "dowker passage arxiv"
For the piece by Lee Smolin and Marina Cortês, google "cortes spin foam causal"
Don't worry about Wieland's paper for now. If you really want it, google "wieland new action".

Dowker's point is that our physics has to understand our experience of the present and the passage of time.

So there has to be a process of causation, a confused "top layer" where the past is giving birth to new space-time atoms.

Once events or space-time atoms have been born in place and joined to the crystalline past we no longer experience them. Because our experience is part of the process of causation, where the old is constantly giving birth to the new.

Fay Dowker's teacher, Rafael Sorkin, calls this process "asynchronous becoming". It is impossible to "time-slice" it. The birth of new spacetime atoms (I think of them as cells of an organic body that grows by cell division on its surface) is not in any definite order. This is the challenging mental leap. The order is physically meaningless or, as Dowker says, "pure gauge". A "gauge" feature is a physically meaningless artifact of the mathematical description. E.g. in GR the particular coordinates used are gauge. Any other reasonable set of coordinates would do as well, but you have to CHOOSE one in order to define and calculate.
Which of many equivalent ones has no effect on the eventual outcome.

"Gauge" is physicist JARGON. It reminds us that in order to make a coherent math or logical description you may need to make some arbitrary choices---their effects wash out and don't affect the physical result or the final outcome. I gather this is a feature of a number of theories of different kinds in different branches of physics, so they have this jargon or slang term for it.

The orderly crystal of the past is covered by a confused frothy layer of becoming.
And the crystal grows by solidification of that layer, which adjoins new atoms (I keep thinking of cell-division and organic growth) to the crystal.
Our experience is only in the confused frothy layer of becoming.

Because our experience involves causation (interaction). So the experience of Now is all immersed in and emerging from this layer. It is a thought conveyed in Fay Dowker's May 2014 essay.

I have to go out, back later. This is all tentative, it hasn't crystallized yet :^)

BRAINinVAT: Dowker doesn't deal with the phenomenon of cosmic expansion AFAIK. She follows Rafael Sorkin's causal sets ideas and is a good presenter/expositor/collaborator. They are not yet at the stage, I think, where they can handle specifics like expansion cosmology.

Marina Cortês and Lee Smolin, with what they call "energetic causal sets" may have taken the theory a step further with more grasp of physical dynamics of how the past grows by this curious confused "cell-division" layer that is more alive. they have more definitive grasp of a possible dynamics, than Sorkin does, I think.
For Cortes-Smolin the little cells are actual tetrahedra behaving acording to some rules, rather than just being abstract elements of a partially ordered set.

But even then I don't see Cortes-Smolin addressing something so specific as expansion cosmology, or bounce cosmology----those would be topics for much later if this model picks up research momentum.

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

The "tutorial" part of this thread was just the first post---taken from an essay by Rovelli in 2006.
I'll go on to discuss some current thinking about one of the issues raised in the 2006 essay. This is partly embodied in recent papers by Dowker, by Cortes-Smolin, and by Wieland. I will give google-tags and links for them

Google "dowker passage arxiv" to get http://arxiv.org/abs/1405.3492
Google "cortes spin foam causal sets arxiv" to get http://arxiv.org/abs/1407.0032
Google "wieland new action arxiv" to get http://arxiv.org/abs/1407.0025

I've included "arxiv" in the google search terms to force it to make the first hit a FREE ONLINE version of the article itself instead of a pay-the-publisher version or an discussion somewhere else ABOUT the article.
If you do not include "arxiv" (the free preprint archive) you will still get the free version as one of the hits, but it might be a few hits down in the list.

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

I think there's a revolution brewing in theoretical physics because the standard "block universe" model of the world (1) is a trajectory as Rovelli pointed out in 2006 and so at odds with quantum theory and (2) has no special place for the experience of the present and the passage of time. The "Physics of Passage" conference in Dec 2012 was just one sign of this stirring at the foundations level.

I think Fay Dowker expresses this very well so I'm going to quote part of her May 2014 paper ("dowker passage arxiv"). Her point is that physics has to fit our experience and if there is a missing element people may ignore it for a long while, but conflicts build up, and eventually there is a foundations change. And she ILLUSTRATES that by pointing out there was this mismatch in NEWTONIAN gravity theory (you don't feel gravity like you feel other forces) which people put up with and fooled themselves about for over 300 years and then there was the 1915 revolution and they realized that it, after all, was NOT a force, it was curvature. You can zero it out by going into free fall. She draws the ANALOGY with today and the block universe mismatch in the "passage" department.

