Today’s insight, a wave is a large sized particle with lot of empty space in-between just like a center of mass of a large number of small sized particles.

**Since I involved myself randomly into this discussion on the web and found certain interesting observations I am going to copy them and from there try to clarify the concerned matter. Indebted to Patrick Das Gupta sir for spotting my mistake and giving a good insight and thanks to Shrey for initiating the discussion. I will copy all of the discussion and follow with my insights.**

**BPP**; Patrick Das Gupta Sir, if in **photoelectric effect**, if I give the incident energy just equal to** work function** and if I don’t apply any kind of potential there to accelerate it, will the electron coming out will just float or what in practical. Also if I am in rest frame and see photoelectric effect happening in accelerated frame will I see something weird like EM wave kind of something?

**PDG**; (**Patrick Das Gupta** not **Particle Data Group**) This is a hypothetical situation. We know that in real life, the work function is not a number but a number with a small uncertainty. Similarly, the incident photon will have an energy along with an uncertainty. So, you can never have incident photon energy to be equal to the work function. As you know, **an accelerated frame is equivalent to a rest frame with gravity**. So, when you see the photon approaching the metal you will see its frequency changing with time due to gravity. (**Edited MD: since gravity strength does not compare with EM strength eg, its only conceptual perhaps?**) Also,** the work function will get modified by a small amount due to the effective gravity.**

BPP; Okay Sir, Thanks.

MD; as you know ~~in relativity energy is a Lorentz Invariant quantity~~.~~ In other words if you know energy in one frame it will be same in another frame.~~ (work function is energy) Since ~~photon’s rest mass is zero~~ (click on link why thats spurious) that means both energy and momentum will be conserved (If I am incorrect Patrick Das Gupta Sir can correct me)

PDG; Manmohan,** in special relativity energy E is not Lorentz invariant, only rest mass is Lorentz invariant.** Energy is the ~~time component~~ [Edited by MD; *rather 4th or 0th component strictly, although Physics students understand whats meant by time component because time is also 4th or 0th component*] of momentum 4-vector, and therefore it will depend on the inertial frame. For example, in my rest frame, I have no kinetic energy but only rest energy. But if you are moving with respect to me uniformly, you will see that I have both kinetic energy and rest energy. (edited by MD: no rest frame for photons)

MD; **Yes you are right I misphrased it. Energy is not Lorentz Invariant, **It will be conserved anyway.. the invariant mass will be zero for photons?

PDG; BP was talking about photons in an accelerated frame, i.e. non-inertial frame. ~~Special relativity is not applicable in such (non-inertial) frames~~. (isn’t strictly correct actually, edited by MD)

MD; Of-course. As you said through **Principle of Equivalence** effects of gravity/acceleration will show up. But from an inertial frame still the problem can be considered and added amount of energy due to accelerated frames has to be considered that would not invalidate Special theory.

[ [… text …] added later; **Just like in classical physics noninertialness is accommodated by considering Pseudo forces eg Coriolis and Centrifugal forces etc. ** See this: Once we go from the idea of noninertialness that is acceleration or force we have energy.** Energy is additive, Hamiltonian and Lagrangian are examples of how energy is added in two different ways to solve all Physical problems,** so jumping from Kinetic energy to potential energy we have total energy H or their difference L, then also we jump from inertial frame (constant Kinetic Energy) to non-inertial frame in the exact same way (non-inertial: constant KE + acceleration, acceleration is **by principle of equivalence** potential energy or force or added form of energy, one can define a constant interval in which the speed is constant and then integrate in any case Principle of Equivalence is equivalence of KE and PE from which follows all other principle of equivalence in Physics such as: x and t, E and B, mass and E etc. So Energy Conservation and PoE are related, breaking of one will invalidate all of Physics, I have proved PoE from Equation of motion, in a couple of lengthy articles, last summer. ]

**The tricky part is invariant mass**. The invariant mass of one photon is zero hence energy and momentum will be equal and conserved. But when there are more particles the invariant mass is not zero. Hence **energy is excessive to momentum**. This is important since this has significance to Quantum Mechanics .. Because whether the particle or wave nature of photon is applicable will be decisive depends on the intensity of photon. If flux of photon is feeble in other words **E=h.nu is small then particle nature is OK**. That means invariant mass will be (actually **can be**) zero. But if the intensity is very high they will come very fast and wave nature becomes imminent hence invariant mass is no longer zero. In any case the quantum mechanical nature is due. In case of wave nature being applicable the interference between different waves will adjust the frequency and this is in line with** invariant mass being non zero** since the momentum will be adding before invariant mass is defined (determined) hence non zero invariant mass. That means everything is consistent with the empirically observed equation of Einstein where if we know the energy of incident photons after accounting for work function the rest is going towards KE+rest-mass of electrons. !!

