First notice that the electron must have a rest mass because it travel less than light speed. Then recognize that the electron can be accelerated by electric fields. Best of all consider that energy of annihilation with positron is precisely measured. Rest mass is found by extrapolation of energy data to zero velocity. So the answer is yes, and by more than one method.

@ Xavier Oudet 

my dear Xavier Oudet  i am unclear about your question..shall you plz explain it in another manner....

@ Hussainsha:In other word the mass of the electron at rest is that of the electron alone in the space, this means that we are unable to observe it. That we observe on the electron always imply a motion. Regards Xavier

@ Xavier Oudet 

my dear Xavier Oudet i think this scenario appears not only to an electron but also appears to all fundamental particles...is it? 

The most accurate determination is the 2014 result by Sturm et. al, to a relative precision of 2.9 x 10-11. What is measured is the ratio between between the electron mass and the mass of C12 atoms (which defines the atomic mass unit).  I believe the measured accuracy is much higher than what can be furnished by the SI kilogram standard. NIST lists a relative uncertainty of 1.2 x 10-8 when the mass is expressed in kilograms instead of atomic mass units u.

http://physics.nist.gov/cgi-bin/cuu/Results?search_for=electron+mass

https://arxiv.org/pdf/1406.5590.pdf

https://www.nature.com/nature/journal/v506/n7489/full/nature13026.html

Strictly speaking, no, this is impossible. You'll have to satisfy yourself with a limiting case of slowly moving electrons.

1. The measurements are made in the laboratory frames, motion of which is totally controllable. Nobody can perform measurements in electron's own frame.

2. Being at rest for the electron means that its momentum is zero, i.e. known exactly. This, of course, requires from the electron to be evenly smothered across the Universe. Experimentally this could not be realized.

Note: Actually, what is measured is mass-to-charge ratio. 

Dear Igor: Thank for your clear answer. Finally it appears that the notion of charge involve the motion. Then it appears normal that Dirac find an electric moment as an magnetic moment.

We can feel there the motion in Dirac’ Theory. Regard Xavier

The last line of Igor comment is correct, but it demands a complement. The first experimental estimate of electron mass was found when Millikan measured the electron charge $e \approx 1.6 \times 10^{-19}$ Coulomb. This is because the electron charge-to-mass ratio was measured by J.J.Thomson in 1897. Note that in Thomson experiment the electrons in the cathode ray are moving with a high speed (typically ~10^6 m/s).

What do you mean by observe? the Millikan e/m experiment has given us an experimental estimation of the rest mass of an electron. 

First notice that the electron must have a rest mass because it travel less than light speed. Then recognize that the electron can be accelerated by electric fields. Best of all consider that energy of annihilation with positron is precisely measured. Rest mass is found by extrapolation of energy data to zero velocity. So the answer is yes, and by more than one method.

The electron's mass is invariant under Lorentz transformations-so it doesn't depend on any particular inertial frame-and the electron isn't confined-that's why measuring it makes sense. So it is possible, in principle and it has been done in practice, as mentioned above. 

@Stam Nicolis. When an electron supposed to be far from a proton is stabilized on it, giving a hydrogen atom, there is emission of one photon. Where do its energy come from?

Do you have another source of energy than the mass of the electron if we suppose the proton at rest?

In the hydrogen atom the electron is bound. Measuring the  spectrum of the hydrogen atom isn't the most efficient way of deducing the mass of the electron-so it's not useful to bring it up.

The (electric) charge of the electron is a property that's distinct from its mass. 

@Stam Nicolis. Thank for your answer. As you know Dirac finds an electric moment as a magnetic moment. So something is missing in the classical approach. If we suppose that the interaction between the proton and the electron is the result of exchanges as fluxes of very small grains mass (see the Wave and the QS), this electrical moment is not difficult to understand. It is the result of the motion of the electron if we suppose the proton a rest.

if, for a bounded system,  Eb2 - pb2 = mb2, how do you split this into constituent parts?

One of the most accurate measurements, see

Dean L. Farnham, Robert S. Van Dyck, Jr., and Paul B. Schwinberg, Phys. Rev. Lett. 75, 3598

consisted in comparing the cyclotron frequency of an electron and a carbon nucleus in the same magnetic field, using a Penning trap in which both were confined. Since the electron velocity in such a setup is very small, we get a very good approximation to the rest mass. Since additionally we know the velocity, we can, I assume, correct for the relativistic effect, though it seems this should be less than the error.

