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Slicing time


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As far as I know the shorter than a second are millisecond > microsecond > nanosecond > picosecond.

 

It’s a picosecond that we can consider the ultimate in time measurement.

 

Or...

 

Perhaps I would consider positive zero - approaching zero from the positive side. More interesting is the square root of a negative zero (approaching zero from the negative side), or 0i...imaginary zero.

 

Any other ideas regarding the shortest slice of time?

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Classically there is no limit to slicing up intervals of time, infinitesimal is fine (as infinitesimal displacements are also ok).

 

However, based on intuition and arguments from quantum theory one expects that space-time will be come noncommutativeor "fuzzy". That is it maybe the case that knowing the position and time of a particle to arbitrary accuracy simultaneously may not be possible. This will depend on the details, but it is analogous to the uncertainty principle in quantum mechanics.

 

A related idea, but I am not sure exactly how is the chronon. It is like a discrete packet of time. It would represent the smallest slice of time interval.

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Classically there is no limit to slicing up intervals of time, infinitesimal is fine (as infinitesimal displacements are also ok).

 

However, based on intuition and arguments from quantum theory one expects that space-time will be come noncommutativeor "fuzzy". That is it maybe the case that knowing the position and time of a particle to arbitrary accuracy simultaneously may not be possible. This will depend on the details, but it is analogous to the uncertainty principle in quantum mechanics.

 

A related idea, but I am not sure exactly how is the chronon. It is like a discrete packet of time. It would represent the smallest slice of time interval.

Thank you for your responce and the links. I think "time" is a measurement of change, without change, there is no time. So time is based on change, so the smallest measure of change would by necessity be the smallest measure of time. Mentally, if change (as an idea) is made, for example, in making a descision, then the smallest measure of time would be one descision, or possible nexus point.

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Classically there is no limit to slicing up intervals of time, infinitesimal is fine (as infinitesimal displacements are also ok).

 

However, based on intuition and arguments from quantum theory one expects that space-time will be come noncommutativeor "fuzzy". That is it maybe the case that knowing the position and time of a particle to arbitrary accuracy simultaneously may not be possible. This will depend on the details, but it is analogous to the uncertainty principle in quantum mechanics.

 

A related idea, but I am not sure exactly how is the chronon. It is like a discrete packet of time. It would represent the smallest slice of time interval.

This is really an incredible information. I found another article to examine http://www.thekeyboard.org.uk/What%20is%20Time.htm

Edited by needimprovement
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Classically there is no limit to slicing up intervals of time, infinitesimal is fine (as infinitesimal displacements are also ok).

 

However, based on intuition and arguments from quantum theory one expects that space-time will be come ... "fuzzy". ...

In fact, time flow is not a series of infinitesimal periods but always a series of finite intervals because for a too short interval of time we cannot get sufficient information - information becomes uncertain, unreliable. Take a film camera and try to increase the rate of frames by decreasing the exposition periods. You will arrive at so short expositions that the information on each frame will be too poor or even absent some times (no photons registered on a frame). On the other hand, time serves to follow changes of information on frames, so for certainty the exposition periods cannot be too short or too long.

Edited by Bob_for_short
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In fact, time flow is not a series of infinitesimal periods but always a series of finite intervals because for a too short interval of time we cannot get sufficient information - information becomes uncertain, unreliable. Take a film camera and try to increase the rate of frames by decreasing the exposition periods. You will arrive at so short expositions that the information on each frame will be too poor or even absent some times (no photons registered on a frame). On the other hand, time serves to follow changes of information on frames, so for certainty the exposition periods cannot be too short or too long.

 

That makes a lot of sense

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But then Bob I am happy looking at infinitesimal (active) diffeormorphisms and the flows they generate. In the mathematical formulation of classical mechanics and general relativity taking infinitesimal changes in time are fine.

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In the mathematical formulation of classical mechanics and general relativity taking infinitesimal changes in time are fine.

Yes, of course, because they are classical theories with abstractions and idealizations. For example, CM is about motion of centers of inertia of macroscopic bodies (3 coordinates suffice). As soon as the body information gets "fluctuating", CM fails. Consider the limit of low intensity of light (few photons per second). The body position gets uncertain due to lack of statistics for good averaging. This is an experimental limitation. In such conditions you cannot collect sufficient information about the initial data and predict the body trajectory with CM.

