Defining Time: Our Everyday Mystery

[Pilot7]

Dimension

Just a note on dimension:

Dimension, at its deeper roots, is a topological construct, meaning it is an aspect of a set (usually infinite). When we say a "space" has n dimensions, we are really saying something about the space's underlying topology.

For those unfamiliar with "topology" and "set theory", you can think of it as the structure that is more basic than that part we quantitatively measure. For example, a balloon and a beach ball and a cube all have quite different measures, but all have identical topology. On the other hand, all these differ from a popped balloon, or a piece of paper or square shape, again all three of which have different geometries, but the same topology. Donuts and a torus again are yet another common topological classes differing from the aforementioned. Dimension in this sense is a topological property with obvious implications for geometry and measure (ie we measure things according to their topological dimensions usually, for example width, height, breadth, but also temperature, mass, charge,... and of course *time*)

So what is going on when we say space is 3-D or 4-D (space-time) is that we are judging from experience a smallest number of dimensions consistently to explain some (but not all) physical data. Some people of course contend with various theories that have required 5 dimensions in the universe, or 9 or even 11 (as I believe is in some string theories for example). And if we count mass a primary quality, that certain would be another dimension.

Now this begs whether these dimensions as such "actually exist" or are they simply intellectual constructs used to explain relationships between data? This was in fact famously debated by Leibniz and Newton and remains an unresolved issue to this day with at least three distinct positions one can take on it.

Of course, we may well wish to elevate certain dimensions (those spatial), since not only does this sort of theoretical construct work remarkably well to predict the way cannon balls and maybe space ships to fly, but it also *seems* to our consciousness to be how the world is. We don't directly perceive mass, we infer that, but distance has a kind of immediate quality to our senses.

It is worth noting here, that the kind of space we perceive is pretty well Euclidean--meaning specifically we intuit using the parallel axiom. However, if Einstein is right, our intuitions are of course wrong, but we can only infer this, we do not directly perceive it as the case. The significance of relativity is not (necessarily) a dimensional change to the universe or our best theories thereof, but to an inversion of one of four dimensions so far as measure is concerned. (I guess there are some GTR models that really do change the topology, like Goedel Universes, but even these do not change the basic set of dimensions).

Now with time, we don't have this exactly, though we have some kind of sense of past experience being variously far past and near past or perhaps near future. Whether one wants to ascribe this a dimension in the same way as space is, I suppose, a matter of taste and convention a la the Newton / Leibniz debates. However, in our experience, we not only distinguish between events separated by measurable distances and times, we also experience their immediate alteration/change.

This change appears to be a primary quality of the universe. The measure of such change might be secondary, for example according to the kind of theory we use to calculate such (GTR, STR or classical). But change in and of itself is not (as far as I have been able to see in my research) reducible to any other primary qualities through any going theory of physics, and it really does seem to be there.

Actually, some interpretations of quantum theory do provide for a foundation of change as a *real* collapse of the wave function--and while I personally favour this sort of theory, it does open a number of serious cans of worms relating to the nature of consciousness in the physical universe and so on.

Final note. One of the features of "psychological time" or change is its apparent direction. One of the great errors of even some quite famously clever physicists (like Hawking) is to conflate *direction* with *asymmetry*. Consider the "arrow" below:

------>

The shape is asymmetric, that is to say, one side differs form the other. But is there any intrinsic direction in the shape? If you say it is "pointing" to the right, consider why. Is this not merely the convention we have associated with the shape? Could not a different culture, for example, associate the opposite direction with such a symbol? Or none at all? The moral here is that direction and asymmetry are different beasts, and while all things that have "direction" as a quality arguably also have asymmetry, it does NOT follow that all things with asymmetry have direction...

Hope my post was not inappropriately pedantic or boring or longwinded... :-)

 

[guillefix]

True the asymetries we find in our universe doesn't directly favour one direction or the other, but may be the nature of our consciouness is related to for example the entropy of our brain, may be the bigger the entropy the more information that our brain has about its cause (the past, when the entropy was lower) than its future, say. We know too little about what consciounes is and how our brain works to know the exact mechanism, but I think what Hawkins means is that we can't have direction without assymetry, now which direction depends on other things (in other cultures, other laws of nature for example).

