To clarify what is meant: the authors do not really claim to violate the usual uncertainty principle, as proved in QM textbooks. They speak, rather, about a statement originally made by Heisenberg, that any measurement of one quantity induces an uncertainty in the conjugate quantity. This is something which is very hard even to formulate correctly in quantum mechanics in today's form. The authors argue that a clear formulation can be made, and that this statement is then theoretically wrong, as well as experimentally so.

None of this, emphatically, has any bearing whatever on the validity of quantum mechanics: the analysis is made in terms of quantum mechanics, and the experimental results agree fully with quantum mechanical prediction. What is shown is that some, historically important, but eventually misguided formulation of the uncertainty principle.

As a matter of record, let me state the uncertainty principle as it is stated today: take a given state and measure, say, position many times. You will get many different results. Of these you can take the average, and the variance, call the latter sigma_x^2. Then, still using the same state, repeat the same process with a measurement of momentum. Call the resulting variance sigma_p^2. Then the uncertainty principle states that

sigma_x^2*sigma_p^2 >= hbar^2/4

The crucial point is that nowhere does one state anything about ``measuring position and momentum at the same time'', or ``perturbing momentum while measuring position''. We simply make many position measurements and observe the scatter, then observe the scatter of momentum measurements on the same state, and the uncertainty principle claims that both scatters cannot be simultaneously small.

No. The Third Assumption of Science, uncertainty (It is impossible to know everything about anything, but it is possible to know more about anything) and the Fifth Assumption of Science, conservation (Matter and the motion of matter can be neither created nor destroyed) are consupponible.

For details see:

Borchardt, Glenn, 2004, The ten assumptions of science: Toward a new scientific worldview: Lincoln, NE, iUniverse, 125 p. (http://www.scientificphilosophy.com)

http://www.scientificphilosophy.com

Dear Glenn

Thank you for interesting link. I am reading your paper "The ten assumptions of science and the demise of cosmogony".

https://www.researchgate.net/publication/221706041_The_ten_assumptions_of_science_and_the_demise_of_cosmogony

I will reply your comment later, after than I finish studying your paper.

Conference Paper The ten assumptions of science and the demise of cosmogony

Well, the authors of that article do not challenge the uncertainty principle. They challenge an unfortunate formulation. Regretfully, the journalists quite often preach it that way. The is no measurement in the uncertainty principle. It holds even if nothing is measured. A wave function cannot be constructed to have precise momentum and coordinate simultaneity. End of story. 

There is another moment also. The energy conserves really only in very special cases. Yet, the energy conservation law is considered a sacred cow. With any time dependent interaction, the energy conservation law is gone. 

To clarify what is meant: the authors do not really claim to violate the usual uncertainty principle, as proved in QM textbooks. They speak, rather, about a statement originally made by Heisenberg, that any measurement of one quantity induces an uncertainty in the conjugate quantity. This is something which is very hard even to formulate correctly in quantum mechanics in today's form. The authors argue that a clear formulation can be made, and that this statement is then theoretically wrong, as well as experimentally so.

None of this, emphatically, has any bearing whatever on the validity of quantum mechanics: the analysis is made in terms of quantum mechanics, and the experimental results agree fully with quantum mechanical prediction. What is shown is that some, historically important, but eventually misguided formulation of the uncertainty principle.

As a matter of record, let me state the uncertainty principle as it is stated today: take a given state and measure, say, position many times. You will get many different results. Of these you can take the average, and the variance, call the latter sigma_x^2. Then, still using the same state, repeat the same process with a measurement of momentum. Call the resulting variance sigma_p^2. Then the uncertainty principle states that

sigma_x^2*sigma_p^2 >= hbar^2/4

The crucial point is that nowhere does one state anything about ``measuring position and momentum at the same time'', or ``perturbing momentum while measuring position''. We simply make many position measurements and observe the scatter, then observe the scatter of momentum measurements on the same state, and the uncertainty principle claims that both scatters cannot be simultaneously small.

I left unfinished the last sentence of the second paragraph: ``What is shown is that some, historically important, but eventually misguided formulation of the uncertainty principle, is to some extent incorrect. This formulation has been often used in popular presentations of QM.''

Dear Igor

There is a mystery for me about "the energy conservation law is gone. ", does it mean that energy is destroyed? From being to nothingness? Or energy decay to other physical existence?

Conservation of energy is strictly valid in systems (classical or quantum) which have time  translation symmetry.  Energy-time uncertainty is exhibited only when the Hamiltonian of the  full quantum system is time dependent, like in the case of two quantum systems interacting for a finite time or an atom interacting with the vacuum fluctuations that causes transition from an excited state to the ground state.  Hence, there is no conflict between this uncertainty and energy conservation.

Dear F. Leyvraz

"You will get many different results." I think this is not only true for subatomic particles, also the measure the length and width of the room is probably true. Am I wrong?

Dear Hossein, this means that the system is no more closed and can exchange energy with other systems, which are usually not specified. Thermodynamics has notions of work and heat. Quantum mechanics does not usually use them. If, for example, the quantum mechanical system is in the field that changes periodically in time, it can absorb energy from the field or give it to the field (here come lasers). The energy is not conserved any more.

The energy conservation law is defined for the system that stays in the same state infinitely long. Noether's theorem demands the uniformity of time. 

Another point. The system does not have to be in a state that is the eigenstate of the Hamiltonian. It could be in the superposition of such states. Such system has only the average energy.

Dear Hossein!

Your tought cannot be denied. But the uncertainty principle is a consequence of the quantum mechanics from the times of Heisenberg.  Mechanical objects (this comprises a very high amount of particles in fixed compound) have a certain and measurable amount of energy. Observeations and measurings do not modify the energy (as a rule).

Always atoms or molecules of gases shows energy distribution resp. variable internal energy. The energy of a gas-particle is not exactly defined and it change every moment by collisions. Just the same as the smaller particles of the microcosm, but their interactions are more different. Basically the β-spectrum is the consequence of variable internal energy resp. the uncertainty principle. Furthermore any observeation or measuring will change the energy of a particle.

