Einstein On Steroids: Dirac, The Higgs, And Speeding Neutrinos
By Johannes Koelman | October 23rd 2011 12:40 PM | 62 comments | Print | E-mail | Track Comments

I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune

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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 Why cling to these dull and outdated theories?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!

I find this article amazingly arrogant. The teleological argument you forward is essentially this: "because the smartest physicists are so very, very smart, there can't be anything that travels faster than the speed of light because then all these very smart people would be wrong." Welcome to the world of scientific revolution.

the Einstein's of today, in the future will find themselves the Newtons of yesterday

To me, this article outlines the main problem with physics. Complacency with theories that, yes, have proven to be hugely successful, but without acknowledgment of their limits and failures and the possibility that there is theoretically a number of theories and as-yet-to-be theories that can describe, explain and predict the behaviour of physical systems.

This is most evident in the incapacity or unwillingness to restate the most fundamental questions about nature.
All dominant physics theories are founded on the axiom of continuity of space, which is the unstated axiom of special relativity. Time dilatation is the unavoidable consequence continuity of space if one poses that the speed of light is constant. Time dilatation is also the most convincing argument supporting that time is a physical dimension.
But if once replaces the axiom of space continuity by an axiom of discreteness of space, then the constancy of the speed of light becomes a direct consequence of the structure of space and there the concept of time dilation becomes irrelevant.

I think the first and greatest blunder of science is it believes that space is continuous despite evidence that everything at some point or another reveals itself to be discrete. The second blunder is to think that the purely relational concept of time corresponds to a physical aspect of reality.

The third blunder is the refusal to question the foundation of dominant theories. I am convinced that this hinders if not entirely prevents the emergence of a theory of fundamental reality that can explain all physical systems at all scales.
That said, I’m willing to take the bet the OPERA results will be replicated and when they are, there will be no choice but to consider a page one rewrite of physics.

Daniel L. Burnstein
www.quantumgeometrydynamics.com

Daniel: fine, if you are right and the 'complacent vast majority' is wrong, no doubt you will get your Nobel prize in due time. Good luck with that, and I will congratulate you sincerey when that happens.

Reason I am reacting to your post is not that I feel the need to argue on the points brought forward by you. Rather, I would like to test if indeed a bet is possible. I am thinking of both of us putting in an amount of approximately \$200. How does that sound? Can you send me a PM, so that we can see something can indeed be worked out with both parties getting a guarantee that there will be a pay-out (which could involve a duration of multiple years).

best, Johannes
If you haven't already you might want to research all the Nobel prizes that have either been flat-out given "in error" or, with the passing of time, seem patently absurd to us now. The point being, one shouldn't always bring up "the nobel prize" as some kind of magic ace card that immediately lends support to an argument.

As for placing a bet, I don't bet on anything, and even if I did betting on something like this would be foolish because I most likely will not agree with whatever the "argument" ends up being that might dispute the neutrino results. In other words, dealing with Quantum physics is in my opinion as much art as science, and I don't think it's wise to bet money on who has the better argument as to which is a nicer painting: a Van Gogh or a Matisse.

Anyway, I still did enjoy reading your piece and found it interesting.

Glad you liked the piece despite your disagreement with some of the content.

What Nobel Prize do you have in mind? The Nobel for Peace?

This is a physic blog, so let's stick to the Nobels for phyics. Keen to hear specific examples if you feel any were awarded in error (i.e. for what appears in hindsight an erroneous piece of work). I am not aware of any: a Nobel in physics gets awarded only if the piece of physics is validated by experiments.
I know there have been nobels awarded in the field of medicine that were later shown to be in error as well as awards that today might seem of questionable value, such as giving an award to the discovers of the lobotomy procedure. The point being that the nobel is not fool-proof but subject to judgements that can later be shown to be not as significant as first thought. I dislike the trend, used more and more it seems, of trying to support an argument or cause by saying "x number of nobel laureates agree." If something makes sense it should make sense even if it hasn't won an award. I wasn't even thinking of nobels for peace or literature which obviously are even more subject to the biases of the voter.