BTW here's her profile:
http://inspirehep.net/author/profile/F.Dowker.1

==quote Dowker http://arxiv.org/pdf/1405.3492.pdf ==

...Sorkin’s suggestion that the birth of spacetime atoms correlates with our conscious perception challenges the view that quantum gravity effects can only show themselves as phenomena in regimes far beyond our immediate reach. The idea is that we may have access, through our intimate experience, to a physical phenomenon that is not present in General Relativity but is part of a more complete theory of spacetime. Lest this seem far-fetched, let me introduce an example from history where an everyday human experience was pointing the way to a new understanding of the physical world, but the lack of a theoretical framework in which to situate and understand this experience meant that it remained (as far as I know) un-articulated until the beginning of the twentieth century.

Every day in the centuries between Newton’s discovery of the Law of Universal Gravitation and Einstein’s discovery of General Relativity, every human being was making an observation with no explanation within the Newtonian theory but which correlates perfectly with GR. This observational fact, was, throughout that time in history, “hidden in plain sight.” I invite you to make the observation yourself. Sit down, close your eyes and spend a few minutes becoming aware of all the sensations on and within your body, with as little “mental commentary” as possible. One of the most obvious sensations is the pressure of your chair upwards on your bottom. One thing that you do not feel is a gravitational force (what we call “weight”) acting downwards on you, though the Newtonian theory tells us that there is such a force: there is a lack of correlation here between experience and Newto- nian gravitational theory. In General Relativity, on the other hand, there is perfect correlation between experience and theory because in GR there is no gravitational force acting downwards on you: we are always, wherever we are, weightless. Perhaps one reason GR is so immensely satisfying to learn is that it accords with our experience in this way.4 The phenomenon of lack of sense-experience of a downwards force of weight occurs in everyday situations far removed from the physical regimes of strong curvature in which the full theory of GR reveals itself. Sorkin is suggesting that partial evidence for a theory of quantum gravity may be similarly close to us, although the full theory of quantum gravity is expected to manifest itself only in extreme regimes.

The experience that a gravitational force downwards is not felt did not rule out the Newtonian physical world view; it did not even count as an observational fact because the theoretical framework in which it can be understood did not yet exist.5 In the Newtonian world view, the feeling of the force upwards on you proves there must be a gravitational force of weight downwards on you, since you are at rest. The feeling of upward pressure is therefore interpreted as the appropriate experience of the force of weight downwards, hence the terminology of “weightlessness” to label the experience of astronauts in space but not our experience on earth. I am aware that this example is threatening to lead into a debate about whether sense- experiences can be completely theory-independent. My own opinion is that they cannot; but what we can decide is whether our sense-experiences find closer correlation with theory X or theory Y which is all that is necessary for our discussion. Now, consider this fictitious conversation:

17th Century Scientist: There is a physical force of weight on you. Look at all the data, celestial mechanics, etc. The Newtonian theory of gravitation accounts for all that data.

17th Century Sceptic: But I don’t experience this gravitational force of weight whereas I can feel mechanical forces of comparable magnitude. Why?

Scientist: The force of weight is physical. So your sense-experience of no force must be an illusion. Neurology, psychology, the way the mind and body work to produce sense-experience must be responsible for this illusion of lack of gravitational force of weight.

Sceptic: Maybe. But maybe this is telling us to look again at our theory, with the lack of gravitational force of weight as a heuristic.

The following is a parallel conversation that may, in the future, make similar sense:

21st Century Blockhead: There is no physical passage of time. Look at all the data, celestial mechanics, etc. The theory of General Relativity with spacetime as a Block perfectly accounts for all that data.

21st century Sceptic: But I don’t experience a Block. I experience a sequence of moments. Why?

Blockhead: The Block is physical, the passage of time is not physical. So your sense-experience of time passing must be an illusion. Neurology, psychology, the way the mind and body work to produce sense-experience must be responsible for this illusion of the passage of time.

Sceptic: Maybe. But maybe this is telling us to look again at our theory, with a physical passage of time as a heuristic.6
======footnotes======
4 I find it interesting that school students often make the mistake of forgetting to include the force of weight on bodies in mechanics problems: one might conjecture that they make this “mistake” because of lack of experience of such a force, in contrast to reaction forces, tension, pressure etc. which can be felt.

5 If there is only a force upwards on you from your chair and no weight acting down on you then you must be accelerating upwards, away from the earth. And so must someone sitting on a chair on the other side of the planet. For everyone on the surface of the earth to be stationary and yet also accelerating away from the centre of the earth requires that the spacetime around the earth be curved.

