We can consider a simple QED process, in which an electron couples to a photon. Electrons are drawn as solid lines and photons are drawn as wavy lines. If they meet at a point it is called the vertex. Four momentum is indeed conserved at fundamental vertices. And photon lines are real at this level.

In the next stage, two vertices can be joined in several different ways to describe a scattering process. For example an electron can emit a photon which is again absorbed by a second electron. Let us consider four momentum of the incoming electron as p1, the outgoing electron as p2, photon four momentum is q. Then using conservation of four momentum at the first vertex we write p1=-p2+q, in the second vertex if p3 is the four momentum of the incoming electron and p4 is the four momentum of the outgoing electron then again applying conservation of four momentum at the second vertex, we write, -p3+q=p4. For the total scattering process, however, q can be eliminated from the two equations. For the total process, conservation of four momentum becomes p1+p2=p3+p4 and q being the four momentum of the internal line, becomes a free parameter. At this stage it becomes a virtual internal line, or a propagator. Because internal lines violate conservation of four momentum at individual vertices, they can exist only for a very short duration, obeying time energy uncertainty relation.

In Physics force fields, such as the electromagnetic field (EM) have 3 properties ; they are defined everywhere, they interact with particles according to their charges and they propagate in the vacuum. This propagation is usually continuous, and on 2 dimensional spheres (the waves). This is what happen when you use your mobile phone : photons do not go from your mobile to the mobile of your correspondent. However in some circumstances discontinuities happen in this propagation, usually in the interaction with a particle (such as an electron going from one level of energy to another in an atom). The discontinuities manifests itself as a quantity which propagates along the same kind of curves as the propagation of the field, and with characteristic which are constant, as well as their energy. This is similar to shock wave in a fluid. These discontinuities, bosons, then interact with particles in a process similar to the field, but discontinuous, and usually disappear. This is a physical phenomenon, which has nothing to do with an "uncertainty principle". Experiment show that boson can have quite a long life !

Remark : in any collision between material bodies it is common to tell that the solution of the problem is given by the conservation of momentum. This is only partially exact : a simple count of the unknown variables shows that the conservation of the translational momentum does not suffice. One needs to add the conservation of rotational momentum. Which is of course a bit ackward for bosons in the relativist geometry.

Dear Biswajoy ,

Do you have any experimental evidence that free electron emit a photon and via exchanging of photons two electron interact? Don't you think that it is breaking causality principle and the conservation of energy? What is the chance that whole QED is based on wrong assertion?

At a classical level virtual photon is breaking energy conservation. We are considering QED, which is quantum electrodynamics, where though expectation values of classical observables behave classically, energy conservation/momentum conservation can be broken within the limits of Heisenberg's uncertainty principle.

Dear Bisawjoy,

Do you have any experimental evidence of verification of uncertainty principle? Are you certain that nature follows statistical average at QM level?

GS> "Do you have any experimental evidence of verification of uncertainty principle? Are you certain that nature follows statistical average at QM level?"

The uncertainty principle is not a simple measurement or staistical problem as is commonly assumed. Uncertainty and the breakdown of the conservation laws at the substructure of quantum level is a fundamental aspect of objective reality. At macroscopic (human) scale the objective reality is just a gross, averaged-out, summed-up and apparently stable superstructure of micro-level quantum uncertainty. Physics needs a revolutionary change of its epistemology - from traditional causality to dialectical materialism; to deal with this new revolutionary aspect of objective reality! The following is a copy from a comment in another forum:

[The conservation laws (of energy/mass) in physics and thermodynamics, including "Ex nihilo nihil fit" of philosophy are assumed a priori truths, but these are only valid at macroscopic scale.

Nature at quantum level is fundamentally uncertain – it is not a statistical aberration – but a fact and a phenomena ascertained by Quantum Electro Dynamics (QED). The law of the conservation of mass/energy of thermodynamics and physics breaks down at quantum level and creation “ex nihilo” is practically feasible! https://www.scientificamerican.com/article/something-from-nothing-vacuum-can-yield-flashes-of-light/

The quantum vaccum is full of ghostly "virtual particle/antiparticle pairs" that continuously pop in and out of existence and their effect on the spectral lines of atoms known as the "Lamb Shift" can be very accurately measured. This effect can also be measured as the Casimir force with much less efficiency. The "virtual particles" can become "real particles" if sufficient energy equivalent to compensate for their mass is available. There is also a finite probability that a "virtual particle" can become "real" (even without sufficient energy for mass equivalence) through a phenomena known as "quantum tunnelling".