Such a measurement requires quite little theoretical input. So I would say it pretty much answers your question positively. The existence of other, for example spectroscopic, measurements which give coincident values (effect of the electron mass via center of mass motion on hydrogen spectrum) gives one, of course, additional confidence.

``Do you have another source of energy than the mass of the electron if we suppose the proton at rest?''

Definitely: if an electron is in an excited state of  hydrogen atom, say, it goes to another state, say the ground state, and emits a photon having a frequency corresponding to the difference in energy between those two levels. So yes, the energy that goes into the photon was in the electron before as some quantum equivalent of our old friends, kinetic and potential energy.

David Bergman and myself have a toroidal model of the electron that is a purely electromagnetic construct (as Poincare suggested might be possible) which is completely in equilibrium and requires no mysterious "binding energy" to keep it from flying apart due to its Coulomb forces.  Instead, it is held together by magnetic pinch forces ... within & without.   And the only laws of electromagnetism used in its construction are Coulomb's law, the Ampere circuital law, the usual formulae for electric and for magnetic energy densities at a point in space, E = M c^2, and its spin being hbar/2.  I attach a preliminary, earlier paper and then a three part paper describing this model in detail.  However, there is an error in the proof that there is zero twisting as the charge circles  the ring, but it is not difficult to patch it ... or else one may simply assume that there is no twisting of the charge.  And there is a fourth paper in the series of electron modeling, but (unfortunately) it contains an error as well.

This question touches the very heart of accelerator design.Should there be an issue,we would not be able to design acceleratgors and use kinematics for analysing experimental data.Is there some problems with these issue?I do not think so.

Yes, it certainly IS possible to calculate the electron rest mass for it being fixed in Newton's Absolute Space (to which the GPS scientists have been forced to return to get their superior accuracy of 15-18 inches) and for being far away from any gravitational mass (which also affects the electron's mass according to the gravitational scale factor), and to calculate many other of its associated constants as well.  I'm attaching a recent Derive 5 spread sheet with this information calculated ... and also much other additional information.

Dear All: there is one point which has not yet tackle, if the photon is the energy lost by the electron, nevertheless the proton and the electron are in interaction and this energy must also concern the proton. The notion of small grain mass to describe the interaction with exchange of flux between the proton and the electron allows an explanation, the energy in question belong to the proton as well to the electron, (see The wave and the Quantum state or the Quantum State and Periodicity). Thanks for your interest Xavier.

Dear All:

About Xavier’s question on photons emitted by the hydrogen atom:  First of all, the photon generation process is very simple.  What you have, as the electron accelerates, is that the Compton wavelets in front of the electron are compressed while those behind it are decompressed.  This results in a potential difference across the finite extent of the electron with an attendant increase in the electric field across it.  This changing electric field results in the generation of a photon.  There is no mysterious exchange of anything from the electron or the proton, other than that the charge difference between them produces acceleration of the electron.  The electron does not give up any of its internal mass-energy.  It only changes its radius and mass due to a very, very minor relativistic correction as it approaches the proton.

This radiation processes covered qualitatively in Sections 1.9 and1.10 of my web page using Figures 1-1 – 1-3.  Qualitatively, it's very straightforward.  Quantitatively, however, it is a little more complex.   I am currently working on a simulation of a Lyman photon using C++.  The simulation is a bit tedious, but doable.

Hence, a revolving point charge model is critical to understanding the basis for radiation, as well as the origin of de Broglie waves and the mass.

There are also several references to relativistic issues with the electron. Hence read about the mass of the electron and its relativistic corrections.   See Eqs. 1-7 and 1-8 on the same web page.

See web page www.tachyonmodel.com.

One other model to take note of:  Alfred Lauck Parsons came up with a revolving toroidal charge model in 1915. This was remarkable for its day, but it seemed to have faded away a long time ago.   Also, it was not unlike Kronig or Ulenbeck & Goudschmidt’s models that came out later.

But since then, high energy scattering experiments have indicated that the charge is a tiny point entity, not a large structure the size of a Compton wavelength.

But even more important, if the toroid is a  continuous stream of charge, how do you know it is moving, our how could it produce current without discontinuities or markers of some kind?  Worse, a revolving toroid will not produce Compton wavelets without a lot of chicanery. 

However, in spite of this, the toroidal model has been revived in the past few years.

That being said, Parsons now has his own Wikipedia page.  Hence, he will be remembered, as he well should be for such an incredible innovation at the time.