6 One could try to develop the analogy further. The lack of a local gravitational force – the equivalence principle – is not the whole of GR, it is only one aspect of it. A great deal of further work needed to be done to arrive at GR, particularly on the precise form of the dynamical laws governing the new spacetime substance. The concept of the birth of spacetime atoms would be only one aspect of quantum gravity: the full theory including its quantum dynamical laws remains to be discovered.
===endquote===

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

Good day to you Marshall!

I sincerely appreciate the amount of time and thought that you put into your posts, and in the number of references you readily cite in support of your arguments. I also like the fact that you have the principle of never denigrating the comments of people like me who make a comment on your posts

I did actually bring up the last three links that you inserted and have to admit that I could not comprehend the subject matter of those links. I feel that I lack what Piaget, the great French teacher of the 1920s, called ‘organisers’ in my brain – those basic fundamental pieces of understanding under which I can subsume, by association, new input to my brain-information stores on the matters you have discussed and referenced. I feel that I am out of my depth.

Having admitted my own personal ignorance about ‘spacetime’, I know I’m going to be sorry for making any comments about your last post, but please accept it in the manner of an uninformed student making an inquiry to an educated professional. You quoted Fay Dowker as “expresses this very well so I'm going to quote part of her May 2014 paper ("dowker passage arxiv"). Her point is that physics has to fit our experience and if there is a missing element people may ignore it for a long while, but conflicts build up, and eventually there is a foundations change. And she ILLUSTRATES that by pointing out there was this mismatch in NEWTONIAN gravity theory (you don't feel gravity like you feel other forces) which people put up with and fooled themselves about for over 300 years.”

Dowker – a pause here – I was going to state that certainly we don’t ‘feel gravity like you feel other forces’, but then I recalled Manfred Clyne (In Sentics: The Touch of Emotions) pointing out to us that gravity seems to have a huge effect on our emotions in the sense that we do feel ‘heavy’ with grief, troubles, personal problems, but we feel ‘light’ with a sense of success or happiness or generally when things are going well with us. However that’s poetic feely feely stuff.

But that was just a thought by association. What I was going to say until that thought entered my mind, was that we do not have to ‘feel’ gravity in order to recognise that if any fragile object falls off a table it smashes, if any object falls over it lands on any surface below it, mostly resulting in some form of damage to the object. Nothing falls upwards. So, in essence, every one of us must have had a concept of gravitational force, even though it took a Newton to explain that to us.

Hey Marshall, I love that expression “hidden in plain sight.” I’m going to use that more often in posts. I tried that experiment – “Sit down, close your eyes and spend a few minutes becoming aware of all the sensations on and within your body, with as little “mental commentary” as possible. One of the most obvious sensations is the pressure of your chair upwards on your bottom.”

I was living proof of ‘hidden in plain sight’ in that I was not aware of the sitting pressure until I read your post further, and then it became obvious. I suddenly became aware of the pressure on my bum and I immediately thought of all those poor invalids with pressure sores. But that simple experiment was sufficient to reinforce my belief that we do not notice the ‘common-place’ every day phenomena so much as we notice the ‘unusual’.
I made a few comments, but I realise that any answers will be ‘off thread’. So I will understand if there are no responses.

The fact I have to face is that I have no comprehension of space-time.

doogles
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### Re: Short tutorial on time (to avoid senseless argument)

People, Dave_O esp.,
It makes it too complicated to try to discuss the old Block model in the same thread with these more recent topics that the tutorial is on.
So if you have things to say involving that please start a separate thread or go to "Dave's support for the Block model" and contribute to the discussion there.
Let's try to make Dave's thread in support of his conception of the Block universe model as lively as the subject allows!

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

Hi doogles,

My response to you was moved here if you want to read it.

Regards,
Dave :^)

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### Re: Short tutorial on time

Thanks for the cooperation! To get a fresh start, let's summarize some essential points from the tutorial at the start of thread. Rovelli describes the historical weakening of the concept of time, from Newton to present day.

By "gravitational field" is meant the GEOMETRY of spacetime, and the the geometry actually influences the curves that objects coast along and the ticking of their clocks if (like good observers) they carry clocks. So the geometry is a SOLUTION of the GR equation and it does not evolve IN time because there is no time until you haves solved the equation and have determined a geometry.

A solution is like a "trajectory" of geometry, describing continuous changes in curvature ripples expansion contraction etc. But lets go back BEFORE all that to the simple Newtonian beginnings. Special Rel was 1905 and General Rel was 1915. Let's go back before 1905, how did we think of time back then?

==excerpts, quoted from starting post==
Before special relativity, one assumed that there is a universal physical variable t, measured by clocks, such that all physical phenomena can be described in terms of evolution equations in the independent variable t.

