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Author Topic: If time is discrete, what happens in between 'packets' of time?  (Read 7763 times)

Offline Ian Scott

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Is time linear or discrete as in packets - as in digital systems that are sampled

What happens in the gaps between times therefore?

Mod edit - formatted the subject as a question.  Please try to do this to help keep the forum tidy and easy to navigate - thanks!
« Last Edit: 24/07/2008 08:50:37 by BenV »


 

lyner

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I don't think there is any need for time to be quantised. Let's face it, the only thing which we need to treat as quantised is energy and, even there, the size of quantum can be vanishingly small, as the frequency involved approaches zero.
All other quantities can be treated as continua (ums?) and it is only in computations that they are treated discretely. This, itself, could be a source of confusion and produce odd results.
 

Offline BenV

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...All other quantities can be treated as continua (ums?) ...

It is 'continua', though I feel 'continuums' is a nicer word to read, write and say.
 

Offline Alan McDougall

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Time to me it just a measure we use to movement. I do not see it as discrete "timesons" but more of an analogue flow

Regards

Alan
 

lyner

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Energy is not a 'dimension'; it is a variable which relates to space, time and mass (dimensional analysis gives us that); we find that it is 'quantised', but only under certain circumstances.
Time is a dimension and there is no reason at all to suggest that it should be quantised.
 

Offline LeeE

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Hmm...  I've no idea whether time is actually quantised or not, but there are some reasons why it might be.

Think of an event occurring over a period of time.  If the period of time over which the event occurs is finite then there must be regions of time both before and after the event where the event was not occurring.  We can say that during the period when the event is occurring the amount of that event occurrence is > 0 and that when the event is not occurring it will be = 0.  So if the duration of the event is not infinite, there will be a point where the amount of occurrence increases from = 0 to > 0.  As the change required to move from = 0 to > 0 must also be > 0 it seems to me that there must be a discrete step, regardless of how small that step is, which implies quantisation.

The Planck time unit also implies time quantisation.

Just out of curiosity, what is the significance of the pictures?  I can't see their relevance to your question.
« Last Edit: 25/07/2008 00:30:06 by LeeE »
 

lyner

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there must be a discrete step, regardless of how small that step is, which implies quantisation
That Mathematical argument doesn't really hold. If an interval can be arbitrarily small, then the  quantity is infinitely variable - or continuous. We assume that we can differentiate safely, for instance, and you can't do that with a non continuous function.

Although the planck time is "the smallest measurable unit" I don't think that forces the conclusion that time, itself is not continuous - just a limitation of measurement. But this is an 'angels on a pinhead' type argument, in any case. Calculations involving time use ordinary Maths and that does not involve quantisation (?) but I could be convinced otherwise. Certainly the quanta of time would be a lot smaller (in terms of the actual values involved) than those of Energy, which are pretty plain to see (literally, on a very dark night).
« Last Edit: 25/07/2008 00:37:41 by sophiecentaur »
 

Offline LeeE

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there must be a discrete step, regardless of how small that step is, which implies quantisation
That Mathematical argument doesn't really hold. If an interval can be arbitrarily small, then the  quantity is infinitely variable - or continuous. We assume that we can differentiate safely, for instance, and you can't do that with a non continuous function.

Although the planck time is "the smallest measurable unit" I don't think that forces the conclusion that time, itself is not continuous - just a limitation of measurement. But this is an 'angels on a pinhead' type argument, in any case. Calculations involving time use ordinary Maths and that does not involve quantisation (?) but I could be convinced otherwise. Certainly the quanta of time would be a lot smaller (in terms of the actual values involved) than those of Energy, which are pretty plain to see (literally, on a very dark night).

While I would agree that the interval can be arbitrarily small and can resolve to any value, it doesn't follow that once resolved it is also infinitely variable.  The interval intrinsically needs to be > 0, otherwise there will be no change and we will still be = 0, but I can see no intrinsic reason for that interval, once established, to vary without reason - without another factor to change the interval size.

Mathematically, we can measure and resolve any point, at any resolution, but the Planck time and size units don't just represent measuring problems.  They mean that anything that actually exists has to operate within the constraints they imply.  So yes, while we can happily do the mathematics for smaller times or sizes, the universe may not take any notice.

