The problem exists because by definition reality is independent of the mind and any abstract mechanism it can create concerning it.  Therefore only way we can be sure the theoretical models created by the imagination have any connection to reality or physicality of the world we see and touch is by connecting it to what we can see and touch. 

This would be true even though they make accurate predictions of all observable events in the environment it describes.
For example Quantum theory makes extremely accurate predictions of particle interactions based on mathematically generated probability functions.   However it also tells us that particles do not exist until a conscience observer looks at them.  In other words it is tells us that reality is completely dependent on the mind because it assumes the act of observation by the mind creates the physical reality of the particle world.

However this also it means there can be more than one reality because if it is completely dependent on the mind each individual mind can create one suited to its needs.

This presents a problem for science because as mentioned earlier it is tasked with defining a unique existence or set of facts describing the world in which we live.

However if existence is only defined by the mind as quantum mechanics suggests then identifying the unique existence of our world would be impossible because each mind can contain many different ones.

Einstein was often quoted as saying “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”

He realized for science to make a claim that they have organized the natural world into a single set of patterns or laws that describes its reality they must be able to physically connect the independent models developed by our minds and imaginations to the world that exists outside of it.

For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”

However Einstein realized he could explain this by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold to explain how gravity “may act upon another at a distance through a vacuum” in terms of a curvature in space and time.   This allowed him to understand the “reality” behind gravity based on a physical image formed by the reality of what we can see and touch in our three-dimension world.

In other words he was able to connect the world he created in his mind and imagination to the “reality” of our three dimensional environment in terms of a physical imaged formed by the observable properties of our world.

Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Einstein.  They chose to look for reality only in terms of abstract mathematics instead of the physical imagery given to us by the reality of what we can see and touch.

One reason may be because it is easier to alter an abstract mathematical environment to conform to an observational inconsistency than it is to alter one based on physical imagery. 

For example Quantum theory makes predictions based on the random properties of a probability function.  However because its abstract properties are not connected to any physical images of our world all observations no matter how inconsistent they are with the physical world it is describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in our three-dimensional environment physically connects it to a four-dimensional space time-environment

For example a mass that was repelled by gravity instead of being attracted by it would contradict the physical model define by Einstein and would be extremely if not impossible to explain according his model because that would mean that we should observe objects rolling up hill in our three-dimensional environment.  In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses gravitational repelling each other impossible to incorporate into it.

If however if some observation happened to contradict the complimentary principal of quantum mechanics such as simultaneously observing both the particle and wave properties of mass it could easily explained in terms of the fact that its probability functions tell us that anything that can happen eventually will.  This makes it impossible to find an observation that would contradict it because it tells us the even the impossible is possible if we wait long enough.  However this can only happen in an abstract environment which is not bound by the physicality of our observational world because in that world we observe that some things just cannot happen.

But why should science put in the effort to understand the physical reality of our world when both the abstract mathematical foundation of quantum mechanics and the physics imagery of Einstein’s theories make very accurate predictions of future events based on the past. 

Because the mission of a science is to define reality which can only be done in terms of what we perceive in the world around us which is not, by definition abstract.

Later Jeff

Copyright 2013 Jeffrey O’Callaghan 

The post The role of reality in science appeared first on Unifying Quantum and Relativistic Theories.

All forms of mathematics are abstract by definition. However scientists feel that it can be used to extract, by quantification the underlying essence of a physical environment and thereby eliminate any dependence on real world objects with which it might originally have been connected.

Many of our most successful theories began as a mathematical study of real world problems. In other words scientists attempt to use mathematics to quantify real world environments and to establish the underlying rules that govern them.

However the fact that one can mathematically quantify an environment does not mean that they accurately defined the “reality” of the rules that govern it.
For example, Isaac Newton made qualitative observations of how objects in a “real world” environment interacted with the earth’s gravitational field. He then used the understanding develop form those observations and his knowledge mathematics to derive a theoretical model that could not only quantity them but also explain the rules as to why they interacted the way they did in terms of those observations.

In other words he was able to provide a direct physical connection between the abstract properties of his mathematics and how the components of his environment interacted through his observations.

However, with the advent of higher mathematics and advance computing technology physicists now feel they have to ability to define the “reality” of what we observe in purely abstract mathematical terms.