**Slight more clarfn: KE already has rest mass in it.**

This is remarkable since this says “**Quantum Mechanics even if it was known later to Relativity was decisive in the formulation of Invariant mass**, Relativity paved the way for Quantum Mechanics by adding,** properly**, the energy and momentum. **Momentum of each particle got added first** before they were subtracted from the** sum of energy (**or** invariant mass** =** **square** of sum of energy** minus square** of sum of momenta)** This was like addition of amplitude”

Physicists especially Einstein did not know Quantum Mechanics (while formulating Relativity) and in-fact A. E. did not believe for long time that its true but he formulated Relativity in a way it welcomed Quantum Mechanics.

It is clear therefore from this analysis that the **wave-particle duality is but different segment of energy-spectrum**. The lower end of energy leads to particle behavior and the higher end due to** interference of many particles** leads to wave behavior. So Photo Electric Effect was the seed of quantum mechanics …

This is the **reason why photon is quantum of em wave** because the em waves are waves of electric field and magnetic fields hence (waves of) the corresponding **forces which therefore give you momentum vectors**. (momentum gets added before squared and subtracted from same of energy, that means its the amplitude of EM waves that decide the invariant mass of photon and hence its size) If mass of photon were not zero this was not possible (the lower end of **amplitude/force/energy/field/E/B** ) and higher end of **amplitude/force/energy/field/E/B** is due to large number of photons which act like wave when interfere (from center of mass of many photons the total size of the photon behave like a wave of particles, **invariance mass of a large number or actually even of two particles is not zero anymore, it gradually increases hence behaves like a large sized particle or wave**) . *Whats size of a particle? Read in the end.*

I just had the insight that **mass of photon is necessarily zero due to Quantum Mechanics and not Relativity alone** (in Relativity alone what was its mass?). Actually the fact that **invariance mass of a single particle could be zero** (in Relativity)** leads to Quantum Mechanics.** Because even if one particle has an invariant mass zero, many particle would add up (like wave amplitudes) and not have a zero invariant mass. Once it is **not zero invariant mass** it means its a wave because there is interference (and extension or size which is dynamically changing). Hence Relativity leads to Quantum Mechanics this way. (any particle that satisfies both wave and particle nature therefore qualifies as a quantum of that force or as is called the force carrier of that force) So Graviton is also hypothesized to be a zero mass because it carries a wave to infinite distance. But~~ gluons~~ and other bosons as force carrier **do not have zero mass** as they do not have to carry the wave to infinite distance. Their invariance mass is not zero and thats no problem to having interference (**so I do not understand this paradox yet as such, how robust is unification: one is mass-less, others are not but they are all short range, these latter bosons**)

I confused myself when I said ~~Gluons do not have zero mas~~s as they do not traverse infinite distance, so I did not publish it here and searched and I see that gluons indeed have zero mass, but its a nuclear range force which is carried by gluons. **Whats up with Physics?** In that case my above analysis that a particle having zero invariance mass is a good qualifier to quantumization (or quantization) of a force is valid. The only that remains is then weak force as its carrier is not zero mass. That means it (any of weak bosons) should not show particle behavior in consistency with all 3 other as per Relativity and Quantum Mechanics !!

Eureka !! **Any particle will be a zero mass iff its energy is arbitrarily small**. If not (energy arbitrarily small) it can have a larger/nonzero mass .. It may be necessary for its infinite range transmission that masses be zero but is not sufficient. **In other words particles with zero mass may not transmit to infinite distance.** In any case the fact that particles can be blessed with arbitrarily small energy (lower end of energy spectrum) and larger energy (or wider spectrum therefore in all total ) is the cause why there is Quantum Mechanics. (eg black-body spectrum) Because then it can behave both as particles and waves (small end of energy spectrum leads to particle behavior and ” larger energy ” leads to** both wave and particle behavior**)

