"Stories of Science, History & Mystery"
Chapter III: God's Particle
«The physicists only defer to the mathematicians, and the mathematicians only defer to God.»
Leon M. Lederman, The God Particle: If the Universe is the Answer, What is the Question?
The friends listened attentively to Valérie's recounting of their story.
March 2010
1.
A few years after going their separate ways from University times in Edinburgh, Chris had set up a reunion meeting at a Highland manor. Liz had gladly taken up the invitation. She needed to get a break from her tenure-track faculty job at the University of Florida. Chris had promised that Daniele would be there too. What's more, Chris had mentioned something about a surprise he had in store. But it was all hush-hush, and she was not allowed to tell anyone.
«So, when will you reveal the big surprise Chris?» Liz asked.
«Glad you asked.» he said.
He came back with a worn book written in Cyrillic characters.
«I would like you to have a look at this.»
Liz and Daniele looked puzzled.
«Would you like us to do a translation for you?» she said ironically.
«Why don't you give us a little backstory?» Daniele said.
«The book you are looking at was authored by the Serbian mathematician Josip Garganov. It is a treatise on Lagrangian density that was written around 1890.»
«Never heard of him.» Liz said. Yet her curiosity was awakened. Lagrangian density is effectively the backbone of quantum chromodynamics, and thus particle physics. She was not sure though what an obscure Serbian mathematician would have discovered before the revolutionary discoveries of the 20th century, which then turned the whole Physics world upside down. She knew one always had to be cautious of Chris' exuberant optimism.
«Have a look at page 28.» Chris said.
Daniele turned the pages. After looking at the page for a few minutes, he said. «I must admit this all looks fuzzy to me.»
«Naturally, being orthodox, it is all in Cyrillic. What's more, Josip was using some very unusual mathematical notation that it makes it hard to decipher. I have attempted to put it in a more modern notation. Go the blackboard and replace the characters shown with the following substitutions.» Chris said.
He gave Daniele a card with instructions. Garganov's original expression made no sense, but as Daniele started writing the revised equation on the blackboard, Liz could barely believe her eyes. It was one of the best-known equations to her; an equation with which her advisor, Peter Higgs, had proven the existence of the Higgs particle, due to a breaking of symmetry in the electroweak interaction. Since this particle was believed to be responsible for the manifestation of mass, some referred to it as God's particle.
«That cannot be right» she blurted out. But after carefully looking it over, she could see that the substitutions indeed gave the correct equation.
«Is this genuine?» she asked. If this was true, someone had beaten her advisor to the punch by a full 70 years. With the discovery of the Higgs boson imminent in the next few years, Higgs was basically assured to the receive the Nobel prize. The stakes could not be higher.
«I'm glad to have your attention, but that is not even the reason that I brought you to here to this remote place.» Chris said. In the meantime, he had fixed himself a cigar, and was about to light it. «Garganov's real discovery is much later in the book. Go to page 91.»
Liz fast forwarded to the relevant page. She could make out a few characters that indicated some multidimensional version of the previous equation. Without an explanation of the terms, it was not obvious to make sense of it.
Chris was delightfully puffing his cigar. It was evident that they needed some help. He switched on an overhead projector with an English translation of the page. There were only a few sentences that showed up, but one in particular was highlighted. «This proves that the four dimensions of the aether are perfectly transposable.»
«What does that mean?» Liz thought out loud. The aether was such a strange 19th century word. Yet she also noticed that the equation, while written in an arcane fashion, could be understood as a four-dimensional representation.
«You tell me, you are the physicist.» Chris said.
«It could in principle mean that matter is composed of four dimensions.» Liz reasoned. «Though that seems an odd assumption, especially at that time. In Einstein's view, there is a three-dimensional space, and time is of course the fourth dimension.»
«Let's assume that he was talking about the Einsteinian space-time. I think the key word here is transposable.»
«You mean that one can simply change time, just like one changes the coordinates in space? That would mean that time travel is possible.» Liz said.
«Exactly» Chris said.
At this point Daniele interjected. «Chris, with all due respect, but have you actually checked the veracity of the proof? Maybe it's just a mistake?» He was always the moderating force in the group. Chris and Liz loved to push each other in their sometimes crazy hypotheses. Daniele did not like to get too carried away before checking that it was actually grounded in reality. The pragmatism of an engineer...
«No, I figured that I would leave that up to you guys.» Chris said cheekily.