For example, String Theory is based purely on mathematically analyzing the quantitative observation of the real world and then, using only that information define its reality. In others words they not only define the quantitative properties of the environment but also the rules for why its component interact in terms of abstract mathematics without physically observing how those interactions are taking place.

Therefore, String Theory does not and cannot provide a physical connection to the observable universe because its description is based purely on abstract properties of mathematics and not on the physical observations as Isaacs Newton’s were, of how its components interact to form the environment they are describing.

These two different approaches to theoretical philosophies are called Empiricism and Realism.

On the surface they both to be appear to be viable methods for defining the rules that governing our observable environment even though their methodologies are different.

This is because Empiricists say that our theoretical models should only be concerned with the quantifiable properties of observations while the Realist tell us that our theories should not only make accurate quantitative predictions of an environment but also allow us to understand why nature behaves the way it does based on the observable properties of the environments they are describing.

For example empiricists feel that as mentioned earlier science should only be concerned with quantifying observations and that they should only be tested against the quantifiable properties of the natural world. In other words they are not interested in or feel that it is important to integrate the observations of how objects interact in the “real world” to create our observable environment. This is the attitude most string theorist take because they attempt to define not only observations but why the nature world behave the way is does in terms of the abstract properties of mathematics.

Realists, on the other hand believe that science should not only be concerned with quantifying experiences but also explaining why the natural world behaves the way it does based on observations. In other words they feel that mathematics should not only be used to quantify an environment but should also explain why object in the “real world” interact the way we do in terms of the observable properties of that environment. This, they feel would give the underlying essence of a physical environment developed by mathematics a stronger tie to its reality.

For example, Einstein who some would call a realist first developed a conceptual understanding of space-time, based, in part on the observation that the speed of light was constant in all reference frames. However unlike the Empiricists he then developed the theoretical structure of Special Relativity by forming a physical image of what it would be like to chase after a beam of light based on observable properties of the “real world” and then translated or transpose that understanding to define how and why matter and energy in motion would interact in a space-time environment. Later he developed the equations that quantified and verified the accuracy of his conceptual model based on observations of speed of light in the natural world.

However, the proponents of Empiricism take the opposite approach to science. They observe the quantitative results of observations and then, through trial and error define a series of abstract equations, which can accurately predict them. They then use those equations to define a theoretical structure which then predicts the reality or rules governing the underlying essence of that environment.

For example, Quantum Theories, which espouses the empiricist approach defines the observations of the quantum mechanical environment of energy/mass based solely on mathematical probability functions or equations. They then use those abstract equations to not only quantify those observations but to define the rules which govern of the environment they occupy.

However this circular method of predicting both observations and operating environments based on only on mathematics does not allow one to determine the physical reality of the environments they define because those mathematically created environments are by definition abstract and therefore are independent of the physical world they are defining.

But is there a way science can verify when a mathematical created environment defines the underlying essence of the “real world” when as just mentioned they are by definition abstract and therefore do not have a direct “physically connect” to it.

The realist answer to this is to connect the abstract environments created by mathematics as Newton and Einstein did to the physical environment they are defining though observations.

For example Quantum theory makes predictions based on the abstract mathematical environment of a probability functions. However because its abstract properties are not connected to any physical images of the “real world” all observations, no matter how inconsistent or bazaar they are can be incorporated into it.

This is in sharp contrast to the space-time environment defined by Einstein because he, as mentioned earlier developed the theoretical structure of a space-time environment based on a physical image of what it would be like to chase a beam of light in the real world. This not only gives the abstract properties of his mathematics a physical connection to the real world it also give science a way of checking its conceptual validity.

For example Einstein’s theory would be invalidated if it was found that something could travel faster than the speed of light because that would contradict the physical model he define.

If however if some observation happened to contradict principals of quantum mechanics such as simultaneously observing of both particle and wave properties of mass it could easily explained of in terms of the fact that its probabilities functions tells us that anything that can happen will eventually happen. However it is impossible to find any observation that would contradict the fact that anything can will and must happen at some time in the future.

Yet this can only happen in an abstract environment which is not bound by the physicality our observational world because in that world we observe that some things just do not happen.

But why should science put in the effort to understand the physical reality behind our world when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein’s theories make very accurate predictions of future events based on the past.

Because the mission of a science is to define reality in terms of what we observe in the world around us which, by definition is not an abstract property of mathematics.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post The reality of our “mathematical worlds” appeared first on Unifying Quantum and Relativistic Theories.