The mass changes. On the possibility of changing gravitational influence. Does the mass of an electron change with its “energy state”

I don't know where I came from, where I'm going, or even who I am.

E. Schrödinger

A number of works noted an interesting effect, which consisted in a change in the weight of objects in the presence of rotating masses. The change in weight occurred along the axis of rotation of the mass. In the works of N. Kozyrev, a change in the weight of a rotating gyroscope was observed. Moreover, depending on the direction of rotation of the gyroscope rotor, there was either a decrease or increase in the weight of the gyroscope itself. In the work of E. Podkletnov, a decrease in the weight of an object located above a superconducting rotating disk, which was in a magnetic field, was observed. In the work of V. Roshchin and S. Godin, the weight of a massive rotating disk made of magnetic material, which itself was a source, was reduced magnetic field.

In these experiments one can highlight one common factor– the presence of a rotating mass.

Rotation is inherent in all objects of our Universe, from the microcosm to the macrocosm. Elementary particles have their own mechanical moment - spin, all planets, stars, galaxies also rotate around their axis. In other words, the rotation of any material object around its axis is its integral property. A natural question arises: what reason causes such rotation?

If the hypothesis about the chronofield and its impact on space is correct, then we can assume that the expansion of space occurs due to its rotation under the influence of the chronofield. That is, the chronofield in our three-dimensional world expands space, from the region of subspace to the region of superspace, spinning it according to a strictly defined dependence.

As already noted, in the presence of gravitational mass, the energy of the chronofield decreases, space expands more slowly, which leads to the appearance of gravity. As you move away from the gravitational mass, the energy of the chronofield increases, the rate of expansion of space increases, and the gravitational influence decreases. If in any area near the gravitational mass the rate of expansion of space is somehow increased or decreased, this will lead to a change in the weight of objects located in this area.

It is likely that experiments with rotating masses caused such a change in the rate of expansion of space. Space somehow interacts with the rotating mass. With a sufficiently high rotation speed of a massive object, you can increase or decrease the speed of expansion of space and, accordingly, change the weight of objects located along the axis of rotation.

The author made an attempt to verify experimentally the assumption made. An aviation gyroscope was taken as a rotating mass. The experimental design corresponded to the experiment of E. Podkletnov. Weights of materials of different densities were balanced on analytical balances with a measurement accuracy of up to 0.05 mg. The weight of the cargo was 10 grams. Under the weighted scale there was a gyroscope, which rotated at a fairly high speed. The frequency of the gyroscope supply current was 400 Hz. Gyroscopes of various masses with different moments of inertia were used. The maximum weight of the gyroscope rotor reached 1200 g. The gyroscopes were rotated both clockwise and counterclockwise.

Long-term experiments from the second half of March to August 2002 did not yield positive results. Sometimes minor weight deviations within one division were observed. They could be attributed to errors arising due to vibrations or other external influences. However, the nature of these deviations was unambiguous. When the gyroscope was rotated counterclockwise, a decrease in weight was observed, and when rotated clockwise, an increase was observed.

During the experiment, the position of the gyroscope and the direction of its axis changed at different angles to the horizon. But this also did not give any results.

In his work, N. Kozyrev noted that changes in the weight of the gyroscope could be detected in late autumn and winter, and even in this case, the readings changed during the day. Obviously, this is due to the position of the Earth relative to the Sun. N. Kozyrev conducted his experiments at the Pulkovo Observatory, which is located about 60° northern latitude. IN winter time year, the position of the Earth relative to the Sun is such that the direction of gravity at this latitude is almost perpendicular to the ecliptic plane (7°) during the daytime. Those. the axis of rotation of the gyroscope was practically parallel to the axis of the ecliptic plane. IN summer time, to obtain the result, the experiment had to be tried at night. Perhaps the same reason did not allow E. Podkletnov’s experiment to be repeated in other laboratories.

At the latitude of Zhitomir (about 50° north latitude), where the experiments were carried out by the author, the angle between the direction of gravity and the perpendicular to the ecliptic plane is almost 63° in summer. Perhaps for this reason, only minor deviations were observed. But it is also possible that the impact was also on the balancing loads. In this case, the difference in weight was due to different distances from weighing and balancing weights to a gyroscope.

