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Mass is one of the most fundamental properties of matter. Nearly every scientific formula relating to matter involves mass in some way. But what is it? What causes it? And how does it relate to the whole business of Relativity?
First, we need to understand that mass acts in two quite distinctly different situations. For this reason it’s often referred to by two quite different terms: inertial mass and gravitational mass. The reason for the first is generally given in terms of the Higgs boson, whereas the latter is defined in terms of curvature of spacetime in the context of General Relativity. The reason for the relationship between these two quite different properties of mass is usually given as a need for consistency between different aspects of the physical realm - not really an explanation at all. As we’ll discover further down this article, both of these different effects are directly attributable to the same property of matter: its energy content.
Now read on …
Inertial Mass
Inertial mass is the property of matter that requires it to receive an input of energy to set it in motion or change its present speed and/or direction of motion. This basically follows Newton’s First Law of Motion: “A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force”. Newton’s Second Law expands on this: “When a body is acted upon by a force, the time rate of change of its momentum equals the force”; in simple terms, the change in kinetic energy of any object is equal to the energy input by a force (force x distance) - and kinetic energy is of course proportional to mass of the object.
This Newtonian view is a slight simplification of the fuller picture, but it’s good enough for all practical purposes at speeds below, say, 1% of light speed; it expresses pretty clearly what we mean by ‘inertial mass’.
The question then is: “What gives rise to this inertial mass, and so to the property of inertia (tendency to continue in uniform motion unless acted on by a force) in all material particles or objects?” The conventional answer is the Higgs boson, but this raises a number of other how?s and why?s, as well as adding yet another level of complexity, totally unnecessarily, to an already over-complicated scenario. The need for this bizarre concept - the Higgs field and its associated particle - evaporates as soon as we recognise that matter is itself formed from cyclic photons - spun light.
Once we see that particles are formed from loops of electromagnetic energy, cycling on the spot if a particle is static and with an added linear component if the particle is moving, then it’s obvious that this linear component could only be added by input of directed energy - a force of some sort acting for a time in the then resulting direction of motion. In the same way, change of speed and/or direction of a moving object or particle would require a change in the linear energy-flow component of that moving object; this again would require input to, and/or reduction of, the present linear energy flow component, both of which require a force acting in a particular direction for a time.
Since any particle or object requires the same amount of formative structural energy (in addition to any linear energy of motion) regardless of its velocity, it follows that the amount of linear energy required to sustain that object at any given speed will be proportional to its cyclic energy content - hence to its inertial mass.
We’ll see all this set out clearly below. First, though, a few words on gravitational mass, and how that too depends on an object’s cyclic structural energy content.
Gravitational Mass
Every particle of matter is formed from one or more photons of electromagnetic energy. Every photon exists in one of an unlimited number of polarisation states; every one of those states can be resolved into a combination of just two: right and left circular polarisation. These can be seen as the fundamental polarisation states.
It follows, then, that every particle consists of a combination of left and right circularly polarised photon energy. Evidence suggests that electric charge and gravitational effects are both artefacts of this polarisation: charge being the result of an excess of one polarisation state over the other; gravitation being a more subtle effect based on the combination of these two states.
Both of these effects will be looked at in detail in a later post. For now it’s sufficient to note that:
(a) Two particles of widely differing mass (such as proton & electron) may have equal (and possibly opposite) charges if the smaller is predominantly or totally all one state of polarisation whilst the larger is an almost-equal mix of both states (so a relatively small differential between those two states);
(b) If gravitation is an artefact of the combination of both polarisation states, i.e. all of the energy in a particle, then gravitational effect for any particle is proportional to the total energy of that particle - which is, of course, proportional to its inertial mass. So it follows that gravitational mass and inertial mass are both based on the same fundamental property of a particle or object - its energy content - so both are equal.
More on this at a later date.
Inertial Mass in action
Back in our earlier post Unlocking the Mystery of Light, we saw how the path of the energy flow forming a static particle could be likened (in simple terms) to the path of an aircraft forming vertical loops repeatedly in the same place (on a far smaller scale, of course!). We could then liken the energy-flow path of a particle in motion to the path of that same aircraft travelling linearly through the air at the same time as forming those loops - effectively a spiral path.
We then put some figures to such a situation by now modelling those two situations with a length of cord wrapped around a circular pipe: the static-particle situation is modelled by loops around the pipe being bunched tightly together, whereas the moving-particle situation is modelled by those loops passing diagonally around the pipe to form a spiral pattern: in the latter case the cord wraps linearly along the pipe at the same time as wrapping cyclically around it.
If we apply some simple maths to the cord wrapped diagonally, we see that each diagonal can be viewed as a component around the pipe and a component along the pipe which combine in accordance with Pythagoras’ theorem to give the length of one half turn of the diagonal cord. If we were to cut those half-turns and join them end-to-end, we’d get the diagonal side of a larger triangle whose horizontal side would be the total distance along the pipe and whose vertical side would be the total distance around the pipe, of all those turns.