Liz was hooked. Daniele was of course right. They needed to check that the proof was correct. That was the first priority. But assuming it was true, a whole new realm of particle physics might open up. She was cautious about the whole space-time interpretation. That was likely wishful thinking on Chris' behalf. Still, more recently string theory proponents had suggested a multi-dimensional universe, composed of perhaps eleven or even more dimensions. So, only one additional dimension did not really seem that far fetched. Plus, the fact that Garganov had come up with the Higg's equation all by himself was truly amazing - assuming the whole thing was not fake of course.
2.
Daniele was bug testing a software to replace the unusual characters with a more modern notation. Chris had previously laid the groundwork by translating parts of the manuscript from Serbian into English. His Russian course at Edinburgh University had proven to be very useful after all. Chris was intrigued by the text, and particularly the four-dimensional respresentation. Nonetheless, the mathematics far surpassed his abilities. For one, he was not a trained mathematician. Moreover, the notation truly was archaic. It was only by coincidence, and due to his photographic memory, that he had noticed the similarities in Garganov's equation with Higg's equation. He did not really know much beyond that, but had hoped that this would be enough to get Liz and Daniele interested. He had a strong hunch that he was onto something big, and his instinct was generally spot on. Still, at this point, he would have to see if his friends could make some headway.
What had taken Chris months of painstaking effort for a few pages of translation, Daniele's program did in a matter of seconds. As the revised pages appeared on the screen, many things clarified quickly. Liz could see that Garganov implemented a spring-theory-type approach for each particle. However, why stop at four dimensions? After a few substitutions in the notation, she realized that Garganov's equations only made sense for bosons. That also explained why the Higg's boson was a natural solution. It took Liz almost the whole night to work through the proof. She did not really consider this a chore. Nights were her favorite part of the day. No-one would disturb you, and you could completely work in peace. It also helped that she was still on East Coast time.
There were no mistakes in Garganov's proof, and one had to recognize that some of the approaches were elegant and well before their time. Then, however, it struck her. The final equations only made sense for particles that had no mass. Sensing her breakthrough, she decided to wake up her colleagues. She let them have a shower and coffee, then called them to the dining room.
«First the good news. I could not detect any problems with the proof.» She could see Chris' excitement, but she quickly added «I'm afraid though, it looks like the proof has little use.»
Chris looked baffled. «What do you mean, little use?»
«The proof only makes sense for the special case of massless particles, otherwise parity-time symmetry is violated. I cannot see how anything insightful would come of that, certainly no general theory on anything.» Liz explained.
«Are you sure? Is that the only interpretation?» Chris asked feebly.
«Absolutely, there can be no mistaking. I'm sorry to be the bearer of bad news.» Liz said.
Chris sat down in his armchair. He looked deflated.
«Don't take it too hard, Chris, it might still be a breakthrough in mathematics that you have unearthed.» Daniele tried to console him.
«I'm going for a walk.» Chris said. The news had shaken him.
Liz was overly tired, and needed a nap. In the meantime, Daniele needed a distraction in the kitchen. He was going to prepare a special treat for lunch, and so they decided to reconvene around noon.
Over lunch, Chris was in unexpectedly good spirits. The other two were surprised by the sudden change in demeanor.
«What's up? Something nice happened on the walk?» Daniele asked. «Some cute lady perhaps?»
«I found a purpose for Garganov's theorem.» Chris said with complete confidence.
Daniele and Liz looked at each other quizzically. It was natural for Chris to put on his usual bravado - that was just like him.
«I understand that you have put a lot of energy into this, but I think you need to let it go.» Daniele said, trying to help him see clearly.
«You will see that this is the most important equation in humankind» Chris exclaimed.
Typical Chris, Liz thought. Always stubborn, and never able to acknowledge a mistake. She needed to talk some sense into him.
«Look, as a particle scientist, I must tell you that considering only massless particles would be completely non-sensical. In the history of the standard model, we have gone to ever-increasing masses. The Higg's particle is next on that list. This flies in the face of history.»
«Liz, what you just said, fits exactly along my line of thinking.»
It was clear to Liz that he just wanted a fight. You want to fight on my turf? Be my guest! Daniele, as usual, looked from afar, to then join the winning side in the end.
«Now it's your turn to explain.» Liz said. She just needed to poke some holes in his arguments, to make it all come apart.
«Like you already said, Garganov's equations only make sense for massless bosons. So, that basically means light.» .
«Obviously»
«Thus, light photons can access a fourth dimension.»
«So what?»
«Let's assume that the assumption of time as the fourth dimension is correct. That would mean that photons could explore the time dimension.»