I cannot see a violation of the energy conservation law by the uncertainty principle.

But the description of β-decay by current theory assumed the violation of the energy conservation law. The appearance of Z- and W-particles violates the called law for a very short time.

Regards

Hans

Dear Glenn

I studied your "The Ten Assumptions of Science"

1- Materialism: The external world exists after the observer does not.

2- Causality: All effects have an infinite number of material causes.

3- Uncertainty: It is impossible to know everything about anything, but it is possible to know more about anything.

4- Inseparability: Just there is no motion without matter, so there is no matter without motion.

5- Conservation: Matter and the motion of matter neither can be created nor destroyed.

6- Complementarity: All things are subject to divergence and convergence from other things.

7- Irreversibility: All universes are irreversible.

8- Infinity: The universe is infinite, both in the microcosmic and macrocosmic directions.

9 - Relativism : All things have characteristics that make them similar to all things, as well as characteristics that make them dissimilar.

10- Interconnection: All things are interconnected; that is, between any two objects there exist other objects that transmit matter and motion.

I agree with your ten assumptions, but I have not its relation with the amount of uncertainty principle.

Dears Patrick, Igor and Hans-G

Thank you for important notes. What I have understood of your descriptions is that the conservation energy law is saved in quantum mechanics too. Am I right?

Or is limited energy conservation by the Heisenberg uncertainty principle?

The uncertainty principle does not violet the law of energy conservation. It helps understanding many quantum mechanical phenomena, like the tunneling effect. The very Quantum mechanics  can be derived starting from the uncertainty principle. 

This question does not exist, or,  this question is not well defined:Heisenberg's uncertainty principle concers a relation between OBSERVABLES, mathematically: self adjoint operators in a Hilbert space. for several models exist a selfadjoint energy operator, but "time" has no representation as such a thing like:  "the variable t is selfadjoint"

Hossein,

I think you are correct that the act of measuring is only because we have to have tolls to do that and on a large scale there is so little affect that we can compensate for the differences but on this scale we can not.

The fact of the matter is that the uncertainty principle in my humble opinion is a case of frustration over not being able to measure sub atomic things at an accuracy that science wants.  

Anyone that understands a light photons at all knows that its velocity in a vacuum is the speed of light.  Yet when that photon strikes a surface we pretend that we do not know where it is and it velocity as it hits.  If we did not know this information most of the information that we are exchanging right now could not happen.

George Van Hoesen 

Hi  Hossein,

 Yes, if there is complete time translation symmetry, even in QM energy is conserved. But we know that systems interact with each other in a time-dependent fashion violating time translation invariance, so that energy is no longer conserved. But what the uncertainty principle tells us is something more: Not only energy is not conserved, but one cannot determine the time-dependent energy accurately. If the systems interact over a time T, then our ignorance in the exchange of energy that takes place is greater than hbar/T. Please see Landau-Lifshitz's book on QM for a precise statement.

Dear Petar and Anton

I agree uncertainty principle is a mathematical and useful tool in quantum mechanics.

Consider that experiment in Canada shows there is not a precise value for the amount of certainty principle.

Dear George

When we are measuring some thing at large scale, might the amount of uncertainty is not considerable, but for sub atomic particles uncertainty has considerable role.

Dear Patrick

Uncertainty principle is used to describe may of unknown physical phenomena such as virtual particles, zero point energy, even big bang theory. What is your opinion?

Hi Hossein, I'm NOT interested in this canadian experiment. A gentleman has better things to do. (Richard Ii)

Heisenberg' principle is basic and fundamental in QM, and there exist NO energy-time uncertainty. Energy and time are NOT conjugate variables and Heisenberg knew that (and told me so).

Quick answer, yes for a short enough time.

Dear Anton

You have noted to an important matter, "Energy and time are NOT conjugate" that I never heard it before, thank you. I will let you know that I am neutral relative the results of this issue, I will know what uncertainty principle means and where is its influence domain.

So, I interest on Canadian experiment, I want know what it is really.

But about energy-time uncertainty, there is ambiguity and important discuss on it.

For examples:

An uncertainty relation for energy and time of the usual ‘‘canonical’’ type does not exist and some of the reasons why people have wanted to see such a relation were shown to be unfounded.

http://www.cce.ufes.br/jair/mq1mest/AJP396_Hilgevoord_Uncertainty_Principle_Energy_Time.pdf

In this paper we have tried to perform a comprehensive summery of Energy-Time uncertainty principle.

http://www.ijera.com/papers/Vol3_issue3/HW3313621364.pdf

Hi H., in the Schrödinger picture we have trivially

Dear Anton

I have found nothing that shows Heisenberg has proposed the "Energy-Time uncertainty". Do you know who was the first provider of "Energy-Time uncertainty"?

@Hossein Javadi:

"You will get many different results." I think this is not only true for subatomic particles, also the measure the length and width of the room is probably true. Am I wrong?

Indeed you are right. But this is something else, namely measurement error. This can be diminished by appropriate measures. Besides, the distribution of your measurement results do not depend on the state of the room, but on the way you measure. For a room, quantum effects are altogether negligible.

In quantum mechanics, depending on the state you measure, you will get a scatter of position values, which no change of measurement procedure will affect. The scatter is determined by the quantum state. So it is qualitatively different. It is this kind of scatter, which cannot be reduced by improving measurement technique, which is the subject of the uncertainty relation.

Dear Leyvraz

I agree that there is an uncertainty in measurement on the behavior of quanta.

You have written; "...which cannot be reduced by improving measurement technique,..." But researchers have performed measurements of photons and showed that the act of measuring can introduce less uncertainty that is required by Heisenberg’s principle.

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.100404

Also, do you know who was the first provider of "Energy-Time uncertainty"?

