Abstract
The proposed structure for theoretical physics posits that ‘Reality’ is subject to measurement and interpretation through a mathematical framework. It argues that fundamental concepts like force, mass, and acceleration are not inherent aspects of Reality but rather theoretical constructs derived from measurements.
Using Newton’s second law as a case study, the text contends that defining force involves a mere mathematical relationship and not an empirical law governing Reality.
This perspective criticises the traditional approach to physics, advocating for a foundational system of measurement to enhance understanding, rather than relying on assumed fundamental qualities that may misguide scientific inquiry.
A proposed structure for theoretical physics
We assume that there is something called ‘Reality’ which we wish to investigate (left column).
We make various measurements to get a limited but objective representation of at least some of the characteristics of the aforementioned Reality (middle column).
The measurements are then interpreted via a theoretical system of a usually mathematical nature in an attempt to delineate quantitative relationships between the various elements (column on the right).
Relationships between the elements confer some sort of ‘understanding’ and such an understanding can be used to formulate new hypotheses and to make quantitative predictions with the regard to further experimental outcomes, that is to say, measurements.
We do not make predictions concerning Reality directly as the only apparatus we have at our disposal is a set of measurement protocols. We therefore make predictions concerning these measurement outcomes under various conditions and then check for consistency via the theoretical framework.
Theoretical physics therefore consists of just this: taking measurements and interpreting them via theory.
We can see that all the properties that we think of as ‘fundamental’ parts of Reality (mass, force, time etc.) are not actually part of Reality at all, but abstract elements within a theoretical framework which are only made apparent via the interpretations of various measurement protocols. We never directly observe ‘time’ for example.
It is obvious in this diagram that force, mass and acceleration are all theoretical elements with well-defined numerical relationships.
This all seems fairly straightforward but seems to have escaped the attention of physicists.
Example: Newton’s second Law
As an example, we can look at Newton’s second Law of motion, which claims to relate a force applied to an object to the product of its mass and acceleration:
Force = Mass x Acceleration
What does this equation actually mean?
Newton’s equation as a ‘definition’
If we use the theoretical framework described above, then this equation appears to be a straightforward definition of a theoretical element called ‘force’ whose numerical value is obtained by multiplying together the numerical values for mass and acceleration (both also theoretical elements derived from measurements).
This is noted by Wikipedia:
Newton’s second law is sometimes presented as a definition of force, i.e., a force is that which exists when an inertial observer sees a body accelerating. – Wikipedia
The phrase ‘sometimes presented‘ seems somewhat dismissive and suggests that the authors do not entirely approve.
The phrase ‘a force is that which exists’ suggests that they are conflating characteristics of Reality with theoretical elements. If Newton’s equation is really a definition then the ‘force’ mentioned is a mathematical construct derived from mass and acceleration and therefore has a speculative relationship with Reality. Theoretical constructs do not ‘exist’ in the everyday meaning of the word.
This is sometimes regarded as a potential tautology – acceleration implies force, force implies acceleration. – Wikipedia
No, a definition is not a tautology. We assume here that we already have well-defined constructs called ‘mass’ and ‘acceleration’ and want to create a third theoretical construct called ‘force’ which is simply the product of the two.
This is fine. The thing called ‘force’ is now simply mathematical shorthand for the product of mass and acceleration and may be used in place of such a product wherever it may appear.
Force and acceleration are two elements of a theoretical system connected by the (usually constant) multiplier of ‘mass’. This is common in mathematical frameworks and should not be considered an anomaly in any way.
Is this a ‘law’?
No, a definition most certainly is not a ‘law’. It is a definition, it defines a single new element of a theoretical framework in terms of already existing elements.
From this point of view, the equation doesn’t really say anything at all about the theoretical framework or about physical Reality. It is just some shorthand mathematical notation, a mathematical convenience which adds nothing to our understanding of either the theoretical framework or physical reality.
Newton’s law as a restricting influence on scientific enquiry
The following passage from Wikipedia references one of the Feynman Lectures on Physics and needs to be taken seriously:
Newton’s second law has also been regarded as setting out a research program for physics, establishing that important goals of the subject are to identify the forces present in nature and to catalogue the constituents of matter. – Wikipedia
Yes, indeed. The law focuses on the relationship between the acceleration of a mass and the ‘magnitude’ of external influences, formulating such influences as ‘forces’ no matter what their origin or nature.