To counter people with a bet is aiming for emotions and polarization, tricking people into assuming that your opinion is what scientists subscribe to (the other side of the bet). I too would not take that bet, but that does certainly not mean that I would agree with anything else here. You are the only guy I have ever seen who claims that his pseudo-science is in line with the scientific consensus. Could you maybe point out (like others here), where your models are clearly non 'Einstein index 300' ones?
(This "zig-zag model" is no more than the old light clock argumentation. It cannot be a fundamentally light-velocity-causal model because the cause for turning zig into zag cannot be Einstein local. In fact, this zig-zag (before it was called such) is why others argue for emergent relativity from an ether, which would allow faster than light particles.)
I too would not take that bet
Doesn't surprise me the least...

pseudo-science...
This "zig-zag model" is no more than the old light clockargumentation. It cannot be a fundamentally light-velocity-causal modelbecause the cause for turning zig into zag cannot be Einstein local. Infact, this zig-zag (before it was called such) is why others argue foremergent relativity from an ether, which would allow faster than lightparticles.
I think you have some catching up to do on Feynman's checkerboard model. Basic stuff really. Referring to Feynman's work as pseudo science puts you deep into what Feynman referred to as 'Cargo Cult Science'.

Your comments are getting more and more the character of plain trolling. Just can't believe you as a trained physicist would really believe the nonsense you are penning down here. Will not react anymore to any of your comments unless you manage to start contributing meaningfully to the discussion.

Best,
Johannes
"I think you have some catching up to do on Feynman's checkerboard model."
Sorry - but that model and similar is the very basis on which relativity may be emergent rather than fundamental. You may not understand the limitation of that model (again: cause of the zig going zag). Telling readers clearly about the limitations of a model and whether something discussed is or is not mainstream is all I am asking for. Thank you.
Daniel:

All dominant physics theories are founded on the axiom of continuity of space, which is the unstated axiom of special relativity. Time dilatation is the unavoidable consequence continuity of space if one poses that the speed of light is constant. Time dilatation is also the most convincing argument supporting that time is a physical dimension.
But if once replaces the axiom of space continuity by an axiom of discreteness of space, then the constancy of the speed of light becomes a direct consequence of the structure of space and there the concept of time dilation becomes irrelevant.
It is interesting that you should assert that if one "replaces the axiom of space continuity by an axiom of discreteness of space" that then one finds "the constancy of the speed of light becomes a direct consequence of the structure of space", because even with "the axiom of space continuity" we find that "the constancy of the speed of light becomes a direct consequence of the structure of space[-time]".  :)

So "the constancy of the speed of light becomes a direct consequence of the structure of space[-time]" is independent of whether one assumes "space continuity" or "discreteness of space".

The only case where this may not hold is in the possibility of "emergent relativity from an ether", or some such.  ;)

David
Wow. An amazingly informative article. Look forward to the 'Einstein on steroids' description of relativity. Thanks!

PS. Phm, it seems you are in for a bet? Put your money where your mouth is! Lol.

Seems to me a theory of mass has to explain why particles differ in their mass? Why does an electron and a muon zig and zag at different frequencies? I am sure the QFT equations tell us why, but your description doesn't capture that part - why particles vary in mass. There is also the question of linear addition of masses when a body is made up by combining (say with electromagnetic binding) other bodies. Mass adds linearly, in fact directly, for this case. Why would zig and zag frequencies sum that way?

Why would QFT need to predict particle masses? Do you also require a theory of planetary dynamics to predict from first principles the periods of the planets? Newtonian dynamics is very successful in predicting planetary positions given a set of initial conditions. It can't predict the initial conditions.

Your requirement on the linear addition of zig-zag transition frequencies is based on a misunderstanding. The zigs and zags don't add up. If multiple Dirac fermions bind together, they continue as individual zigs and zags, while exchanging bosons associated with the binding interaction.

Very noob question here: why is "the speed of light" the same as "the speed of causation"? Couldn't it be that "the (theoretically slightly higher) speed of neutrinos" is actually what should be considered the speed of causation? Does this question even make sense? To rephrase it: perhaps the fastest particles are neutrinos and we have been mistakenly thinking that it was photons, and from now on we should start measuring astronomical distances in "neutrino-years" and so on...? I'd appreciate it if you could explain what is it that makes it so that light (and not something else) ought to be the fastest-moving thing in the universe.

It's actually a logical question to ask, and one that has been considered extensively. The short answer is that observations constrain the mass of the photon to Mphoton < 10^-18 eV. Don't mind the units: for comparison the three neutrino flavors combined are constrained to Mneutrino < 0.3 eV, and an electron has Melectron = 5 x10^5 eV. If the photon has mass, it is a very, very tiny mass.