One can imagine the following mechanism for weight change. The rotation of gravitational masses and other objects and systems in the Universe occurs under the influence of the chronofield. But rotation occurs around a single axis, the position of which in space depends on some factors that are still unknown to us. Accordingly, in the presence of such rotating objects, the expansion of space under the influence of the chronofield acquires a directional character. That is, in the direction of the axis of rotation of the system, the expansion of space will occur faster than in any other direction.

Space can be imagined as a quantum gas that fills everything even inside atomic nucleus. Between space and material objects, within which it is located, there is an interaction that can be enhanced under the influence of external factors, for example in the presence of a magnetic field. If the rotating mass is located in the plane of rotation of the gravitational system and rotates in the same direction with sufficient high speed, then along the axis of rotation space will expand faster due to the interaction of space and the rotating mass. When the directions of gravity and the expansion of space coincide, the weight of objects will decrease. With the opposite rotation, the expansion of space will slow down, which will lead to an increase in weight.

In cases where the directions of gravity and the expansion of space do not coincide, the resulting force changes insignificantly and is difficult to register.

The rotating mass will change the tension gravitational field in a specific place. In the formula for the gravitational field strength g = (G· M) / R 2 gravitational constant G and the mass of the Earth M cannot change. Consequently, the value changes R– the distance from the center of the Earth to the object being weighed. Due to the additional expansion of space, this value increases by Δ R. That is, the load seems to rise above the Earth’s surface by this amount, which leads to a change in the strength of the gravitational field g" = (G· M) / (R + Δ R) 2 .

In the case of slowing down the expansion of space, the value of Δ R will be deducted from R which will lead to weight gain.

Experiments with weight changes in the presence of a rotating mass do not allow achieving high measurement accuracy. Perhaps the rotation speed of the gyroscope is not enough to cause a noticeable change in weight, since the additional expansion of space is not very significant. If similar experiments are carried out with quantum clocks, then higher measurement accuracy can be achieved by comparing the readings of two clocks. In the area where space is expanding faster, the tension of the chronofield increases, and the clock will move faster and vice versa.

Information sources:

  1. Kozyrev N.A. On the possibility of experimental investigation of the properties of time. // Time in Science and Philosophy. Praga, 1971. P. 111...132.
  2. Roshchin V.V., Godin S.M. Experimental study of nonlinear effects in a dynamic magnetic system. , 2001.
  3. Yumashev V.E.
Remember from the course general physics What are Galileo's transformations? These conversions are some way to determine whether this case relativistic or not. The relativistic case means movement at sufficiently high speeds. The magnitude of such speeds leads to the fact that Galileo's transformations become impossible. As you know, these coordinate transformation rules are just a transition from one coordinate system, which is at rest, to another (moving).

Remember that the speed corresponding to the case of relativistic mechanics is a speed close to the speed of light. In this situation, Lorentz coordinate transformations come into force.

Relativistic impulse

Write out an expression for relativistic momentum from a physics textbook. The classical formula for momentum, as is known, is the product of the mass of a body and its speed. In the case of high speeds, a typical relativistic addition is added to the classical expression of momentum in the form of the square root of the difference between unity and the square of the ratio of the speed of the body and the speed of light. This multiplier must be in , the numerator of which is classic performance impulse.

Pay attention to the form of the relativistic momentum relationship. It can be divided into two parts: the first part of the work is the ratio of the classical mass of the body to the relativistic addition, the second part is the speed of the body. If we draw an analogy with the formula for the classical impulse, then the first part of the relativistic impulse can be taken as the total mass characteristic of the case of motion at high speeds.

Relativistic mass

Note that the mass of a body becomes dependent on the magnitude of its speed if we take general form masses of relativistic expression. The classical mass in the numerator of the fraction is usually called the rest mass. From its name it becomes clear that the body possesses it when its speed is zero.

If the speed of the body becomes close to the speed of light, then the denominator of the fraction of the expression for mass tends to zero, and it itself tends to infinity. Thus, as the speed of a body increases, its mass also increases. Moreover, from the form of the expression for the mass of the body, it becomes clear that changes become noticeable only when the speed of the body is sufficiently high and the ratio of the speed of movement to the speed of light is comparable to unity.


