Ghosts lurking around in advanced physics

Jack Dikian

February 2012

Lurking deep at the core of Gauge Quantum Field Theory are two Russian ghosts called Faddeev and Popov - somewhat reminiscent of the ghost monsters in the old video game; Munchkin. Luckily for us, these ghosts are also thought to be “good ghosts”. The bad ghosts, which apparently also exist in the strange and schizophrenic world of quantum mechanics are another thing altogether.

As the theory goes, these ghosts where send for so as to avoid the over-counting in the complex area of theoretical physics, to fix gauges and make path integrals right.

In high school, we were taught classical mechanics (remember fiction, momentum, force, gravitation, etc) and one of the things we learned was that the path of say a moving object (think of a ball thrown across the room) was that for which the action is a single unique trajectory, i.e., a stationary action [formulation].

In the world of the quantum mechanics, however, the stationary action formulation of classical mechanics extends to the path integral formulation, where a physical system follows simultaneously an infinity of possible trajectories with associated probability amplitudes for each path being determined by the action for the path. Now, path integral formulation should yield unambiguous, non-singular solutions; which they don’t. To modify the action such that these calculations yield applicable results, the good ghosts are used to break the gauge symmetries and make things right.

So every gauge field has an associated ghost, and where the gauge field acquires a mass, the associated ghost field acquires the same mass in some cases.

The Search for the God particle in Europe

Jack Dikian

December 2011

The Higgs Boson, nicknamed the God particle is the quantum of the theoretical Higgs field expected to have a non-zero vacuum expectation value thus, as the theory goes giving mass to every elementary particle that couples with the Higgs field, including the Higgs boson itself.

Experiments attempting to find the particle are currently being performed using the Large Hadron Collider at CERN. Now, CERN may have confirmed this theory. Scientists hunting for Higgs boson say they've found "intriguing hints" but not definitive proof that it exists, narrowing down the search and hope to reach a conclusion on whether the particle exists by next year. So if it does exist, it can help explain why there is mass in the universe.

It seems the data indicates the particle itself may have a mass of between roughly 114 and 130 billion electron volts. One billion electron volts is roughly the mass of a proton. The most likely mass of the Higgs boson is around 124 to 126 billion electron volts.

Project Tuva and Feynman Lectures

Jack Dikian

November 2011

I was first introduced to the work of the great Richard Feynman when I came by Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character) when I was 15 or 16. I can’t remember if I borrowed the book from my high school library, bought it at a place called the White Elephant or found it amongst hundreds of old Reader's Digest copies left behind in the family house we moved into around that time.

One thing is for certain. The book was truly enthralling – especially to a boy who grew up building Crystal radio sets, spending summer nights looking at the night skies, reading Parabola and cherishing the wonder of all. So coming across Surely You're Joking, soothed by it’s comforting and lighthearted tone was truly a discovery of a lifetime.

Fast forward – we’ve all debated the features and benefits of Microsoft over Apple, some of us have even queued for hours outside an Apple store in the hope to buy their latest gadget; impress our friends, impress ourselves.

Regardless of our biases there is one thing that musts be said about Microsoft. Their Project Tuva which is an enhanced video player platform released to host the Messenger Lectures series titled The Character of Physical Law given by Richard Feynman in 1964 is a must for all who are interested in theoretical physics and in a strange way history. I say history because apart from a good introduction to topics that are still current in physics there is pleasure in seeing how a college campus looked in the fifties,

The project was a collaborative effort between Bill Gates and Microsoft Research that is designed to demonstrate the potential of enhanced video to teach people about the "core scientific concepts" of Feynman's lectures using interactive media.

According to his video introduction, Gates saw the lectures when he was younger. He enjoyed the physics concepts and Feynman's lecturing style, and later acquired the rights to make the video available to the public. He hopes that this will encourage others to make educational content available for free.

Feynman in his The Character of Physical Law lectures makes the most on-point remark dealing with the difficulty of understanding Quantum mechanics. James Bradford DeLong (commonly known as Brad Delong) in the course of something or rather suggests that the theory of relativity really isn’t all that hard. At least, if your standard of comparison is quantum mechanics.

He goes on – ‘While relativity has a reputation for being intimidatingly difficult, it’s a peculiar kind of difficulty. But anyone who studies the subject appreciates that it’s a series of epiphanies the theory are models of clarity. Quantum mechanics is not like that.”

And Feynman:

There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics.

You can get to project Tuva and the lectures at

http://research.microsoft.com/apps/tools/tuva/

I Am Convinced God Does Not Play Dice

Jack Dikian

March 2011

Introduction

The Copenhagen interpretation of quantum mechanics proposes, generally, that the outcome of any measurement cannot be measured with certainty. This leads to the situation where measurements of a property performed on two identical systems can give different answers.

However, can a deeper reality, hidden beneath quantum mechanics, described by a more fundamental theory predict the outcome of measurement with certainty. Einstein, a proponent of a deeper reality (hidden variables) hidden famously insisted that, "I am convinced God does not play dice”.

Quantum mechanics puzzle

Quantum mechanics creates the puzzling situation in which a measurement of one system can "poison" the measurement of the other system, no matter what the distance between them. One could imagine the two measurements were so far apart in space that special relativity would prohibit any influence of one measurement over the other.

For example, say, in a neutral-Pion decay, where two photons travel some light years apart – if the spin of one photon is measured, quantum mechanic suggests that that measurement instantaneously forces the second photon into a state of well-defined spin - even though it is light years away from the first.

Einstein, Podolsky, and Rosen (EPR) argued that elements of reality must be added to quantum mechanics and postulated that the existence of unknown properties should account for the discrepancy – that there is a deeper reality.

