The relativistic electron

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If we start with a hydrogen atom that is stationary, relative to our reference, the electron is nevertheless traveling with relativistic velocity. As such, the electron should be defining relativistic mass, distance and time due to its velocity, even though the atom, as whole, is stationary in our reference. So essentially the hydrogen atom is a combination of two distinct references.

The electron is also hard to pin down in the space within the 1S orbital. This uncertainty of location is expressed by the Hiessenberg uncertainty principle. This principle is needed because there are two distinct reference affects, but we traditionally model the electron using only the stationary reference of the nucleus. This results in one ending up with a level of uncertainy because the electron is not exactly within the zero reference, except via the wave function of the orbital. A more complete analysis needs to include the stationary and the relativistic references.

Anyone who would like to develop this historic problem is welcome to it.

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So, how is this an historic problem?

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The first energy level of hydrogen is -13.6eV. So an electron with more than 13.6ev will escape. This is very small compared to the mass of 511kev/c2 (ie. a factor of about 37,000), so the bound electron in a hydrogen atom is most certainly not relativistic.

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My interpretation is coming from conflicting accounts about the speed of electrons in atomic orbitals. I have read anywhere from 1/137 th of C to where relativistic affects should be evident. Does anyone know what the velocity of the electron is in an atomic obital? We can plug that into the equations to see if it is in the range of uncertainty.

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My interpretation is coming from conflicting accounts about the speed of electrons in atomic orbitals. I have read anywhere from 1/137 th of C to where relativistic affects should be evident. Does anyone know what the velocity of the electron is in an atomic obital? We can plug that into the equations to see if it is in the range of uncertainty.

Severian gave you all the nessacary information...

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Relatavistic effects would be quite small, even at 1/137 C. The Lorentz factor, denoted by gamma, , is extremely small. Infact, its 0.99997336. An electron, about 9.109 3826(16) × 10^−31 kg is mass, going at 1/137 C, would have a relatavistic mass of 9.109625281 x 10^-31. Thats a difference of 2.4268066 x 10^-35, Which is extremely small.

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If we do the calculation a little deeper the difference between 9.109 3826(16) × 10^−31 kg and 9.109625281 x 10^-31kg is about 1 in 25,000 more or less. As Servian pointed out, the mass of an electron has 37,000 times more energy value than the 13.6 ev escape velocity. If we combine all this, that amount of relativistic mass adds to roughly 13.6 ev. This is within the range of uncertainy. This assumes 1/137th C. This does not even take into account the potential energy in distance and time.

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The calculation was rounded downward (estimation math) since I am still not sure of the consensus speed of an electron. In any case, it is sort of interesting that the relativistic mass is in the range of ionization energy.

If we go back to the Hiesenberg uncertainty principle, it is no so much concerned with uncertainty in mass as it with uncertainy in distance and time. One can not really pin the electron down without alterring its energy. This is true because it is modelled as one reference. Distance and time relativity are also off by a factor of 1 in 25,000. If we assume two references we should be able to lower the range of uncertainty. Some math wizz may be able to get us zero uncertainty.

If we look at an electron in orbitals it not only has velocity but also has a constantly changing velocity vector due to the EM force and acceleration that keeps it in orbital space. With respect to relativity, the electron is contracting distance and dilating time within orbital space, with its affect maximized at the electron.

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What makes you think these two sentences are compatible?

As Servian pointed out, the mass of an electron has 37,000 times more energy value than the 13.6 ev escape velocity.

In any case, it is sort of interesting that the relativistic mass is in the range of ionization energy.

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My math was rounded down to make it more conservative. I was too lazy to do the real calculation because hard numbers based on approximation is better served with a math approximation. But if the mass of the electron converted to energy via E=MC2 ends up being 37,000 time more than the 13.6 ev, and the relativistic mass increase at 1/137 th C is about one part in 25,000, I figured 37/25 times 13.6. But I rounded down to 13.6 instead of use the value 20 ev. I don't know the electron speed, for certainty, so I was being very conservative. I do not believe this number has anything directly to do with ionization energy but I thought that it was sort of interesting.

Let me continue the idea of two references with another observation. An electron-positron pair can form from very energetic photons. But it does not lead to the net production of electrons, since the/or/a pair will annihillate with the release of energy. With the electron-positron, so similar, but differing in charge, this is an example of what happens when both charges are in the same reference. With the proton and electron in slightly different references, they can interact via EM force, but will dance around but can not easily combine into pure energy. I am sorry about this last assertion but I hope I can make it clearer.

If we look at a photon, it has no mass but expresses itself with distance and time, that we call wavelength and frequency. What is strange about this output arrangment is evident in special relativity and relative reference. Something traveling at C in our reference should be showing max distance contraction and max time dilation, yet what we see is the photon expressing something finite in distance and time. I believe that the energy of the photon is the amount of energy needed to maintain its finite references in distance and time apart from what a C reference should actually be. I call the energy of a photon a combination of distance and time potential, since it has no mass, and no mass times infinite gamma (V=C) is still zero and therefore the mass (less) aspect is consistent with the C reference. For example, a gamma ray has a tiny time interval or high frequency. It takes a lot of potential energy to maintain what should be an infinite time reference as an infintessimal time increment.