SPECIAL THEORY OF RELATIVITY 3 - MASS AND ENERGY

In the above work on Einstein's theory of relativity (see p. 163), it was proven that the mass of a body depends on its speed and if energy is imparted to the body, its mass increases, and with the loss of energy its mass decreases.

Mass is a measure of inertia, i.e. the property of a body to maintain a state of motion or rest. Einstein proved that the mass m of a body depends on its speed υ in accordance with the equation m = γ m 0, where m 0 is the rest mass of the body, γ is the Lorentz factor equal to (1 - υ 2 /c 2) - 1/2 .

Energy is the body's ability to do work. The scientist proved that if a body is given an amount of energy ΔE, its mass changes by Δm in accordance with the equation ΔE = Δtc 2, where c is the speed of light in vacuum. Any body of mass m has a total energy E = mc 2

Changes in mass due to changes in the amount of energy are insignificant for chemical reactions and movements of objects relative to the Earth.

In order for a body weighing 1 kg to break away from the Earth and leave it, it needs to be given an energy of 64 MJ, which will increase the mass of the body and the Earth by an insignificant amount.

In typical chemical reactions Energy changes on the order of an electron volt (1.6 x 10 19 J) are observed. In this case, the mass changes by an amount much smaller than the mass of the electron.

Changes in mass caused by changes in energy are significant in nuclear reactions, where extremely powerful forces hold protons and neutrons together, overcoming the electrostatic repulsion forces of the protons, unless the unstable nucleus decays. In nuclear reactions, energy changes occur on the order of MeV per nucleon, which is approximately a million times greater than in chemical reactions. Consequently, the change in mass with a change in energy by 1 MeV is quite significant relative to the rest mass of the nucleon. The mechanism due to which the mass of a body changes with a change in energy is not yet completely clear, although there is much experimental evidence for the equation E = mс 2.

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For a long time quantum mechanics confidently believed that when the speed of a body changes, its mass changes. This mass was called “relativistic” to emphasize its variability. Currently, this optimism has faded a little.

Previously, many venerable scientists, with all the power of their genius, tried to show why and how body mass should increase with increasing speed. And this was partially successful and it turned out that the mass always increased according to the relation m = (1).

This phenomenon, for example, was confirmed in Kaufman's experiments with particles. But no one understood why the mass of a body suddenly increases with an increase in the speed of the body, and even increases to infinity. Few people were interested in where this mass comes from. No one could explain this phenomenon, so many scientists and ignoramuses did not believe it. They believed their eyes, their experience - mass is a constant quantity. There is no “relativistic mass”, period. But both those who believe in the presence of such a mass and those who do not believe with the greatest tenacity admit that the photon does not have mass. When you read about this, you see how not far we have moved from the Neanderthal. If someone had told a Neanderthal sitting in a cave that there was a waterskin in his cave, he would never have believed it. He would point to a mammoth skull and say that there is not a drop of water in the cave. No matter what you told him about humidity, evaporation, molecules, no matter what formulas you gave him, he would probably remain unconvinced. So do we - a photon has momentum, energy, speed, but not mass. We know that an electron has mass, and everyone knows this. We all know, except the orthodox, that an electron emits photons. Well, the electron emitted one photon, changed its speed, accelerated it again, it again emitted some photon, etc. This can be done in the collider without difficulty. And what? Does the electron remain the same after all the radiation? Or did the energy fly away, but the mass remained? succeeded in Large Collider squeeze all the energy out of an electron and get the Higgs boson?

Do you see what a mess? Understand whether this mass exists, or it doesn’t, or it’s somehow different. Someone has already proven or convincingly suggested that the mass of a particle does not depend on its speed and is an invariant. This means that expression (1) does not make sense.

Everything falls into place if you understand that a photon has mass. True, this is a very small quantity and we cannot measure it, just as a Neanderthal could not measure the amount of water that evaporated. R. Feynman in his QED says that force gravitational interaction “...between two electrons is 1 with 40 zeros times weaker than electric (possibly with 41 zeros)”.