 

[Pilot7]

...may be the nature of our consciouness is related to for example the entropy of our brain, may be the bigger the entropy the more information that our brain has about its cause (the past, when the entropy was lower) than its future, say. We know too little about what consciounes is and how our brain works to know the exact mechanism, but I think what Hawkins means is that we can't have direction without assymetry, now which direction depends on other things (in other cultures, other laws of nature for example).

Yea, this is the question. But while entropy has a funny relationship with information (I guess the latter has been curiously defined as the inverse of the former in certain engineering circles--a definition with a very ironic origin actually), information is not consciousness, or to be more precise, it is not "intentionality" to use one technical term. Interestingly, this term comes from the latin "intendere" (roughly) meaning to "point at". I don't see how entropy or its gradients could, *even in principle*, fully explain what is going on with consciousness or memory or psychological time. True there is much we do not know, but even if we did not know the process by which beer is fermented, we might still reasonably infer that it does not come from an enchanted river upstream... The first part of getting to know about something mysterious is often getting clear on what it cannot be. In this way, IMHO, looking to entropy, and its apparent temporal asymmetry, is very much barking up the wrong tree.

On Hawking, I could dig it up, but actually he is quite confused on certain topics, consciousness and psychological time being one of them. Look up "Hew Price" and "Hawking" and "arrow of time" or some such, there is sufficient literature on it. I know criticizing Hawking is something of a holy cow, but I have been astonished how little weight he gives to consciousness (or philosophy)--he is really an old school positivist in many respects. But that scientific program has some real problems, not just consciousness, but many others. Anyhow, I am (unsurprisingly) not a positivist :-)

 

[sophiecentaur]

You could look upon time in the same way as you can look at Mathematics. They could both just be constructs of our brains to help to explain what we experience. By introducing time into our perception of the World, we have a small chance of feeling that we may 'Understand' a little bit about what is going on (and there, unfortunately) I have had to use an implied 'time' in my explanation. But we have no option. There are forms of Art that portray some processes with the various states presented in the same picture and we can sometimes remember temporal experiences as one entity - for instance, we remember some films and plays as a single entity and it's only when we run over them in our minds or try to describe them that we actually introduce time. Also, we draw graphs with time along one axis but we don't have to wait to see the variables changing - the graph shows them over a range of times all at once.

 

[sophiecentaur]

And, talking of time - didya notice that this is my 3000th post? And it seems only a day or two since my first.. . .
Must crack upen a bottle of fizzy water tarrraaa .

 

[Pilot7]

You could look upon time in the same way as you can look at Mathematics. They could both just be constructs of our brains... There are forms of Art that portray some processes with the various states presented in the same picture and we can sometimes remember temporal experiences as one entity...

Yes, could be... BUT, roughly in the words of Lotze, either we need to explain the nature and origin of an illusion or accept that it is more than illusion. Yes, the raw experience of process and change might well be due to our curious perspectives as human beings, but this remarkable illusion itself cries out for explanation. For example, the color of red has no direct correlate in the physical world, beyond its tentative association with a certain frequency of EMR, which upon closer analysis is quite superfluous to the experience itself (all one needs to do is excite certain cones in one's retina to produce the experience of red). In the same way, our explanations are quite lacking until we can find some kind of theory to account for this phenomenon.

Process itself is a very atomistic notion often overlooked. If indeed it is not a fundamental feature of the cosmos, which is to say that the cosmos is in itself static, I find myself troubled indeed to explain how such could even in principle be derived from any set of static components whatsoever.

Kant came closest to giving time a basis in reason in some ways, which is roughly what you are suggesting, that the phenomenal empirical world does indeed appear to be temporal, mostly because of a faculty he called the "intuition". And like you, Kant suggests that the noumenal, real world, which mostly lies outside of our intuitive faculty to discern, is... somehow perfect, Platonic, and unchanging. However, it is a part of his reasoning that definitely depends on a "miracle", for whether one tries ontologically to reduce consciousness to a static cosmos, or if one tries, like him, to explain epistemically how the universe must be to account for our experience, process itself is like a big hot coal that one can neither swollow away nor spit out.