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If one considers time inevitably linked to change as measurement parameter, let’s add absolute zero into the equation and theory. This would give us no movement and yet we would still have time! Hmmm.

I got your point.

 

My friend in Chicago said that the smallest "slice of time" was defined by the interval between a traffic light turning green and the guy behind you honking his horn. :lol:

 

But your point is very good.

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If one considers time inevitably linked to change as measurement parameter, let’s add absolute zero into the equation and theory. This would give us no movement and yet we would still have time! Hmmm.

There are things above T=0K that do not feel time: the conserved functions of motion, for example, the total energy, the total momentum, the total angular momentum, etc., that do not change in time despite motion.

The listed explicitly functions are well known and are additive in particles, but there are the integrals of motion in CM that are not additive in particles. Their number is equal to the number of initial data, I think.

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A related idea, but I am not sure exactly how is the chronon. It is like a discrete packet of time. It would represent the smallest slice of time interval.

Can you help me understand (in common man parlance) how the chronon differs from Planck time? All I really managed to grasp from the wiki is that the chronon is roughly twice as long. I'm fairly sure I'm missing a relatively basic contextual, categorial, or semantic difference, but I'm wholly uncertain at this point what that is.

 

Cheers.

Edited by iNow
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Can you help me understand (in common man parlance) how the chronon differs from Planck time? All I really managed to grasp from the wiki is that the chronon is roughly twice as long. I'm fairly sure I'm missing a relatively basic contextual, categorial, or semantic difference, but I'm wholly uncertain at this point what that is.

 

Cheers.

 

I am not really sure what a cronon is. One definition, as given on wiki is the time taken for a photon to travel across the classical electron radius. ( Lévi, Robert (1927). "Théorie de l'action universelle et discontinue". Journal de Physique et le Radium 8: 182–198. and Margenau, Henry (1950). The Nature of Physical Reality. McGraw-Hill.)

 

To me this sounds more like a technical barrier rather than some fundamental limit. It could be a useful unit of time. It is roughly [math]7 \times 10^{-24} [/math] seconds.

 

The Planck time is the time taken for a photon to travel a distance of one Planck length. This is roughly [math]5 \times 10^{-44}[/math] seconds. I don't know if you should really interpret Planck time as the smallest possible time interval. It really signifies, in four dimensions the time scales on which you would expect quantum gravity to become important. It could in reality be a much longer time scale if we have, for instance more dimensions than 4.

 

Now, quantum gravity is going to have something to say about time. We don't really know what.

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Thanks, ajb. I'll look into the topic more closely as time permits. I also need to apologize for my ridiculous math error above. Ten to the negative 24 is NOT roughly half of ten to the negative 44. Good grief. That particular statement fails in a few different ways. :doh:

Edited by iNow
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In fact, time flow is not a series of infinitesimal periods but always a series of finite intervals because for a too short interval of time we cannot get sufficient information - information becomes uncertain, unreliable. Take a film camera and try to increase the rate of frames by decreasing the exposition periods. You will arrive at so short expositions that the information on each frame will be too poor or even absent some times (no photons registered on a frame). On the other hand, time serves to follow changes of information on frames, so for certainty the exposition periods cannot be too short or too long.

So time has a constant velocity (minimum), like the speed of light , so there is a minimum 'speed of time'.

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Sir William Thomson (Lord Kelvin) said, "In physical science the first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be." [PLA, vol. 1, "Electrical Units of Measurement", 1883-05-03]

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  • 3 weeks later...

Time is relative.

An infinitesimal slice of time for you can be a lot of time for another observator.

The same goes for distance.

Current popular theories in physics such as quantum gravity, string theory, and black hole thermodynamics all predict that spacetime is quantized. That is, there is a smallest possible length which is on the order of quantum length. So the shortest possible distance between the two dots is the Panck length.

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Current popular theories in physics such as quantum gravity, string theory, and black hole thermodynamics all predict that spacetime is quantized. That is, there is a smallest possible length which is on the order of quantum length. So the shortest possible distance between the two dots is the Panck length.

 

Typo. You ment Planck length.

 

Well, if everything is relative, Planck length must be relative too.

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