Transferring this to the formative energy-flow of a moving particle, it follows that total linear energy-flow and total cyclic energy-flow combine in accordance with Pythagoras’ theorem to give the overall total energy-flow for that particle, over any given time interval. This translates into rates of energy flow: linearly, cyclically and overall.
This perspective matches precisely the conventional view as given in the Relativistic Energy-Momentum Relation, demonstrated countless times in the phenomenon of Compton Scattering (for which Compton won a Nobel prize). The linear (motion) wave component was confirmed by Davisson & Germer in their Nobel-winning discovery in 1927, with electrons bounced off a crystal lattice showing interference patterns typical of waveform behaviour. The cyclic (structural) component is evident from Compton scattering, which defines an associated wavelength for any material particle; this also confirms the constant amount of that structural component, whatever the speed of motion - a significant aspect of the working below.
Reaching for infinity …
In any uniform state of motion the dynamic structure of an elementary particle is self-sustaining; the electromagnetic interactions across the interior of a particle hold that structure in whatever form it happens to be – as a static particle or as a particle moving at a given speed in a given direction.
It follows, then, that the electromagnetic forces in any particle must be perfectly balanced to maintain that structure – elementary particles of matter are in general very stable. If a particle is in motion then some of its energy is ‘externalised’ as linear motion, leaving less energy in the form of cyclic flow to hold the particle together. From this we can work out some simple principles.
To balance this reduction in cyclic structural flow more energy has to be added to the total energy-flow for that particle to maintain its structure as a moving, rather than just a static, energy system - this is the energy input referred to above. Since a particle needs a fixed amount of cyclic energy flow to hold its structure, we can work out the total amount of energy flow that’s needed for a particle at any speed compared to that same particle when it’s stationary.
As its speed increases, the proportion of total energy-flow externalised as energy of motion also increases. This leaves a smaller proportion as cyclic flow to maintain structure. The total amount of energy must be increased so that this smaller proportion matches the energy content of the particle when it’s stationary.
The spiral energy flow of a particle in motion can be resolved into cyclic and linear components, corresponding to formative structural energy and energy of motion for that particle, respectively. [Note: whilst energy is a scalar quantity and so doesn’t have a direction, energy flow clearly does – as demonstrated by a laser.] The speeds of those two energy flow components can be represented as the sides of a right-angled triangle whose diagonal side represents the overall flow speed, c, of the energy that is the moving particle - see the rope-around-pipe illustration above.
[If you have difficulty visualising components, think of trying to swim straight across a river whilst the current carries you downstream: your swimming action gives a cross-stream component whilst the current gives an along-stream component; your resulting motion follows a diagonal path, across the stream and along the stream at the same time.]
We can see the linear and cyclic components of a moving light-formed particle as here:
If we’re considering the amount, not just the speed, of energy in each of these components then we need to take account of the flux density. Just as two streams may be running at exactly the same speed but one carries twice as much water per second because it’s twice as wide (or twice as deep) as the other, so the amount of energy flowing around any particle depends not only on the flow speed but also the ‘thickness’ of that energy flow.
When we’re considering the flux density of the three components of energy flow in that last triangle, the direction of flow for each component will (of course!) be the same – so a triangle showing the amounts of energy flow in each of these components, per second, will fit the same shape as that previous triangle. [Technical note: the amount of energy flow in each component, and so also in the overall energy flow, is directly proportional to the frequency of that energy flow.]
The vertical side of this triangle represents the amount of cyclic energy flow per second that gives each particle of an object its structure To ensure the stability of each particle in the object and so ensure the structural integrity of the object itself, that amount of cyclic flow per second must remain constant (as confirmed by the Compton effect).
This means that side of the triangle must remain the same length no matter what speed the object is travelling at. If the amount of cyclic flow per second changes then the electromagnetic structure-holding interactions within each particle will also change, and that’s bad news for the structural stability of those particles.
The simplest situation for an object is when there’s no motion at all, in other words when the object is static. In that case there’s no linear flow to worry about and the total energy flow is the same thing as the cyclic energy flow. This is shown by the zero-width ‘triangle’ – no linear flow – in diagram (a) below.
As the object starts moving and then begins to move faster, the linear flow component (horizontal side of the triangle) stretches the triangle. This leads to an ever-increasing total energy flow, as shown in triangles (b) and (c) below. In each of these triangles the vertical side (cyclic flow component) is the same as in diagram (a), to ensure structural stability.
Triangle (b) shows a linear flow component that’s about half the size of the total energy flow, i.e. the horizontal side of the triangle is about half the length of the diagonal side. Since both these flows are the same ‘thickness’, this means that the linear flow speed – which is the object speed – is also about half the actual full flow speed, that is, half the speed of light.
At this object speed the diagonal side of triangle (b) is about 15% longer than the vertical side. In other words, the total energy needed for an object to travel at half light-speed is about 15% more than the cyclic energy that makes up that object when it’s not moving, as shown in (a).