Now, the effect of a small finite mass on the relative lengthening of the travel time (compared to a massless photon) is given by an equation quadratic in the ration between the mass and the energy: dt/t = (Mc^2/E)^2/2. If you put in a photon mass of 1 10-18 eV (worst case) and a photo energy of 10^-6 eV (assuming again a worst case of long wavelength radio waves), you find dt/t = 0.5 10^-24. Over a distance of 730 km (Geneva to Gran Sasso) this corresponds to a change in path length of 0.4 10^-18 m. Less than the dimeter of an atomic nucleas and way less than what would be needed to explain the OPERA anomaly.
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.
Gosh Johannes, I don't find your logic here at all reassuring, it reeks of everything I dislike about the scientific community and their consensus forming tendency towards innovation crippling groupthink.
Philosophers of science argue over the epistemological limits of such a consensus and some, including Thomas Kuhn, have pointed to the existence of scientific revolutions in the history of science as being an important indication that scientific consensus can, at times, be wrong.

Groupthink
is a psychological phenomenon that occurs within groups of people. It is the mode of thinking that happens when the desire for harmony in a decision-making group overrides a realistic appraisal of alternatives. Group members try to minimize conflict and reach a consensus decision without critical evaluation of alternative ideas or viewpoints. Antecedent factors such as group cohesiveness, structural faults, and situational context play into the likelihood of whether or not groupthink will impact the decision-making process.
The primary socially negative cost of groupthink is the loss of individual creativity, uniqueness, and independent thinking.
Social scientists are very aware of the enormously negative impact of groupthink, it seems that theoretical physicists are lagging behind and lack the same self-awareness of their inevitable bias?

Isn't it simply possible that man made, oscillating neutrinos traveling through matter, can move faster than light traveling through a vacuum, with a bit of help from the Mikheyev–Smirnov–Wolfenstein or matter effect and gravity and even Cherenkov radiation? Couldn't they also be using Dirac and Majora masses in a see saw or 'zig zag' mechanism?

Why aren't you theoretical physicists discussing and analysing the alternative possibilities of what could cause tachyon neutrinos and what the repercussions would be if they do exist, instead of analysing the gambling skills of highly conformist PHD female (!) theoretical physicists? The proof of these high ranking, theoretical physicists' conformity to conventional thinking being, by your own admission, their highly coveted and career cushioning Einstein Index and their ability to only feel safe if they are backing the favourite horse in a race.
My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
I discover again and again that people who make remarks about 'groupthink' in the context of the exact sciences have had direct interactions with surprisingly few, if any, exact scientists. Anyone who deals with these nerds on a daily basis knows that these creatures are highly individualistic, always eager to find an alternative explanation, and don't let go if the spot a (perceived) weakness in someone's argument. If a group of many thousands of these non-conformist, despite their eagerness to discover a loophole everyone has overlooked, agree on something, it is indeed a safe bet to follow them on this.

But the key point is: you don't need to. You can form your own opinion. I have tried to provide the readers of this column with some simplified tools to do so. If despite this, you or anyone else wants to adhere to thoughts at odds with scientific consensus, that's fine with me. However, I will not react any further to such remarks as the resulting discussions are pointless.

Scientific consensus can be wrong at issues dealing with the frontiers of science. Physicists are very well aware of such, and take that into account in their reasoning. You see lots and lots of question marks in the above quantum gravity jigsaw puzzle. These are there for a reason. I am not aware of a single case in the history of theoretical physics where an established fundamental consensus was ever proven wrong. Some concepts on which consensus was reached got refined later to render them applicable to a wider class of phenomena. But wrong? What examples do you (or Popper) have in mind?

I find it surprising that no sensible person challenges any of the more easily comprehendible physical theories such as Newton's equations. As soon as relativity theory is put on the table, that mode changes drastically. A key question to ask yourself: why is no-one accusing physicists of 'groupthink' on Newton's theory? Could it be because most people have some intuitive understanding of this theory?

Best, Johannes
Actually, what I'm trying to say is that I find the possibility of superluminal neutrinos a very interesting subject that I have been following closely and I have even written a blog once speculating about the possible unknown effects of oscillating neutrinos. So I am becoming bored to death with reading articles saying why the scientific community's consensus is that OPERA has almost inevitably made a mistake and that tachyon neutrinos almost can't possibly exist.