Finally, I highly recommend that those of you that have a reasonably well developed electron or other model should put it on a web page for all to see and debate.  It makes discussions much easier.

The electron's structure is a function of (1) its velocity relative to absolute space [that, of course, presupposes an absolute frame of reference; see Spec. Sci. Tech. 3, 57 (1980b)], and (2) of the ambient gravitational potential.  The (1) can be calculated via (e.g.) the S. Marinov chopped light experiment while (2) can be calculated using the measured gravitational potential at the surface of the Earth since atomic clock slowing determines it and this has been done by the GPS people very precisely (see the attached paper by Ronald Ray Hatch, a key GPS engineer who invented the Hatch filter).  Thus, one can calculate the electron's structure as (a) fixed in absolute space and as (b) being alone in the universe so that then no ambient gravitational field exists (see my web page for this calculation and other such calculations).

Dennis:

Where is your web page?

It's on ResearchGate.com.  My full name is Dennis P. Allen Jr.

GPMB  Yes, old fashioned Copenhagen quantum theory only allows for two orientations of the electron, namely, up and down.  However, See Prof. William Happer's work at Princeton for a more modern approach.

Graham:

You might want to look at the Gabrielse Group at Harvard University. They have done some impressive work on trapping electrons in a Penning trap.  See

http://gabrielse.physics.harvard.edu/

ELW:  Yes, I know about that, but the Penning trap obviously is composed of electromagnetic fields; and my calculation is for (1) no outside electromagnetic fields and for (2) no gravity either.  And also, it is for (3) fixed with respect to absolute space ... or, if you prefer, with respect to an absolute reference frame that Ron Hatch's GPS work shows must exist ... even if Einstein says no.  [See attached paper (for example) on page 14 where Ron discusses an "absolute ether frame".]

GPMB:  Thanks for the reply.  I realize that the Bergman-Allen spinning ring electron model is a three dimensional construct, and I've previously attached 4 papers by Dave Bergman & myself concerning this.  I don't have them available to attach at the moment, but they all appeared in his little journal: "Foundations of Science" that may be accessed on line at Common Sense Science. 

However, the Copenhagen quantum theory is now quite dated, but scientific political correctness is such a huge factor nowadays that the old theory is held in place in the physics journals and in the university courses by will power alone, unfortunately. 

And this is philosophically referred to as both "positivism" (i.e. My will is law!). and "nominalism" (i.e. What I will is good because I will it!).  Of course, both isms are condemned by Holy Scripture, but Holy Scripture has been ousted from scientific debate because is is claimed to be mere superstition; and out & out will-power-nonsense has been its replacement, unfortunately.

God Bless, Denny

GPMB:  Yes, please let me know if you have any questions on the Bergman-Allen electron-positron-proton-antiproton model.

GPMB:  Yes, I have attempted many times to explain to Bill Lucas that Faraday's law of induction fails for (e.g.) a plasma, and that this then explains why the ITER hot fusion people have not been able to succeed in magnetically confining their hot plasma properly, but Bill won't listen.  (I think he simply feels that it's too late for him to turn back now ... as he's written and published so much using the Faraday law up to the present.)

In Dr. Jeremy Dunning-Davies's and my "Neo-Newtonian Mechanics ... : Part 2: Radiative and Inductive Effects" in the first appendix, there is a short prof that Faraday's law fails in general to fully account for magnetic induction.  And J.P. Wesley's, "Scientific Physics," explains just why the magnetic vector potential A vector is the right magnetic vector, not the usual B field, where B = curl(A).

And the positive electron (or positron) -- one of Dirac's anti-particles -- arises from the Bergman-Allen electron model by (1) changing the negative algebraic charge sign to the corresponding positive value of the same magnitude, and (2) changing the energies, both magnetic and electrostatic, to have negative signs instead of the usual positive signs. And this latter is, of course, fully in accord with Dirac's brilliant idea that his antiparticles must have negative mass-energies!  [Note that in the various Bergman-Allen model equations, charge appears both to the first power and also to the second power, and so changing the algebraic sign of the charge changes its sign when to the first power, but not when it is to the second power!]

And, yes, a concrete model -- such as the Bergman-Allen one -- has many, many advantages.  Ronald Ray Hatch, the GPS guru, has a similar electron model; but it is not as concrete as the Bergman-Allen one; and I think that this is unfortunate as then one cannot calculate as much based upon it.  It then can only really be used as a qualitative guide.

