The Idea of Energy
If arriving at this page from an earlier link, this discussion is primarily an exploration of the idea of energy rather than an attempt to formulate a new speculative proposal. However, we might still question what we really understand by the word ‘energy’ especially as it seems to have been a concept that was not totally clear to one of the most respected physicists of the 20^{th} century:
'Energy is not something perceptible, but a quantity that is calculated using a set of rules. The concept of energy remains open to future modification and, in effect, I can't say what energy is, I simply know how to calculate it effects’. Richard Feynman
This said, while there may be some ambiguity on the fundamental description of energy, we appear confident enough to talk about its effects and assign names to its many perceived forms. However, given the somewhat general scope of this discussion, we shall try to limits the discussion to just its most fundamental forms, e.g.
[1]
Based on [1], we can see that our idea of energy is closely linked to the fundamental unit of mass, although we might also question what is really understood by the label of ‘mass’. As suggested earlier, many speculative proposals only challenge some of the details of an accepted theory, whereas any questioning of the idea of energy might also suggest some questioning of the most fundamental concepts in physics, i.e. the very quantities used to described the dynamics of the physical universe. From a classical starting point rooted in the MKS system of units, we might cite 4 basic quantities:
- Time - seconds
- Length -metres
- Mass - kilograms
- Charge -coulombs
However, developments in quantum mechanics that subsequently led to quantum field theory might appear to ultimately question the idea of any form of mass particle beyond its mathematical description as a point particle. If so, this might also bring into question the common description of charge, as a property normally associated with a particle, e.g. electron or proton, where charge might simply be described as another manifestation of potential energy in space.
But what implications follow if we try to remove the idea of mass?
Well, at one level, we might initially consider Einstein’s mass-energy equation, e.g. E=mc^{2}, which is used in [1] as the definition of rest mass energy, i.e. m=E/c^{2}. Of course, negating the idea of mass quickly runs into the problem in that energy appears to always be defined in term of mass:
[2]
Again, in [2], we have an example of the preference of Western culture to label things with a noun, e.g. a Joule. Of course, it might be argued that this is simply a convention to honour famous scientists of the past, but clearly energy might be more analogous to a process and therefore more suited to the verb-orientated languages of Eastern cultures. However, putting the issue of semantics to one side, it is unclear that the implied definition in [2] helps us to quantify energy, if mass [m] is no longer a valid concept at the most fundamental level of reality. However, being persistent, we might consider Planck’s frequency-energy equation, e.g. E=hf, as an alternative definition in which energy exists in some form of a waveform with an associated frequency [f]. However, again, examination of the standard units involved only appears to lead us back to energy being defined in terms of mass:
[3]
Note: See discussion entitled 'A Matter of Semantics' that attempts consider the idea of energy within the context of a wave model. Within this model, a point in space is defined in terms of a quantum harmonic oscillator that support both potential and kinetic energy. Later, in equations [4] and [5], there is the suggestion that the Planck constant [h] might simply be masking some of its real physical attributes.