There are hardly any articles discussing the unlikely possibilities and effects that would result if OPERA hasn't made a measuring mistake and we really are generating tachyon neutrinos at the Large Hadron Collider. Why not? I want to read some speculation as to what it would or could mean to theoretical physics if tachyon neutrinos are really being generated at the LHC but I can't find this anywhere :~(
My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
There are hardly any articles discussing the unlikely possibilities andeffects that would result if OPERA hasn't made a measuring mistake andwe really are generating tachyon neutrinos at the Large hadronCollider. Why not? I want to read some speculation as to what it wouldor could mean to theoretical physics if tachyon neutrinos are reallybeing generated at the LHC but I can't find this anywhere :~(
Where have you been hiding? ;) Just search for tachyon on arXiv: yields hundreds of (mostly speculative) preprints.

I'm talking about articles and blogs about the possible causes and effects of superluminal neutrinos and tachyons, not arxiv papers, after all I am a laywoman not a theoretical physicist.
My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
Proves the point: if you feel the need to accuse anyone of 'groupthink', it is probably the blog community and not the science community you should aim your arrows at.
Please correct me if I'm wrong, but I thought that a large part of this article that you have written here was explaining how the world's top theoretical physicists, mainly identified by their Einstein indices would refuse to take on a bet of \$300 from you based on the assumption that within five years from now neutrinos have been proven to be capable to overtake light traveling in vacuum if, within the same timespan the OPERA experiment gets busted, and no sign remains of superluminal neutrinos, she has to pay you \$ 100.

All that the bloggers and their articles are doing is backing the same top theoretical physicists' viewpoints and the same favourite horse. In my not so humble opinion, it is the theoretical physicists job to at least theorise about the alternatives to the OPERA physicists having made an error and probably the bloggers job to try and translate these alternatives into laywoman terms.

Now surely sometimes theoretical physicists are also bloggers but so far I can't find anything much outside of the Arxiv papers you linked to, speculating on the various causes and effects of the outsider horse Tachyon Neutrino beating the favourite horses Opera Error and Speed of Light through a Vacuum to the finishing line? Yes, I thought that maybe groupthink was coming into play, but I don't really want to fire arrows, I just want to read some interesting theoretical physics hypothesising about alternative possibilities, is that too much to ask?
My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
More to the point, if you don't actually know what the "group" thinks, then perhaps you shouldn't be so accusatory and desirous of wandering off into speculations that you don't understand.
Mundus vult decipi
My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
You never learn.
Mundus vult decipi
And you rarely ever understand what I'm saying. If the 'group' thinks differently to what the bloggers are reporting then why aren't the bloggers reporting it? Johannes is clearly explaining here what all of the highest ranking theoretical physicists think, that OPERA has made a measurement error. I want to know what the repercussions to physics are if they haven't made a measurement error?
My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
Helen -- I think you are missing the point here. There are lots of theoretical physicists who will try a certain alternative approach, even without really believing in it. They do the work with an open mind and an attitude of "let's see what results, and if I can get this model consistent". I think most science bloggers (but unfortunately not all) apply a fair judgment on whether the work in question is promising or not, and write only about results that they feel could lead to 'something big'.

So don't assume that if you witness many hundreds recent articles on tachyons, that tachyons have entered mainstream.

On the Einstein index cut-off of 100: that was not the main point at all. (By the way, an index of 100 was suggested in order to stand a fair chance of separating out any pseudo-scientists. A world class theoretical physicist will have a much higher index running into several 1000's or even beyond 10,000.)

The key point I want to get across in this blog post is to give people an intuitive understanding of what relativity really is. It is no surprise that with the benefit of hindsight we can conclude that Maxwell was the first to derive a relativistic theory. Deep down relativity and QFT are about what happens 'on the light cones'. Anyway, more about this in follow-up blog posts.
Well thanks for your explanations Johannes, I'm looking forward to your follow-up posts and what happens 'on the light cones' or even better outside them!
My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine

Nice article. I never "got" the work of Dirac. This clears up a few things.

What amazes me most in the "pseudo-sceptics" rants against Science, is not that they accuse scientists of the faults they themselves exhibit: extreme group think and lack of openness. But their unwillingness to accept experimental data. They deride scientists for building theories using the things you actually measure.

