A Jewel at the Heart of Quantum Physics

Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality. “This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work. The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression. “The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.” (via Physicists Discover Geometry Underlying Particle Physics | Simons Foundation)

Why Time? “Dilates”?

Time dilation is very likely the best-known connected with the relativity effects as a result of the twin paradox. Listed here the scenario: An astronaut leaves on a manned rocket journeying at near the speed of light. After zooming all around the galaxy she comes back to discover that her (non-identical) fraternal twin sibling on Earth is an old individual with a lengthy beard though she herself is without a doubt young. Today it is overwhelming. So why might time pass even more slowly simply simply because you are actually moving? Just what physical explanation will we find with regard to that?

Intuitive explanation. The explanation is actually once again built upon the field character of matter, defined by the field equations. Consider 2 atoms in an interplanetary rocket (or in its contents). Suppose that a single atom generates a field disruption and the minute that intrusion meets the 2nd atom something happens. (It is the interaction among atoms, it goes without saying, that induces everything to happen.) Now if the spacecraft transport is actually moving, the 2nd atom is going to have gone even farther ahead, thus the disturbance must travel a greater distance to get there, even after taking the F-L constriction into account. Given that fields travel at a preset rate, it is going to consequently take longer for the disorder so as to reach the second atom. (Disturbances that propagate in the backward direction have a shorter distance to travel, but this effect turns out to be not as great.) Simply put, things happen much more slowly and gradually when you’re moving because the fields have to go a greater distance.

An analogy. Consider two men on a raft who exchange information by calling back and forth to each other. Suppose further that this exchange of information determines the evolution of events on the raft. That is, when B receives information from A he makes certain things happen, and when B calls back to A, other things happen. The problem is, it takes time for the sound waves to travel from A to B and by the time the sound reaches B, he will have moved to a new position B’. The sound must travel through a greater distance and the communication will take longer than if the raft were at rest.


My first Feynman diagram! Actually excited! (And momentarily not even wondering why I’m doing this.)

I’m just gonna be honest. That was pretty freakin complicated. Turns out these things are just abstract pictorial representations of the terms you get when you approximate a big integral equation that tells how a wave equation will evolve. I suspect though that we’re headed in the direction of just taking the little arrows and calling them particles.


How Lengths Contract Through Dynamics

The suggestion concerning contraction was initially submitted by a relatively unknown Irish physicist, George Francis FitzGerald. FitzGerald shared his concept in a brief report to the American journal Science in 1891, a decade after Michelson’s 1st reported result, and he suggested a cause.

I propose that just about the only hypothesis that is able to resolve this [conflict] is that the span of form changes, conforming while they are travelling through the ether as well as across it, by an amount according to the square of the ratio of their velocities to that of light. We know that electric forces are affected by the motion of the electrified bodies relative to the ether, and it seems a not improbable supposition that the molecular forces are affected by the motion, and that the size of a body alters.

While FitzGerald described the ether, which was believed to be the carrier for light waves during the time, the objective viewpoint holds with or without the ether. A little bit later his rather timid suggestion that molecular forces are probably impacted by motion was actually repeated as well as fine-tuned by the most popular physicist of the time.

Though FitzGerald was actually little known outside Ireland, the Dutch scientist Hendrik Lorentz was acknowledged as the greatest physicist since Maxwell. In 1902 he and Pieter Zeeman received the 2nd Nobel Prize ever awarded for identifying the “Zeeman effect” that brought on the discovery of electron spin (Chapter 6). Einstein referred to Lorentz “the most well-rounded and harmonious personality he had met in his entire life” (P1982, p. 169). Upon Lorentz’s passing, Europe’s greatest physicists attended the funeral and 3 minutes of silence were actually observed all throughout Holland.

Lorentz had actually not seen FitzGerald’s study, nevertheless he too recognized that Michelson’s strange result would definitely make sense if the apparatus contracted along the direction of motion. He went further than FitzGerald; he did the calculation (not an easy one) using Maxwell’s equations. When he found that the theoretical contraction exactly compensated for the extra traveling distance, this was surely one of the great “Eureka” moments in physics, equal to those of Newton and Einstein.