From this respect, the only interesting aspect of gravity is that it constitutes a ‘force’ when influencing ‘matter’. The nature of gravity itself and the actual mechanism by which it affects objects are not addressed by Newton’s equation. Gravity itself is now referred to as The Gravitational Force and takes upon a theoretical status identical to that of pulling an object along with a piece of string.
The setting out of research goals therefore has the advantage of focusing attention in one particular direction, but subsequent labelling of forces as ‘fundamental’ and of gravity in particular as one of the ‘four fundamental forces of reality’ do not in any way help our understanding.
By identifying these concepts as ‘fundamental’ scientists are actually discouraging further investigation, for if gravity is fundamental then there can be no underlying mechanism and any such a notion will surely be labelled as pseudo-scientific.
How can there be any proof at all of the ‘fundamental’ nature of gravity if its nature is unknown?
Do forces cause acceleration?
No! Both forces and acceleration are elements of a mathematical theoretical framework. Abstract theoretical elements are not part of Reality and therefore cannot cause anything to happen in the real world.
Force = Mass x Acceleration
There is no causation symbol within Newton’s equation or within theoretical physics in general.
This means that causality cannot be defined within such a framework and so cannot be discussed or quantified.
Note that theoretical physicists have gotten by perfectly well for hundreds of years without any causality notation which implies that such a thing is not strictly necessary.
The idea of causality comes from philosophers who themselves can provide no coherent definition.
A system of measurements
If we are to calculate a theoretical value for force from Newton’s equation we must first obtain theoretical values for both mass and acceleration. We therefore need a consistent System of Measurement.
A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Instances in use include the International System of Units or SI (the modern form of the metric system), the British imperial system, and the United States customary system. – Wikipedia
A system of measurement is used to define the fundamental quantities of the theoretical framework such as time, distance mass etc.
Each physical quantity will be measured via a well-defined measurement protocol to ascertain a numerical value which will then be used to perform calculations within the mathematical framework.
As an example, we could define the mass of an object as the numerical readout of a triple-beam balance of a precise and specific manufacturing specification which compares our object against a specific reference mass.
Important: This will precisely define the quantity called ‘mass’ which will be used in our theoretical system.
This is the system used by commerce and is the only sane way to proceed with a theoretical system, but unfortunately is not the approach adopted by most texts on physics.
If I order a kilogram of an expensive substance from you then we must surely have some documented agreement as to what constitutes a kilogram. We cannot each claim we have a better method of measuring the same quantity, we must define a kilogram as the outcome of a mutually agreed measurement protocol.
The ‘traditional’ approach
In the sane and logical approach outlined above, theoretical quantities are obtained initially as the outcome of a specific measurement protocol and then further theoretical quantities (e.g. force) are determined by calculations performed within a mathematical framework.
The outcomes of the measurement protocols can be said to constitute the fundamentals of the theoretical system with all other quantities being ultimately derived from these fundamentals.
However, reading educational texts on physics, we find that a completely different approach is adopted.
Here we find that mass, distance, force, gravity etc. are all declared somewhat arbitrarily to be fundamentals of reality. The idea is that they exist independently of any measurement protocol and it is the job of the scientist to somehow find out what they are by devising ever more accurate instruments and techniques.
Mass is regarded as a fundamental quality to be measured in its own right instead of being defined as the outcome of an existing and well-defined measurement protocol.
There are many problems with this approach:
- How do we know when we have obtained the correct measurement?
- How do we choose between different measurement protocols?
- How do we know that these quantities are ‘fundamental’?
- None of these fundamental properties of reality can actually be measured directly but emerge as calculated results from measurement outcomes. They are therefore really theoretical quantities anyhow.
We are left with the situation where different instruments might give different measurements for the same quantity and we have no way of deciding which one is best or even defining what ‘best’ actually means.
This is wholly inadequate.