While it might appear that we are going in circles at this point, it does highlight an anomaly as to why the definition of energy is predicated on mass, even when it is described as existing in the form of radiation. For example, if we describe this radiation propagating at light speed [c] through a vacuum, special relativity would prevent the inclusion of any rest mass. Of course, we might have to consider the argument that radiation acquires a form of kinetic mass by virtue of a relativistic propagation speed, such that we might have to consider the relativistic energy equation:
[4]
In [4], we see the expansion of the momentum quantity [p=mv], which then requires the use of the subscripts [m_{0}, m_{K}] to distinguish between the idea of some sort of rest mass [m_{0}] and the notion of an implied kinetic mass [m_{K}]. Normally, the form of [4] is used to described a particle with some rest mass [m_{0}], which has a velocity [v] that can only approach, but never equal [c]. In this case, we might generalise the relationship between the rest mass [m_{0}] and it kinetic mass [m_{K}] as follows:
[5]
However, in the case of radiation, [4] collapses to a different form because there is no rest mass [m_{0}] and [v] must equal [c], such that we will need another approach to define the initial idea of kinetic mass [m_{K}] associated with radiation [E=hf]:
[6]
However, by referencing [3], we see that the inclusion of Planck’s constant [h] will once again only return us to an energy definition based on mass [kg]; although we might glimpse the idea that energy, even when described in terms of a radiation frequency [f], has an attribute that can be likened to mass. If so, it might be argued that mass is an emergent property of energy, not the other way round, such that mass cannot really be used within the basic definition of energy. This said, it would seem we are not getting anywhere with this approach, as a description of energy predicated on an underlying conceptual mass [kg] appears to be deeply rooted into the accepted scientific paradigm. Therefore, let us simply consider a speculative idea in which we redefine the original list of 4 fundamental quantities as follows:
- Time - seconds
- Length -metres
- Energy - joules
For the moment, we will just put the idea of charge on the back-burner, until we qualify some of the arguments behind the revised list above in which energy is simply assigned units of Joules, although this label-name may infer no obvious physical meaning. Within the scope of this speculation, we might start with a visualisation that space and time, as previously discussed, simply provide the physical stage on which all events play out, while within this analogy, energy will be the source of any drama. In this context, we shall initially assume that time is subject to the arrow of time, as defined by thermodynamics, while the basic idea of length provides us with the fundamental measure of space, i.e. the metre, plus the concept of area, i.e. metres^{2}, which in practical terms can only be physically realised within the construct of a 3-dimensional volume of space, i.e. metre^{3}. As such, we shall defer any notion of n-dimensional space until required and proceed with the idea of a ‘stage’ defined in terms of 3-dimensional space plus time. On this stage, we now introduce the idea of energy defined only in terms of its SI unit of a Joule, as per [2], in order to avoid any inference of mass.
But how can we now describe the nature of energy?
At this point, we might simply re-affirm the accepted description of energy as a scalar quantity, but in order to describe the idea of a particle with rest mass, its associated energy would have to be confined within some defined volume of space, i.e. length^{3}. In this context, we would always end up with a description of an energy-density:
[7]
Let us just stop at this point to consider the speculative idea that energy, as a scalar quantity, cannot be defined in terms of any of the previous equations because it is analogous to trying to define length in terms of velocity and then having to argue that velocity is a fundamental quantity, i.e.
[8]
While both equations in [8] are mechanically consistent, only (a) describes the fundamental relationship, such that velocity is the composite quantity defined in terms of the rate of change in distance with time. Likewise, the initial idea of energy, as a fundamental quantity, can only be given a name, as it is not really a composite of any other quantity with the possible caveat that the existence of energy can normally only be realised within some finite volume of space, i.e. as an energy-density.
Note: It might be argued that all manifestations of energy have to ultimately be traced back to potential energy, which can be then converted into kinetic energy of motion.
So how would the kinematics of a system be described in this model?
First of all, let us try to put the scope of the current speculation into some focus. There is no suggestion that the classical description of particles has to be generally abandoned, other than at the most fundamental level of reality. As such, this speculative idea still has to conform to all the experimental verification of Newtonian mechanics at some appropriate scale. However, we might now be a little more descriptive about our idea of the mass of some given particle in terms of the volume of space it occupies:
[9]
In terms of [9], what we normally describe as a particle essentially aligns to an energy-density, which usually has a perceived geometry, e.g. radius [r], which helps define its volume. In the case of radiation, this geometry may not appear to exist as per a particle, although we might still be able to detect a heated plasma as a manifestation of energy within a given volume.
But what is the source of the dynamics within such a description?
The idea of some minimum potential energy state might be described as a general concept, originally developed within classical physics, but which might be extended to all systems irrespective of size. As a very broad generalisation, we are simply describing the ‘tendency’ of a system to converge towards some definition of its minimum potential energy due to the 2^{nd} law of thermodynamics, which states that the entropy of a system will be a maximum when energy is in equilibrium. As such, any variation in the energy-density within any given volume of space is a potential source of dynamic change given the ‘tendency’ of energy to ‘flow’ into some lower energy-density state.
Doesn’t the ‘flow’ of scalar energy still require a mechanism to move in space and time?