Sergei Semikov, a passionate admirer of the emission theory of Walter Ritz, in the article “On the nature of mass and time” (article published in the magazine “Engineer” No. 5, 2006) writes:

“Since the electrical interaction F of two electrons is 1042 times stronger than the gravitational interaction G, then one electron should contain approximately the same number of rheons. In this case, it is clear why an electron, constantly emitting myriads of rheons, loses almost no weight.”.

For some reason he called them reons "particles that carry electromagnetic influences, as Ritz puts it.

And I intuitively want to believe this. Now hardly anyone believes that the electron is some kind of monolith. The assumption that an electron consists of 100, 1000 or even a million small particles does not warm the soul either. If there were 100 or 1000 constituent parts in an electron, it would manifest itself in something.

Common sense says that if a part of something is taken away, then it has lost part of what was taken away. If it was a mass, then it is now smaller. Not to be confused with the pit: there we select one thing, and another is added. Thus, we can assume that after the emission of a photon (this can be many quanta), the electron did not “get heavier”, but, on the contrary, “lightened”. And when a photon is absorbed, a real, not conditional, “weighting” of the electron occurs. So the electron mass is quite an additive quantity. How can you even see this “weighting”? Where could it have come from? Perhaps this was observed in the accelerator. If you accelerate an electron in an accelerator, you will notice that obtaining acceleration by the same amount at a speed of 10 km/sec and 1000 km/sec requires different power for the accelerating unit. From this it is easy to conclude that the mass of the electron has increased. And indeed it has only increased not absolutely (it has decreased absolutely), but relative to the force giving it acceleration. How did this happen? Let's imagine a flat, or close to it, electric field; this will always automatically happen if the accelerating field is larger in area than the electron field. It gives acceleration to the electron. After the photon is emitted, part of the mass (charge) is lost. And the charge is distributed in the electron in inverse proportion to the square of the radius. As a result, the mass will decrease more slowly than the cross section of the charge, i.e. electron. This means that per unit mass, for the same acceleration, an increasingly greater and greater density of the accelerating field will be required. Hence the appearance of “weighting”. If the force were not distributed, but point-like, then such an effect would not be observed. To be fair, it should be said that all this can be calculated and this hypothesis can be confirmed or refuted. And it would be desirable to do this, since the situation is very bad, especially in the field of education.

In the methodological collection “To help teachers and students,” published by POIPKRO, 1998, No. 6, pp. 106-111. Co-author N.V. Ryabtseva published an article How the myth of the “relativistic mass” arose. It says:

“The idea that the mass of an electron depends on the speed of its movement was put forward by Kaufmann in 1896-98. They carried out experiments on the deflection of cathode rays in a magnetic field. Naturally, in his calculations he used classical expressions for the momentum and kinetic energy of the electron (another 7-9 years will pass before the creation of SRT). Kaufman's calculations led to a formula from which it followed that the specific charge of an electron, e/m, depends on its speed. And since Faraday formulated the conservation law electric charge, then Kaufman suggested that the mass of the electron depends on the speed”.

And what conclusion is drawn from this quote? Anyone who has not read this article will never guess. There is only one conclusion: the concept of relativistic mass was introduced before the appearance of SRT. Those who wrote this article were not interested in the fact that The specific charge of an electron e/m depends on its speed. Which physical phenomena occurred, which led to a change in the charge-mass ratio? What has changed in the electron itself? What force and how did it act on the electron? Why did they decide that in this relationship it was the mass that changed, and not the charge, or both? These and other questions did not interest them. And even the fact that the photon, in their opinion, has no mass, is accepted as an immutable fact, although there is no justification for this. The word “relativistic” is perceived as “green”, “high” or any other way. “Relativistic” means relative. Relative - in relation to what? Regarding the force accelerating this mass. The mass does not have to increase absolutely, assuming the force is constant. The mass can absolutely decrease, but the force can decrease even faster and it turns out that the mass increases relative to the force. This is what Kaufman saw, and this confirms the existence of the phenomenon of mass relativism. When in a collider or any other accelerator the total power is increased and increased in order to accelerate a particle, then less and less power gets to the share of this particle, and it seems that its mass is growing.