The gravitational constant
As an example of the absurdity of this approach consider the case of the Gravitational Constant. The value of this constant is seen to change in a cyclic fashion over the years and even to change on a daily basis and according to location.
The response of the mainstream is to declare that the constant itself cannot be changing but that there must be some problem with the measuring technique. This is absurd; the only empirical knowledge we have of the supposed constant is a set of measurement outcomes and so if those outcomes suggest variability, then variability is what we must conclude.
The scientists are suggesting that there is some aspect of reality that they ‘know’ is constant despite all empirical evidence to the contrary.
The only solution that the scientists can come up with now is to keep altering the measurement techniques until they get the answer that they want!
Goal oriented science at work.
Wikipedia on forces
We described Newton’s second law above as a definition within a mathematical theoretical framework and found that this was reasonable and theoretically consistent.
We introduced the idea of a System of Measurement to define the initial values of a theoretical calculation.
However, if a beginner were to attempt to understand physics by reading standard texts, neither of these ideas are explained and the result is a horrific mess of ill-defined or nonsensical ideas, circular arguments, a general lack of structure to the framework and repeated conflation of Reality and theory
Wikipedia explains Newton’s Law thus:
The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed. – Wikipedia
Ok, but what is a force?
In physics, a force is an action that can cause an object to change its velocity or its shape, or to resist other forces, or to cause changes of pressure in a fluid. In mechanics, force makes ideas like pushing or pulling mathematically precise. – Wikipedia
- A force is described as an action but an action is not defined
- The action can cause a change which means that it may not!
- We seek precision but a force is defined in terms of something less precise than itself
- A vague definition cannot make anything mathematically precise
- Mathematics is part of the theoretical realm but forces are described as in the physical realm
- Some forces are described as ‘fictitious’!
- In order to quantify the magnitude of a force we need to measure it and so we need a well-defined measurement protocol, but none is supplied
- The language of causality is used but the concept never defined
The claim is made that a force is a Real Entity capable of causing Real Effects in the Real World. The claim is that the effects are ‘proportional to the force’ but this is like saying that flavour is ‘proportional to the apple’. Just nonsense.
A force will have an effect proportional to its numerical magnitude, but this is either a theoretical construct or a measurement result and not a physical process.
Because the magnitude and direction of a force are both important, force is a vector quantity (force vector). The SI unit of force is the newton (N), and force is often represented by the symbol F.
Force is a ‘vector quantity’ and requires arbitrary units to be quantified. This is an admission that a force is a mathematical theoretical construct and not an element of physical Reality.
The International System of Units
The newton is the unit of force in the International System of Units. Expressed in terms of SI base units, it is 1 kg⋅m/s2, the force that accelerates a mass of one kilogram at one metre per second squared. – Wikipedia
So despite physicists trying to explain that ‘forces’ are some fundamental aspect of physical reality, we find that for practical purposes, they are best expressed as simple numerical values obtained by multiplying mass by acceleration.
Newton’s famous equation is exposed, not as some wonderful insight expressing a fundamental Law of Nature, but a simple convenience equation which can be used to economise on ink.
Force = Mass x Acceleration
We were sold the idea that a ‘force’ existed somewhat independently of mass and acceleration, that we could somehow measure it empirically in order to verify the truth of Newton’s Law.
As it turns out, however, such empiric verification is neither necessary nor possible as the definition of force is completely dependent upon mass and acceleration, with the consequence that it will always be true by definition.
If an equation is always true by definition then it cannot be saying anything about Reality.
Summary
This is the sort of confused, hand-waving nonsense from physicists to which we are now becoming accustomed. They so much want to believe that they are uncovering the fundamental secrets of the Universe that all reason has abandoned them.
- Newton’s Law is merely a definition, not a Law
- The Law has little to do with Reality, being merely theoretical
- Forces are not ‘fundamental’ and not even ‘real’
- The definition of a force depends entirely upon measurements of mass and acceleration and is not independent of them
- The fundamentals of a theoretical system do not necessarily indicate a fundamental entity of physical reality
- The entire of physics should be founded upon a well-defined measurement system and not upon the imagination of physicists
- A simple theoretical definition such as this contributes nothing to our understanding of the Real World