If we return to the classical description of energy, the dynamics of a system are often described using the concept of a ‘force’ that might be simply quantified as a rate of change of energy [dE] with distance [dx]:
[10]
However, the general definition of a force in [10] has been extended to include Newton’s 2^{nd} law of motion plus Newton’s gravitational law, both of which are expressed in a form requiring mass. What ‘flows’ from the equations in [10] is the idea that a change in energy can manifest itself as a force, however, because the conservation of energy does not allow energy to be destroyed, only converted into another form, we might qualify this description with the following equations:
[11]
At this point, it might be useful to give a very fundamental example of [10] and [11] in action. Within a conceptually empty volume of space, a particle of mass [m_{2}] is so far from a huge mass [m_{1}], e.g. a notional black hole, that the ‘force’ of gravity is virtually, but not quite zero. Classically, we might describe mass [m_{1}] as a source of potential energy, which manifests itself as a force, as per [10], which causes mass [m_{2}] to start accelerating [a=g] towards it. In so doing, mass [m_{2}] acquires kinetic energy, although the total energy is conserved at the expense of potential energy, as per [11]. In this example, the particle [m_{2}] would ultimately disappear behind the event horizon of the black hole, where the acquired kinetic energy would be ‘absorbed’ as an increase in gravitational potential of the black hole, which would also result in a miniscule increase in its Schwarzschild radius.
But does this description really help explain the mechanisms at work?
While the basic form of [10] and [11] allow calculations to be performed, which is often enough for the ‘shut-up and calculate’ school of thought, we seem to have once again ended up with a description rooted in the idea of mass, which possibly has no substance at the lowest level of reality. Of course, at this point, we might switch to the description of general relativity in which we can replace the idea of a potential gravitational field extending out towards spatial infinity with the idea that space around the black hole being subject to a gravitational curvature, such that the particle might be described as effectively rolling down hill towards the black hole; although we might still ask:
What causes the particle to roll ‘down-hill’?
At this point, we appear to have ended up with various descriptions based on different semantics, i.e. forces and spacetime curvature, both somewhat dependent on the idea of mass. So while the existing equations are able to make predictions about some future state of the system, they do not necessarily give us a clear or even rational explanation of the mechanics at work.
So what alternatives might exist?
If we return to the basic premise that mass does not exist at the most fundamental level, there may only be one physical mechanism that is able to transport energy from one point in space-time to another, i.e. a wave, driven by some sort of energy-density gradient. Purely from a general descriptive perspective, it can be argued that any basic wave description also provides an efficient mechanism for spatially distributing an excess of potential energy originally confined within some smaller region, i.e. a higher energy density. Again, the following animation is only tended as a visualisation of the distribution of energy, analogous to a pebble being drop into a pond.
So what sort of wave is actually being suggested?
While this question needs to be addressed head-on, at this stage, the scope of speculation is primarily trying to table questions, which appear to arise within the current accepted model, but do not necessarily have any obvious answer. Therefore, based on only deductive reasoning, i.e. premise leading to some conclusion, the first speculative premise being suggested is:
Ultimately any form of physical particle has to be predicated on a description of energy and not on any form of tangible mass. |
Of course, if we accept the possibility of this premise, it is clear that it may well lead to other questions related to the nature of charge and spin, which are normally described as a particle attribute. However, for now, we are simply pursuing the logic that follows from the premise above, such that we must return to the relationship in [7], i.e.
[12]
At this point, we cannot use Einstein’s rest mass energy equation, i.e. E=mc^{2}, which might therefore only leave us with Planck frequency-energy equation, i.e. E=hf; although we will now need to constrain the units of Planck’s constant to the form [h=Joules-seconds]:
[13]
Based on [13], we might speculate that the frequency associated with some waveform also reflects the energy density by virtue of Planck’s equation [E=hf], where higher frequency waves with shorter wavelength might be visualised as fitting into a smaller volume, such that the energy density would increase with frequency. However, we would also have to provide some explanation of how a waveform could be localised in space, as required by the wave-particle duality description in quantum mechanics, e.g.