What I am saying is what we are observing is whats happening in nature but there are some erroneous conclusions we are drawing from what we are observing. (which is apart from what I am explaining here, which I do not think any one has explained so far and for sure I was never taught, Physics isn’t taught often very well) example of erroneous: A zero mass particle is a long range (infinite range force) and the reasoning is given by Uncertainty Principle (I think the text Perkins? and Nuclear Physics Wong?) I think something like Uncertainty Principle which describes pretty much everything we observe in Quantum Mechanics is kind of heuristics and empirical. Its mathematical apparatus is theoretical and comprehensively taught in all text books and world wide famous even through all sorts of cartoons. (eg of Heisenberg and Schrodinger) But recently I am hitting upon some discrepancies, since I haven’t made sure of everything I am not unto talking much about them, let alone publishing them. And there are many other pending Physics work that needs to be finished. I don’t think these new findings of min will contradict anything that we know popularly but will shed light how loosely sometimes we do Physics that the perhaps it only hinges on a condition like **“necessary and sufficiency logic of mathematics “** just like the one I am citing here: zero mass is not sufficient for infinite range transmission, the reverse is valid in case of zero mass but its necessity will be clear if we find gravitons as reality of nature. So for now the only example for the latter case of infinite-transmission range with zero mass carrier quantum is EM force. The gravity force hasn’t shown any experimental evidence of its “**hypothesized**“quantum Graviton. Similarly perhaps the uncertainty principle hinges on necessity of non-Commutation but non-commutation does not suffice to stand in favor of Uncertainty relation. (Uncertainty can come from two commuting operators if they are physically dependent/correlated? eg **energy and speed will share an amount of uncertainty with time?** In other words due to energy-time there is also speed-time hence speed-distance etc uncertainty? But the later variables are commuting?)

Apart from the analogy what I am actually mentioning here is uncertainty relation is not enough to draw all sorts of conclusions that are merely experimental, eg I had written one article why we find arbitrary values for lifetimes of elementary particles through observation/experiment and why uncertainty relation is about uncertainty on that rather than the mean value of such life time. (which is why the life time and range of force that was based on such might be erroneous, it just has to be corroborated by what we observe experimentally in case of EM force it is, the only other example which is still open is Gravity Force, Strong Force is closed?)

Well Weak force is closed but it does not have a zero mass carrier. So as I explained that means its going to show both wave and particle character and qualifies as a carrier quantum. But the particle nature corresponds to a large size (invariant mass) of the** force/particle**. The wave is due to interference of more than one particle hence even bigger extension (**center of mass of invariance masses**) and also the** interference therefrom**.

Thats the whole idea of the size of a particle. Consider nature/universe like a big sugarcane machine or a grinder of sorts of any kind of fruits. It goes on grinding/chopping and produces all sized grains, particles, juices, drops, droplets whatever. To the extent that energy or size of these can diminish we expect a variety of these. Same with nature. It goes on diminishing the energy of the system in various phenomena. That occurs through quantum mechanics or the laws and processes of the small. Sometimes it happens that the particles are alone. Sometimes they occur in large bunches. (now they are called waves if large number of particles occur, because their relative extensions and motions will keep on changing in space and time just like oscillation of anything you observe) They will occur singletons (or a second will show up either after a long time has elapsed or a long distance has been covered by the first occurrence of particle) That means the wavelength or the separation between two particles is large hence their energy and frequency of occurrence is really small. Thats what I am talking about. The processes in nature can be such that very very small or feeble amount of energy can travel and hit a scene. If energy of this bunch is small it is equivalent to being only one single particle because even two will have size-ably more energy. The moment energy is small momentum of such has to be really small. Because if one of momentum or energy is bigger the size of the particle is going to be much bigger. Its the difference between the square of the energy and the momentum which is called the size or invariant mass of the particle. So thats a Pythagorean properties. Imagine a slice of cheese thin on one side and a bit long on another probably in the shape of a triangle whose one side is longish and another smaller. In effect its bigger therefore. For any cheese slice to be really small in size both sides have to be really small so the hypotenuse or the longest side is really small. That means having arbitrarily small energy would produce single or small sized particles or waves. ( a very small chunk) But having larger energy or momentum would mean a larger invariance mass or larger chunk. The larger chunk is therefore addition of many smaller chunks but imagine them flying and floating indifferent oscillation much like snow flakes. Since their interconnectedness is now an oscillation they are called waves. So a tiny little single chunk is a small oscillation of a large part or wave whose other parts are coming on to us slowly.

The fact that zero mass particles exist simply might be a coincidence of nature, that a very small energy was produced randomly. Again since it transmitted a longer distance or infinite distance might only happen for EM force only because of the nature of phenomena. Probably we need to think more why, what are any fundamental differences between different fundamental forces.

For now Relativity and Quantum Mechanics seem to be in perfect union. Perhaps we will realize one day absolutely zero mass particles are only a mathematical ideal. Our experimental sensitivities might show us a very small and tiny yet nonzero mass for all particles. Then we will know more about how to reformulate our understanding of what lies beneath the smaller than the small. Perhaps new laws will be discovered. It will be an unified effort of phenomenology, empiricism, mathematics and experiment and fundamental physics as we know it.

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