So what is the deal with this 'cosmic speed limit'? Is it really unthinkable that neutrinos move faster than light?

You might want to try an experiment. Go to a nearby ATM, and draw \$300 from your account. Now go to the nearest person with a PhD in theoretical physics, and ask her what is her Einstein index. If her index doesn't reach a three-digit figure, wish her success with her career, and go to the next physicist. If, however, her index is expressed in three or more digits, you have found a suitable test candidate. Congratulate her with the respect shown by her peers, and show her the \$300. Now ask her if she would be willing to participate in the following bet: if within five years from now neutrinos have been proven to be capable to overtake light traveling in vacuum, you will pay her the \$300. If, however, within the same timespan the OPERA experiment gets busted, and no sign remains of superluminal neutrinos, she has to pay you \$100.

Ok, no matter how hard you try, at the end of the day you will take the \$300 back home. No takers.

Yes, this guy needed steroids: with some QFT and a bit of Higgs he looks way more convincing

Interestingly, there will be plenty of takers for a reverse bet that makes them receive money in case the OPERA results get debunked. There are even takers who would be willing to bet the value of their house on the wager that the OPERA anomaly is the product of a systematic error. Others have promised they will eat their own boxers shorts live on television in case the OPERA results get proven correct.

What makes these physicists so convinced and narrow minded? Surely they have boxed themselves in! Why cling to these dull and outdated theories? Why ignore tachyons and various other interesting theories? Would the universe not be much more interesting if a cosmic speed limit did not apply?

The thing is: the physicists you have proposed the wager to, are all very aware of the amazing achievements of these 'narrow and dull theories'. And what's more: they thoroughly understand the rock-solid foundation on which these theories are build. An important component in this foundation is formed by a principle formulated by a patent clerk more than a century ago. But the foundation itself runs much deeper. The physicists who refuse your wager understand that stripped down to its barest essentials, physics is not about particles moving at given speeds. There is a deeper level that tells us that physical reality is all about causations. Causations that propagate at only one speed. The speed we refer to as the speed of light, denoted by the magical symbol "c". Nothing goes faster, and nothing goes any slower. Our universe knows only one speed, "c", the speed of causation.

So forget particles. Physics deal with causations described by mathematical constructs known as 'fields'. Such fields are studied down to sub-microscopic length scales. These are length regimes where quantum effects dominate and causations travel as discrete field excitation that we observe as massless particles. Welcome to the wondrous world of Quantum Field Theory (QFT)!

That's all fine, but how do massive particles, particles that travel at speeds less than the speed of light, fit into a causation description?

Ok, to answer that question we need to have a closer look at QFT. But first we need to understand how the various theories fit together.

# Quantum Gravity Puzzle

Theoretical physicists are puzzle solvers. The puzzle that keeps them busy already for generations is the question how to derive a quantum theory incorporating gravity. Solving the quantum-gravity puzzle will bring us the 'Theory Of Everything'. But it is a hard puzzle. Probably the hardest puzzle mankind has ever attacked.

Imagine this quantum-gravity puzzle to be a jigsaw puzzle. A jigsaw that is rectangular in shape. Instead of a picture, imagine each piece to be encoded with two values: a value denoting the occurrence of gravitational effects, and a value that describes the importance of quantum effects. When solved, the puzzle will show gravity to be zero along the left edge of the puzzle, and attain increasingly larger values away from that edge. Quantum effects will be zero along the bottom edge of the puzzle, and increase in the upward direction. Away from both edges, both gravity and quantum effects play a role in describing the physics.

A first step in solving this puzzle was made in 1865 when James Maxwell, without even without having a clue about the full extend of the puzzle, identified the bottom-left piece. This corner piece represents the unified theory of electromagnetism. This theory describes the zero-gravity, non-quantum physics world of electricity, magnetism, light, radio waves, X-rays. The whole shebang. A truly amazing result.

But there was more to come. Much, much more. Forty years later Albert Einstein made an amazing move. He turned over Maxwell's corner piece and low and behold: the flip side described particle motions in a world where the motion of light is absolute and time and space are relative. A startling result. Startling but convincing: the theory nicely unified the kinematics of material bodies with electromagnetism and appeared consistent in a most elegant way. And more importantly: well over a century since Einstein formulated his theory, we can conclude that time and time again experiments have verified Einstein's theory.