Our scientists are truly amazed:

“It was only in 1977 that a university textbook on SRT by V. A. Ugarov was published, in which for the first time in our educational literature the concept of RM was not only not used, but also a special paragraph was included in which the absence of any physical content in RM was logically shown. But school and university physics programs, extensive popular science and any other literature related to SRT continued to enthusiastically discuss the dependence of the mass of a moving body on the speed of its movement. It took the intervention of the prominent Soviet theoretical physicist L.B. Okun, who published a large article in the international journal “Advances in Physical Sciences” entitled “The Concept of Mass” (1989). Then the journal “Physics at School” published an article by one of the authors of this message entitled "Is there a relativistic mass? (1994). His textbook was published earlier (G.A. Rozman, Special Theory of Relativity (1992). These and other publications about RM forced the compilers of school and university programs And teaching aids finally eliminate the concept of PM. New school textbooks have appeared (“Physics-11” edited by A.A. Pinsky, “Physics-11” edited by N.M. Shakhmaev, “Physics-10” by S.V. Gromov), setting out the foundations of SRT in modern scientific and methodological level. Let’s hope that the new generation of teachers will not use the concept of RM and physics will forget another myth associated with the interpretation of SRT.” .

I don’t know how respected V.A. Ugarov logically showed “absence of any physical content in the Republic of Moldova”, but I think it’s not “more logical” than Mr. Rozman proved that a ball in any ISO will look like a ball. We will not analyze this example, only note that Rozman’s logic is that signals from all points of the cube, to the eye or other recording device, arrive simultaneously, which is only possible from a photograph of the cube.

Our Skolkovo will not soon turn into Silicon Valley if we study using such textbooks.

Yustai Igo

Does the mass of an electron change with its “energy state”?

When an electron absorbs a photon, it moves to a higher energy state and enters the upper orbit/shell.

Does (or should) this absorption of energy affect its mass (albeit incredibly little)?

Can we measure the mass of an electron while it is still bound to the nucleus?

Aron

Depends on what mass you are referring to... Are you talking about gravitational mass or inertial mass or rest mass?

Jeffrey

@Aron This is a very misleading statement. I even want to say that this is completely wrong, since, as far as we know, inertial mass and gravitational mass are the same. Moreover, unless you're trying to differentiate them with some big subtlety (like mass-energy density), rest mass is also equivalent to the other two terms. I'm not sure what you're trying to achieve, but I think it really confuses the problem at hand.

Aron

@Geoffery. You are very wrong. Rest mass and inertial mass are NOT equivalent except when at rest. Simple SR. Yes, inertial mass and gravitational mass in massive particles are equivalent to a few parts per million, but I'm not sure about concepts like holes.

Ruslan

@Aron No, You very wrong. According to the principle of equivalence of general relativity, the inertial and gravitational masses are absolutely identical. And they are equal to the rest mass. If you show otherwise, it will be a major discovery.

Pelto

Let's just add that for electrons interacting with a lattice of atoms (especially in semiconductors), there is also the concept of "effective mass". This is simply a device for summing up the interaction effect (more or less like "relativistic mass"), but it is useful when working with crystals.

Answers

John Rennie

This is really an extended comment on Jeffrey's answer, so please describe Jeffrey's answer rather than this one.

Hydrogen atom mass 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353270 × 10 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> - 27 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">1.67353270 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">× 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">10 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">- 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">27 kg. If you add the mass of a proton and an electron together, they 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353272 × 10 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> - 27 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">1.67353272 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">× 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">10 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">- 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">27 kg. The difference is about 13.6 eV, which is the ionization energy of hydrogen (although it should be noted that the experimental error in masses is not much less than the difference, so this is only an approximation).

This shouldn't surprise you because you have to add energy (in the form of a 13.6 eV photon) to split a hydrogen atom into a free proton and electron, and this increases the mass according to known equation Einstein E = m c 2 " role="presentation" style="position: relative;"> E E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> = m With E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> 2 E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;">E E = m c 2 " role="presentation" style="position: relative;">= E = m c 2 " role="presentation" style="position: relative;">m E = m c 2 " role="presentation" style="position: relative;">c E = m c 2 " role="presentation" style="position: relative;">2 So this is a direct example of the increase in mass that you are describing.

However, we cannot say that this is an increase in the mass of the electron or proton. This is an increase in the mass of the combined system. The constant masses of the electron and proton are constant and do not depend on whether they are in atoms or freely moving. The change in mass occurs from a change in the binding energy of the system.