Heisenberg conducted a thought experiment as well. He considered trying to measure the position of an electron with a gamma ray microscope. The high-energy photon used to illuminate the electron would give it a kick, changing its momentum in an uncertain way. A higher resolution microscope would require higher energy light, giving an even bigger kick to the electron. The more precisely one tried to measure the position, the more uncertain the momentum would become, and vice versa, Heisenberg reasoned. This uncertainty is a fundamental feature of quantum mechanics, not a limitation of any particular experimental apparatus.

Heisenberg outlined his new principle in 14-page a letter to Wolfgang Pauli, sent February 23, 1927. In March he submitted his paper on the uncertainty principle for publication.

Niels Bohr pointed out some errors in Heisenberg’s thought experiment, but agreed the uncertainty principle itself was correct, and the paper was published.

The new principle had deep implications. Before, it had been thought that if you knew the exact position and momentum of a particle at any given time, and all the forces acting on it, you could, at least in theory, predict its position and momentum at any time in the future. Heisenberg had found that not to be true, because you could never actually know a particle’s exact position and momentum at the same time.

The uncertainty principle soon became part of the basis for the widely accepted Copenhagen interpretation of quantum mechanics, and at the Solvay conference in Brussels that fall, Heisenberg and Max Born declared the quantum revolution complete.

https://www.aps.org/publications/apsnews/200802/physicshistory.cfm

There is nothing about "Energy Time Uncertainty", in Heisenberg paper.

Dear Anton

You have written: "Energy and time are NOT conjugate variables and Heisenberg knew that (and told me so). "

I found an article that contains:

Heisenberg also discusses the classically conjugate variables of time and energy and defines a time operator through the, quote, ”familiar relation”

[E, t] = (Et − tE) = −i h-bar (4)

On the basis of this commutation relation, Heisenberg assumes a time-energy uncertainty relation (TEUR)

Delta E Delta t ~ h-bar (5)

page 1 of following article:

http://iopscience.iop.org/article/10.1088/1742-6596/99/1/012002/pdf

Seems Heisenberg has not ignored uncertainty relation Energy- Time.

What is your opinion?

Once more: the PRL you quote in no way contradicts the uncertainty principle that follows from quantum mechanics. It does contradict a historically important formulation, which states that any attempt to measure one observable induces an uncertainty in the conjugate one. This is not even easy to formulate unambiguously in quantum mechanics as it is now formulated.

Any given state has a given scatter in position, and a given scatter in momentum. They cannot have a product less than a certain value, and the PRL you quote emphatically does not deny that.

I think that much of the problem stems from the problem of why we measure things differently at different gravitational potentials.  Much of this is because of the problem we have with dealing with mass, gravity, and the speed of light.  

If for instance we measure something using a clock that uses the frequency vibrations of an atom at a given temperature we should understand that as the potential of gravity increases the clock physically changes as the force that is exerted changes.  The reason for the time difference is not that time changes but that gravity affects the movement of, or the vibration of matter.  Our notion of time changes then go to zero as it is just an additional force that changes things not that time changes.  Time is not changing but our ability to measure it is changing.

What this means for the uncertainty principle is that the uncertainty is affected by our inability to accurately measure things in a gravitational field.  Einstein gave us a better picture than Newton but it does not tell the correct story of what gravity really is and how it works over distances.

In my humble opinion the science is just not correct and therefore the uncertainty is needed to explain the inability to explain other things with the old theories.

dear Hossein,

you may create for every observable of dimension p^nxq^m a "partner-observable" of dimension hxp^-nxq^-m and put this pair into a uncertainty relation.

in the beginnig also W.Heisenberg did this with energy and time. in this time the "foundation of quantum theory" war barely developed and mathematical physicists like J. von Neumann explained that this above is only a necessary condition of being  a conjugate pair of observables. Heisenberg was smart enough to accept this.

In standard Schrödinger theory the basic terms in this relations are:

= t^n and h bar is zero. (time is a "c-number")

the same is tru in the Heisenberg picture.

of course, you may construct a new Lagrangian, Hamiltonian, ... and a tricky time operator t = t(t',p,q) which is now conjugate to a new "energy".

I wish you good luck in preceding!

Tony

Dear Anton

Thank you, I agreed that there is not the unique formulation of uncertainty in quantum mechanics.

Dear Dr. Leyfraz, I appreciated your information about what's going on in Canada' s experiment.

however ... we talk about simultaneous measurement uncertainty of position and momentum of a quasi free incoming and outgoing electron. This is done by the standard slot experiment, also to demonstrate the de Broglie character of a wave function. the results are indeed very well known and are basic for the axiomatic formulation of QM

have a nice day

Tony

@Anton Schober: you say that results concerning the ``simultaneous measurement of position and momentum'' are well-known. Maybe you should attempt to formulate them here. To my mind, in ordinary quantum mechanics, when one measures an observable, one cannot, in a well-defined manner, speak of the values of the conjugate observable. If we measure position x, then we get a probability density \rho(x) with a given scatter. If we measure momentum, we get a distribution \tilde\rho(p), with its scatter. But there is no way to obtain a common distribution function \rho(x, p). The Weyl quasidistribution will of course do something similar, but it cannot be interpreted as a probability. My claim is that the usual interpretation of QM, and of the uncertainty relation as it is mathematically shown, refers to the product of the scatters of \rho an \tilde\rho, and as such do not refer to simultaneous measurement.

What the Canadians claim, is to have invalidated a form of the uncertainty relation used by Heisenberg, that involved the effect of the measurement of one variable on the value of the other. I am not aware how to make this rigorous in the formalism of QM, though I am reasonably sure there must be a way. But ``welll-known''? It would be nice to hear what you have in mind,

in contrast to a classical state a quantum state is a vector of a separable Hilbert space over the complex numbers and the "observables" are elements of the set of selfadjoint operators on this Hilbert space. All is unique up to isomorphism. We measure (parts of) the spectrum of such a selfadjoint operator. Each selfadjoint operator A has a real spectrum, which may be discrete or continuous or mixed. The measured value is in obvious notation. Next we have to preparate a "physical state". e do this by fixing a Hamiltonian H ( or Lagrangian, other ...). It is necessary to check that this Hamiltonian is "selfadjoint", for instant at the Coulomb problem. This Hamiltonian has for instant a continuous (possible unbound) spectrum >0, a discrete part

http://arxiv.org/pdf/1208.0034.pdf

This the publication??!!