In the same way, triangle (c) shows the total flow for the same object travelling at about 80% of the speed of light – the linear flow (horizontal line) is about 80% of the total flow (diagonal line). At that speed the total energy needed by the object, as shown by the diagonal side of the triangle, is almost 70% more than the energy needed by the object at rest (as shown by the vertical side).
Let’s follow this pattern and see how it continues as we get significantly closer to the speed of light, right up to the point where an object’s speed of motion is on the very edge of light-speed itself.
Triangle (d) below shows the energy flows when the object is moving at 98% of the speed of light - the horizontal side (linear flow) is 98% of the length of the diagonal side (total flow). Here the total energy needed by the object works out to about five times the energy that provides the structure of the object at rest – the longest side (total flow) is about five times the length of the vertical side (cyclic flow). [Note that cyclic flow component is the same as for a, b and c.]
At 99.99% of the speed of light the base of the triangle would have to be 99.99% of the length of the diagonal side. That triangle would have a diagonal side over seventy times the length of the vertical side. I.e. the total energy flow in our object travelling at 99.99% of the speed of light would be over seventy times the energy in that same object at rest.
At 99.999999% of the speed of light, the diagonal of our triangle would be over seven thousand times the length of the vertical side. Our object would need over seven thousand times its rest-energy to achieve that speed.
For the base of our triangle to get closer and closer to the length of the diagonal, that triangle has to be made longer and longer. Unless our triangle has a height of zero - no cyclic flow - then that triangle would have to be infinitely long to get its base and its diagonal equal in length.
So we see why that object can never reach the speed of light, c, and why the energy within it increases towards infinity as it approaches that speed. As every particle’s energy always includes the vertical formative-energy flow component, the horizontal component can never be equal to the diagonal; transferring that fact to the triangles on these two pages, this means that the horizontal velocity component v – the particle’s speed through space – can never be the full energy- flow velocity c as represented by the diagonal line.
As we pump more and more energy into that particle the horizontal and diagonal lines in triangle (d) get ever longer, ever closer together – but are always held slightly apart by that vertical particle-forming energy-flow component; so the particle’s total energy rises towards infinity as its speed rises towards, but never reaches, that unattainable goal of speed c.
This also means that it takes more and more energy to gain each additional metre/second as the speed inches ever more slowly towards that elusive target: the effective mass, even of a single particle, also increases towards infinity as its speed approaches the speed of light.
And there you have it. Any material object would take an infinite amount of energy to reach light speed. And as it gets closer and closer to that speed it takes ever greater amounts of energy to increase its speed even by a tiny fraction. Whilst light itself, having no cyclic flow, has absolutely no trouble travelling at light speed.
Inertia, then, is the need to keep the same amount of cyclic energy to maintain the structure of an object whilst energy is ‘externalised’ as the linear-motion component of the object’s energy-flows. This requires an increasing input of energy to progressively increase an object’s speed; changing its velocity in any other way similarly requires appropriate energy input (or output).
So how does this fit in with the Higgs boson?
Put simply – it doesn’t.
The Higgs Field and associated Higgs boson are a proposed mechanism to deal with a rather different view of mass: resistance to changes in velocity as viewed from the perspective of Special Relativity (SR). In SR every uniform state of motion may validly be seen as a state of rest. Those ‘states of rest’ are regarded as being (hyperbolic) rotations in spacetime relative to one another.
The role of the Higgs Field, then, is to resist rotation of an object through an angle in spacetime from one inertial reference frame to another. To do this, as described by one leading physicist, it acts like a sort of ‘molasses’, holding back objects from changing their velocity. The difficulty with this is that every object in the cosmos, whatever its present speed, is held at that speed by those molasses – so those molasses have to be static relative to every state of motion in the universe at the same time. That’s quite a big ask!
The Higgs Theory is an example of a Gauge Theory, used to define the effects of forces in a universe that’s assumed to have no universal rest state. Needless to say, the maths can be pretty tricky; they’re also unnecessary if that universal rest state does exist – as pointed to by the spun-light understanding of material reality and also by the Cosmic Microwave Background.
Of course the Higgs boson is reckoned to have been found, resulting in award of the 2013 Nobel Physics Prize to Peter Higgs and François Englert. It’s true that a particle has been found that has various characteristics that the boson would have to have (though reports at the time and since have said that it has insufficient energy to do the job alone) but no evidence is known of by the author that shows this particle actually conferring mass on other matter.
The ancient Greeks, who believed that the earth was the centre of the universe, developed a convoluted system of mathematics to explain the convoluted orbits of the planets and other celestial bodies. That maths became irrelevant and the calculations became far simpler once it was realised that it was the movement of the observer that caused most of the complications in their observations.
This might just turn out to be a case of history repeating itself.
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In the next post we’ll unpack the most famous equation of all time, the equation that’s almost universally regarded as the hallmark, the definitive confirmation, of Relativity Theory. And we’ll derive it from scratch, with absolutely no reference whatsoever to Relativity Theory.
In the meantime, be sure to check out Transfinite Mind for books plus free articles and presentations.