# Can DEL-t exist without INT-t existing

1. Oct 17, 2011

### skeleton

Can DELTA-time exist without INTEGRAL-time existing

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SUBJECT:

My following question derives from a motivation to explore the notion that (accumulated) time, as a physical entity, might not exist in reality.

However, an associated paradox would thus arise: there are numerous real physical parameters which characterize a time-rated characteristic. As an example: the following parameters are time-rated:
- Half-life of radioactive isotopes, t_1/2: s
- Gravitational constant, G = 6.67E-11 m^3/kg/s^2
- Spring constant, k: kg/s^2

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CONUNDRUM:

Where a physical parameter occurs which is time-rate dependent, then time can be mathematically isolated by integration of its denominator of time.

Here, I mean a time-rated parameter to be a physical parameter that defines a rate of physical quantity per unit of time. Example: speed being displacement per unit of time (mph, kph, etc). In calculus, this would be represented as:
V = delta_x / delta_t

Also, I mean an accumulated-time would arise where delta_t could be integrated over its own domain (time).

Consider a generalized flow-like parameter:

Given
q = delta_Q(t) / delta_t

Where
Q(t) = flow function
q = flow rate
t = time

Then
delta_t = delta_Q(t) / q

Integrate over t
INT [delta_Q(t) / q] = INT [delta_t]
= (t.f - t.i)

Where
q.i = flow at initial state
q.f = flow at final state
t.i = time at initial state
t.f = time at final state

Thus, in the above manipulation, a duration of time (t.f - t.i) is seen to transpire. However, a mathematical manipulation does not necessarily prove the realism of its result.

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CONJECTURE:

Perhaps time is a fictitious parameter. Where the time parameter arises in standard equations of physical mechanics (etc), perhaps some other implicit parameter is actually responsible. For example, perhaps where time appears in a time-dependent parameter, the real dependent parameter is something else, like energy.

An example can be seen in the parameter, speed. A vehicle can have its speed quantified as displacement per unit time (km/hr). But the evolution of time is not what propels the vehicle. Rather, the speed of the vehicle is really the result of its consumption of fuel. So, the vehicle speed could be alternatively quantified as displacement per unit of fuel (km/liter_of_fuel).

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QUESTION:

Can flow-like parameters (ie: time-rated) exist while mandating that accumulated-time must not sensibly existing?

This is equivalent mathematically to asking (but pertaining to the physical world):
Is it possible for delta_time to exist without Integral(delta_time) having any real meaning?

This question could be applied, for example, to speed. This would ask: can speed (time-rate of displacement), being physically real, exist while any implied elapsed time would not physically exist?

Consider the previous example of a vehicle burning fuel to propel it at a given speed. After it has consumed a known quantity of fuel, it will have traveled a determinable distance. In human terms, some time has elapsed. But I am considering the notion that time did not elapse in a physically real sense, only in a perceived sense. The elapsed time is physically not to be found. But the traveled displacement is physically observable in itself, as is the consumption of fuel.

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Last edited: Oct 17, 2011