- #1
nightcleaner
OnTime
If we use the speed of light, c, as a basis unit of value one, then it immediately follows that at the speed of light one unit of length is equal to one unit of time. In order to make this idea local and thereby avoiding the question of universal curvature, we can make the definition that at c one Planck length is equal to one Planck time.
Then at velocities less than c, the number of Planck lengths per Planck time is less than one. We might express velocites as percentages of c, as .9c or .75c and so on. The question then is, what is zero c? In order to preserve background independence, and in accordance with the idea that there is no preferred frame of reference, we then set zero c to be in the frame of reference of the observer. To keep things uncluttered, we may think of an observer in some flat region of space far from any fields of acceleration.
Setting velocity, V=kc, where k is a value between zero and one, and considering k as L/T, where L is a number of Planck lengths and T is a number of Planck times, we can see that in the frame of the observer, that is in the rest frame, L/T=zero. Note that L and T are both counting numbers, that is, they are positive integers.
There are two conditions under which a ratio such as k can approach zero. One is the condition in which L is very small and T is very large. The other is when L is zero and T is any number. Since we are using only the counting numbers, neither L nor T can be less than one, so the second condition is not considered.
So we may say that the frame of the observer is that frame in which L is very small and T is very large, keeping in mind that L and T are positive integer numbers of base units. Under this condition, we will not be able to consider the state of motion of the entire universe, since in that case L, for the observer, would be large.
Now it is common for all observers to experience a flow of time and a sense of volume in space. Even in the rest frame, where volume may be taken to be constant, there is a flow of time. We may imagine, then, that every volume in space experiences an increase in its sum of instants in time. This could be thought of as an increase in time density. In this sense, each volume in space contains an ever increasing amount of time.
Holding the spatial volume as a constant, we then must imagine an infall of time into space. An object can be thought of as containing more time as time passes. Since this would have to be a change in time per time, we are talking about an acceleration. Also, there would have to be a flux of time across the surface of the object, and this flux would be directed inward.
If there is a flux, then we may think of the flux being due to a difference in density of time across the surface. The density of time outside the surface must be greater than the density of time inside the surface, since the flux is directed inward.
Now we may ask, what is it about an object that makes the time density within it less than the time density outside of it? We must keep in mind when asking this question that the observer is also an object. What is an object?
In the most trivial sense, an object is that which can be observed. We may wish to limit our idea of objects to those objects which are irreducible, that is, to fundamental particles. Complex objects, like atoms, may then be built up of fundamental objects, and observers are built of atoms, and observers may imagine non-material objects, such as, for example, a category, perhaps the category of all atoms. While the atoms may be said to be the sum of their parts, the category, as an object, may be more or less than the sum of its parts. Catagories are not irreducible in this sense, so are not included directly in this discussion, although additional rules for catagories and other non-fundamental objects may be formulated elsewhere. For now, let us limit the discussion to physical objects, and further to fundamental objects.
A fundamental object, then, at very least, occupies space and experiences an increase, an acceleration, in time. This acceleration can be thought of as a flux across the surface of the object, and the density of time in the object can be thought of as increasing.
If the time density in the object is increasing, will it ever reach the density equivalent to the density outside the object, and so stop the flow of time across the surface of the object? Is this the condition of the object accelerated to c, in which the flow of time, relative to the observer, is said to cease?
What is it about an object that causes the time density in the object to be less than the density outside the object? Two possibilities. The acceleration of time inside the object is for some reason less than the acceleration outside the object. Or, there is within an object some mechanism for reducing the density of time within the object. Objects are, fundamentally, time sinks.
Why would the acceleration of time inside the object be less than the acceleration outside the object? Perhaps it is because the object is moving, as all objects must move, even though we have invoked the fiction that the object is in a rest frame. Then the movement of an object somehow reduces the accelleration of time in the object, that is, reduces the rate of time flux across the surface into the object. Then we might expect to be able to see a difference in time flow on different surfaces of an object moving on one direction. There would be a "front" side of an object as it moves through time and a "back" side. We should be able to notice a difference. But we do not notice any such difference in objects under motion. Perhaps we can discount the idea that motion causes the difference in acceleration of time.
Then perhaps the other idea is the better one. There must be some mechanism within objects that reduces the density of time within the object. Objects are time sinks, and contain a drain out of which time escapes the object. Where does it go? Are some time units different from other time units, such that some of them go out the drain and others do not? Are new time units somehow different from old time units, so that the old time units dissappear or get used up somehow?
Oh well. Something to think about while cleaning behind the grill.