That makes these "pseudo-sceptics" non-scientists. As you can only be a scientist if you accept experiments as the ultimate judge of theory. They are more like religious believers, who will not be swayed from the true path by reality, in this case, mere experiments and observations.

Btw, this is whole neutrino controversy is a new illustration of this truth by Francis Crick:
'if a theory explains all the facts it is likely to be wrong because some of the facts will be wrong'

Let as consider a compound system (body), a "chubby" one. It has the center of mass (always assositaed with the body itself) and different constituents around it. This body can "internally" oscillate. Whatever the system velocity is in some direction, the CM cannot get in front of the body constituent that moves in the same direction and is in front of the CM. The limiting velocity is about impossibility to get in front of something, isn't it?

We often think of electromagnetic waves and of charges as of independent systems (as if they belonged to different, parallel spaces). But we know well they interact, they interact permanently, so they are features of a compound system. If we understand them correctly, then there is no problem in admitting the CM velocity to be "limited" somehow. With running fast, you cannot get in front of your nose anyway. ;-)
First let me say, I have no issue with EM fields propagating at C, nor that em fields in the SM propagate at C. What I don't understand is why it's presumed that Gravity, the Strong and the Weak forces have to propagate at C as well. Maybe there's been some experiments that have measured these forces and confirmed this?

Also, I took 1 second of Planck time * Planck length which came out to 192,104 miles, or 192,104 miles/sec, That would be a bit (3.28%) faster than C, which would make sense, as the EM field would take some time charging space. But that (it seems to me) leaves the possibility that the other forces propagate at a value unique for each field.
Never is a long time.
Mi Cro:

By the very definition of Plank time and Plank length, "1 second of Planck time * Planck length" can never yield anything other than exactly one (1) light second of distance!  So the only way you could have obtained anything different would be due to roundoff error(s).

Sorry, this simply doesn't work.

David
Well, that explains that (though that appears to be a lot of rounding error).
Never is a long time.
It all goes back to the definitions.

Exact mathematics with the exact definitions yields the exact result.  Approximate mathematics, especially with only approximate values in place of the definitions, can't help but result in roundoff errors.
I think that you'll find by looking closely that some of the pieces have been forced into the puzzle that don't quite fit or belong there, and that's the only reason that the complete puzzle wasn't framed and mounted over the fireplace long ago.  The difference between Dirac’s hole theory and quantum field theory is one place where this shows up, and I'm pretty sure that this is because the negative energy states have been misinterpreted when Dirac's theory was formulated in the wrong background.  As I understand it, negative mass absurdities wouldn't even exist if this was fixed, because the negative mass solutions to Einstein's equation are simply referring to ordinary mass energy that  is less dense than ordinary matter so it has negative pressure and comprises the expanding vacuum.

http://arxiv.org/abs/hep-th/0401208
Dirac’s hole theory and quantum field theory are generally thought to be equivalent. In fact field theory can be derived from hole theory through the process of second quantization. However, it can be shown that problems worked in both theories yield different results.

And therein lies the problem that has not been resolved by any “reinterpretation” of the vacuum state, and so the quantum expectation for the energy density of the vacuum is about 120 plus orders of magnitude^ greater than it should be without the assumption of an “ad' hoc” suppression mechanism to cover this “little” discrepancy.  The problem goes back to the negative mass absurdity that falls from the Dirac equation, and QFT’s “ad hoc” assumption has also assumed the flaw, rather than to fix it, which only carries and compounds the problems when extended to quantum gravity theories of all varieties.

My two cents...
Richard:

I'm reasonably certain (recalling my advanced Quantum Mechanics of over two decades ago :/ ) that the problem is not so much about negative mass solutions, but negative energy solutions.  (Yes, I know, E = mc2, and all that, but there is a distinction, especially when one drops the deprecated concept of "relativistic" mass, and recognizes that Dirac's equation has only an invariant rest mass term.  Both the positive and negative energy solutions have the same Dirac/rest mass.)

Now, I don't know what you are referring to when you assert that "the negative mass solutions to Einstein's equation are simply referring to ordinary mass energy that  is less dense than ordinary matter so it has negative pressure and comprises the expanding vacuum."  What "negative mass solutions to" what "Einstein's equation"?