Heisenberg’s “uncertainty principle” is not just a statistical problem as is commonly assumed; but much more than that. This fact has both scientific and philosophical foundation:

Scientific: "Are you certain Mr. Heisenberg"? https://phys.org/news/2012-01-heisenberg-deepen-quantum-uncertainty.html

https://www.nature.com/articles/nphys2194

Article Real/Virtual Exchange of Quantum Particles as a Basis for th...

Philosophical: The quantum vacuum, the "virtual particles and their transformation to "real particles" may be understood in terms of the "Being-Nothing-Becoming" of Hegel's ontological triad : "The Philosophy of Space-Time: Whence Cometh Matter and Motion?": https://www.amazon.com/Philosophy-Space-Time-Whence-Cometh-Matter/dp/984041884X

In fact it is possible that this spontaneous creation (ex nihilo) of fundamental particles from the quantum vacuum (and not through the Big Bang) is how the galaxies (along with all other things) evolve, “come into being and pass out of existence” and maintained throughout this infinite and eternal universe as asserted by dialectics: Article Ambartsumian, Arp and the Breeding Galaxies*

Dear Abdul

Please see the uncertainty principle proof in any standard QM book. It has been proven using mean and variance. Unfortunately, nature does not follows statistical rule. The existence of well defined band structure is the living testimony of determinism of nature and its electrical and magnetic properties.

About the uncertainty principle and quantum mechanics

In physics, as in many sciences, we want to know the state of a system over some period of time or area of space. The states are characterized by variables which take a value at each point. What characterizes the state is not the value at each point, but the function. Because there are infinitely many points, the variable, that is the function, is estimated by a statistical procedure from a finite number of observations. To do it one chooses a simplified version of the function depending from a finite, usually small, number of parameters. This is an observable. There is an unavoidable uncertainty due to the choice of a specification amongst many others. But, when the mathematical model meets some general conditions, one can prove that the observable has many properties. Notably the result of the measure follows a probability law which is just the well known relation between the value of the observable and the genuine value of the variable. Moreover when the system depends on time, but the choice of the origin of time is arbitrary, we have an evolution operator and the variable follows a law similar to the Schrödinger law. All these results can be proven : this is just mathematics (see my paper on Quantum Mechanics revisited). There is no assumption about the physical reality or the real world. Just the fact that any measure meeting some general conditions has specific properties similar to the "axioms of Quantum Mechanics". In Quantum Electrodynamics there are physical assumptions, notably about the photon, so this is a physical theory, of the EM field.

Of course one can blame Nature for the uncertainty of our measures : if we can only estimate finite sets of data, this is because Nature is built from finite subsets. This is more comfortable, well in line with the dominant conception of physics, and it is always rewarding to discover or invent a mystery. But the purpose of science is to find answers, not invent riddles.

Dear Jean,

If you lookup the system closely then you notice that conjugate variables can not measured together with full precision has experimental limitation. Because measuring one influence the others. This does not mean that in system both conjugate variables are not defined by nature with absolute precision . They infact defined but we can not measure due to unavoidable influence by the one conjugate variables over other. The existence of flat band at the Fermi energy level which participate in superconductivity, and the existence of well defined electrical conductivity which can be very well defined using DFT band structure are the living testimony of the determinism of the nature. The probabilistic math that scientist has developed to explain the experimental data has no final saying. Sooner or later, scientist are bound to accept that nature is fully deterministic

Dear Gokaran,

I agree with you that we must assume that Nature is deterministic, even if there are phenomena that we cannot explain presently (natural decay of nuclei with weak forces).

There is another point about simultaneity of measures,. A measure is an experiment where we use a known system to probe another system. The value of a variable is measured with respect to the known value of another variables which is used as a gauge. So actually the problem raised by Dirac never happen : we cannot measure simultaneously two unknown variables.

Gokaran Shukla , I think that you are making a too hasty judgment of my comment without considering the references I provided. The point of view I indicated in my comment has both scientific and philosophical foundation, it is just not an arbitrary opinion. The historical development of natural science itself including the recognition of evolution in Nature (both material and biological) and the quantum phenomena have collectively and inexorably shown that the dynamics of the universe and Nature at all level of existence (from the microcosm to the macrocosm) are mediated not by the determinism of cause and effect leading to a “first cause” of creation by God; but by dialectical chance and necessity.

What you are saying about determinism and “standard QM books” are but the mathematical idealism based subjective opinion of conscious or unconscious apologists of Anglo-American lead monopoly capitalism; like Einstein, Mach, Popper et al., masquerading as physics! This “science” based on the “continuous field” (“Matter is a Myth”) concept of objective reality was coined as a reactionary ruling idea after theology lost much of its appeal and after Darwin’s theory of evolution and particularly the quantum phenomena demolished all notions of certainty, determinism, causality etc. of rationalism, theology and classical materialism. This is a naïve attempt to subdue and imprison the “Evil Quanta” within the thick fluids of “continuous fields” like “spacetime”, “QF”, “Higgs” etc. ad nauseum.