In special relativity, this notion of time is weakened. Clocks do not measure a universal time variable, but only the proper time elapsed along inertial trajectories. If we fix a Lorentz frame, nevertheless, we can still describe all physical phenomena in terms of evolution equations in the independent variable x0,..

In general relativity, when we describe the dynamics of the gravitational field (not to be confused with the dynamics of matter in a given gravitational field), there is no external time variable that can play the role of observable independent evolution variable.

The field equations are written in terms of an evolution parameter..., but this coordinate, does not correspond to anything directly observable.

The proper time τ along spacetime trajectories cannot be used as an independent variable either, as τ is a complicated non-local function of the gravitational field itself.

Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable. This does not mean that GR lacks predictivity. Simply put, what GR predicts are relations between (partial) observables,...

... A single solution of the GR equations of motion determines “a spacetime”, where a notion of proper time is associated to each timelike world line.

But in the quantum context a single solution of the dynamical equation is like a single “trajectory” of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues. Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory.

==endquote==

Each historical advance in our world-theory, from Before SR, to SR, to GR, and now as we approach QGR (quantum gravity, quantum general relativity, quantum space-time geometry) has involved a WEAKENING of the concept of time. Or if you prefer, moving to a less NAIVE more sophisticated idea of time.

The major landmark development, which Rovelli did not discuss in the 2006 essay here, and which will very likely come with the reconceptualization of time in QGR (quantization of GR, moving to a fully quantum theory of geometry and matter) will be to make a place in the theory for the PRESENT MOMENT and the experience of the PASSAGE of time.

The past will be a dead chunk of spacetime, a frozen fossil record of geometry, which is living and changing only at a live FRONTIER, where new cells or atoms of spacetime are proliferating.

this is how Dowker describes it. this proliferation of new spacetime cells is what she calls the passage of time. Notice that all EXPERIENCE involves INTERACTION. And interaction (between geometry and matter, between different cells of geometry, between objects and observer...) is precisely WHAT IS HAPPENING AT THE FRONTIER.

The frontier present must be described in terms of interactions. We have to be able to list them mathematically and calculate their various quantum amplitudes of happening.
As all of us here know well, a model that is only vague ideas and metaphors, or cartoon imagery, is garbage, so what we see theory folks now working hard to develop is a mathematical description of the frontier.
This is why I'm currently interested in getting a better understanding of the papers you get when you google
"cortes causal spin foam" and "wieland new action", just in case you are curious.
Marina Cortes and Wolgang Wieland are two young people who just recently got their PhDs and are putting a lot of energy into this enterprise. They are from Portugal and Austria.
If those google links don't get you the arxiv.org versions free online, just add "arxiv" to the search terms and google "cortes causal spin foam arxiv" and "wieland new action arxiv".

Marshall
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### Re: Short tutorial on time

Interesting life history. Marina is from Lisbon, Portugal. She started out to be a classical ballet dancer but a Carl Sagan book got her interested in theoretical physics so switched as undergraduate from Conservatory to University.

PhD in circa 2010, University of Edinburgh (advisor Andrew Liddle)
postdoc UC Berkeley, 2011-2012
postdoctoral research fellow at Edinburgh 2013-present
https://cosmoaims.wordpress.com/2011/04 ... as-cortes/
http://www.ph.ed.ac.uk/people/marina-cortes
http://www.roe.ac.uk/ifa/people/cortes.html
http://www.perimeterinstitute.ca/people/marina-cortes
http://inspirehep.net/author/profile/M.Cort.s.1

Marshall
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### Re: Short tutorial on time

This thread started out as just one post, a short tutorial on how the concept of time has changed historically from Before SR, to SR(1905), to GR(1915), to Quantum GR.
It's useful to keep in mind how the concept has been weakened over time.

the thread developed into discussion of CURRENT PROFESSIONAL RESEARCH papers dealing with some of the issues that Rovelli raised, and some that were raised by Fay Dowker at the Dec 2012 conference on bringing the passage of time into physics theory.

If you have ideas to present, they should be from the professional research literature (not your own personal ideas). In that case, please give links to the scholarly articles that you are paraphrasing and discussing.

Marshall
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### Re: Short tutorial on time

This will be a little technical. I want to give an idea of the "post-Sorkin" development of Causal Sets that merges somewhat with the spin foam models of LQG. Work by Cortes Smolin Wieland. I think they are working on a new paper now, so what I say is very provisional and also not expert. The math structure used to base the world theory on is called a simplicial complex, consisting of Edges, Triangles, tetrahedra and the 4d analogs of tets , call them "pents" they are the simplest 4d figures, chunks of space-time.