Jeffrey

The rest mass of a particle never changes. Its mass is a natural constant, and one of the numbers that uniquely identifies it (such as its rotation). On the other hand, the invariant mass of an atomic system does increase when the electron becomes excited, bringing the atom into a higher energy state. In this sense, the atom (rather than the electron) becomes "heavier" due to the increased energy of the internal configuration of the particles.

Yustai Igo

So the atom as a whole becomes heavier, while the material of its composition remains the same mass? By material I mean it is particles. So the increase in the total mass of an atom absorbing photons increases due to its energy component and not due to the increase in particle mass?

Jeffrey

Basically yes. The conceptual explanation is based generally E = m c 2 " role="presentation" style="position: relative;"> E E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> = m With E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> 2 E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;">E E = m c 2 " role="presentation" style="position: relative;">= E = m c 2 " role="presentation" style="position: relative;">m E = m c 2 " role="presentation" style="position: relative;">c E = m c 2 " role="presentation" style="position: relative;">2 idea. Roughly speaking, increased atomic energy is translated into increased atomic mass through relativistic effects. I think John's answer is an excellent explanation.

dmckee♦

Correct only if you are using text from the Eisenhower administration (to quote the regular edition of Physics SE) Invariant mass remains invariant. This answer is also not useful for a bound electron, which does not have a well-defined momentum.

Yustai Igo

I thought there was no such thing as "invariant mass" since all matter in our universe is in a constant state of motion. So the whole "rest mass" thing is a little misleading if you keep the big picture of the cosmos in mind. No?

HolgerFiedler

@YoustayIgo: Great.

Jeffrey

@YoustayIgo This idea, which you explain in your comment here, is a common misconception caused by what people hear about moving particles becoming more massive. Within special theory relativity, a fast moving particle is generally more difficult to accelerate than Newton's laws would predict, which are often - and misleadingly - like increasing the particle's mass, when in fact it is simply a fact of relativistic mechanics that it not Newtonian mechanics. Relativity is marvelous new world. Take it on your terms.

dmckee♦

@YoustayIgo The invariant mass of a particle or system is defined as the length of the energy-momentum vector four. As such it is a Lorentz scalar and is measured the same in any reference system. All Lorentz scalars (including proper time) have this property, so people who take relativity seriously rely heavily on them because they are just all kinds of calculations. Most relativists say only about invariant mass, abandoning the unnecessary, outdated and misleading concept of “relativistic mass”; which does not mean that this concept cannot be defined and used.

Dzidza Mawuli Yao Emmanuel

I performed an experiment to get frequency data circular motion(f) and how it relates to the length (L) of the pendulum. In the experiment, the pendulum is shifted through a large angle to make a horizontal circle. Ten revolutions are timed.

From observation it is clear that the frequency f is inversely proportional to the length L of the pendulum, but directly proportional to the speed v of the circular motion.

f - kV/l. Introducing f --_w / 2pi and V-- rw f-- V/2pirL. From this equation, frequency is inversely proportional to radius r.

This math from my experiment had implications for the atom and its electrons that: 1. Electrons close to the nucleus have high kinetic energy and they move at high speed, while those far away have high potential energy, and they move at low speed. Thus, kinetic energy decreases with increasing radius. 2. This confirms the uncertainty principle, which focuses on the position and momentum of electrons and their location in this moment time. Electrons close to the nucleus have high momentum, so the uncertainty of their position is high, but those electrons that are far from the nucleus have lower momentum, so the uncertainty of their momentum is high. This is caused by the frequency of their circular motion. 3. The observation explains why the size and mass of atoms increase per group in the periodic table because the radius of the atoms increases and the frequency of electron circular motion decreases. 4. The observation points to the fact that the mass and size of electrons depend on their distance from the nucleus, therefore electrons in the same atom have different masses, although the difference is insignificant and has different sizes. So electrons have size, although they may be point particles. I'm still working on the experiment. This experiment explains some of the absurdities in solar systems and their location.

My name is Dzidza Mawuli Yao Emmanuel from Ghana in West Africa. Lives in Volta. Teaching in high school high school Agbozume - Southern District Ketu. Email: [email protected]