There is nothing in it on dE.dt??!!

and it describes what dr Levraz wrote the extra uncertainty in 2 conjugate variables because of the measurement

@Anton Schober: ``the term "at the same time" is missleading: I know my p-distribution if you tell me your x-distribution.''

By no means: if you know the x-distribution, by taking the square root you know |psi(x)|, but from this only follows

psi(x) = sqrt(rho(x)) exp(i phi(x))

where phi(x) is unknown. phi(x) in fact significantly influences the p distribution.

In fact, it is not even enough to know both the x and the p distribution function to determine the state psi(x) uniquely. This is not obvious, however.

No.

1st you have to prepare the state which also.means fixing the Hamiltonian.

2nd construct a possible set of eigendistributions.

3rd find the symmetry algebra and fix a subset of commuting elements which fixes the state: here [A, B] = 0

4th: because the observables are in the Lie Algebra we have always [A', A''] =iA'''.(Heisenberg's "uncertainty")

5th The Lie group acts as a unitary transformation like a general Fourier transformation on  the representation space - "wave function" - and on the Lie algebra - "observables".

Bohr's interpretation of the uncertainty principle.

Bohr writes: According to the quantum theory, just the impossibility of neglecting the interaction with the agency of measurement means that every observation introduces a new uncontrollable element. Indeed, it follows from the above considerations that the measurement of the positional co-ordinates of a particle is accompanied not only by a finite change in the dynamic variables, but also the fixation of its position means a complete rupture in the causal description of its dynamical behavior, while the determination of its momentum always implies a gap in the knowledge of its spatial propagation. Just this situation brings out most strikingly the complementary character of the description of atomic phenomena which appears as an inevitable consequence of the contrast between the quantum postulate and the distinction between object and agency of measurement. Como Lecture

http://members.tripod.com/~Glove_r/Folse4.htm

The uncertainty principle is due to the effects that a Fourier transform has on the wave function of a particle. This Fourier transform maps two parameter spaces onto each other. One is the configuration space, which is a simplified version of what we experience as our living space. The other parameter space is the parameter space of the Fourier transform of the wave function. The wave function is a complex probability amplitude distribution. Its squared modulus represents the probability of detecting the owner of the wave function at the location in configuration space that represents the parameter value of the wave function. Owning a Fourier transform involves owning a displacement generator. The displacement generator represents the quantum physical momentum of the owner of the wave function. These are all pure mathematical relations or physical interpretations of these mathematical relations. The uncertainty relation now states that the product of the square root of the variance of the detection of the position and the square root of the variance of the detection of the momentum is a fixed number that relates to Planck's constant. Apart form the interpretation of the term "detection" this has a pure mathematical significance. Physics enters the story when we interpret the squared modulus of the wave function as a location detection probability distribution and the squared modulus of the Fourier transform of the wave function as a momentum detection probability distribution.

@Hossein: reading Bohr is interesting if you want to know about the *history* of QM, and particularly if you have an extensive knowledge of, and clear ideas concerning, quantum mechanics. It is quite a bad idea if you want to know the way in which people interpret QM today. The lecture you quote was given in 1927, that is, at a time when von Neumann's book, which cast QM in its modern form, had not yet appeared. A lot of experiments were also not yet done, and many theoretical developments (entanglement, decoherence...) still lay in the future.

So if you want to know about QM as it is practised and interpreted nowadays, you should look at different books. Leonard Susskind and Art Friedman, ``Quantum mechanics: the theoretical minimum'' comes to my mind as a good place to start. It does require a bit of math, but not much, and is accurate as far as the philosophical underpinnings go.

Dear F. Leyvraz

I am thankful with your guidance.

I would not study the interpret of QM, I want to know how the uncertainty affects of our observations.

@Hossein: then i suggest a modern textbook of quantum mechanics. The reference I gave earlier I believe to be OK. If you find it too complex mathematically, you should probably get some background in linear algebra in finite dimensional complex vector spaces from the net. Infinite dimensional spaces are required for some purposes, but Susskind and Friedman limit themselves to finite dimensional spaces and get their points across very nicely.

Best wishes,

Francois

Dear F. Leyvraz

Thank you for suggestion. My problem is beyond of uncertainty principle. In the classical derivation of Lorentz transformations there is no real solution for speed greater than light so thought has stopped at speed of light. But the physical realities such as vacuum energy and virtual photon showed that the speed of light and visible particles isn’t the end of physical spaces.

Also, uncertainty principle is used to describe many of unknown physical phenomena such as virtual particles, zero point energy, even big bang theory. So, seems physicists have stopped at light speed and uncertainty principle.

In quantum field theory, forces are transmitted by particles, and fields are associated with particles which transmit the forces. The particles of the electromagnetic field are the photons. In quantum electrodynamics all electromagnetic fields are associated with photons, and the interaction between the charged particles occurs when one charged particle emits a virtual photon that is then absorbed by another charged particle. The photon has to be a virtual photon, because emission of a real photon would violate energy and momentum conservation. If, for example, an electron initially at rest emitted a photon, the final state would consist of an electron and a photon moving off in opposite directions, a configuration which necessarily has more energy than the initial at-rest electron. But the uncertainty principle prevents a contradiction.

http://electron6.phys.utk.edu/phys250/modules/module%206/standard_model.htm

Zero-point energy, also called quantum vacuum zero-point energy, is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have associated zero-point energy, a consequence of their wave-like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential as well. This results in motion even at absolute zero. If the zero point energy in space (vacuum) exists, how can we explain the zero-point energy without using the uncertainty principle?

