Model for Measurements without Space or Points

by Steven Gibson July 2005

This paper postulates that points with zero dimensions are never accurate models for measurement and calculation. Any point under observation is a measure of an area. On a fine level absolute points do not exist. Of course when moving to human scale we can work with objects that behave like classic points. But this is because we are then measuring complex objects composed of sets of measurable objects.

This method proposes changing our conception from discrete core objects to continuous (state based) measurement objects.

Viewing points as having zero dimensions leads to several unnecessary paradoxes. For example, an infinite number of points don't get you anywhere. You never get to a physical object or distance. It’s turtles all the way down.

This model is supported by models based on information. For us to measure anything in this world requires information to be received. Information is a selection out of uncertainty. We are immersed in information and we select a specific bit of it for our measurement. Since measurement selects some bit of information that has physical traits, so any object we can work with will also have physical traits.

So this model suggests viewing points as measures of areas. Likewise space has no existence separate from measurements. We should define space as an object defined by measurement of a set of objects.

Selections of an actual object from the potential objects depend on evidence obtained from a measurement. This model will formally describe how the number system is built from measurement. The mathematical formalism of numbers mapping to points on a line should be changed to view numbers as probabilistic objects in a cloud that are found by measurements of information.

This model leads to the idea that the real numbers do not represent a full set of useful numbers. Real numbers are viewed as existing along a linear space

I would suggest numbers can be seen like a cloud of representational objects filling a volume of space.

This proposed model may change our view of imaginary numbers. I have suggested that the set of numbers should not be viewed as a linear set. Instead the set of numbers should be seen more like a cloud of representational objects filling a volume of space. So a subset of the number set could be abstracted out that represents the old number line. -n to +n, but I would suggest numbers could exist like 1-1+n and 1+1-n With that model we would find a number that when raised to a power of 2 will result in -1

x2 = -1

This model may unify our modeling of numerical systems from numbers to probability to logic. This model suggests the set of numbers is a cloud of information extracted from uncertainty. Perhaps probability can be viewed as a specialized model of this information pulled from uncertainty. Probability statements are about the likelihoods of outcomes: one exact event either occurs or does not, and you can bet on it. This measurement model does not select exact events out, but instead models the representations of events.

The model supports the idea that 2 valued logic is just a subset of more complex views of logic. Probability involves methods of measure of uncertain events or knowledge or defining selection of future events. Logic can be viewed as a specialized model relating to probability theory. I suggest viewing logic as a model for the representation of data range selection. We can use this data range interpretation for the management of real systems. It helps model decisions by selecting ranges of choices instead of only allowing one choice. Data ranges allow us to handle complex systems. Boolean logic, which most people are familiar with, is a subset of more generalized logic. In Boolean logic, we are limiting ourselves to data ranges that only include two values.

What seems like a discrete point in everyday life, like our body, a car, or a tree are measures of complex sets of objects.

This model may even address the Many Worlds vs Copenhagen view of Quantum Change. Since this model postulates there is no such think as a discrete point, so perhaps each world variation created by Quantum change is like a probabilistic possibility that exists and is not solidified until a measurement is taken. So I would postulate that there is a temporary many worlds existence that is created constantly. Then when information is selected out of the probabilities the possible worlds collapse back to one.

Does Schrodinger's cat split?

Consider Schrodinger's cat. A cat is placed in a sealed box with a device that releases a pellet of catnip if a certain radioactive decay is detected. For simplicity we'll imagine that the box, whilst closed, completely isolates the cat from its environment. After a while an investigator opens the box to see if the cat has catnip or not. According to the Copenhagen Interpretation the cat neither has catnip nor does not have it until the box was opened, whereupon the wave function of the cat collapsed into one of the two alternatives (catnipped or non-catnipped). The paradox, according to Schrodinger, is that the cat presumably knew if it had catnip “before” the box was opened. According to many-worlds the device was split into two states (catnip released or not) by the radioactive decay, which is a thermodynamically irreversible process. As the catnip/no-catnip interacts with the cat the cat is split into two states (catnip happy or not happy). From the catnip happy cat's point of view it occupies a different world from its non-catnip receiving version. The onlooker is split into two copies only when the box is opened and they are altered by the states of the cat. The cat splits when the device is triggered, irreversibly. The investigator splits when they open the box. The catnip happy cat has no idea that investigator has split, any more than it is aware that there is a unhappy cat in the neighboring split-off world. The investigator can deduce, after the event, by examining the catnip mechanism, or the cat's memory, that the cat split prior to opening the box.

According to this proposed measurement model I would say that the potentialities of the cat getting captnip or not are temporarily split during the passage of time and the potentialities resolve to one by the event of the box being opened.