A. Thomson's model considered the atom as a plum pudding, in which positive and negative charges were mixed together.Some students mixed up ideas coming from different models: 10% of them described Thomson's atom as a planetary model, and 3% of them stated that it had a nucleus with protons and neutrons.For example:A. It had a positive nucleus and electrons rotating around it.A. It had a positive nucleus made of protons and neutrons, and elliptical orbits on which electrons rotated.A. Definitely the conservation of energy.Probably also momentum, but I do not know why.On the other hand, 72% of students used both the conservation laws for explaining the Compton effect.It is interesting to note how, for many students, the photoelectric effect and the Compton effect are seen as two completely distinct phenomena: in the photoelectric effect the photon is in fact "absorbed" by the electron (43%), while in the Compton effect the electron is "bumped and pushed away" by the photon (49%).17% of students recalled the fact that, dealing with photons, the relativistic formulas must be used, while 21% of them highlighted that the photon must be considered as a small material body.A. The photons, colliding with the electrons, behave like small material bodies, and for this reason both momentum and energy are conserved in the collision. Moreover, several students (51%) referred to the quantization of energy:A. In the photoelectric effect and in the Compton effect, Planck's hypothesis and the conservation of momentum and energy are used.No students described the two effects as the same phenomenon, at different energy values.Teachers' answers 22% of teachers used both the conservations laws for the photoelectric effect, compared to 88% for the Compton effect, in line with the percentages related to textbooks.Only 9% of teachers focused on the difference in energy between the two phenomena:A. The principle of conservation of energy and momentum are requested in both (as in all elastic collisions).The only difference is the energy involved in the two phenomena.A. The energy involved in the Compton effect is higher than the one involved in the photoelectric effect.Only 4 people recalled the aspects related to the three-bodies problem:A. Considering both the conservation of energy and the conservation of momentum, it turns out, at some point, that the equations are incompatible unless the energy is zero (there would be no interaction!).And this is because we have three bodies and not two: namely, the photon, the electron, and the metal.In addition to this, 15% of teachers mentioned the quantisation of energy:A. For both the phenomena, the quantisation of energy introduced by Planck is required.
A. Thomson's model considered the atom as a plum pudding, in which positive and negative charges were mixed together.Some students mixed up ideas coming from different models: 10% of them described Thomson's atom as a planetary model, and 3% of them stated that it had a nucleus with protons and neutrons.For example:A. It had a positive nucleus and electrons rotating around it.A. It had a positive nucleus made of protons and neutrons, and elliptical orbits on which electrons rotated.A. Definitely the conservation of energy.Probably also momentum, but I do not know why.On the other hand, 72% of students used both the conservation laws for explaining the Compton effect.It is interesting to note how, for many students, the photoelectric effect and the Compton effect are seen as two completely distinct phenomena: in the photoelectric effect the photon is in fact "absorbed" by the electron (43%), while in the Compton effect the electron is "bumped and pushed away" by the photon (49%).17% of students recalled the fact that, dealing with photons, the relativistic formulas must be used, while 21% of them highlighted that the photon must be considered as a small material body.A. The photons, colliding with the electrons, behave like small material bodies, and for this reason both momentum and energy are conserved in the collision. Moreover, several students (51%) referred to the quantization of energy:A. In the photoelectric effect and in the Compton effect, Planck's hypothesis and the conservation of momentum and energy are used.No students described the two effects as the same phenomenon, at different energy values.Teachers' answers 22% of teachers used both the conservations laws for the photoelectric effect, compared to 88% for the Compton effect, in line with the percentages related to textbooks.Only 9% of teachers focused on the difference in energy between the two phenomena:A. The principle of conservation of energy and momentum are requested in both (as in all elastic collisions).The only difference is the energy involved in the two phenomena.A. The energy involved in the Compton effect is higher than the one involved in the photoelectric effect.Only 4 people recalled the aspects related to the three-bodies problem:A. Considering both the conservation of energy and the conservation of momentum, it turns out, at some point, that the equations are incompatible unless the energy is zero (there would be no interaction!).And this is because we have three bodies and not two: namely, the photon, the electron, and the metal.In addition to this, 15% of teachers mentioned the quantisation of energy:A. For both the phenomena, the quantisation of energy introduced by Planck is required.
In 1897, Thomson demonstrated that cathode rays (observed to be emitted from the cathodes of vacuum tubes) were in fact charged particles which he called electrons. Thomson proposed that the atom consisted of a positively charged sphere in which were embedded negatively charged electrons. Rutherford subsequently found in 1911 that the electrons orbited at some distance from a central positively charged nucleus. Rutherford proposed that electrostatic attraction between the nucleus and the electron was balanced by the centrifugal force arising from the orbital motion. However, if this were the case, then the electrons (being accelerated inwards towards the center of rotation) would continuously radiate all their energy as electromagnetic waves and very quickly fall into the nucleus. In 1913, Bohr postulated two important additions to Rutherford’s theory of atomic structure: 1. Electrons can orbit the nucleus in what are called stationary states in which no emission of radiation occurs and in which the angular momentum L is constrained to have values: 2. Electrons can make transitions from one state to another accompanied by the emission or absorption of a single photon of energy E = hf thus leading to absorption and emission spectra.