Mysteries Still Evading Explanation through Quantum Field theory

Even with the many successes of Quantum Field Theory, there are five unexplained enigmas or “gaps” that may perhaps someday be filled:

Renormalization is important since Quantum Field Theory does not explain exactly how an electron (or various other charged quantum) is impacted by its own self-generated EM field.

Field Collapse is actually of two varieties: spatial collapse, anytime a spread-out quantum suddenly is suddenly sucked in or possibly becomes localized, and also internal collapse, when the spin or other interior feature of a quantum instantly changes. Collapse can likewise happen by having two or maybe even more entangled quanta. Quantum Field Theory does not illustrate the way in which and when this takes place, despite the fact that it can calculate probabilities.

Whys and Wherefores. Quantum Field Theory does not offer an explanation for why the masses and interaction strengths regarding the various fields are what they are.

Dark Matter and Dark Energy are generally thought to exist in deep space thanks to astronomical proof. They similarly are not explained by the recognized areas of Quantum Field Theory.

Consciousness is undoubtedly something that transpires behind our noses, nevertheless is not explained by Quantum Field Theory.

… How dare physicists talk about “theories of everything" when they can’t explain what goes on behind their very noses! But please know, by consciousness I don’t mean simple information processing, such as might be accomplished with the assistance of the computer. I mean the spirit consisting of awareness, the sensations, the feelings that human minds encounter on a daily basis— originating from the color red to the charm attributed to a Mozart sonata or perhaps the discomfort of a toothache. These sorts of sensations are called qualia. Most physicists really don’t wish to be inconvenienced by the question, and it it is left to theorists such as Charlie Chaplin to worry about it: "Billions of years it’s taken to evolve human consciousness … The miracle of all existence … More important than anything in the whole universe. What can the stars do? Nothing but sit on their axis! And the sun, shooting flames 280,000 miles high. What? Wasting all its natural resources. Can the sun think? Is it conscious?”— C. Chaplin (film “Limelight”).

I see consciousness as a much more critical issue than the concern concerning exactly why the field constants contain the values they do, and I would definitely trade a hundred field collapses in order to get an explanation of precisely why people see colors. Among those physicists who are inclined to consider the challenge, several think that consciousness arises from the complexness of human brain— that our brains is nothing more than a remarkably complex computer or even robot could do. (A physicist has been defined as “the atom’s way of thinking about atoms.”) This is referred to as the Artificial Intelligence (AI) explanation. Nonetheless presently there are a few physicists who are convinced that the marvel of consciousness transcends our current knowledge: “”Of all the areas of experience that we try to link to the principles of physics by arrows of explanation, it is consciousness that presents us with the greatest difficulty. We know about our own personal conscious emotions directly, without needing the intervention of the senses, so precisely how will consciousness ever be brought into the ambit of physics and chemistry? The physicist Brian Pippard … has put it thus: “What is surely impossible is that a theoretical physicist, given unlimited computing power, should deduce from the laws of physics that a certain complex structure is aware of its own existence.” I have to confess that I find this issue terribly difficult.”“— S. Weinberg.

To me it is perfectly obvious that consciousness consists of more than electric or electro-chemical signals, as in a computer or robot. If I took the most skilled carpenters in the world, gave them an unlimited supply of wood and said, “Take this wood and make a television set, but don’t use anything except wood”, I know they couldn’t do it. We can’t even define these sensations, much less know how to create them from computer parts.

Some scientists justify their belief in the AI explanation by asking “What else? Why is this so difficult to believe in regard to consciousness?

Will we ever find an explanation?

Too many rigors, not enough prose,
too much Einstein, not enough Bose.

Well, I spent half the day working through the first fifteen or so pages of Professor Hugh Osborn’s lecture notes in Advanced Quantum Field Theory. So of course that means it actually turned into an afternoon spent reviewing reviewing the basic formalism of Quantum Mechanics. Making good use of a long walk to work this fall, I managed to get about halfway through the Dover edition of Albert Messiah’s classic Quantum Mechanics textbook, so I’m feeling alright about these lecture notes so far. I’m a little worried though, because I got lost very quickly when Messiah jumped into spin and the Pauli exclusion principle. Spinors and tensor spaces might just be difficult, but it’s a very formal presentation that doesn’t offer much help to the uninitiated! I might put these lecture notes on hold long enough to do some homework and get up to speed on spin.