Electrons do not “jump” or teleport from one energy level to the other

Neil deGrasse Tyson, you gotta fix this!

I am very happy that Neil Tyson made the series “Cosmos”, where it is another way to communicate science to people, which is necessary in this era. I, personally, haven’t watched it, because I’m a physicist and the guy usually talks about things I learned academically. However, my wife watched it… and she told me once: “Neil Tyson said that electrons disappear from one orbit and appear in another”… and she continued talking, while I interrupted and asked… what?! How could a physicist say that? That destroys the simplest rule in relativity!

And yes, he did say that, which is crazy actually, and I’m pretty shocked that this kind of mistake would come out of such a famous scientist. Look for yourself:

Why is that wrong?

Simply, because there is no reason to believe that this is the case. Back then, when Bohr provided his semi-classical solution of the hydrogen atom, those transitions were not understood very well, and they would’ve lead to such conflicts. But, do we still deal with Bohr’s model? Definitely not! We now know Quantum Mechanics.

Before delving into Quantum Mechanics, let me pose this question: Is there any experimental evidence that electrons “teleport” from one orbit to the other as Neil Tyson said? The answer is: NO! And if there is, please let me know about them in the comments.

So, even if we would assume that Bohr made a successful model that explains the hydrogen energy levels in steady state, does that mean that it can be blindly extended to explain the dynamics of electronic transitions? Definitely not! That’s not scientific at all.

Why is this not scientific? Because in science, we create models of natural phenomena, and then test them and try to disprove them. Now what we see in the case of Bohr’s model, is that it successfully explained atomic energy levels to a good accuracy, but there is no part in Bohr’s model that talks about transitions. Therefore, inferring blindly that electrons are only in those levels is… crazy!

On the other hand, this easily breaks special relativity’s main result: Particles do not exceed the speed of light. So, what does this mean? This means that if what Neil Tyson said is true, then Quantum Field Theory, which is a superset of Quantum Mechanics, agrees that nothing exceeds the speed of light, but the very simple hydrogen atom in Quantum Mechanics… does not. How crazy is that?

Quantum Mechanics and the hydrogen atom

Explaining the Quantum Mechanics (QM) model, the QM model comes up when solving the Schrödinger equation (time independent version of it), and the result from solving that is a wave-function, where this wave-function is directly related to the probability of finding an electron spatially somewhere.

In the case of a hydrogen atom, the Schrödinger equation is solved for simply a negative electron and a positive proton. The result of this problem is presented in a wave-function that uses complicated mathematical functions, called Legendre Polynomials and Spherical Harmonics. The result is presented in a nice picture that I found on Wikipedia.

Hydrogen_Density_PlotsNotice that the solution is not “black and white” like Neil Tyson described it. There’s a key on the right, where a $+$ and $-$ can be seen. The $+$ represents higher probability than the $-$ regions. The first row shows the typical spherical orbits that we understand from classical mechanics (the Bohr model), while the other rows show more complicated solutions that involve angular momentum.

Notice that in those solutions, the wave-function is never zero anywhere but at infinity and specific points (lines, or nodes) in space that are infinitely small (Thanks to Lance for making me notice that more nodes exist in the wave-function)! So, according to our current knowledge of the hydrogen atom, why should we believe that electrons disappear from level to another? I think there’s no reason whatsoever.

A little more detail on transitions

Many atomic physics books treated the problem of atomic transitions in a model called “Dipole Transitions”. The model is usually accurate with relative accuracy of around $10^{-6}$. In that model, the problem of transitions is very well understood. For example, in the book Optically Polarized Atoms: Understanding light-atom interactions, there is a section called “Visualization of atomic transitions”. In it, the author shows that a transition from one state to another can be well modeled with a simple time evolution operator that incorporates the two involved states.

For a transition from state $\left|2P\right\rangle$ to the state $\left|1S\right\rangle$ can be modeled with a simple wave function

$$\psi=a_{1}\left|1S\right\rangle +e^{-i\frac{E_{2}-E_{1}}{\hbar}t}a_{2}\left|2P\right\rangle$$

where $a_1,a_2$ are normalization factors, and $E_1,E_2$ are the energies of the states. We see that an oscillation of frequency (in units of energy) $E_2-E_1$ would happen, leading to the production of a photon. Then, again, why should we ever believe that electrons teleport from one atomic state to the other?

Is it just simplicity?

Probably some people will argue that Neil Tyson was simplifying the atomic model for common people, but then I would ask the question: When did simplifications start to communicate false or wrong information? I think simplifying does not justify giving people wrong information at all.

Another simpler mistake

One more simple mistake Neil Tyson did in that video, is that he claimed that spontaneous decays are not understood (with why they happen). This is actually not true. In the same book I mentioned above, a discussion was put on that spontaneous decays happen due to spontaneous quantum fluctuations, that act as a stimulus for atoms and hit them. Therefore, technically, spontaneous decays do not exist; they’re just another form of stimulated emission.

This is not a big deal, though. I think this is an advanced issue, and claiming that “we don’t know” is better than posing wrong information.

Conclusion and discussion

I didn’t make this article to blame Neil Tyson, and actually he’s done a very good job with Cosmos. But I made this article because I found it common in social networks that people use this wrong information, and it has to be cleared out. I actually would be very grateful to him if he would fix this mistake and replace the episode.