I wonder, how answer on this question  may affect work of electron and proton accelerators. To begin with, should this issue be a REAL problem, there would be no chance to design any accelerator. To my knowledge, such accelerators work remarkably well. If this is so, then, the answer to posed question would shed new light on what? 

GPMB:  Yes, mathematics is often misused in the physical sciences.  In Dave Bergman'a and my electron modeling. it turns out that there is a mathematical singularity where no physical singularity exists.  And, also, sometimes one can have an integral that is infinite, but its "principal part" is finite and has a physical meaning which is important.  That's one of the main reasons why a good physical underlying theory is so important; it can then serve as a guide through the corresponding mathematics that enables one to obtain the correct physical answer ... even though mathematical singularities & other mathematical problems may still arise.

Graham, I don't believe in black holes, and Ronald Hatch concludes in his 2007 gravity paper that they do not exist. (See attached)

Graham> As CERN noted...".. they are making black holes albeit 😎😂 little one's"

Can you please point us to where CERN (as an official institution) noted that? With smileys and all??

Dear Dr. Oudet,

David Bergman and myself have successfully modeled the electron as a spinning torus of negative charge and the proton as a spinning ring of positive charge, and out articles are attached. These rings of charge are very smoothly embedded in the ambient vacuum so there are NO messy, messy boundary conditions and there is also no mysterious binding energy to keep them from flying apart due to strong Coulomb forces. Thus they have reality as they ate in equilibrium under electromagnetic forces. This is in line with Poincare's meta-theorem that all physical theory was ultimately electromagnetic.

God Bless,

Dennis P. Allen Jr., PhD (UC Berkeley 1968)

Dear Dr. Oudet,

I accidentally did not add my attachments, and they are below. (See also my ResearchGate.com web page.)

No, it is not possible to observe the rest mass of electron because electron can not stay at rest position.

Dear Dennis Allen,

Thank for your comment. In your paper “Foundation of Science, November, 1999,V2 N4in section Spin page 7 you wrote: The rest mass of an electron is almost equally divided between its electrostatic and magnetostatic energies. This of course gives Magnetic moment of one half Bohr magneton for the first quantum state. As a result if Bohr had known your approach the need of an additional h/2 quantum unit as introduce by Uhlenbeck and Goudsmit would never been suggested!

This also gives an answer to: “The one question science cannot answer: What is the magnetic field made up of?” of Emmanouil Markoulakis. In a different approach I also propose this kind of sharing with the hypothesis of small grains mass “The symmetry of the motion, the mass and the quantum state”.

Thank again Dennis for your very interesting result.

Xavier

Dear Xavior,

Many thanks for the thoughtful reply. You know, I'm not very familiar with modern quantum mechanics, as I prefer to attempt to redo it using Dave's and my electron and proton modeling with a neutron being an electron ring and a proton ring with the smaller proton ring having the same center of symmetry as the larger electron ting and both also having the same planes of symmetry but rotating in opposite directions so their currents are in the same direction ... and thus they "mutually spin pump" each other so as to create the extra energy equaling the (postulated) neutrino's energy in the neutron decay into a proton, an electron and an (assumed) neutrino.

I'm attaching three further files, the first relating to applying Dave Bergman and my electron and proton modeling to my minimally generalized mechanics (i.e. Neo-Newtonian mechanics) that does not assume that a point particle having inertial mass does not change this mass during certain types of motion ... and especially under non-linear accelerated motion. The second attached contains this mechanics of mine as Chapter 4; and I also attach a completely worked out, elementary example of a high spin, simple gyroscope that is assumed to be steadily precessing (without nutation) in a horizontal plane and its shaft having a fixed pivot point.

Finally, I attach some applications of this new mechanics to some inertial induction experiments such as those of Harvey Morgan, H. W. Wallace, and the Russian, V.N. Samokhvalov.

God Bless,

Denny

You are welcome my respected sir

Dear Preston Guynn,

I have given a look to your paper “Thomas Precession is the Basis for the Structure of Matter and Space” it is interesting but I am first an experimentalist and spent a lot of time with experiments. In fact with the theory I am often in difficulty with the thought experiments. There are no evidence that the reality is the same, nothing can replace the reality. At the differential scale SR seems to be correct since the wave equations give correct result.

With best regards,

Xavier

There is this 1967 Witteborn, Fairbank classical experiment: xdel.ru/downloads/lgbooks/fairbank_falling_electrons.pdf with "force was shown to be less than 0.09mg" conclusion.