I wouldn't like to comment on the idea of a 'quanta of time', at least as any sort of particle or type of physical entity, but if time is quantised then the interval would have to be very small indeed and undetectable in any case, as it would be like trying to measure the length of a piece of string using that piece of string itself.

Although having said that, using quantum entanglement to synchronise relativistically moving clocks might show some anomalies.
 

lyner

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How would you actually define a continuous range, then?
I did an 'Analysis' course in my first year Maths (1963!!!!) and such matters a open intervals, closed intervals, continuous functions etc etc came into it. There are some very rigorous arguments involved.
Of course, Maths is Maths and Time is Time but, if you use Mathematical arguments to discuss the nature of Time, you need them to be watertight.
 

Offline LeeE

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How would you actually define a continuous range, then?
I did an 'Analysis' course in my first year Maths (1963!!!!) and such matters a open intervals, closed intervals, continuous functions etc etc came into it. There are some very rigorous arguments involved.
Of course, Maths is Maths and Time is Time but, if you use Mathematical arguments to discuss the nature of Time, you need them to be watertight.

Hmm...  I'm not sure I see the relevance of your question, but fwiw I'd define a continuous range in mathematics as being the ordered region between two limits where any number between those two limits can be found.  In the real world it's more complicated though.  For example, if you think about your computer screen, you could divide it into regions as small as you like - into millionths of an inch if you wish - but the resolution of your screen will be limited either by the number of pixels, for an LCD display, or the dot pitch if it's a CRT device.  Similarly, current IC fabrication techniques are around the 35 nanometre range but while you could mathematically work out yoctometre ranges, you couldn't build such a device.

Just how much mathematics is there in a comparison between being exactly equal to zero and not being exactly equal to zero?
 

lyner

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If time is discrete, what happens in between 'packets' of time?
« Reply #10 on: 25/07/2008 18:56:52 »
Quote
Just how much mathematics is there in a comparison between being exactly equal to zero and not being exactly equal to zero?
That is probably a hue can of worms!
A TV picture is not a good example to use because it is fundamentally Sampled, in the first place. A continuous variable would be the varying  voltage from a microphone. Better still, the progress of an object through space. The measurement of the distance can be arbitrarily accurate, depending upon the resolution of your measuring equipment and the time you take over the measurement (to eliminate thermal noise). To follow your argument / definition, the position of the object could take any value between A and B - same as our continuum of numbers; the measurement being 'just' another issue.

aamof, information theory tells us that you can measure to any degree of precision you want as long as the signal to noise ratio is good enough. So a yactometer of change would still represent a (albeit very small) change in phase of a Terraherz signal, which could, in principle, still be measured.
 

Offline LeeE

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If time is discrete, what happens in between 'packets' of time?
« Reply #11 on: 26/07/2008 22:57:37 »
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A TV picture is not a good example to use because it is fundamentally Sampled, in the first place.

This is a fair comment regarding TV displays, where the broadcast resolution matches the display resolution, but I don't think it applies so well to computer displays where different people use different display resolutions and where the resolution of an image may be much greater (or smaller) than that of the device it's displayed on.

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... Better still, the progress of an object through space.

Or how about spacetime?  ;D

Quote
aamof, information theory tells us that you can measure to any degree of precision you want as long as the signal to noise ratio is good enough. So a yactometer of change would still represent a (albeit very small) change in phase of a Terraherz signal, which could, in principle, still be measured.

I wouldn't argue with the theory, as an abstraction, because it works in the abstract, but there can be problems applying unlimited resolution theories to the real world.  So talking of making yactometre scale devices or device features is silly because at 10^-24 metres they would be much smaller than the simplest atom, or even just atomic nuclei, which start at around 1 femtometre, or 10^-15 m.  While you may, in principle, be able to measure a 10^-24 degree of change in a terahertz (10^12) signal, the resolution of the universe, in terms of the size of the atoms making your measuring equipment is going to get in your way when you actually try to do it.
 

lyner

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If time is discrete, what happens in between 'packets' of time?
« Reply #12 on: 27/07/2008 16:20:57 »
Displaying an image which was  sampled at one rate and then displayed at another rate involves the assumption that it is, in fact, continuous. The 'best' standards conversion involves some fancy filtering. The image is never, in fact continuous but the assumption is made that it is. Vector graphics and text characters (Truetype, Postscript) ,  are drawn at the time and the 'original' is assumed to be continuous.