Once he discovered the significance of both sides of Maxwell's puzzle piece, Einstein was unstoppable. He, more than anyone else, realized Maxwell's puzzle piece to be the corner piece of a larger puzzle that should incorporate gravity. He worked for almost twelve years. When he was done, the whole lower edge of the quantum gravity puzzle fell in place. Einstein had figured out gravity.

In the meantime quantum physics started to take shape, and the questioned popped up: how to extend the puzzle into the quantum domain? Twelve years after Einstein came up with his theory of gravity, Paul Dirac made a start with the left edge of the puzzle. His equation for the electron forms the left edge puzzle piece just above Maxwell's corner piece. Both pieces fitted snugly.

Later on Feynman and countless others extended the left edge of the puzzle by building on Dirac's theory. Thus QFT was born. Many believe that by now the whole left edge has been put in place, and they refer to this edge as 'the standard model'. So should all our attention shift away from both edges and should we solely focus on putting the interior region of the puzzle together? Not really. Undeniable fact is that some puzzle pieces high up along the left edge, most noticeably those related to supersymmetry (SUSY) and the Higgs, have not been validated yet. The thought that in less than twelve months the LHC might indicate the upper left edge of the puzzle to be wrong or incomplete and to require a modification or extension, is an intriguing one. Soon we will know more.

the quantum gravity puzzle and its key contributors

Key point here is that around the  lower left corner an edge of nicely fitting puzzle pieces has formed. Although the full puzzle is obviously far from finished, the edge pieces around the lower left corner are here to stay with us. They represent theories that are extremely well tested. We have reached a point where attempts to discover new phenomena and thereby disprove current physical theories is no longer feasible for single nations, let alone for single individuals. If you want to demonstrate any pieces of the puzzle of modern physics to be wrong or incomplete, you not only need a bright idea for novel tests, but you also need to be able to put hundreds of millions or billions on the table.

Yet, it is very well thinkable that some day we learn that the bottom edge put in place by Einstein is to be extended to the right, or that the left edge needs to be extended upward. And it is everyone's  hope that some day we will learn how to put the whole puzzle together. But fact is that the left corner piece has been in place for one-and-a-half century. Furthermore, this corner piece has triggered a whole rim of snugly fitting puzzle pieces. Even in his wildest dreams Maxwell could not have anticipated his theory of electricity and magnetism to be the first puzzle piece in a magnificent jigsaw display extending in directions unthinkable at the time when he published his theory. And that is exactly the sign of a solid theory: it goes much deeper than even the designer of the theory would have ever thought possible.

# What is mass?

Now let's go back to the question "how does mass fit into all of this?". It is Dirac's puzzle piece that provides the key insight here. According to many, the puzzle piece that Dirac put in place is the most beautiful piece of all the puzzle pieces identified so far. It describes the electron in terms of causations. How does this work? Roger Penrose, in his book 'The Road To Reality' gives an insightful description of the electron in terms of massless 'zigs' and 'zags'. If we limit the number of spatial dimensions to one (that is: if we study an electron that is constrained to move along a line), this description reduces to Feynman's checkerboard model of the electron.  In this model, an electron is nothing more than an alternation between two types of causations: a right traveling 'zig', and a left traveling 'zag'. These causations are referred to as zigs and zags as they form a nice zig-zag pattern when represented in spacetime.

Zig-zag description of the electron

The zigs and zags are causations, and can be interpreted as massless particles that behave like photons. So, according to Dirac's theory an electron is nothing more than a massless particle that cycles ad infinitum between steps forward (zigs) and steps backward (zags), both executed at the speed of light.

So where does the mass enter? According to Dirac's theory the mass enters as the frequency at which the turns between zigs and zags take place. This makes perfect sense, as the presence of transitions between zigs and zags causes the overall motion to slow down to speeds below the speed of light, as should be the case for particles that have mass.