You are, however, absolutely correct that there is a "problem" wherein "the quantum expectation for the energy density of the vacuum is about 120 plus orders of magnitude^ greater than it should be" (where "should be" is presumably a comparison with the apparent value of the cosmological constant).  (Actually, the formal value for the "energy density of the vacuum", as given by Quantum Field Theory, is infinity!  So we only get to the finite, though "120 plus orders of magnitude" too large, value by assuming such calculations break down at about the Plank scale.)  However, this expectation is generally (if I remember correctly) not obtained via negative energy or "hole" solutions to Dirac's equation, but due to Quantum Mechanical zero point energy of harmonic oscillators, upon which second quantization is based.  (Actually, I believe the "problem" is even more slippery than that, since the "problem" appears to morph when one views the nature of the vacuum, and its oscillations, from any of a number of various perspectives.)

So, while there is a "problem", the cause of the "problem" is far from anything close to being so apparent.  Hence, the "correct solution" is even more obscure.

By the way, thanks for the link to the arXiv article.  I'll get to it when I can.  (I have my suspicions of what's "going on".)

David

David, you are correct, but the two equations, $E=mc^2$ and $E^2=m^2 c^4$ …are only different if there is a physical meaning to the negative mass and negative energy values, where the second equation allows for both positive and negative mass-energy solutions.  The expression arises from the fact that the magnitude squared of the momentum four-vector is given by, $m^2 c^2=p^2-E^2/c^2$ .  In the case of a body at rest, $p=0$, which leads to, $m^2=E^2/c^4$.  The concept of negative mass arises by analogy with electric charges, where the formula for the energy of a relativistic particle, $E^2=m^2 c^4+p^2 c^2$ derives that a particle with a certain positive energy but no momentum could theoretically have a positive or negative mass.

Dirac’s “hole theory” rationalized these negative energy solutions by reinterpreting the vacuum state so that all of the negative energy states are filled, and all of the positive energy states are empty.  Dirac’s theory was flawed though, in spite of its success at predicting the existence of the “positron”, because it can’t fully account for particles of negative energy, since it is restricted to positive energy particles, and yet, the quantum field theory representation for this is not an accurate representation of Dirac’s negative energy states.

Richard:

So, I suppose that these equations were what you were referring to as "Einstein's equation"?

However, these equations, in their squared forms (as all but one are shown), have very little relevance to Dirac's equation, and, a fortiori, to his negative energy solutions.  To wit:  Dirac's equation is analogous to the square root of .

I'm sure you can recognize that there are two solutions, of opposite sign, for the energy in the square root of that equation.

The thing to absolutely fix in your (and anyone else's) mind is that the negative energy solutions to Dirac's equation are for exactly the same mass, including the same sign.  So, there is no need for a concept of negative mass, to still have a concept of negative energy.*  In fact, the situation is more like being the opposite of what you have asserted.

Now, Dirac's "hole theory" wasn't so much about "rationalizing" these negative energy states—they exist within the equation, and they get "mixed" together when one adds external fields to the system, so it's not like one can simply "exclude" them (as one can do with infinite energy solutions to the heat equation)—as it was taking their existence for "granted" (in a sense), and seeing where that would logically lead.

The result of any hypothesis of an unlimited (infinite, if you will) number of increasingly negative energy states, along with the observed fact that systems tend toward the lowest available energy states, leads to the conclusion that the observation of only positive energy states must stem from having this "sea" of negative energy states all filled, since any positive, or even zero energy particle would gladly fall into any available negative energy states.

This then leads to an analogous situation we see in solid (condensed) state matter, like semi-conductors, with filled states below the band-gap, and free available states above.  Where excited states are exhibited as particle-hole pairs (where an excitation of a filled, below the band-gap, state results in a missing below band-gap particle—a hole—and a free, above the band-gap, particle).

However, the Dirac "hole theory" goes one step further.  Since the Dirac equation not only has negative energy particle solutions, but also positive energy anti-particle solutions (can be found using Charge-Parity-Time [CPT] symmetry, for instance), one can "turn it on its head", with "holes" in the negative energy "sea" of anti-particles being what we see as (positive energy) particles!  (Try that duality on for size. ;) )

So I don't quite "grock" your assertion that "Dirac’s theory was flawed though, ..., because it can’t fully account for particles of negative energy, since it is restricted to positive energy particles":  As already stated, it is most certainly not restricted to positive energy particles—verily, it even introduced negative energy particles.  However, it "fills" a "sea" of negative energy particles in order to accommodate the observation of only "positive energy particles".