I do agree as to the nonsense of measuring to that ridiculously fine accuracy. However, the lower limit is, essentially, a practical one and not a fundamental one - even Heisenberg doesn't put a limit as long as you are only measuring one dimension.

But Maths is merely a construct / model and isn't 'real'.
 

Offline LeeE

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If time is discrete, what happens in between 'packets' of time?
« Reply #13 on: 28/07/2008 23:37:12 »
Displaying an image which was  sampled at one rate and then displayed at another rate involves the assumption that it is, in fact, continuous. The 'best' standards conversion involves some fancy filtering. The image is never, in fact continuous but the assumption is made that it is. Vector graphics and text characters (Truetype, Postscript) ,  are drawn at the time and the 'original' is assumed to be continuous.

I do agree as to the nonsense of measuring to that ridiculously fine accuracy. However, the lower limit is, essentially, a practical one and not a fundamental one - even Heisenberg doesn't put a limit as long as you are only measuring one dimension.

But Maths is merely a construct / model and isn't 'real'.

It can be quite convoluted with images - when I render my 3D stuff I have to think about whether I'm going to be using sub-pixel super-sampling, stochastic or geometrical object anti-aliasing, combined with specific image texture anti-aliasing, and then when I'm displaying the image it'll quite likely be scaled, usually using cubic interpolation, and then it might finally be anti-aliased once again depending on my video card settings - but yes - you're right - it's not a continuous image but pixel-based, even if the meaning of 'pixel' can become a bit blurred (pun not intended).

As to whether any lower limit would be a practical one or a fundamental one comes down to what you're trying to do.  For example, scaling down an IC with 90 nanometre features to use say, 9 nanometre features is only not possible for practical reasons, which are likely to be overcome, but scaling that IC down to using 9 yactometre features is not possible for fundamental reasons that cannot be overcome.

In the end, I think the issue is precisely all about Maths being a construct/model and not being real.
 

lyner

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If time is discrete, what happens in between 'packets' of time?
« Reply #14 on: 29/07/2008 10:45:13 »
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In the end, I think the issue is precisely all about Maths being a construct/model and not being real.
Which makes me wonder - somewhere else in the Universe, could someone be using an entirely different kind of Maths? I don't mean a more advanced sort but a Maths which is different from the very start - but not a dead end like the Roman number system.
For instance, an organism with no skeleton / digits might never have started to 'count' as we did, yet would still communicate and have a Maths.
 

Offline LeeE

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If time is discrete, what happens in between 'packets' of time?
« Reply #15 on: 29/07/2008 22:49:43 »
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Which makes me wonder - somewhere else in the Universe, could someone be using an entirely different kind of Maths?

That's a very interesting question.

The concept of integers seems to be fundamental, regardless of the base being used, and from that, counting.  Fractional/non-integer bases and powers could be interesting too, especially for irrational numbers such as pi or e.

It also seems to me that there is an inherent dimensionality to many mathematical operations.  For example, addition and subtraction are one-dimensional whereas multiplication and division can be two-dimensional.  Addition and subtraction is like joining pieces of string together, or cutting bits off, so that the final length of the piece of string is different.  Multiplication and division in maths is normally used to imply multiple additions/subtractions, which once again just produce a different length of string, but in physics it can be more like defining an area where the product can't be represented in terms of multiple numbers of it's factors - how many feet are there in a square foot?  Power is expressed in Watts, as Energy divided by time, so not only is the product different in nature to it's factors, but both the factors are different in nature to each other.
 

lyner

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If time is discrete, what happens in between 'packets' of time?
« Reply #16 on: 01/08/2008 23:53:40 »
You say that digital arithmetic is fundamental. Say there was a group of organisms which were completely amorphous (no fingers, toes or limbs) and varied hugely in size. Imagine that they always operated in groups - there were, basically, no individuals. They operated by making decisions based on group 'feeling', which were weighted by an individual's size, age etc. Their planet is the only one orbiting around their Star and it rotates, like our Moon does around the Earth. They would have no 'days' no 'years' and no 'seasons'. There would be no integral measure of time.
They would have no technology as we know it.
Would they necessarily use any digital calculations? Yet they may be fantastically adroit in complex logic and 'something completely different'.
 