Chapter I The origins of quantum physics I The Compton effect — a strange dichotomy in the nature of electromagnetic radiation In a series of experiments conducted between 1919 and 1923, Arthur Holly Compton (Figure 1.1) investigated the scattering of monochromatic (single-wavelength) X-rays from graphite targets. He found that the radiation scattered at an angle 0 to the incident beam contained, in addition to radiation of the same wavelength as the incident radiation, a second component with a considerably longer wavelength. The existence of this second component in the scattered radiation could not be explained by the well-established theory of the scattering of electromagnetic waves by electrons. Compton considered instead the process illustrated in Figure 1.2, in which a particle of electromagnetic radiation, collides with a slow moving electron, which then recoils absorbing some of the X-ray particle’s energy. Treating the process as a collision between particles, and using only the (relativistic) conservation laws of energy and momentum, Compton was able to account for the effect completely. However, at the same time, in the same experiment, Compton was using interference effects, depending wholly on the wave model, in order to determine the wavelength of the scattered radiation. So here was an experiment which apparently required the simultaneous use of both the wave and particle models of electromagnetic radiation for the interpretation of the results! The existence of this strange dichotomy in the nature of electromagnetic radiation was just one indication of the need for a radical revision of views regarding the physical world.
The idea of the photon has stirred the imaginations of physicists ever since 1905 when Einstein originally proposed the use of light quanta to explain the photoelectric effect. This concept is formalized in the quantum theory of radiation, which has had unfailing success in explaining the interaction of electromagnetic radiation with matter, seemingly limited only by the ability of physicists to perform the indicated calculations. Nevertheless, it has its conceptual problems—various infinities and frequent misinterpretations. Consequently an increasing number of workers are asking, “to what extent is the quantized field really necessary and useful?” In fact the experimental results of the photoelectric effect were explained by G. Wentzel in 1927 without the quantum theory of radiation. Similarly most electro-optic phenomena such as stimulated emission, reaction of the emitted field on the emitting atom, resonance fluorescence, and so on, do not require the quantization of the field for their explanation. As we will see, these processes can all be quantitatively explained and physically understood in terms of the semiclassical theory of the matter–field interaction in which the electric field is treated classically while the atoms obey the laws of quantum mechanics. The quantized field is fundamentally required for accurate descriptions of certain processes involving fluctuations in the electromagnetic field: for example, spontaneous emission, the Lamb shift, the anomalous magnetic moment of the electron, and certain aspects of blackbody radiation. (The Compton effect also fits here, but see later under references 8b and c.) Here we will outline how the photon concept originated and developed, where it is not required and is often misused, and finally where it plays an essential role in the understanding of physical phenomena. In our discussion we will attempt to give a logically consistent definition of the word “photon”—a statement far more necessary than one might think, for so many contradictory uses exist of this elusive beast. In particular consider the original coining of the word by G. N. Lewis: “[because it appears to spend] only a minute fraction of its existence as a carrier of radiant energy, while the rest of the time it remains an important structural element within the atom…, I therefore take the liberty of proposing for this hypothetical new atom which is not light but plays an essential part in every process of radiation, the name photon!” (our exclamation point). Clearly the present usage of the word is very different.
The description of the physical and chemical properties of matter is a central issue that has occupied the minds of scientists since the age of the ancient Greeks. In their route to dissect matter down to what cannot be divided any further, they coined the term atom , the indivisible . Matter became then a collection of atoms. More than twenty centuries had to pass until the development of a more precise concept of atom, thanks, amongst others, to the systematic studies of Mendeleyev and the establishment in 1869 of the periodic table of the elements (Mendeleyev, 1869). The discovery of the electron in 1897 and the first modern model of the atomic structure by Sir Joseph Thomson were soon refined by his student, Sir Ernest Rutherford, who in 1910 showed that an atom was made of a positively charged small nucleus and a number of negatively charged electrons that neutralize the nuclear charge. Much in the spirit of planetary systems, and drawing from the analogy between gravitational and electrostatic interactions, scientists in the beginning of the twentieth century built an image of the atom that consisted of a number Z of electrons – of elementary charge – e – orbiting around the nucleus of charge Ze . A number of experimental observations, though, were incompatible with this idea of orbiting electrons. In particular, according to the successful electromagnetic theory, charged electrons in orbital (radially accelerated) motion should radiate energy, thus decelerating and eventually collapsing onto the nucleus. Clearly, such a picture would imply that matter is essentially unstable, in flagrant contradiction with our everyday experience of the very existence of matter.