Now, as for your assertion that "the quantum field theory representation for this is not an accurate representation of Dirac’s negative energy states":  Does this rely solely upon the single arXiv paper you have linked to, above?  If not, I would appreciate any additional references.  If so, I expect to find this statement on very shaky ground.

David

*  Besides, General Relativity does some very strange things with negative masses!  ;)

P.S.  Your equation has the wrong sign (and certainly doesn't jibe with your other expressions).

Let me cut to the chase as I think that we may be talking past each other a little bit:

In Dirac hole theory the vacuum state is the state where each negative energy state is occupied by a single electron, and each positive energy state is unoccupied.  It is my contention that each negative energy state is occupied by ordinary mass energy that is less dense than ordinary matter, having rho<0, therefore, negative pressure, so the negative energy states that comprise the vacuum mimic the antigravitational negative mass characteristics of a negative mass object until the mass energy is condensed down over a finite enough region of space to attain the matter density.  At which point it has rho>0, so it no longer has negative pressure and no longer produces the anti-gravitational characteristics of negative mass and THAT is why the "anti-electron" has positive mass.
Richard:

You are correct that
In Dirac hole theory the vacuum state is the state where each negative energy state is occupied by a single electron, and each positive energy state is unoccupied.
However, again "in Dirac hole theory" all those negative energy states have positive (rest) mass.  Additionally, only two of those (infinite number of) states (two spin states) have zero momentum (so E = - mc2), for a given type of Dirac particle.

This is the "reality" of Dirac's hole theory.

Now, you then claim
It is my contention that each negative energy state is occupied by ordinary mass energy that is less dense than ordinary matter, having rho<0, therefore, negative pressure, so the negative energy states that comprise the vacuum mimic the antigravitational negative mass characteristics of a negative mass object until the mass energy is condensed down over a finite enough region of space to attain the matter density.  At which point it has rho>0, so it no longer has negative pressure and no longer produces the anti-gravitational characteristics of negative mass and THAT is why the "anti-electron" has positive mass.
OK, but that's most certainly not Dirac's hole theory, nor even Quantum Field Theory (QFT).  This is also far from anything like a reasonable (let alone good) application of General Relativity (GR).

Do you really want me to get into how bad this "assertion" is from the standpoint of GR, or even just plain old ordinary classical physics?
That there may be a number of mathematical solutions to a problem doesn't not necessarily mean that each corresponds to a physical possibility. Mathematics is an essential tool to model physical systems, but they can't dictate to them.

Daniel:

You are correct to say (ignoring the double negative, of course)
That there may be a number of mathematical solutions to a problem doesn't not necessarily mean that each corresponds to a physical possibility. Mathematics is an essential tool to model physical systems, but they can't dictate to them.
However:
1. You were the one that brought up the whole idea of Dirac's "hole theory"
2. You were the one that advocated using the negative energy solutions, as suggested by Dirac's "hole theory", as a real, actual "vacuum" (though you were also, apparently, having problems with "negative energy" vs. "negative mass"—which I have been trying to help you get over)
3. In the particular case of Dirac's equation (from which the negative energy solutions stem), the majority of physical situations to which his equation can be applied, "mix" both positive and negative energy solutions in order to obtain physical solutions.  So it doesn't work to simply dismiss these negative energy solutions (as was desired, initially, since they were deemed "obviously non-physical!").
Now, since the problems with your "contention" extend far beyond any issue with solutions to Dirac's equation, I ask again:  Do you really want me to get into how bad this "assertion" (the one I quoted in my previous post) is from the standpoint of GR, or even just plain old ordinary classical physics?
Hi David,

Richard brought up the issue. Not I.

I was just pointing out a problem many have of not being able to distinguish the mathematical models from the systems they are meant to describe. Often with the result of wanting to impose purely mathematical results upon reality. Or, in other words, confusing mathematical rigour with physical truths.

Daniel:

You point out (quite correctly, I note)
Richard brought up the issue. Not I.
My Bad!  :'(  That's an absolute OOPS!  :{

I'm terribly sorry I mistook the source.  Please accept my most abject apologies.

