What is exactly non-deterministic in our universe?

What is determinism?

Determinism is the concept that the physical world that we live in is wound like a clock. The concept says that if we would know every law that governs the universe, and we have the computational power to compute those laws; then, we may know the future with 100% certainty.

Bad news is…

This universe is non-deterministic. We know this, now, with great certainty, and with many experiments and many successful models that have shown, so far, that this is true. In fact, Einstein had fought his last 20 years, before his death, to disprove this fact, and he failed.

Will someone else disprove it? A Nobel prize awaits this Genius, if he could do it!

Main question of the article

What if an observer lives outside our universe and monitors the universe from the outside, and knows the internal parameters that control our universe. Will he be able to determine the future infinitely precisely?

It’s a very complicated question in fact to think about. However, in order to answer the question, we have to understand what is non-deterministic in our universe.

How can we tackle this question?

In order to understand the answer to this question, we have to understand what it is that we have to predict. And understand why uncertainty shows up in the first place.

Where does uncertainty come from?

Uncertainty comes mainly from the fact that we deal with a world governed by some classical parameters. For example, we deal with energy and position. Those parameters, if known very well, describe our systems very accurately.

In other words, in the simplest form, if we know the positions and energies of a set of particles; we may, as well, predict the future and dynamics of the system very accurately.

What is it that we’re uncertain about in our universe?

Here comes the problem. When we go to the microscopic level of particles, we find that the macroscopic (large scale) description of systems is very different. In quantum mechanics (QM), systems are defined by the so called “wave packets”. They’re not anymore “objects” like we thought of them before.

The above picture shows that a particle in its microscopic description is not a particle, as we had learned about it before. It’s a wave packet. If we try to look at this wave packet from our classical view, the transition from the wave description to the macroscopic, classical description, will suffer uncertainties. Look at the particle at the bottom. While the wave on the top is very clear and well defined with no uncertainties whatsoever, the bottom, classical, picture of the particle suffers uncertainties.

The problem is the transition

Our particles are described by wave packets in the microscopic level. But in our world, we don’t deal with wave packets. We deal with particles. We deal with well defined energies and well defined positions. Therefore, we need a transformation that will take our wave packet from its wavy picture, to a picture that is compatible with our classical observations. This transformation is called in QM the expectation value. When performing this transition, there is no way we can do it without uncertainty. For example, in the particle seen in the picture, we can never, ever, define a single point that characterizes the position of the particle. There’s no position! The particle is smeared over a volume of space. Therefore, the transformation from the QM picture, with wavy properties, to the classical picture, is the cause of uncertainties.


The reason of non-determinism in this world is not that we don’t know the characteristics of a particle in its wave nature. The main problem causing uncertainty to appear is that the description of particles in their microscopic form is always coherent with uncertainties, due to the incompatibility of the world views when taking the step from the microscopic world to the classical world.

Answering the main question: Will someone outside the universe, who knows the parameters of those wave packets, be able to predict the future with 100% certainty? The answer is NO. Because the fact that a transformation from the wavy form to the classical form contains uncertainties is not related to our physical world. It’s rather related to the mathematical nature of this transformation, which inherently will cause uncertainties to appear, independent of the knowledge of the entity performing this transformation.


Physics models nature, it doesn’t find its laws

One huge misconception of physics is that it seeks laws that are presumed to exist in it

No! Physics does not presume that nature has laws and tries to find them. Physics simply studies a phenomenon, and then tries to create a law that is accurate enough to reproduce the phenomenon, or at least to predict its existence in the future.

Do those sound not different from each other?

They are very different! In the assumption that nature contains laws that we try to find, we assume that the laws that we find in nature are 100% accurate. Not only this, but we also assume that the laws of physics represent the system in its roots. Both assumptions are not true!

Why is this wrong?

Because the laws of physics that we create depend solely on our observations of those phenomena. With no doubt, our observations are simply a projection of reality and not reality.

Has there been incidents that show that this is the case?

Yes! Along the history of physics, we have always seen that the laws we discover are simply a superset of older laws. For example, take a look at Newtonian Mechanics (NM) and Quantum Mechanics (QM). In NM, we created a physical quantity called “Energy”, and this energy played like the very main role in everything in classical physics, starting from simple motion, Lagrangian and Hamiltonian mechanics and ending with fundamental thermodynamics laws. However, in QM, we found tha energy, that we thought is fundamental, is not fundamental anymore! Not only that, but we also found that positions are not fundamental, and those characteristics that we used to use in classical mechanics and were absolute, do not work in QM anymore, not absolutely. Consequently, uncertainty principles showed up for position and energy.

Subatomic particles are waves. What’s the position of this particle?


Newer concepts

This means that the observable physical quantities that we see are not real! They’re not how nature fundamentally works. Those concepts that we use are nothing but approximations to reality. A newer concept came in the field called “A wave function”. It describes the behavior of our systems in a better way than before. The Ehrenfest theorem showed also that Newtonian mechanics is nothing but a special case that is true as an approximation of the more general case found in quantum mechanics. The journey, actually, doesn’t end there. After quantum mechanics, Quantum Field Theory (QFT) came up to provide a deeper view of nature’s phenomena, destroying another concept in physics, time order, and saying that time order isn’t really as absolute as we thought it’s. After that, string theory came up and claims (it’s not tested yet) that dimensions are not as fundamental as we think they are. It claims that the dimensions that we live in are nothing but a special case of a more general concept.

Conclusion: Are we ever going to find the ultimate laws of nature?

My discussion doesn’t say that we may never find the ultimate laws of nature. It simply says that the claim that nature has a single set of laws that we think is ultimately what physics is looking for (Theory of Everything), is simply wrong. Even if physicists dream of this coming up eventually, this doesn’t mean that this is what we’re doing. And as Feynman said when asked the same question, “if nature turned our to be a multi-layer onion with more, and more layers that come when we dig deeper, then that’s the way it’s”. We simply don’t know.

Physics doesn’t presume anything. Right now we try to unify the laws that we know with the parameters we think are right. No one knows what kind of parameters govern the universe. We simply try to model the universe with the simple picture that we can understand with our small, simple brains. It could be true that positions, time, energy, and everything we use to model our universe is probably nothing but superficial parameters that approximate the real parameters that govern the universe.

Are we ever going to know? Let’s dig further and find out!

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.