But yes, for God, perhaps in His/Her perfection beyond the celestial sphere, time and process as we know it have no meaning... But how He/She gave rise to the cosmos... replete with process? Miraculous, indeed!

(BTW I am waxing poetically here with strong metaphors)

It might be added that if, on the other hand, one does regard process as essential, even to God, then we are really going to have to rework how some of our best physical theories work. On the other hand, given the incongruence between our best two theories (QM and GTR), perhaps we haven't lost so much as we thought anyways!

 

[sophiecentaur]

"Perfect, Platonic and unchanging" are terms which I feel to be a bit loaded and angled to shoot dead any serious arguments along my lines before they are started. I do have a problem with quoted ideas from Philosophers from hundreds of years ago. With the best will in the world, these guys were not aware of a lot of evidence that has emerged long after their deaths. Whilst I totally respect their intellect, I can't always understand how their ideas are so often used out of the context of 'their' worlds.

If the expression ''relationship between quantities" is used as a substitute for 'process' then time (a very elastic quantity in any case, now that we use Relativity) may not, in fact be regarded as any more than a construct. But, there again, perhaps we could say that about a lot of other ideas too.
Time I went to bed now!

 

[Pilot7]

Well it looks like my response got eaten by the entropy deamons in the void...

"Perfect, Platonic and unchanging" are terms which I feel to be a bit loaded and angled to shoot dead any serious arguments... Whilst I totally respect their intellect, I can't always understand how their ideas are so often used out of the context of 'their' worlds.

Such admittedly extreme terms are not intended as straw men, rather the opposite. I am quite open to looking at another term, a more relaxed sort of theoretical proposition of some sort. I ask myself then: How does this term differ from the sort of extreme paradigm above? If a difference can be shown or even suggested, then I look further there, because that is likely going to be the source of new and better understanding.

I think there may be something of a culture gap here (philosophy/physics)--often certain schools of thought or some idea is associated with its founder, who might well actually have had quite a different view on the matter. For example Plato and what we have since come to associate with Platonism, which itself means quite different things in various contexts (eg mathematics, physics, ethics, etc.). But this is also done in physics, though less often since most of the best physicists also happen to be relatively recent. But by example, consider the expression "Newtonian Physics" or "Newtonian space" or "Newtonian time". Yet, were to actually go back and look at Newton's words, we would find a diverse number of ideas that seem quite foreign to what we now normally associate with the above terms. For example Newton says of time:

Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...

Similarly, we will find other oddities with space and physics itself. His calculus is not even used today (we use Leibniz's notation and arguments). And similar cases will be found with other pre-20th century physicists (eg Galileo, Copernicus,... Archimedes, etc.) Aristotle is usually really tossed under the bus for some of what he said in most freshman physics textbooks, which is a pitty, since his ideas were in many places quite a bit more sophisticated. Anyhow, for sure, we need to bear such context in mind when we read such old sages and when we talk about contemporary views that are associated with whichever figure.

Perhaps the two views of time as we have toying with here are best rendered as the "Heraclitean" and "Parminedean" views, but it is dubious we can say either person really held the views we now associate with them in any detail. (Indeed, how would we know, we have barely more than a page of rather cryptic writing from either of them to tell us!)

If the expression ''relationship between quantities" is used as a substitute for 'process' then time (a very elastic quantity in any case, now that we use Relativity) may not, in fact be regarded as any more than a construct. But, there again, perhaps we could say that about a lot of other ideas too.
Time I went to bed now!

This gets to the heart of the issue as best as I can tell. I am not ready to accept that:

process = relationship between quantities

I am not even ready to accept that

process = a quantity.

I will accept that:

experienced process = a quality

and it may be that:

process (in itself) = a qualitative feature of the cosmos that is static

but I want to know how such an illusion resolves or reduces ontologically speaking. Even in principle, even as a hypothesis or a guess of a shadow of a guess of it might look.