If we carefully review a pair production and decay and the results of high energy particle collisions, from the relation E= mc2 this question will be raised whether in addition to being convertible of energy into mass and vice versa, the other concepts can be derived as well. Are there common rules in the energy structure and elementary particles? If we continue to believe that in the Standard Model, elementary particles are point particles and unstructured, we cannot resolve ambiguities in modern physics. This is my attempt to answer these questions.

"Energy" can be scaled. In QFT we subtract the infinity of the vacuum energy, so these "vacuum fluctuations" (or zero point energy) are not a very important affair. on the other hand the theory is pretty simply: for "free" particles and fields we have no problems at all. For interacting particles all physics consists of the set of all well defined Feynman diagrams. third: At a closer look, there are no "free particles", so all particles and fields interact always and are a bit off the mass shell or light cone, will say, there are only virtual particles and fields. 

why not vacuum fluctuations ....

Dear Anton

""Energy" can be scaled."

What is electromagnetic energy really? There are many explanations and mathematical equation about electromagnetic energy in physics. Also, concept of photon has an interesting history. Photon refers to photo-electric effect that is explained by Einstein. Einstein wrote in 1951:

“All these fifty years of pondering have not brought me any closer to answering  the question, What are light quanta?” 

 http://arxiv.org/pdf/hep-ph/0602036v2.pdf

 Beside of duality concept,  in addition to carrying energy, light transports momentum and is capable of exerting mechanical forces on objects. About mass of photon; While the concept of the massless photon is an assumption, physicists have not stopped on assumption of massless. There are more attempts made to clarify the massless photon in theoretical and experimental physics. There are good theoretical reasons to believe that the photon mass should be exactly zero, there is no experimental proof of this belief. These efforts show there is an upper bound on the photon mass, although the amount is very small, but not zero.

In quantum electrodynamics (QED) a charged particle emits exchange force particles continuously. This process has no effect on the properties of a charged particle such as its mass and charge. How is it explainable? If a charged particle as a generator has an output known as a virtual photon, what will be its input?

In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume. There is nevertheless a distinction between elementary particles such as electrons, photon or quarks, which have no internal structure, versus composite particles such as protons, which do have internal structure. According to the quantum mechanics that photon is an unstructured particle, how can we explain the relationship between the photon energy and frequency, and also pair production and decay?

QED rests on the idea that charged particles (e.g., electrons and positrons) interact by emitting and absorbing photons, the particles of light that transmit electromagnetic forces. These photons are virtual; that is, they cannot be seen or detected in any way because their existence violates the conservation of energy and momentum. If the electromagnetic field is defined in terms of the force on a charged particle, then it is tempting to say that the field itself consists of photons which cause a force on a charged particle by being absorbed by it or simply colliding with it - as in the Photo-electric effect. The electric repulsion between two electrons could then be understood as follows: One electron emits a photon and recoils; the second electron absorbs the photon and acquires its momentum. Clearly the recoil of the first electron and the impact of the second electron with the photon drive the electrons away from each other. So much for repulsive forces. How can attraction be represented in this way? The uncertainty principle makes this possible. The attraction between an electron and a positron may be described as follows: the electron emits a photon with momentum directed away from the positron and thus recoils towards the positron. This entails a degree of definiteness in the momentum of the photon. There must be a corresponding uncertainty in its position - it could be on the other side of the positron so that it can hit it and knock it towards the electron. Is there a way to explain virtual photon (in fact interaction between charged particles) without using the uncertainly principle?

https://www.researchgate.net/publication/280491440_Reconsidering_relativistic_Newton%27s_second_law_and_its_results

Article Reconsidering relativistic Newton's second law and its results

No-the uncertainty principle does not imply that energy isn't conserved, i.e. that the average value of energy isn't well-defined-it is a statement about the fluctuations of energy about its average value.  Quantum fluctuations are, in this regard, exactly like thermal fluctuations in a canonical ensemble of temperature hbar. Just like in the canonical ensemble the average value of energy is well-defined as are its fluctuations, same here. Planck's constant sets the scale of the quantum fluctuations, just like temperature sets the scale of the thermal fluctuations. The difference is that the microscopic degrees of freedom, whose dynamics describe the thermal fluctuations, are commuting degrees of freedom, whereas the degrees of freedom, whose dynamics describe the quantum fluctuations are non-commuting degrees of freedom.  

In quaternionic quantum physics, a combination of an infinite dimensional separable  quaternionic Hilbert space and its companion Gelfand triple is used as structured storage media. The storage implies parameter spaces as well as continuums that can be represented by quaternionic functions. This enables the possibility to store a representation of the whole history and future of the universe in this combination of Hilbert spaces.Smarter is to work with an ongoing embedding of the separable Hilbert space into its non-separable companion.

This idea applies a special version of the generalized Stokes theorem that separates the history from future and uses the current status quo of the universe as the border between the two. This is achieved by requiring that all relevant physical operators feature well-ordered eigenspaces. This means that all real parts of the eigenvalues occur only once and that the resulting real parts are used as enumerators of the eigenvalues and eigenvectors.

This procedure completely hides the future and keeps the past untouched. All dynamics occurs at the rim between past and future.

For the uncertainty principle it means that forecasting is forbidden and thus the uncertainty principle cannot be used for the relation between progression and energy in a dynamic fashion. 

http://vixra.org/abs/1511.0074

There is a qm book by heisenberg, which deals very intuitively with the 

uncertainty relation, in the energy time, or frequency time cases. He uses the

Fourier transform, and this interestingly leeds to the uncertainty principle not only

in physics, but there is also a version in mathematics. Almost the same, except that the planck constant does not appear.

Juan,

if you want to apply the uncertainty principle at the current instant, then you are partly forecasting the future. So your model of physics must tolerate this forecasting.