A conundrum

How do we reconcile the fact that the second photon "knows" that the spin of the first photo has been measured, even though they are separated by light years of space and far too little time has passed for information to have traveled to it according to special relativity?

We can accept the postulates of quantum mechanics its seemingly uncomfortable coexistence with special relativity, or we may believe that quantum mechanics is not complete:

A second universe

Jack Dikian

January 2011

Paul Adrien Maurice Dirac (whilst not a household name) is considered by many to be the greatest British theorist since Sir Isaac Newton. All the great minds that pioneered atomic physics were left trailing by Dirac. When Einstein read a paper by the young Dirac, he said, I have trouble with Dirac – "this balancing on the dizzying path between genius and madness is awful..".

In 1925, for reasons only known to himself, he set out to unite the two most difficult and counter-initiative ideas in history – Quantum Mechanics and Special Relativity (where as a fall out, objects behave differently as they travel at speeds approaching the speed of light). It must be remembered that by the late 1920’s quantum mechanics was consistently producing erroneous results for calculations describing electrons as they traveled at high speed.

As well as this, Dirac had an additional aim. Dirac had a much more esoteric motivation. He was once quoted of saying “a physical theory must have mathematical beauty”. For him, the fact that quantum mechanics and relativity weren’t reconciled was more that just an inconvenience – it was ugly.

Around 1925 he put his extra ordinary mind on the problem of bringing together the two new ideas of twentieth century physics. It is said that he worked on this problem alone for some three years before in 1928 he honed in on one mathematical formulation – an entirely new description of what goes on within the atom. Dirac knew it was right partly because it had mathematical beauty (see equation above).

As far as human achievements go it up there with Shakespeare's greatest works (something which by the way a very dear friend constantly reminds me of) and the Origin of the Species. Dirac’s equation describes how reality works at the fundamental level.

But, incredibly when Dirac looked at his own equation he noticed something that can only be said to be shocking. He later said, his equation [knew] more than he did.

In essence his equation was telling him that there is another universe that we had never noticed before. That’s because instead of his equation having one answer, it has two. The first describes the universe we know…the second describes a kind of mirror image to our universe made of atoms whose properties are reversed. As well as matter, Dirac’s equation predicts the existence of antimatter.

Dirac seems to be saying that for every piece of matter in our known universe, there can exist a corresponding piece of antimatter. Just like a world in a mirror a universe made of antimatter would look and work just like ours.

The Cheshire Cat's Grin, Alice in Wonderland, and Information Loss

Jack Dikian

December 2010

Introduction

As I was trying to fall asleep last night – I thought about a thought experiment that I’ve gone back to over and over again. In fact, since I was a boy. Rocketing away in a spaceship and looking back at my house, my street, my suburb and friends.

After a while, they become scarcely distinguishable and not much more than mere inhabitants, faceless beings without person or form. I’ve always felt I’m taking away with me the knowledge of the frequent earth-born misunderstandings, the eagerness of people to kill one another, their hatreds, imagined self-importance, and the delusion that we have some privileged position in the Universe as this tiny pale blue home disappeared in the vastness of the countless stars.

As I got older and learned more about cosmology and exotic phenomena such as black holes, I would wounder how it would be if trapped in a black hole. And overtime, I’d wonder if there was a way to let my friends know what I once knew. Is the knowledge (actually information) I’m carrying destroyed as gravitational forces pull me apart?

Conservation of information in quantum mechanics

Quantum mechanics incorporates a principle that information about a system is encoded in its wave function, and that the evolution of the wave function is determined by a unitary operator implying that information is conserved (in the quantum sense). Here, quantum determinism, and reversibility are at play.

Any deterministic time reversible theory must conserve information and the evolution of the wave function satisfies this. However, whenever an observation is made it would seem that new information is created, and reconciling this, with the absolute conservation of information in the physical universe is not necessarily straight forward.

Causality of information as a subjective human interaction of the mind may be the source of common confusion. A mind act has no information momentum to transfer to the system. A momentum change as a cause of observation was/is always the physical meaning of information. A change in system as an observation then allows the effect of all as information conservation.

Black Holes and Singularities Acting As Sinks

In the 1970s, Stephen Hawking showed that black holes evaporate by quantum processes. He also asserted that information, such as the identity of matter pulled into black holes, is permanently lost thus challenging a fundamental tenet of quantum mechanics - information cannot be lost. Hawking renounced the idea later but unable, as other weren’t able, to show the mechanism for how information might escape a black hole.

More recently, a team of physicists at Penn State, led by Abhay Ashtekar (and his collaborators, Victor Taveras, a graduate student in the Penn State Department of Physics, and Madhavan Varadarajan, a professor at the Raman Research Institute in India) announced they have shown a mechanism by which information can be recovered from black holes. They say their findings expand space-time beyond its assumed size, thus providing room for information to reappear.

To explain the issue, Ashtekar used an analogy from Alice in Wonderland. "When the Cheshire cat disappears, his grin remains," he said. "We used to think it was the same way with black holes. Hawking's analysis suggested that at the end of a black hole's life, even after it has completely evaporated away, a singularity, or a final edge to space-time, is left behind, and this singularity serves as a sink for unrecoverable information."

The researchers suggest that singularities do not exist in the real world and "Information only appears to be lost because we have been looking at a restricted part of the true quantum-mechanical space-time". Once you consider quantum gravity, then space-time becomes much larger and there is room for information to reappear in the distant future on the other side of what was first thought to be the end of space-time."

To conduct their studies, the team used a two-dimensional model of black holes to investigate the quantum nature of real black holes, which exist in four dimensions. That's because two-dimensional systems are simpler to study mathematically. But because of the close similarities between two-dimensional black holes and spherical four-dimensional black holes, the team believes that this approach is a general mechanism that can be applied in four dimensions.