But for sure I cannot see how:

process (in itself) = a quantity (of anything)

that just doesn't even make sense to me.

Perhaps you can elaborate?

For now, I wish you good dreams.

 

[sophiecentaur]

Fair enough on the Philosopher bit. Of course, using their names as a description is fully justifiable. Was I being too prickly? Possibly - but I am going through an "annoyed by Philosophers" phase - a separate issue and my problem entirely!
What I am getting at is, of course, only statable as as an analogy. Our apparent 'motion' through time needs to be no more than 'apparent' and a convenient ruse to help with understanding. My tie-in with Maths applies here because Maths is a very similar thing which can be thought of as external to the real world but which gives us a way of understanding things.

If you plot a graph of the path of a projectile in horizontal and vertical planes, the whole process (/ situation?) is there, in front of you with no reference to time at all. If you want to plot it from the results of the equations of motion, as we know them, then x and y displacements are related to time. but the relationship between them doesn't include time. You could plot a number of trajectories on the same piece of paper but they could be describing different situations at very different (what we call) times. We don't need to know the times at or the order in which which any measurements were made. So time is, in a sense, outside, the description.
Could it be that the only thing that could make time something more than 'just Maths' could be the fact that we all agree on the direction in which we are using it and that all our experiments seem to indicate a single arrow of direction?

I appreciate your struggle with the definitions at the end of your last post. We are approaching the regions of "what do we mean by mean by mean?" (was it Monty Python?).

 

[Demystifier]

All the confusion about time stems from the existence of two different notions of time, only one of which has to do with physics:
http://www.fqxi.org/data/essay-cont...f?phpMyAdmin=0c371ccdae9b5ff3071bae814fb4f9e9

 

[jeebs]

I'm reading through that paper, and there's a passage I don't understand:

'In particular, nothing in physical equations that deal with time says that the past is more
certain than the future, just like nothing in physical equations that deal with space says
that the left is more certain than the right, or just like that nothing in physical equations
that deal with temperature says that a lower temperature is more certain than a higher
temperature. In other words, nothing in these equations says that time, unlike other
variables, has a property of “lapsing” or “flowing”.'

What is meant by "more certain" in this context? the paper goes on about "time lapsing" all the way through so I'm stuck here.

 

[3nder]

we needed something to measure 'now', 'then' and 'after'. that's all time is, a measurment

 

[MJA]

The only thing more certain than the past or the future is now.

=

 

[Pilot7]

All the confusion about time stems from the existence of two different notions of time, only one of which has to do with physics:
http://www.fqxi.org/data/essay-cont...f?phpMyAdmin=0c371ccdae9b5ff3071bae814fb4f9e9

Yea, I dare say this is definitely the orthodox view. However, this paper is quite weak on several points and arguments, and it fails to reference a number of points even raised in its own bibliography. I will try to offer a critique in more detail when time (!) allows.

In a nut shell though: Yes, there are (at least) two times. And physics clearly concerns itself with one of those. The question of whether it concerns itself with the second is, however, an open question. It certainly is easier to just sweep it under the rug and give it to the "psychologists" to sort out (and I assure everyone that they have produced *nothing* up to around 2001 when I last checked carefully). But there are several problems in physics that may require a better development of our theoretical concept of time, including the so-called "Problem of Time" in quantum gravity and cosmology. But also QT generally (eg quantum zeno effect). Or the relationship between information in quantum systems over time.

I also take quite some issue with the hand waving reduction of all the so called "arrows of time" (most of which we should call "asymmetries in time") to Newton's 2nd Law. That is not so clear, and just because a few cited physicists think it so, don't make it so, and certainly not when it remains an open issue with advocates on both sides. For example the K-Meson I believe is an instance where something quite otherly may be going on. In any case, I will offer a more rigorous critique or cite a paper (mine, now that i think of it) later.

 

[Pilot7]

Fair enough on the Philosopher bit. ...but I am going through an "annoyed by Philosophers" phase - a separate issue and my problem entirely!
...My tie-in with Maths applies here because Maths is a very similar thing which can be thought of as external to the real world but which gives us a way of understanding things.
...
Could it be that the only thing that could make time something more than 'just Maths' could be the fact that we all agree on the direction in which we are using it and that all our experiments seem to indicate a single arrow of direction?