Some differential equations provide solution sets that include advanced and retarded solutions. One of these equations is the wave equation. What do you do with solutions that come from the future? 

Hans

Where did you get this from? You always fourier transform over a finite period of time.

For a wave with a perfecty defined frequency, you must have an infinetely long time.

@Juan Weisz "For a wave with a perfecty defined frequency, you must have an infinetely long time"

this is generally not tru:: f.i. a function: sin wave from t(0) till t(t') and zero outside this interval has a continuous Fourier k-decomposition in k-space. In other words: the Fourier transforms of functions of these standard distriution classes exist and are in the dual space. 

Juan

The wave function is a complex number valued probability amplitude distribution. Its squared modulus can be considered as a continuous distribution that characterizes the density of the locations where the owner of of the wave function can be detected. It is not clear whether this distribution characterizes a distribution of actual locations where the owner was or that it just represents a fuzzy description of where the object is detected when that detection actually happens. The location density distribution has a Fourier transform. On movement wave packages have the tendency to disperse. However, that does not occur to the wave function. This can only be explained when the density distribution characterizes a coherent swarm of locations that is recurrently regenerated. In that case the location density distribution can keep its shape and does not disperse. The fact that the location density distribution has a Fourier transform means that the swarm has a displacement generator and that at first approximation the swarm can be considered to move as one unit.

The fact that the swarm is recurrently regenerated means that the locations in the swarm in fact represent a hopping path of a point-like particle. The swarm represents the spatial map of its hectic dynamic hopping.

In conclusion: the wave function might be no more and no less than a continuous description of the hectic hopping behavior of the point-like owner of this wave function. In that view it is false to draw to far going conclusions from the Fourier transform of the wave function. The fact that the wave function does not disperse on movement is an indication that the above suggestion might be right. The observed particle-wave duality of elementary particles is a further indication that there is more to the wave function than is usually presumed. 

If you want to investigate much deeper, than try the link below.

http://vixra.org/abs/1511.0074

Anton,

You may be technically correct, but that is how I think about it physically.

I do not know what mathematicians think, but in math physics we often use

Integral from minus intinnity to infinity of exp(i omega t) over the time varable

divided by 2 pi is the delta function of omega.

That would be the math expression of what I say. On the other hand I have not

seen rigorous mathematical derivation.

I suggest you look at pages 152 to 154 of my book Nonrelativistic Quantum Mechanics where  discuss in detail the time energy uncertainty relation.

Dear Anton Zizi Capri

Why don't you scan in the 3 pages and attach it here at ResearchGate?!

Here are the pages I mentioned, written in Latex format

\section{Time-Energy Uncertainty Relation}

The inequality (\ref{7.12}) states that for classically conjugate variables

(i.e. those satisfying $[p,q] = i\hbar $) we have the Heisenberg uncertainty

or indeterminacy relation

\begin{equation}

\Delta p\Delta q \geq \hbar/2 \; .

\label{7.30.3}

\end{equation}

Such a relation holds also for the time and energy variables even though

they do \emph{not} satisfy a commutation relation

\begin{equation}

[E,t]= i \hbar \; .

\label{7.31}

\end{equation}

This commutator might be conjectured from the fact that in the

time-dependent Schr\"{o}dinger equation the ``energy operator''

appears as \index{energy operator}

\begin{equation}

E = i \hbar \frac{\partial}{\partial t}\; .

\label{7.31.1}

\end{equation}

As we now show equation (\ref{7.31}) is \emph{false} for any physical system.

The reason for this is that the energy for a physical system must have

a finite lower bound. Otherwise the system would wind up in the

lowest state of negative energy at $E=-\infty$ (by radiating its energy

away) and stay there forever. No perturbation would be strong enough

to excite the system from $E=-\infty$ to a finite value. This being the case

we must have a finite $E_{0}$ with all energies $E\geq E_{0}$ and thus there

can be no self-adjoint extensions for an operator $t$ satisfying the

commutator equation (\ref{7.31}). (See problem 7.10.) \footnote{If the

energy is also bounded above, then $t$ has a one-parameter family of

self-adjoint extensions. In this case, however, the spectrum of the

$t$-operator is discrete.} Hence time could not be an observable if

equation (\ref{7.31}) were to hold.

We now show directly that if there exists a finite lower bound $E_{0}$

(the lowest energy eigenvalue of $H$) such that all eigenvalues $E$

satisfy $E\geq E_{0}$ then we obtain a contradiction from equation

(\ref{7.31}) if both the Hamiltonian $H$ (total energy) and the time $t$ are

to be observables.

Let $\phi_{0}$ be the energy eigenfunction corresponding to the

lowest energy $E_{0}$ .

\begin{equation}

H \phi_{0} = E_{0} \phi_{0} \;\; .

\label{7.32}

\end{equation}

Now pick any positive frequency $\omega$ and define the operator

\begin{equation}

b = e^{i\omega t}\; .

\label{7.33}

\end{equation}

Then, (see problem 7.12)

\begin{equation}

{[H,b] = -\hbar \omega b}\; .

\label{7.34}

\end{equation}

So,

\begin{equation}

Hb\phi_{0} = bH\phi_{0} - \hbar\omega b\phi_{0}

\label{7.35}

\end{equation}

or

\begin{equation}

H(b\phi_{0}) = (E_{0}-\hbar\omega) (b\phi_{0}) \;\; .

\label{7.36}

\end{equation}

Therefore, either $E_{0}$ is not the lowest eigenvalue of $H$ or else

\[b\phi_{0} = 0 \;\; .\]

But, if $t$ is to be an observable then $\omega t$ must be self adjoint and

$b = e^{i\omega t}$ must be unitary. As a consequence

\[b\phi_{0} = 0 \;\;\;\;\Rightarrow \;\;\phi_{0} = 0 \;\; .\]

Thus, we have to conclude that the commutator (\ref{7.31}) is false.