As I will explain in later blog posts, in terms of zigs and zags the whole theory of relativity becomes trivial. All of the the counter-intuitive aspects of relativity theory, Lorentz contraction, time dilation, the twin paradox: all of this can be understood based on a zig zag model of motion. So by diving into some insights that are central to QFT, good old relativity theory becomes trivial. As soon will become evident, the zig zag description presented here will give true insight into relativity theory. By viewing massive particles as what they really are according to QFT, alternations between zig and zag causations, we have put Einstein on steroids. Everything concerning relativity becomes easy and effortless. Soon you will be a relativity theory expert!

For now, let me suffice by stressing again that the simple zig zag picture makes it clear that nothing can go faster than light. When measuring instantaneous speeds, there is only one speed: the speed of causation also referred to as the speed of light. However, averaged over long time intervals that cover multiple zigs and zags, speeds smaller than the speed of light will result.

Now what about neutrinos? Like all fermions, neutrinos are described by the same Dirac formalism. Interestingly, neutrinos have so far only been observed as zigs. Zag neutrinos have never been observed. If neutrinos only zig, and never zag, that means they are massless. Whether that is indeed the case, is a question that experiments like OPERA are supposed to answer.* However, as we all now by now, an unexpected anomaly came in-between.

You now know this anomaly must have to do with some small systematic error, either in the timing or in the distances measured. Like all particles, neutrinos move at each instant at the speed of light. If en-route from Geneve to Gran Sasso they perform some zig zags, they would arrive later than their instantaneous light speed would suggest. However, they can not arrive any earlier than a single zig or a single zag would do, as there is no zig-zag mechanism that can cause particles to arrive quicker than by zigging (or zagging) alone.**

If anyone tells you neutrinos can move faster than the speed of causation, show them your \$300 and ask them if they want to wager \$100 in a three-to-one bet. What the heck. If those folks are really convinced about the neutrino's superluminal capabilities,  they should be willing to enter a bet at even stakes. Any takers?

Now what about the Higgs? Is the Higgs field not supposed to give particles like the electron their mass? If zig zag transitions represent mass, where does the Higgs fit in?

Well, posing the question is answering it. In the Dirac formalism the mass of the particle is put into the equation as a zig zag transition likelihood. The Higgs mechanism clarifies the zig-zag transitions as scattering interactions with an omnipresent Higgs field.

So if the Higgs is not discovered at the LHC, then the whole card house of physical theories will tumble down?

Not at all! If there is no Higgs, the whole zig zag picture will be unaffected. Yet, a new  mechanism will need to be constructed to explain the mass parameter in the zig zag picture. This means that the left hand edge of the quantum gravity puzzle will need some modifications along the top of that edge.

So what is the take away point of all this?

Physicists are involved in solving the ultimate jigsaw puzzle. They have progressed over the years, and the contours of the whole puzzle is becoming visible. Each piece added to the puzzle got accepted only following a critically review. Whenever the addition of the new puzzle piece  led to an avalanche of other pieces falling in place, the confidence of the first piece being correct grew. Only when subsequent experiments validate the new piece, the confidence turns into acceptance. The result of this process over many generations of physicists and following many Nobel prizes, is that lots of pieces are firmly in place. Other more recent additions are less certain and are being examined critically. One piece of the puzzle has a special status as being the most certain and best validated of all pieces: the piece in the bottom left corner. This is where the puzzle started, and where the first avalanches of nicely fitting additions originated. Sure, it would  be wonderful if we would obtain dramatic new insights that allows us to completely reshape the puzzle. And yes, you can question the validity of even the bottom-left corners piece, but you better bring extraordinary evidence to support your claim. A single anomalous result from a complex and error prone experiment falls way short of that.

## Notes

* The full story is a bit more complex. If transitions between different types (referred to as 'flavors') of neutrinos are possibles, these transitions ('oscillations') must occur as zig-zag transitions. If such neutrino oscillations are observed, neutrinos must carry mass.
**  Of course, if you earn your money in Hollywood, you might want to entertain speculations about neutrinos not moving faster than light, but capable of taking shortcuts through extra dimensions. It happens in movies all the time!