Offline LeeE

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If time is discrete, what happens in between 'packets' of time?
« Reply #17 on: 02/08/2008 14:05:02 »
Heh :) - I said "seems to be" - not "is"...

It sounds like you're describing a 'hive mind' there (although it could be close to describing a society too).  If there was only a single such hive mind on the planet it might be possible but even then, I think that the planet on which they lived could only have a single example of any feature it might have i.e. one hill, one ocean (with no waves), one plant (with just a single trunk, branch & leaf) and once source of food etc.  The death of individual elements of the collective could cause problems as there could only be a single corpse.  Hmm... having said that though, perhaps it could work if they/it viewed multiple occurrences of things, such as grains of sand, as being unique by virtue of them being in a different spatial locations, treating locations as intrinsic properties of the objects occupying them and not as a co-ordinate reference system where many locations can exist.

As far as I can imagine, I think they'd have problems with logic.  If everything was viewed as unique it's difficult to see how they could conceive of alternatives.  They'd be aware that something 'is' but I'm not sure they'd be able to conceive of something that could be but isn't - if they could it might lead to a > 1 number of alternatives, which would in turn lead to counting, so they'd be aware of '1' but not '0'.

The SF novel 'Flight of the Dragonfly' (AKA Rocheworld) by Robert Forward (http://en.wikipedia.org/wiki/Rocheworld - recommended reading) is about an expedition to an almost featureless Roche type double planet where there's just a single type of lifeform, the Flouwen, who are more or less featureless blobs and who spend their time either playing and surfing or contemplating complex mathematical problems.  However, they are self aware as individuals and can count.
 

Offline Soul Surfer

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If time is discrete, what happens in between 'packets' of time?
« Reply #18 on: 02/08/2008 17:45:02 »
To get back to the original question. 

For there to be any significance in a short period of time one needs to resolve events that happen in it

The existence of quantum mechanical uncertainty sets lower limits on space and time because to resolve things that happen in smaller spaces and times it higher energies are needed and in the limit the energy will be so high that whatever happens will exit our universe by creating a black hole.  this may just as quickly evaporate but science can never be performed with precisions greater than this.

This gives rise to the Planck system of units  for details go to

http://en.wikipedia.org/wiki/Planck_units

The shortest possible time the Planck time is 10e-44 seconds

This is the time that it takes light to cross the Planck length which is 10e-35 metres  or about as many times smaller than a nucleus, as a nucleus is to the universe, ie incredibly tiny.

The energies involved to do this are very many orders of magnitude greater than the highest energy cosmic rays which are themselves much higher than the highest energies that we can reach or are ever likely to reach with accelerators.

This gives the shortest possible times but when we are considering quantum processes it is not possible to know precisely what happens during the transition but we can in effect measure how long it takes to complete the process.

This is again due to the application of the uncertainty principle.  Some of the best known quantum processes are those associated with the emission of spectral lines of light as an electron jumps between two energy states in an atom.  If you observe this process very carefully for a specific transition at a very low temperature and pressure it is possible to see that there is a slight variation in the frequency of light emitted and the spectrum line has an absolute lower limit of bandwidth.  This can be related to the transition time in the process of emission. Quick transitions produce broad spectrum lines and slow transitions produce narrow ones.  This is why the spectrum lines chosen for frequency standards are very carefully selected to be very narrow and precise spectum lines.
« Last Edit: 02/08/2008 17:50:25 by Soul Surfer »
 

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If time is discrete, what happens in between 'packets' of time?
« Reply #18 on: 02/08/2008 17:45:02 »

 

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