I appreciate your struggle with the definitions at the end of your last post. We are approaching the regions of "what do we mean by mean by mean?" (was it Monty Python?).

With a name like sophiecentaur, how can you be too down on philosophers? ;-) Unless of course you are one, in which case I quite sympathize <grin>. If not, please forgive the slight :-)

The maths analogy is a very interesting one in this context. I have just been over reviewing various blogs on Cohen's axiom of choice work, so I am a bit primed (no pun intended). However, at root of basic mathematics (ie forget all that fancy infinite cardinality stuff--just intuitionist mathematics), most of it does reduce to a complete and consistent first order logic, meaning we don't need to speculate about the Platonic heavens. However, Peano's fifth axiom, corresponding to "mathematical induction" is crucial to get the sort of mathematics we need for basic physics to work (including Hilbert spaces, etc.). This axiom is really an infinite number of first order axioms, and so it is really an article of faith that we accept it is true. A closer look at it, we find that is has an uncanny parallel to something like a Kantian intuition of time... (BTW--this is not my idea, I think it was Poincare who first published something on this). And it is this "axiom" which also makes arithmetic Goedel incomplete... So whether coincidence or serendipity...

Yes, I also came to this kind of conclusion about the direction. I worked this angle in a paper/talk some years ago, arguing that direction should perhaps be adopted as kind of quality in physics (but not this or that direction, just that some set of phenomena have *some* direction). Trying to make "process" sharp without digressing into the meaning of "meaning" and "is" has been very difficult--this is what I was really trying to do in PhD work. Sadly, I was not successful, but I would have to go way out on a rather esoteric limb about why it seems so difficult. And of course I might fall off that limb in the process :-)

 

[MJA]

One Axiom

There is only One mathematical equation
That defines nature truly or absolute
The solution is only =
Or equal
And the lion simply One.
Beyond this simple equation
There is only theoretically division
Complexities faiths and uncertainties
The quantum mechanics of a lost mankind.

=
MJA

 

[sophiecentaur]

And that's Physics?

 

[WannabeNewton]

One Axiom

There is only One mathematical equation
That defines nature truly or absolute
The solution is only =
Or equal
And the lion simply One.
Beyond this simple equation
There is only theoretically division
Complexities faiths and uncertainties
The quantum mechanics of a lost mankind.

=
MJA

Say what?

 

[Pilot7]

One Axiom... The quantum mechanics of a lost mankind.MJA

Planet physics and planet poetry
Surely we have license to live on either, neither or both
tho anyways and always turning about the same sun
held in check by some mysterious, ineffable oath

No doubt, every momentous angle only an allegory
and every sun rise purely theoretical
yet still do our days proceed
a matter also practical

So true 1x1=1 no more, no less than One's division with itself
and perhaps it is rather a lion lying behind the curtain
the wizard but a trick for those on a trek who seek
brains, heart, courage or what we might call certain

But tell me this and tell me true
since when was mankind lost?
and wherever did we lose him?
and whatever were we thinking?

 

[sophiecentaur]

If it's not the cough that carries you off, it's the coffin they carry you off in.
And that's Phisic.

 

[Pilot7]

You can lead a horse to water but you can't make him drink.
And that's physics,=

You can ALSO sing to him... Sooner or later, he will drink! Probably when he forgets himself. Or just gets really thirsty.

But in truth, I suspect the trick of it all lies in timing...

 

[pallidin]

"Time" is a quantifiable measurment of "change"
Without "change" time does not, and can not, exist...

Think about that for a few minutes :)

 

[Pilot7]

"Time" is a quantifiable measurment of "change"
Without "change" time does not, and can not, exist...

Think about that for a few minutes :)

Okay, I'll byte. However, I find both its miraculous event-ness and my ignorance of its true nature remain... unchanged.

Somewhere under the phenomenology of watching a clock (during, for example, a physical experiment) we have an experience like "clock hand pointing to 2" along with the experience of a "memory" (whatever that is) of an experience of it point to 1, possibly also a certain fuzziness in our present experience that seems to corraborate or reinforce our intuition that "another experience is coming and will likely involve the hand point to 3" or some such.