The conceptual problem this may create for others is due to our perception of time and distance. These standardized human measures are new with respect to the universe, i.e., over the past several hundred years. But ever since the beginning of evolution, photons have been creating standarized increments of distance and time. Maintaining these standards apart from C creates potential in distance and time. If we pump energy into an atom, the electron will increase distance and will take time to return to steady state. The release of energy restores the time and distance potential back to the photon.

If we go back to the creation of the electron-positron pair, the distance and time potential of the original photon, is converted to mass or what I call mass potential (V of the photon needs to fall from C), special relativity affects in distance and time, and distance and time potential phenomena that we call charge and EM force.

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Something traveling at C in our reference should be showing max distance contraction and max time dilation,

I think you missunderstand something. If something is travelling at c, it is massless, and travels at c in ALL frames...

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We are both correct. To travel at C it must be massless. The photon is massless and travels at C. But it still creates an affect in space and time that does not display the reference affects of something traveling at C. The affects we see are wavelength and frequency. There is a spectrum of these photons, all traveling at C. The combinations of D (wavelength) and T (frequency) all multiply to C. The departure from what should be V=C in distance and time, defines the energy of the photon. It sounds upside down but it is consistent with observation.

For example, if we had a particle of mass=0+, it could approach C before mass got infinite. It would also show near max distance contraction and max time dilation which will be defined by its velocity. Bump it up to C (and remove the mass), all of a sudden the max distance and max time is not all that forms. There are also things like gamma rays with minimial distance and time expressions. Since this is furthest from the logical extrapolation of max, max, it defines very high energy potential. On the other hand, the infinite wavelength from the event horizon of a blackhole is sort od what one would expect at C. These have essentially zero energy since there is no departure from the time and distance reference expected at C (one should see infinity pulled to a point).

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If we look at a photon, it has no mass but expresses itself with distance and time, that we call wavelength and frequency. What is strange about this output arrangment is evident in special relativity and relative reference. Something traveling at C in our reference should be showing max distance contraction and max time dilation, yet what we see is the photon expressing something finite in distance and time. I believe that the energy of the photon is the amount of energy needed to maintain its finite references in distance and time apart from what a C reference should actually be.

You should read that back. It just does not make sense. I don't mean in physics terms, I mean in linguistic terms, the last sentence in particular.

I call the energy of a photon a combination of distance and time potential, since it has no mass, and no mass times infinite gamma (V=C) is still zero and therefore the mass (less) aspect is consistent with the C reference.

Oh dear. Look, the relativistic calculations of m/(sqrt(1-v^2/c^2) do not apply to photons, or massless particles. You cannot cite zero times infinity is zero, that just is not a legitimate piece of mathematics or physics.

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It is a bit esoteric. One of the conceptual problems that I believe many are having is that it is generally assumed that distance and time are merely variables for measuring location in space and time. The photon demonstrates that measures of distance and time are not only quantitized but can travel through all distance and time references, while mainitaining the integrity of distinct distance and time quanta. This occurs because distance and time (wavelength and frequency) are also potential quanta. Maybe using distance and time as the two aspects of energy potential is leading to some confusion, but it is that simple. These same two potential quanta are also responsible for other phenomena like EM force.

Getting back to the esoteric, we have a particle with mass, at V=C-, relativistic distance and time will become nearly maximized. Picture the same mass particle at V=C-, but now only showing half distance contraction and half time dilation. One would say that is impossible since the mass is still almost infinite. But that is what photons do. Even though they are massless they are traveling at C, so distance and time should be experinecing maximized special relativity, but instead they show fractional variations of the max,max. Blackholes, at the event horizon, suck all but the lowest increment of potential out of photons giving them the expected max, max in distance and time, i.e, infinite wavelength.

The infinite wavelength energy quanta, with nearly zero energy value, imply that the time and distance potential of photons is actually zeroed at the speed of light reference. Deviation from the speed of light reference in distance and time gives the photon energy potential in distance and time. Although this appears backwards, it makes sense since matter contains potential which can only exist if it deviates from the speed of light. While the more the distance and time expression of photons deviate from the C reference, the more energy they define.

I am not just trying to be different for the sake of being different. This orientation has practical value. The two references of the atom is due to differences in time and distance potential. This is not vigorous math but it does help outline the task.

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Here is another area called speculation, even though the electron moves with significant speeds around a nucleus to be slightly relativistic, which can account for the uncertainty. Maybe the problem was my trying to introduce the MDT model of physics. What makes this model different than all the rest is simplicity. It only takes a shifting in perspective. It does not need to speculate other dimensions, speculations which are not censored seeing there is no tangible proof only mathematical necessity.

Personally, I have no problem with that because it is a good academic exercise that can open up the imagination, even if it is hypothetical. Is there a monopoly on hypothetical?

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Here is another area called speculation' date=' even though the electron moves with significant speeds around a nucleus to be slightly relativistic, which can account for the uncertainty. Maybe the problem was my trying to introduce the MDT model of physics. What makes this model different than all the rest is simplicity. It only takes a shifting in perspective. It does not need to speculate other dimensions, speculations which are not censored seeing there is no tangible proof only mathematical necessity.

Personally, I have no problem with that because it is a good academic exercise that can open up the imagination, even if it is hypothetical. Is there a monopoly on hypothetical?[/quote']

It's speculation, in part, because you have not yet done the simple calculation of the electron speed in the Bohr model. You have asked others to do it, and you appear to not like the general answer you've gotten, because you still insist that the electron is relativistic. If you are unable to do the calculation, you really have no business complaining that your posts have been removed from the physics boards.

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