In addition to the references cited above, please see my comments in two long running RG forums on Einstein’s theories of relativity, particularly the very last comment (posted few hours ago) at: https://www.researchgate.net/post/Is_Any_Effective_Refutation_of_Einsteins_Theories_of_Relativity_Possible

Some call it pseudo-particle, some virtual-particle and particle physicist call it gauge boson. What a dreadful set of names! That is just because they all are confused. Listen to me, I am not confused! Photon is not a particle but an EVENT. Event of jumpy, momentary transfer of energy between EM field and matter (or vice versa). That is all. There is no size nor path of a photon, people are confusing photons with wavepackets or light pulses, but that is NT a photon. If you "cook" a piece of matter in a soup of wavepackets, nothing needs to happen for a while. But when there is a transfer o energy between any of those packets and matter THAT is the photon. Note that, photon appears at random time and place that is why it confuses people who think of it a s a particle, and that is why they give it crazy names like pseudo-something.

Photon has dual wave/particle nature. Wave because it displays interference phenomenon, corpuscular because it displays photoelectric effect. In fact after Young's double slit experiment proved that photon has wave nature, it was settled for all and nobody raised the issue of corpuscular characteristics, until Einstein's proposal for the explanation of photo electric effect, which earned him Nobel prize in 1905.

Dear Biswajoy,

Photon does have a wave nature. EM theory is very correct. But photon is not a virtual particle. Photon does not violates conservation of energy and causality at any time and length scale.

@Gokaran Shukla, QED is generally accepted as a correct description but there are many loose ends and there remains ample room for criticism.

Gokaran Shukla

GS> "But photon is not a virtual particle. Photon does not violates conservation of energy and causality at any time and length scale."

Photons can be both real and virtual particles depending on the mass-energy content (it has some finite mass) and like other bosons are also their own anti-particles. It is possible to explain wave/particle duality of photons and other quantum entities based on their particle nature alone, Please see: Article Real/Virtual Exchange of Quantum Particles as a Basis for th...

The formulation of QED by Heisemberg’s matrix mechanics and Dirac’s incorporation of complex conjugates to accommodate fractional spin constitute its principal basis. Later positivist incorporation of the mathematical tricks of so-called “Path Integral” and “renormalization” (which Dirac never accepted, and described this practice as sweeping the dirt under the rug) by Feynman et al. were mere corruption of QED with mathematical idealism and mysticism.

The "spacetime continuous field" as the basis of objective reality formulated by Minkowski-Einstein constituted a reactionary attempt to undermine the materialist foundation of physics by incorporating mathematical idealism and to deny the quantum uncertainty in Nature. Official physics and the followers of Einstein and the positivists led by Bohr collectively hijacked quantum physics and led it to the fantasy and mystical world of mathematical idealism and has led physics to astray and to the present blind alley. Monopoly capitalism and theology are taking full advantage of this “science” by making it their "ruling idea" world wide. They are buying off the "experimental proofs" of these fantastic theories using the lure of fame, fortune and funds - "Higgs boson", "gravitational waves", "discovery of black holes" are more recent cases.

Physics has to un-learn all those mysticism and the practice of "shut-up and calculate” and must go back to its traditional materialist base, to make any progress at all. The high priest Einstein himself realized/admitted this folly near the end of his life when he wrote to his friend Michele Besso in 1954, “I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics” A. Pais, Subtle is the Lord …” The Science and the Life of Albert Einstein”, Oxford University Press, (1982) 467,

The concept of Force fields has been introduced at the end of the XIX° century to account for the electric and magnetic phenomena, and avoid the idea of action at a distance which is part of Newton's Physics. Force fields have 3 properties : they exist everywhere, they interact with material bodies, they propagate in the vacuum. Usually the processes of interaction and propagation are continuous (such as for the gravitational field) but it can happen that a discontinuity occurs. The classic case is the interaction of the EM field with an electron in an atom. The continuous process is a vibration, if the field is strong enough another equilibrium is found by the transfer of an electron on another orbit, or even an ejection of the electron. The propagation of the field in the vacuum is the process by which the field keeps its own equilibrium, the discontinuity propagates in the vacuum. This is similar to a shock wave in a medium, but, because the field propagates on 2 dimensional surfaces in the 4 dimensional universe, the discontinuities propagates along 1 dimensional lines. Moreover they keep some of their basic characteristics so they look like particles : we have a boson. Bosons can themselves interact with particles, and usually disappear in the process.

The representation of force fields by gauge fields (connections in the 4 dimensional universe) explains quite well the phenomenon and gives the characteristics of bosons.

I agree with jean claude Dutailly