This is what it is happening when we look at the grand daddy of clocks, such as one that measures Cesium decay or whatever it is that they use these days. We have a memory of state A, we have an experience of state B, and that experience itself has a fuzziness or unreliability about it that suggests a state C.

This begs some questions: what (really) is a memory? And how is that the fuzziness of measure in the case of time nevertheless seems to lead us to speculate on some other exact measure?

Notice, I don't bother with the usual question of what is experience here--still a valuable question to answer in physics no doubt, but not the only way to crack this egg.

What is a memory? You are not allowed to make references here to the various neurons of the hippocampus or whatever, for what we mean by memory is the experimenter's memory, a phenomenological state which defines what we mean by experiment results. To require a reference to biology or psychology is thus throw the whole of all experimental physics under the bus of conjecture, since its certainty and veracity can be adduced to be no more than is accorded the current neurophysiological model of brain and memory...

In addition, in all the instances in physics where there is an uncertainty of measurement, there are normally two kinds: those based on epistemic ignorance typically resulting in bell curves for best modelling; and quantum uncertainties, which usually offer further boundary conditions for the uncertainty (eg we know an electron will "exist" within some region according to some probability distribution, but we may know definitively that it is not a certain points. Okay, this sort of uncertainty might be epistemic or metaphysical, depending on one's interpretative preferences for wave collapse and the measurement problem. There is also a third kind of uncertainty that is not really physical, but philosophical, for example regarding certain choices made GRT about paths or the many interpretive issues that result in quantum theory.

But the "fuzziness" of time (or "now") does not look like any of these three other kinds of fuzziness. When we see a clock hand at 2 in a "fuzzy" way, we mean to say not just that it IS probably not 2, but likely closer to 3, even that "it is 3". This is an odd kind of uncertainty, for we find ourselves rather certain of the real result while watching the hand creep forward. I am of course trying to characterize the "flow of time" in a physical way here...

Okay, I've ruminated too much now, and the hour grows late :-)

 

[nasijen]

Time is life.

 

[Selraybob]

But the "fuzziness" of time (or "now") does not look like any of these three other kinds of fuzziness. When we see a clock hand at 2 in a "fuzzy" way, we mean to say not just that it IS probably not 2, but likely closer to 3, even that "it is 3". This is an odd kind of uncertainty, for we find ourselves rather certain of the real result while watching the hand creep forward. I am of course trying to characterize the "flow of time" in a physical way here...

Pilot, I still don't see how all this 'fuzzy' talk has anything to do with Time. It might have something to do with how well we can lock something down and how accurately we can count the changes that the counters are counting, but nothing I see about Time. So even though there are a lot of super smart people who've thought about this a whole lot more than I have. It all still comes down to this:

Change --> Count --> Time --> Speed

It happened it that order, not going backwards from C or little t to get some deep mystical meaning. It started with change. It doesn't matter if it's a movement change or some chemical state change or the number of electrons change. Something's changing.

Then someone saw the changes that seemed to repeat and started counting them. It could be moons or suns or electrons spitting off. Someone saw the sun move, compared it to the end of the earth, and thought, huh, the sun's at the end of the earth.

After people started noticing the changes, they started noticing the ones that repeated, then putting marks on the wall or somewhere to record the counts of those changes. They thought, huh, I think something in this acorn in my head's telling me that I saw that sun over the horizon before now. I'll mark the wall every time I see it, just to make sure my acorn's working okay.

And then some brilliant person went and announced to everyone that all these marks we see on the walls are called Time, and not counts of the sun going down.

And once you had Time and people started dividing the days into little pieces, you started to get speed (and rate, frequency, velocity too) -- the count of distance divided by the so-called change in Time, which is just a count of some counting device. To get speed you needed two counts.

Which is why Heisenberg was right. You can't get speed at anyone time, because you need two counts, and when you divide those two counts, you get the calculated speed BETWEEN the two counting spots, not at the end of one or at the beginning.