In spite of the absence of a ``time-energy commutation relation'',

\index{time-energy!commutation relation} a time-energy uncertainty

relation holds. \index{time-energy!uncertainty relation} This

relation is extremely useful and it is important to understand what it

means. It is for this reason we have given such a lengthy discussion

above. We now proceed to the derivation of this relation.

The ``time'' involved in the time-energy uncertainty relation is not the

time parameter \index{time parameter} in the Schr\"{o}dinger equation,

instead it is the ``time of a process'' associated with an observable

$\mathcal{A}$. We therefore define the evolution time $T_{A}$

associated with the observable $\mathcal{A}$ by

\begin{equation}

T_{A} = \frac{(\Delta A)_{t}}{\left|\frac{d\langle A\rangle_{t}}{dt}\right|} \; .

\label{7.38}

\end{equation}

To see what this means consider the change in the expectation value

$\Delta\langle A\rangle_{t}$ of the observable $\mathcal{A}$ in a time

interval $\Delta t$. This is

\begin{eqnarray}

|\Delta \langle A\rangle| &=& |\langle A\rangle_{t+\Delta t} -

\langle A\rangle_{t}|

\nonumber\\

&\approx & \left|\frac{d\langle A\rangle}{dt}\right| \Delta t \;\; .

\label{7.39}

\end{eqnarray}

Now for the change $|\Delta \langle A\rangle|$ to be measurable requires

that $|\Delta \langle A\rangle|$ be at least as large as the

uncertainty $(\Delta A)_{t}$ in the observable $\mathcal{A}$. This

gives us the length of time $\Delta t$ which we must wait to be able to

``see'' any change in $\Delta \langle A\rangle_{t}$ . Equating

$|\Delta \langle A\rangle|$ with $|\Delta \langle A\rangle_{t}|$ we

find

\begin{equation}

\Delta t = \frac{(\Delta A)_{t}}{\left|\frac{d\langle

A\rangle_{t}}{dt}\right|} = T_{A} \; .

\label{7.40}

\end{equation}

But this is just the time $T_{A}$. So $T_{A}$ is the time required for

the expectation value of $\mathcal{A}$ to change by an amount equal to the

uncertainty in $\mathcal{A}$.

Returning to the time-energy uncertainty relation we find according to

(\ref{7.30}) that

\begin{eqnarray}

\left|\frac{d\langle A\rangle_{t}}{dt}\right| &=& \frac{1}{\hbar}|(\Psi

,[H,A]\Psi)|

\nonumber\\

&=&\frac{1}{\hbar}|(\Psi ,[H',A']\Psi)|

\label{7.41}

\end{eqnarray}

where as before

\begin{eqnarray}

H' &=& H - \langle H\rangle

\nonumber\\

A' &=& A - \langle A \rangle \;\; .

\label{7.42}

\end{eqnarray}

Then, by the same sequence of steps used to obtain the general

uncertainty relation (\ref{7.12}), we get:

\begin{equation}

\left|\frac{d\langle A\rangle_{t}}{dt}\right| \leq \frac{2}{\hbar}

\Delta H \Delta (A)_{t} \; .

\label{7.43}

\end{equation}

Writing $\Delta E$ for $\Delta H$ and solving for $T_{A}$ we find

\begin{equation}

\Delta E T_{A} \geq \hbar/2

\label{7.44}

\end{equation}

or writing $\Delta t$ for $T_{A}$ we have

\begin{equation}

\Delta E\Delta t \geq \hbar/2 \; .

\label{7.45}

\end{equation}

This is the famous time-energy uncertainty relation. Its meaning is

clear from the derivation. Namely, let $\Delta E$ be the uncertainty (RMS

deviation from the mean) in the total energy and let $\Delta t$ be the minimum

time required for a measurable change to occur in a given observable

evolving according to the Hamiltonian describing the total energy.

Under these circumstances the relation

\begin{equation}

\Delta E\Delta t \geq \hbar/2

\label{7.46.0}

\end{equation}

holds.

dear Anton Z (to distinguish you from Anton Schober with an S)

Thanks though hard to read

What I can follow sounds like the reasoning of PW Atkins with respect to the fact that t is not an observable but a parameter. What I like of Atkins that he provides a very good example of the lifetime of a non-stationary (excited) state that is not a time-independent state and thus has not a fixed and associated time-independent constant energy.

FYI Atkins' book is on the web for free 

The Cambria Math font contains many characters that make scientific formulas reasonably readable.The comment editor can cope with Cambria Math. Further, you can put formulas in a small pdf file and attach them to the comment. Longer texts may be linked to the comment.

@ Juan Weisz: "That would be the math expression of what I say. On the other hand I have not seen rigorous mathematical derivation" Here a kind of "derivation":

1st: QM takes place in H, Hilbert space, which is  isomorphic to H', its dual space. (dual space V' = vectorspace of linear maps of V (= vectorspace) into the reals)

2nd: your exp(ikx) is not square integrable, so not in H, but in a distribution space named E, and its Fourier transformed distribution, the delta function (not (!) in H), is in E', dual space of E.

3rd: f(x) = exp(ikx) for - say - |x| < 1, and zero outside this interval is the product of exp(ikx) times two suitable theta functions (theta(x) = 1, for x > 0 and  = 0 for x < 0). f(x) is in D, distribution with compact support (and H (!!!)), and its Fourier transformed (integral from minus till plus infinity !!!): exists and is in D', dual space, and clearly in H. In physics, those functions (similar f(x)) are called "wave packets"

4th: these dual pairs (D,D'), (S,S') and (E,E') are studied in elementary functional analysis textbooks, readable easily for mathematical physicists. H is in S (=Schwartz functions): D in S in E. E' in S' in  D'.

Dear Hosein Javadi,

Much as I admire Heisenberg and his work, he was wrong in this instance. There is no time operator such that  [E,t] = i h-bar. You can see the proof of this in my book on the pages I mentioned before. I am attaching these two pages from my book with the proof.