They actually correspond to a set of simple INTERACTIONS of tetrahedra, each involving 5 Tets like one in and four out or two in and three out. The interactions are called Pachner moves.

The gist is that the space-time past is being built up out of Pachner move interactions of tetrahedra . Every 4-simplex added to the body of the past represents a Pachner interaction involving 5 tets . there are 4 possible interactions 1↔4, or 2↔3
The reason we can say this is that in the causal spin foam the 4-simplices are dual to vertices and the tets are dual to edges and the edges are TIME-ORIENTED. So at each vertex we can identify the incoming and outgoing edges . So the vertex is an interaction.

Basically we are talking about a new "ontology", a way of thinking the world. there is no instantaneous 3d space, but there is (past) spacetime. And (past) spacetime is made of interactions (that have happened).

There's a swarm of tets and they are constantly interacting and becoming different ones, 4 might collide and 4→1 become one, or one might explode 1→4 and become 4. the AMPLITUDES for these moves haven't been thoroughly worked out. But Wieland has treated the swarm of tets as a classical system and proposed a Hamiltonian. That is what the "new action" is about.

Once some tets have interacted, they are DEAD and become part of the fossilized or crystallized PAST. The past is something you can't affect any more, you can't interact with it, and it can't cause anything more than it already has and is already in progress. So it is immaterial in a sense. You can only see and feel and touch what you can INTERACT with.

Our experience is in the present, in a kind of confusion of interacting tetrahedra which have not finished interacting yet. Since we equate interactions to 4-simplex "cells" or "atoms" of space-time, these 4d cells are still forming. Or in the language of Sorkin and Dowker, the atoms are being born.
The order in which the past is covered over with a new layer of interactions is, as Dowker says, "pure gauge". It is not physically meaningful in which order it happens because you can't interact with the order. There isn't time. There isn't time to discriminate between different orders of interactions freezing up. This is the experience of the present moment, and the PASSAGE OF TIME.

The reason Cortes-Smolin "causal spin foam" and Wieland "new action" papers are significant is basically because they find a way to represent our experience of the passage of time in the context of Covariant Lqg (CLQG) aka Spin Foam QG

This is a bit rough, I don't have time to improve the wording and add explanation, like what is the DUAL of a simplicial complex. I'll have to get back to it later. Family stuff to do now.

Marshall
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### Re: Short tutorial on time

Operationally, time is a COUNT of some periodic process. You need an oscillator and a counter to measure time. If you cannot measure it does it have any meaning? If below some range of duration, or above some range of frequency, you cannot measure it, if it is not measurable even in principle, does it mean anything?

Causation is more basic than time. It is not quantified except by itself. A sequence of events that follow each other immediately according to the discreteness of the world. Each causing the next. Is there a smallest separation, a shortest duration? But if those amounts cannot even be measured, all there is is the sequence. Number. Below some critical scale, which might be (say) Planck scale, how would you build a clock? Even in principle.

The proliferation of space-time cells constituting a causal set does not happen IN time. It is causation itself. It provides a basis on which things like clocks and concepts like time can be constructed.

I am thinking of the orderless commotion at the frontier of the past, where new interactions are occurring, new events happening, new cells of space-time (which wieland identifies with basic geometric interactions) are accumulating and accruing to the past. The vital frontier of causation itself.

Let's think of building up a partial order by adjoining nodes in a certain sequential order. the same partial order (think of a tree diagram) may be able to be built up in several different sequential orders. If, of two events, it is impossible (even in principle) to say which happened first, then the sequential order is "pure gauge" physically meaningless, merely a matter of mathematical convention. This is why I'm describing the frontier as an orderless commotion. an arbitrary choice of sequential order may be useful for description, but permuting the sequential order of construction (as long as the causal set itself is unchanged) makes no physical difference.

Dowker points out the analogy with GR, which has "diffeomorphism invariance" aka "general covariance". In both cases, if you are careful you can mess around with the description (whether it is building sequence or a system of coordinates) and it does not change the physics.

Marshall
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### Re: Short tutorial on time (to avoid senseless argument)

See James recent post over in a related non-sticky thread.
viewtopic.php?f=2&t=28020&p=270664#p270660
==excerpt==
I think what he argues is that this overview (a God's eye view) cannot physically be arranged, so it shouldn't be used to draw ontological conclusions... Science, it seems to me, has to return to the observational framework. To speculate ontologically from a model that can't be observed invites incredulity even if it works, instrumentally. ...
...
==endquote==
Relativity does not imply that the future already exists: a counterexample

It is one of several landmark papers helping to free us from the block universe model and lay the foundations for a growing universe model.

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