Thanks for being here. Comments welcome.
nc
If we use the speed of light, c, as a basis unit of value one, then it immediately follows that at the speed of light one unit of length is equal to one unit of time. In order to make this idea local and thereby avoiding the question of universal curvature, we can make the definition that at c one Planck length is equal to one Planck time.
Then at velocities less than c, the number of Planck lengths per Planck time is less than one. We might express velocites as percentages of c, as .9c or .75c and so on. The question then is, what is zero c? In order to preserve background independence, and in accordance with the idea that there is no preferred frame of reference, we then set zero c to be in the frame of reference of the observer. To keep things uncluttered, we may think of an observer in some flat region of space far from any fields of acceleration.
Setting velocity, V=kc, where k is a value between zero and one, and considering k as L/T, where L is a number of Planck lengths and T is a number of Planck times, we can see that in the frame of the observer, that is in the rest frame, L/T=zero. Note that L and T are both counting numbers, that is, they are positive integers.
There are two conditions under which a ratio such as k can approach zero. One is the condition in which L is very small and T is very large. The other is when L is zero and T is any number. Since we are using only the counting numbers, neither L nor T can be less than one, so the second condition is not considered.
So we may say that the frame of the observer is that frame in which L is very small and T is very large, keeping in mind that L and T are positive integer numbers of base units. Under this condition, we will not be able to consider the state of motion of the entire universe, since in that case L, for the observer, would be large.
Now it is common for all observers to experience a flow of time and a sense of volume in space. Even in the rest frame, where volume may be taken to be constant, there is a flow of time. We may imagine, then, that every volume in space experiences an increase in its sum of instants in time. This could be thought of as an increase in time density. In this sense, each volume in space contains an ever increasing amount of time.
Holding the spatial volume as a constant, we then must imagine an infall of time into space. An object can be thought of as containing more time as time passes. Since this would have to be a change in time per time, we are talking about an acceleration. Also, there would have to be a flux of time across the surface of the object, and this flux would be directed inward.
If there is a flux, then we may think of the flux being due to a difference in density of time across the surface. The density of time outside the surface must be greater than the density of time inside the surface, since the flux is directed inward.
Now we may ask, what is it about an object that makes the time density within it less than the time density outside of it? We must keep in mind when asking this question that the observer is also an object. What is an object?
In the most trivial sense, an object is that which can be observed. We may wish to limit our idea of objects to those objects which are irreducible, that is, to fundamental particles. Complex objects, like atoms, may then be built up of fundamental objects, and observers are built of atoms, and observers may imagine non-material objects, such as, for example, a category, perhaps the category of all atoms. While the atoms may be said to be the sum of their parts, the category, as an object, may be more or less than the sum of its parts. Catagories are not irreducible in this sense, so are not included directly in this discussion, although additional rules for catagories and other non-fundamental objects may be formulated elsewhere. For now, let us limit the discussion to physical objects, and further to fundamental objects.
A fundamental object, then, at very least, occupies space and experiences an increase, an acceleration, in time. This acceleration can be thought of as a flux across the surface of the object, and the density of time in the object can be thought of as increasing.
If the time density in the object is increasing, will it ever reach the density equivalent to the density outside the object, and so stop the flow of time across the surface of the object? Is this the condition of the object accelerated to c, in which the flow of time, relative to the observer, is said to cease?
What is it about an object that causes the time density in the object to be less than the density outside the object? Two possibilities. The acceleration of time inside the object is for some reason less than the acceleration outside the object. Or, there is within an object some mechanism for reducing the density of time within the object. Objects are, fundamentally, time sinks.
Why would the acceleration of time inside the object be less than the acceleration outside the object? Perhaps it is because the object is moving, as all objects must move, even though we have invoked the fiction that the object is in a rest frame. Then the movement of an object somehow reduces the accelleration of time in the object, that is, reduces the rate of time flux across the surface into the object. Then we might expect to be able to see a difference in time flow on different surfaces of an object moving on one direction. There would be a "front" side of an object as it moves through time and a "back" side. We should be able to notice a difference. But we do not notice any such difference in objects under motion. Perhaps we can discount the idea that motion causes the difference in acceleration of time.
Then perhaps the other idea is the better one. There must be some mechanism within objects that reduces the density of time within the object. Objects are time sinks, and contain a drain out of which time escapes the object. Where does it go? Are some time units different from other time units, such that some of them go out the drain and others do not? Are new time units somehow different from old time units, so that the old time units dissappear or get used up somehow?
Oh well. Something to think about while cleaning behind the grill.
Thanks for being here. Comments welcome.
nc
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