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**Physics, Astronomy & Cosmology / Re: How fundamental is time?**

« **on:**11/01/2019 16:50:14 »

Change and time are not equivalent. Time is a dimension, and change refers to differences within one dimension.

This is most well defined within calculus (sometimes called the math of change), where the symbol ∂ (sometimes d) is used to denote microscopic change, often relating the change of one thing with respect to the change of another.

In this way, we can define instantaneous (microscopic) change of position along a spatial dimension (x) with respect to instantaneous (microscopic) change in time (t) as ∂x/∂t which is equivalent to the velocity in the x direction.

Although time is a very common dimension (variable) to compare changes against, it is not the only one. For instance we can look at the change in altitude with respect to change in forward distance traveled ∂y/∂dx (slope) or the change in cost of making chocolate with respect to the change in the cost of labor ∂$

What I am trying to learn in this thread is whether our concept of velocity (or any other rate of change with respect to apparent time) is best described as a ∂x/∂dt, or if there is a more fundamental variable (I believe I called it α earlier in the thread) such that ∂t/∂α is well-defined, and ∂x/∂α holds up better to the boundary condition that the big bang appears to impose on ∂t.

This is most well defined within calculus (sometimes called the math of change), where the symbol ∂ (sometimes d) is used to denote microscopic change, often relating the change of one thing with respect to the change of another.

In this way, we can define instantaneous (microscopic) change of position along a spatial dimension (x) with respect to instantaneous (microscopic) change in time (t) as ∂x/∂t which is equivalent to the velocity in the x direction.

Although time is a very common dimension (variable) to compare changes against, it is not the only one. For instance we can look at the change in altitude with respect to change in forward distance traveled ∂y/∂dx (slope) or the change in cost of making chocolate with respect to the change in the cost of labor ∂$

_{chocolate}/∂$_{labor}etc. etc.What I am trying to learn in this thread is whether our concept of velocity (or any other rate of change with respect to apparent time) is best described as a ∂x/∂dt, or if there is a more fundamental variable (I believe I called it α earlier in the thread) such that ∂t/∂α is well-defined, and ∂x/∂α holds up better to the boundary condition that the big bang appears to impose on ∂t.

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