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Old Apr 25th 2017, 06:08 AM   #1
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Instants: real or abstractions?

They say that instants are only convenient mathematical abstractions. That no real fact occurs only "in an instant". But when I throw a pebble vertically upwards, it has a highest point in its trajectory. The pebble is not in that position for a milisecond, because a milisecond is a time interval and the pebble does not levitate. But the trajectory has a highest point, that is a fact. So the pebble is in that position for an instant, and this is a real instant, not a mathematical abstraction. Is this wrong?
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Old Apr 25th 2017, 07:28 AM   #2
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Events in Time

Sir Castilla,

I suppose the purpose of science is to predict future occurance of events.
This includes the "null event," nothing happens, the abstract of which is
permanence. Observation and math tools are used as descriptions of real
behavior.

However, at the beginning and end, all this involves human observation,
observation not quite precise.

I wrote a little about time and description of events in time.

1.21 Events and Time | THERMO Spoken Here!

Good Luck with your studies... JP
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Old Apr 25th 2017, 10:23 AM   #3
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You are quite right with your pebble example.
In the example the trajectory of the pebble is continuous, that is both the distance axes and the times axis taken on a continuum of values from start to finish.
And at any instant, not just the apogee of the trajectory, the pebble can be said to possess certain properties including height and distance coordinates, velocity etc.

As an aside I will observe that modern theory is undecided as to whether the real universe is continuous like the mathematical modle above or granular ie the axes are actually made of very very very tiny segments of distance and time.
This is embodied in the uncertainty principle of the quantum theory, where you can never know both the distance and time with infinite precision.

But this is not what is meant by in an instant or instantaneous in science.

This description refers to the propagation of disturbances or changes to the system which take time to get from one place to another.

Here is a brilliant video that shows this effect.

A man hangs a spring by its top and releases it.

The bottom does not move in an instant but hangs there in space for a short time before beginning to fall.

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Old Apr 25th 2017, 11:59 AM   #4
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Cool video!

The idea of an "instant" and that an object can have certain properties that vary continuously with time is at the heart of the calculus. Not only is the pebble precisely motionless for only one instant in time, it also has other exact values of velocity for only an instant as well. For example when you throw it upward at 10 m/s there is only one instant in time when it has an upward velocity of exactly 5 m/s, or 4.13762 m/s, or whatever value you want. Each of these "instants" are defined by the when it is that the slope of the displacement versus time graph is exactly equal to the particular value of velocity in question. Calculus is about taking a continuous function (like displacement versus time) and calculating discrete values of the rate of change of that function at discrete moments in time by calculating the limit of the change in position divided by the change in time as the change in time goes to zero. The change in time can never be precisely zero however, because then the pebble's velocity would be 0/0, which is undefined. It took mathematicians hundreds of years to rigorously resolve the paradox of determining the precise slope of a curve at an instant in time, when slope is meaningless if the change in time is zero. All of which begs the question you posed - whether mathematics is a true description of the physical world or merely a pedagogy that models the world and conveniently gives useful results has been a matter of philosophical debate for a long time.
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Old Apr 26th 2017, 05:31 AM   #5
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Your example of the pebbles trajectory to illustrate an instant in time implies that a precise position can be defined for the pebble.
However we know that at a quantum level, the position and momentum of the pebble cannot (both) be known completely absolutely precisely.
I am not entirely sure, but I think that there is a similar uncertainty inherent in the positioning of an instant in time.
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