Of course you are absolutely correct to point out
I was just pointing out a problem many have of not being able to distinguish the mathematical models from the systems they are meant to describe. Often with the result of wanting to impose purely mathematical results upon reality. Or, in other words, confusing mathematical rigour with physical truths.
On the other hand, of course, this should never be construed to suggest that one may play "fast and loose" with the mathematics, and expect to have something that means anything, let alone anything with regards to "physical truths".

David
No problem, David. Made that mistake myself before.

Enjoying the discussion and valuing your opinion.

Daniel

Based on what?
Mundus vult decipi
I once had a discussion with a colleague of me about the existence of tachyons he is very into new age believe so he is convinced about the existence of tachyons and of course its healing properties.
I didn't believe him and tried to convince him that it is a hypothetical particle made up by mathematicians and physicists for their research ,but my colleague couldn't be persuade to an other opinion.
Anyway when the big news came a few days later about the faster then light neutrinos and the possible time travel on the tvjournals and a lot other tvshows the day after at my work that same colleague came
to me with a big smile saying : you see I told you so tachyons exist there's your proof from OPERA Italy.
Ha ha ha in the world of pseudo-science, new age hippies and believers they have now al the proof they need and want :) about tachyons.

Can you direct your colleague to this site? I still need some folks willing to bet in favor of superluminal neutrinos.

I had a few takers, but with messages like this coming in, one after the other throws in the towel. It seems I have only one taker left...
Johannes:

The link ("messages like this coming in") appears to be blank.

What messages were you trying to refer to?  (Just curious.)

David
Thanks for letting me now. (That link somehow got completely scrambled.) Now fixed.
Well I don’t think that bet will work with my colleague you can have all the evidence in the world for someone with strong beliefs in whatever religion, is it New age or Christianity or any other god and maybe some Star trekkies :) they will just believe whatever the result will be in favor or against superluminal neutrinos/tachyons in the existence of the faster than light particles.
You can only win the bet from someone who understand the evidence, seems to me someone with enough skills and experience in mathematics and physics.
But hey probably that’s the reason you have no takers yet :) as you already stated in your writing

Why the vulgar intrusive popup ad? If you want, I can spring for a donation.

As a layman who loves reading about physics (but letting others do the math), this is one of the best articles I've ever read. The zigzag description is the most clear and eloquent description of causation I've ever read. Thank you.

Was just taking a look to see if perhaps you've read today's news on Nature.com
Apparently the measurement has been replicated by OPERA, this time with what appears to be a higher level of accuracy...

As a physics student who's still in his bachelor years I was wondering if you had any new thoughts on the topic.

P.S. I've been following your blog for a few months now, and enjoy it VERY much! Thank you for taking the time to update it, and continually explaining complicated topics in simple language.

Avner

"Apparently the measurement has been replicated by OPERA, this time with what appears to be a higher level of accuracy... As a physics student who's still in his bachelor years I was wondering if you had any new thoughts on the topic."

The OPERA collaboration has been able to reproduce their systematic error(s) with a much increased accuracy. This gives us good hope the error(s) will soon be identified. In the meantime it is amusing to witness the newspaper and blog titles triggered by these results.
COOOOOOOL! I should try this with my photos! Thank you for sharing. :D

Wheeew....! the stuff here are nervewracking! Information overload. But it is all worth it to read all the stuff written here. I honestly surprisingly enjoyed reading it. The visual aids are helpful. Great!

ok.so we have zitterbewegung,brownian motion.is "t"(time) in schrodinger really T=TEMPERATURE?no "zag" for neutrinos?does this look much as wheeler's "one electron world" and feynman answer "there are no equal amount of positrons"(electrons cutting the other way the world line)?how about "sphere eversion"?

Hi.

On a Feynman checkerboard, do the zig-zaggers have unique identities?

If two "electrons" were positioned next to one another, and they switched positions at every time-step (like a shoe lace), without a way to measure identity, are there two valid observations? 1) switching, 2) staying still.

Or is the entire concept of "switching" or "moving" or "velocity" absurd without the concept of "identity".

---
I really appreciate hearing about Feynman's checkerboard. It is very intuitive and helps to alleviate some of the weirdness I felt about relativity. Now I feel like I can take another look at Feynman diagrams and have a shot of understanding them.

Thanks,
Wm