The conclusion of this article, is that electrons do not teleport from one energy level to the other. There’s no evidence on that whatsoever! Electrons are, also, not strictly bound to those energy levels. According to our understanding of the quantum world, electrons have a probability cloud; and an electronic transition (dipole transition) will just make this cloud oscillate continuously from one energy level to another one continuously.

Should we trust eBay? Short answer: No!

Unlike all large corporations that try to become famous and trustworthy through good products, eBay proves, day after day, that they become famous by monopolizing the internet selling business.

Every time, and I really have to say this clearly: Every time I sell something on eBay there has to be something hidden in the deal. From the outside, they write that your offer costs: 0.00. But would it end there? Definitely not! You sell your product and you’re happy, but eventually you get an invoice that you have to pay something like 3%-5% of the price of whatever you sold.

If one reads the policy of eBay in their help section, one will find that they clearly state that personal selling is free for up to 20 items per month. What does this mean in the real world? Nothing whatsoever! They still charge you.

In the following picture, you see that I sold components from my older computer. They charge me for them, although I’m not selling them as commercial.

 

eBayInvoice
eBay charges you for personal transactions, even though they clearly say that there are no charges for up to 20 items of noncommercial deals (click to view full size).

I’m not happy as a customer. What should I do? Of course, they have no e-mail to contact, because although they suck millions from customers through a robot server that practically doesn’t cost anything, they can’t hire some customer service to answer your questions! So, if you have a problem, please use the non-free phone number, where they’ll make you pay more than the amount you’re complaining about with your phone!

Is this the only time? Not really… I don’t remember once when I sold stuff with eBay peacefully with no problems.

Let me top that with a nice story. Like a few years ago, I was stupid enough not to use PayPal and buy a processor for 400 euros. The seller didn’t send anything and it turned out it’s a scam. How did the guy do it? He simply put an external picture (from outside eBay) which was white. And after the payment, he changed the external link to contain text that says “The item will be sent with no insurance, and the buyer will be responsible”. I realized the trick, and informed eBay. Did they help? Actually they didn’t even try! They made me pay around 45 euros for phone calls with them, but they did nothing! They didn’t cooperate in any way, and my money was gone.

The morale out of this? Don’t use eBay unless you must. Because there’s always something hidden in their “copy of the rules” that you won’t know about until you’re given a good hit.

Peace!

Tired from LaTeX tedious coding? Try LyX!

I was really tired from latex and it’s extremely tedious way of writing every equation. Of course, the resulting documents from latex are wonderfully organized and perfect for all scientific purposes.

For example, writing equations with latex is horribly complicated… It’s almost a rule whenever you use latex that you miss a bracket that your latex compiler complains or you get the wrong equation. So what’s wrong with the philosophy “What You See Is What You Get”? Nothing except that people often feel they don’t have the same degree of freedom.

The question is: Is there a way to use the full power and facilities of latex, without the suffer one has to live with it? I think the answer is Yes! The answer is LyX.

LyX is a software that’s based on latex, where it codes latex in the background. It can do everything latex does, with all the freedom you require in latex (that could go to the level of looking into the source), while at the same time, you could work in an environment of “What You See Is What You Get” (at least for equations). LyX in reality uses the philosophy “What You See Is What You Mean”, which is the same philosophy of latex but with no coding, except that you can see how your text looks like in the parts that matter, like text style and equations and figures.

In the worst case, if LyX has a function does not have a function that latex has, one can still write latex code inside lyx!

People who’re used to using latex will definitely complain and say “latex for the win”, while I agree that it’s a matter of taste. But I’m a person who likes dedicating more time on the idea rather than on styling, especially when it comes to documentation. There’s no doubt that making the same document on LyX takes much less time than it does on LaTeX. Therefore, the question rises: Why should I spend more time on coding when I still can do the same with a better tool?

Try lyx, and try to make use of it. It does nothing but make you spend half as much time you do to write an article in a scientific journal.

Faith is the enemy of science

As cliché as this phrase would sound, I had the luxury of learning it from practice rather than from hearing.

I spent 3 years of my life working on optically pumped vapor cesium magnetometers in the nEDM (neutron Electric Dipole Moment) experiment at PSI. For almost 10 years, it was believed by experts that cesium magnetometers are absolute magnetometers, with 100% accuracy, and it was believed that a magnetometer is only limited by its sensitivity.

This was believed in an experiment where the relative precision of the measurement required is $10^{-10}$. After spending three years with this belief, which was as long as 10 years for others in my group, and while I was investigating another quantum mechanical effect called “The Quadratic Zeeman Effect”, I stumbled upon an effect that relates the laser power to an absolute shift that could reach 100 pT; which is a relative accuracy shift of $10^{-4}$. Yes, 6 orders of magnitude were omitted for all those years, just because an inherited belief was carried on from one person to the other; with no experimental measurement that proves that cesium magnetometers are really absolute magnetometers.

Although I left religions long years ago, where I realized back then that faith never leads to anything related to the truth; I never realized that faith could find its way into my life again, in some other way.

Opposing faith while seeking the truth about reality is one of the greatest challenges a researcher could face. One would never realize where faith could sneak into your science career to ruin something you’re doing.

Be aware of it!

Cheers, I learned my lesson 🙂