«Even if that were true, it could never be proven. That is also the whole problem with string theory. It's beautiful math, but there is no experiment that can prove or disprove it.»
«But, there is Liz. Think about it. Let's assume that we send a photon through time. We just need someone on the other side to detect it.»
«Sounds easy. Why don't we just send Daniele to the future, so he can collect those photons.» she said sarcastically.
«Not to the future, to the past. And replace photon with message.»
It dawned on Liz that Chris might have a point. «Are you suggesting that we send a message to the past, and that this sort of biblical message would be reported in history?»
«That is precisely what I am suggesting.»
Liz had to admit that the idea was not completely crazy. However, there were many technical challenges to overcome.
«I could see how we could make a message appear by some kind of laser etching. According to Garganov's theorem, the light would appear at a different time, but exactly at the same location in space. The particle accelerator at CERN is probably the only place in the world where during particle collisions space-time is bent sufficiently to access the time dimension. However, it is located 100 meters underground. No-one lives there, and no-one lived there in the past either. How could anyone then receive the message?»
Daniele sensed that Chris was winning the overall argument. Liz was at least considering the possibility of this hare-brained scheme. He was also aware of recent developments in laser technology that could assist them.
«Well actually, a far infrared laser could work for this. At that wavelength, most rock is basically transparent; and thus the light will go through it. But if you focus it enough, you could etch a message in a building at ground level. » he explained. «Not clear though what building one would target.»
«As chance would have it, there is a building above the CERN beamline that would be perfect. One building was spared when the invaders from Berne razed Pouilly to the ground in 1536 - the church.» Chris said.
Liz and Daniele gasped. What had looked like a crackpot idea was suddenly taking form. Not only might it be possible to communicate a message to the past, this was the pretext for sending such a message to a willing receiver.
«We would warn people of the imminent attack. Genius!» Liz said.
«...and being thankful, they would build us a monument.» Chris added.
«Let's not get overexcited here. How much is one of those lasers Daniele?» Liz asked.
«It's really state-of-the-art. Plus, you would need multiple lasers. It could be 5 million, perhaps even 10 million all in.»
«I guess I could write a proposal to the Gates foundation» Liz joked.
«That would not really keep it a secret, would it?» Chris said. He had become all serious all of a sudden.
«How are we going to finance it then?»
«I will» Chris said, without a hint of irony.
His friends were taken aback. Chris, the guy with the old banger? The guy they had at times taken pity on, because he did not have the discipline to finish his thesis? In fact, it had all been part of a carefully crafted persona. Christopher Harrison is not exactly an uncommon name in England. But the Harrison clan in Suffolk is of true blue blood, with a traced lineage back to Richard III. He was the heir to a landowning dynasty estimated at half a billion pounds. The Scottish manor that he had invited them to was not rented, it was family property.
To Liz, it explained a few things. Chris only pursued projects that were of interest to him at that time. If he got interested, he would pursue it with all his energy. She remembered how impressed she was when it came to his ability for quickly accumulating knowledge. The first time they had met, she had referred him to some literature on particle physics. When they met again a few weeks later, they had discussed the current state of the field of particle physics for hours. He seemed to know more about the field than some of the graduate students she was working with. Yet he could also very quickly lose all interest. When he had lost interest in his PhD thesis, he simply shelved it for something else. Liz had mistaken this for a mere weakness in character. It was also a luxury he could afford.
Liz felt betrayed. She thought they had been intimate about everything, since they were best friends. It seemed disloyal to keep secrets from one another. Then again, the fact that he had gone to Edinburgh suggested that he had wanted to get far away from his nobility life. Perhaps, he just wanted to be someone normal, having normal relationships with other people? Being a wealthy heir will get you a lot of friends, but not true friendship.
Everything seemed to fall in place so neatly, almost too neatly. What they were going to embark on was dangerous. People kill for that kind of information. She wondered if anyone else might be onto the same idea.
«Could anyone else get wind of this?» she pressed Chris.
«No way!» he said firmly.
«How can you be so sure? I know Garganov was obscure, but still.»
«This is the only copy of the book.» he said. Before his friends could ask, he added «I had the others destroyed.»
A darker side of Chris showed through. Liz felt a bit uneasy, but the adrenaline rush was intoxicating. She did not want to spoil the moment.
«Let's hope that the historians got the date of the raid right, otherwise our message will fall on deaf ears.» she said, with a laugh.
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© Credit for the art work goes to my children Emile and Winnie. All rights of this work are protected.