- EM radiation has a particle-like nature as defined by the photon description.
- Electron particles have a wave-like nature defined by its deBroglie wavelength.
While the energy of a photon, i.e. [E=hf], is now well-established in scientific literature, we might wish to table a question about the structural volume of a photon in respect to [10]:
What volume of space does the energy of a photon occupy?
Clearly, the argument in support of [13] suggest that energy is a scalar quantity, which might only be quantified in terms of an energy-density, i.e. the energy must be contained within some given volume. However, it is not clear that science currently offers up any clear answer to the question above, which we might wish to take into consideration in any subsequent speculation.
To date, as far as is known, no photon has ever been detected in propagation, such that any measurements are only quantified in terms of some energy/momentum exchange at the target location. It might also be highlighted that not all EM waves appear to have any obvious photon behaviour. For example, radio waves never seem to show any particle-like behaviour, even though visible light is relatively close to the radio bands. Again, we might question whether the idea of a photon is simply a reflection of a desire to give names to ‘things’ we do not fully understand. |
Of course, this ambiguity does not seem to apply in the case of particles, such as electron, although we might still wish to seek some clarification even here:
Does an electron have a definite physical radius?
You might find a figure for the classical radius of the electron specified to quite remarkable accuracy, e.g. 2.8179403267(27)*10^{-15 } metres, in sources such as Wikipedia. However, examination of the assumptions supporting this figure might have to be questioned a little further in light of deBroglie’s hypothesis. Of course, if we pursue the premise that physical mass ceases to have any meaning at this scale, the idea of a fundamental particle having any physical geometry, which resembles a ball-bearing, might be questioned. With these doubts raised, let us return to the inference that all particles have some sort of wave-like nature, which we might first extrapolate in the form of the Compton wavelength [λ_{C}]:
[14]
Compton’s original experiment, in 1922, was seen as a verification of the particle-like nature of radiation, i.e. the photon, which had first been speculated in Einstein’s photoelectric effect paper of 1904. However, deBroglie’s hypothesis was trying to show the opposite, i.e. the wave-like nature of particles, albeit anchored in the same momentum [p] premise as shown in [14]:
[15]
However, it is highlighted that while the Compton wavelength is linked to the rest mass [m_{0}] energy of a particle in [14], the deBroglie wavelength is linked to only the kinetic energy of a particle with velocity [v]. As such, we could use [14] and [15] to calculate the Compton and deBroglie wavelengths of an electron, if we assume some arbitrary velocity:
[16]
For the purposes of the deBroglie calculation in [16], the velocity [v] corresponds to the ground state orbital velocity of hydrogen, as originally defined by the Bohr model in 1913. Today, the idea of this orbital velocity would be questionable, but for now, we can just assume this velocity to be some arbitrary value for comparison. Based on the figures in [16], we might also want to make some comparison of the energy associated with each wavelength on the assumption that its relationship to frequency is still quantified via a propagation velocity defined by [v=fλ]:
[17]
So based on Planck’s equation [E=hf], we might now calculate the associated rest mass energy and the kinetic energy of an electron for the velocity [v] assumed:
[18]
At this stage, we will try to avoid drawing too many conclusions from what amounts to little more than a series of speculative hypotheses, originated in the early part of the last century. However, we might realise that the velocity [v] used for the deBroglie frequency is essentially non-relativistic and therefore the relativistic energy equation in [4] might be expected to be dominated by the rest mass energy, as implied by [18]. Of course, the more challenging and speculative issue is the shape of any particle-waveform, which might explain both the Compton and deBroglie wavelengths co-existing within some wave structure.
While this discussion will not pursue this issue, other than to highlight that the form might resemble a beat wave packet, it should be noted that this waveform would have to exist in 3-dimensional space and time.
Note: See the Wave Structure of Everything for a more speculative discussion of potential 3D waveforms.
So while some of this speculation might appear questionable, the question really being tabled by this initial discussion still remains:
If the idea of mass has no meaning at the most fundamental level of reality, what physical structure or mechanism might account for the emergence of particles within the sub-atomic realm?