This short note proposes that the conserved substance of physics is action, not energy. Energy conservation is, by Noether's theorem, the exact statement of a uniform flow of time — an assumption that fails, even if only slightly, in a relativistic universe where clocks run at different rates in different places. Read the other way, Planck's relation becomes a conservation law rather than an empirical input: Eτ = h, one quantum of action processed per cycle of a local resonance, with ordinary energy conservation recovered as the special case in which the period τ is held fixed. The note carries exactly one assumption beyond the algebra, stated plainly rather than smuggled in: the vacuum is a medium of such resonances, and a particle is a persistent, self-closing cycle within it. Angle and capacity The invariant has two faces. The law pins the magnitude at h — the capacity — leaving the accumulated phase φ as the only freedom: dS = ℏ dφ. Every familiar conjugate pair is this one statement read along a different axis of advance — energy against time, momentum against position, angular momentum against orientation — three orthogonal accounts of one accumulating phase, each closing one unit of capacity per cycle: Eτ = h, pλ = h, L·2π = h. This split is where classical and quantum mechanics part ways. An open trajectory reads the phase continuously, and its stationary-phase condition is the principle of least action; a closed resonance can only count whole turns, and closure quantises. Quantisation is a property of closure, not a property of the phase — the boundary between classical and quantum is a change of topology, not a change of law. What follows mechanically From the capacity law alone, with no further postulate, three familiar structures are recovered. A resonance at rest turns at the Compton frequency ωC = mc²/ℏ, so that one full turn spends exactly one quantum, EτC = h: mass is nothing but a resonance's cycling rate. Driven through the medium, a resonance meets an increased flux that scales as the Lorentz factor; conserving its fixed action budget under that load forces its geometry to yield — contraction along the direction of motion, dilation of its internal period — recovering special relativity as mechanical equilibration rather than a postulate about coordinates, with no rest frame ever exposed because the same yielding that would reveal one also defines the observer's own rulers and clocks. Requiring the accumulated phase along a worldline to stay coherent, expanded in the weak-field limit, returns the classical Lagrangian directly, −Mc²dτ = (T − V − Mc²)dt: least action is not minimised as a primitive rule, it is what capacity conservation looks like when a resonance crosses a gradient of the medium. And the Heisenberg relation σxσp ≥ ℏ/2 is read as the ordinary bandwidth (Gabor) theorem for a wave and its Fourier transform — a floor on occupancy for a phase-locked resonance, not a ceiling on knowledge. Gravity, without a graviton The most interpretive claim in the note, flagged as such throughout: if the metric's invariant is Eτ = h rather than a fixed energy, the metric carries no absolute clock, and the phase-lock condition forces its temporal and spatial responses to be reciprocal, giving the bipolar exponential line element ds² = −e−2ξc²dt² + e+2ξdx². The conceptual point is what this reframes: the decades-long search for a quantum theory of gravity has sought a graviton by quantising the metric on a fixed background, when gravity is the background. On this reading there is no separate field to quantise — the medium's deformation is already quantised at h per cycle, and gravity is simply the shape of phase accumulation across its gradient. The problem is not solved so much as dissolved: relocated from “how do we quantise the metric” to “the metric was never a separate thing to quantise.” Scope The note is deliberately bounded, and says so explicitly rather than leaving the boundary implicit. It derives special relativity, the principle of least action, and the bandwidth reading of the uncertainty relation from the capacity law alone; it advances the gravitational reading as a stance to be tested against its consequences, not a completed theory. It does not derive the particle spectrum, specific masses, electric charge, colour, or the numerical values of G or α, and makes no cosmological claim. This separation is intentional: a conservation principle should be judged on its own terms. A companion note reports a closed-form numerical identity for the proton mass as a separate, independent empirical fact; the two are meant to be read, and to stand or fall, apart.
Classical mechanics, which gives a fairly accurate description of large systems (e.g., solar system) as also of mechanical systems in our every day life, however, breaks down when applied to small (microscopic) systems such as molecules, atoms and nuclei. For example, (1) classical mechanics cannot even explain why the atoms are stable at all. A classical atom with electrons moving in circular or elliptic orbits around the nucleus would continuously radiate energy in the form of electromagnetic radiation because an accelerated charge does radiate energy. As a result the radius of the orbit would become smaller and smaller, resulting in instability of the atom. On the other hand, the atoms are found to be remarkably stable in practice. (2) Another fact of observation that classical mechanics fails to explain is wave particle duality in radiation as well as in material particles. It is well known that light exhibits the phenomena of interference, diffraction and polarization which can be easily understood on the basis of wave aspect of radiation. But light also exhibits the phenomena of photo-electric effect, Compton effect and Raman effect which can only be understood in terms of corpuscular or quantum aspect of radiation. The dual behavior of light, or radiation cannot be consistently understood on the basis of classical concepts alone or explained away by saying that light behaves as wave or particle depending on the kind of experiment we do with it (complementarity). Moreover, a beam of material particles, like electrons and neutrons, demonstrates wave-like properties (e.g., diffraction). A brief outline of phenomena that require quantum mechanics for their understanding follows.