Quantum physics uses Hilbert spaces in order to store physical data in the form of numbers or continuums into the eigenspaces of operators that reside in these spaces. It is possible to store all data about universe in just two Hilbert spaces. One is a separable Hilbert space and it stores all discrete numerical data. The other is a Gelfand triple, which is a non-separable Hilbert space. All infinite dimensional separable Hilbert spaces own a companion Gelfand triple. The Gelfand triple can store continuums in the eigenspaces of corresponding operators. I this way, these Hilbert spaces are nothing more and nothing less than structured storage media. Physics describes the embedding of the separable Hilbert space into its non-separable Hilbert space as an ongoing process. The past is left untouched. The future is considered to be yet unknown. On the rim between history and future operate controlling mechanisms that feed the separable Hilbert space with discrete data that contain new locations of discrete objects. These mechanisms are not mentioned by any current physical theory. Without their activity nothing would happen in universe.

http://vixra.org/abs/1511.0074

Anton Z

you attached only one page and upside down

The generalized Stokes theorem generalizes both Stokes theorem and the divergence theorem to multiple dimensions.

This should include quaternionic manifolds. which are manifolds that are characterized by quaternionic functions that use quaternionic number systems as their parameter spaces.

A special application of the generalized Stokes theorem is the usage of the spatial part of the quaternionic parameter space as the boundary that encapsulates part of the full quaternionic parameter space.

∫∭dω=∰ω

Here the first integral on the left restricts the real part of the quaternionic parameters from zero to a certain "time" T. On the right side ω concerns the static status quo at progression instant T. dω is the exterior derivative of manifold ω.

If quaternions are interpreted as dynamic geometric data with the real part as the progression stamp, then the above application of the generalized Stokes theorem can be interpreted as a description of what happens in a quaternionic space progression model on the rim between past and future. Here the "boundary" describes the static status quo of the model at a selected progression instant.

This model resembles the way that we describe universe. However, the above model is a strict Euclidean model. 

https://en.wikipedia.org/wiki/Stokes%27_theorem#General_formulation

Dear Anton

I'm sorry for being late. My computer was corrupted.

Thank you for attachment, but as Harry said, you attached only one page.

Very good question and the subject of talks. But: due to ISIS+Russia+USA it has lost its value. What can be important at the edge of nuclear war? 2) The reduced uncertainty tells me, what David Bohm theory for Quantum Mechanics is correct. The energy do conserve in closed system. But in Bohm interpretation it is not conserving due to "quantum potential". So, the system is open. Therefore, there is God. Short and simple argument, isn't it?

@Dmitri Martila

too fast, this god's existence proof contains a fallacy: you imply we overlook the full system. Still we don't know what happens in the very small and the very large

Dear Anton

"Still we don't know what happens in the very small and the very large". I agree with you, only for directly detection. We can analyze observations and compare them with direct experience to get good results.

https://www.researchgate.net/publication/270339919_Interactions_Between_Real_and_Virtual_Spacetimes?ev=prf_pub

Article Interactions Between Real and Virtual Spacetimes

There is an order in the Universe and that order can be called God.  This is in all systems not just closed or opened.  That being said there is a way to prove this just using logic and a few scientific facts.  Matter exists and gravity works.

The argument over God is only by each persons thought of what "God is" not that this order exists.  As a child I learned that God was there and that my parents thoughts on the issue were in line with many about heaven and hell.  I grow up to understand that the books of religion most certainly had to be wrong as I turned into logic and science as a bases for my understanding.  This did not mean that I should not understand that the Universe is a highly ordered place in what appears to be total chaos.

Therefore order exists and on the largest of scales the conservation of energy and mass are correct.  The uncertainty principle my seem to show that there is a violation but I think not. 

@George E. Van Hoesen

many people  admire "order", why not calling this "god"? I prefer sex and wine and my goddes is Venus (and Dionysios)

Dear George

  Before starting talking about gods, we must specify which of gods we are having in mind. There are many gods, and they are all equal (as Orwell would put it), but my is the most powerful one. (I cant prove it, but you have to believe me!).

  As for the equality Order = God, I must say it should be taken with a grain of salt. I recently came across a paper (as referee):

S. Zorba, "God is random, a novel argument for the existence of God", European Journal of Science and Theology, February 2016, Vol. 12, No 1, 51-67, 

with the telling title.

  Anyway, discussions on the existence of God seem to  me a bit obsolete.

        After all, present day world is atheistic. Thanks God!

Dear Anton Schober

I totally agree with your preferences. Even physicists enjoy the carnal pleasures of this life , especially as we grow too old to do good physics.

Anton Capri

What is wrong in saying that  d/dt does not commute with t ?

Dear Juan,

It is true that d/dt does not commute with t. Why do you ask what is wrong?

Anton Capri

In your answer to Javadi you say there is no time operator

such that [E,t] = i hbar

What did you mean? I think you mean that somehow this is not an adequate

basis for the uncertainty principle?

The time operator is just to multiply by t

@Juan Weisz

of course, by substituting E = i hbar d/di you represent the above commutation relation. But this is only a NECESSARY condition for this "uncertainty" relation! In addition, both objects (="operators") have to be a conjugate pair. This is - as I pointed out above - not the case.

@Anton Zizi Caprì · 

"Even physicists enjoy the carnal pleasures of this life , "

so far o.k., but this is only the smallest part of the story: sex is a principle of live, eventually universal. In my opinion, it ranks higher than this "universe"

@ Anton Zizi Capri

would you please explain What physical system you have in mind which has a negative infinity lowest energy, to which you apply your arguments against the existence of time-operator?

Regards

Dear Rajat Pradhan,

That is precisely the point. There is no system without a lower bound on the energy. All physical systems have their energy bounded below. Thus there is no system with infinite  negative energy.

Dear Anton

"All physical systems have their energy bounded below. " I agree with you.

What is this bound?