Higher contact-like structures and supersymmetry

In my latest preprint “Higher contact-like structures and supersymmetry” I provide a novel geometric view of N=1 supersymmety in terms of a polycontact structure on superspace. The preprint can be found at arXiv:1201.4289v1 [math-ph]

The conception of the idea to describe supersymmetry in terms of some contact-like structure came from understanding SUSY mechanics in terms of a contact structure. See my preprint “Contact structures and supersymmetric mechanics” arXiv:1108.5291v2 [math-ph] and an earlier blog entry here.

Young Researchers in Mathematics Conference 2012

Royal Fort House, University of BristolRoyal Fort House, University of Bristol. Picture courtesy of the YRM 2012 committee.

The Young Researchers in Mathematics Conference is an annual event that aims to involve post-graduate and post-doctoral students at every level. It is a chance to meet and discuss research and ideas with other students from across the country.

 

I will be attending the Young Researchers in Mathematics Conference 2012 to be held at Bristol University 2nd-4th April.  I have offered to give a talk and right now awaiting confirmation that my talk has been accepted. My talk would fit into the Geometry and Topology tract.

 

I will post more details in due course.

 

Link

YRM2012

 

 

 

 

Mathematics the langauge of Physics

It is a rather indisputable fact for physicists that mathematics really is the correct language   of physics.  Without mathematics one could not formulate physical theories and then make prediction to be tested against nature.  Indeed, the formulation of physical theories has required the development of new mathematics.  Theoretical physics is really the construction of mathematical models to describe nature.

Even the experimentalist cannot avoid mathematics.  One has a lot of analysis of results and statistics  to preform in order to make sense of the experiments.

It is rather clear then, that without mathematics one will not go very far in physics. Any understanding of nature is going to be rather superficial without some mathematics.

A little deeper than this I believe that mathematics is more than just a language for physics, or indeed all science. The structures, patterns and rules of mathematics can guide one in constructing/analysing theories. The notion of symmetry is so fundamental in modern theoretical physics and at its heart is group theory.  Understanding physics can be driven my mathematical beauty. Given a new theory the first question to ask is what are the symmetries?

One has to ask why mathematics is the language of the physical sciences? Can we understand why mathematics has been just so useful and powerful in structuring our understanding of the Universe?

Eugene Wigner in 1960 wrote an article The Unreasonable Effectiveness of Mathematics in the Natural Sciences which was published in Communications on Pure and Applied Mathematics.  Wigner argues that mathematics has guided many advances in the physical sciences and that this suggests some deep link between mathematics and physics far beyond mathematics simply being a language.

A very extreme version of this deep interconnection is Max  Tegmark’s mathematical universe hypothesis, which basically states that all mathematics is realised in nature.  What this hypothesise also suggests is that the Universe really is mathematical. We uncover this mathematical structure rather than impose it on nature. This would explain Wigner’s “unreasonable effectiveness”.

We are now close to having to think about the philosophy of mathematics and in particular Platonism. I am certainly no big thinker on philosophy and so will postpone discussion about the philosophy of mathematics.

I would not go as far as to say I believe in Tegmark’s hypothesis, but it is for sure an interesting and provocative idea.  It certainly makes one think about the relation between mathematics, physics  and the nature of our Universe.

 

Wikipedia Links

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Mathematical universe hypothesis

What is wrong with engineers?

Here are a few comments on understanding engineers. I will tell you that an engineer sent them to me.

 Understanding Engineers: One


Two engineering students were walking across a university campus when one said, “Where did you get such a great bike?”
The second engineer replied, “Well, I was walking along yesterday, minding my own business, when a beautiful woman rode up on this bike, threw it to the ground, took off all her clothes and said, “Take what you want.”
The first engineer nodded approvingly and said, “Good choice; the clothes probably wouldn’t have fit you anyway.”


Understanding Engineers: Two


To the optimist, the glass is half-full.
To the pessimist, the glass is half-empty.
To the engineer, the glass is twice as big as it needs to be.


Understanding Engineers: Three


A priest, a doctor, and an engineer were waiting one morning for a particularly slow group of golfers.
The engineer fumed, “What’s with those guys? We must have been waiting for fifteen minutes!”
The doctor chimed in, “I don’t know, but I’ve never seen such inept golf!”
The priest said, “Here comes the green-keeper. Let’s have a word with him.”
He said, “Hello George, what’s wrong with that group ahead of us? They’re rather slow, aren’t they?”
The green-keeper replied, “Oh, yes. That’s a group of blind firemen. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free anytime.”
The group fell silent for a moment.
The priest said, “That’s so sad. I think I will say a special prayer for them tonight.”
The doctor said, “Good idea. I’m going to contact my ophthalmologist colleague and see if there’s anything he can do for them.”
The engineer said, “Why can’t they play at night?”

Understanding Engineers: Four


What is the difference between mechanical engineers and civil engineers?
Mechanical engineers build weapons. Civil engineers build targets.


Understanding Engineers: Five


The graduate with an engineering degree asks, “How does it work?”
The graduate with a science degree asks, “Why does it work?”
The graduate with an accounting degree asks, “How much will it cost?”
The graduate with an arts degree asks, “Do you want fries with that?”


Understanding Engineers: Six


Three engineering students were gathered together discussing who must have designed the human body.
One said, “It was a mechanical engineer. Just look at all the joints.”
Another said, “No, it was an electrical engineer. The nervous system has many thousands of electrical connections.”
The last one said, “No, actually it had to have been a civil engineer. Who else would run a toxic waste pipeline through a recreational area?”


Understanding Engineers: Seven


Normal people believe that if it ain’t broke, don’t fix it.
Engineers believe that if it ain’t broke, it doesn’t have enough features yet.


Understanding Engineers: Eight


An engineer was crossing a road one day, when a frog called out to him and said, “If you kiss me, I’ll turn into a beautiful princess.”
He bent over, picked up the frog and put it in his pocket.
The frog then cried out, “If you kiss me and turn me back into a princess, I’ll stay with you for one week and do ANYTHING you want.”
Again, the engineer took the frog out, smiled at it and put it back into his pocket.
Finally, the frog asked, “What is the matter? I’ve told you I’m a beautiful princess and that I’ll stay with you for one week and do anything you want. Why won’t you kiss me?”
The engineer said, “Look, I’m an engineer. I don’t have time for a girlfriend, but a talking frog, now that’s cool.”

 

 

 

Response to "String Bashing" by M.J. Duff

If you have read Smolin’s and/or Woit’s books arguing against string theory then please read Duff’s response  here.

Duff’s “String and M-theory: answering the critics” is quite accessible and does a good job explaining why people are interested in string theory, both from a physics and mathematics point of view. One major point he makes is the unfair coverage of “anti-string theorists” and  works that are wrong.

For example, Lisi’s theory of everything based on \(E_{8}\).  This theory is mathematically wrong, it does not describe  the correct matter content of the universe.  Also, the use of the exceptional groups  in theories of everything, including string theory pre-dates    Lisi’s work.  I would say that the media and the “blogosphere”  was too quick to hail Lisi’s work and too slow in pointing out the errors.

Duff also points out how quickly the attacks on string theory become personal attacks on string theorists.

Is it important that the general public has a reasonable understanding of string theory and supports such reserach?

I would have to say  yes.

Not that science or mathematics is a popularity contest that will be won via the general media, it will be won via peer-reviewed papers. However, the general public pays for almost all fundamental science research and thus it is vital to keep the public on board. There will always be speculation, disagreements and conflicting points of view in science at the frontiers of our knowledge, but this should not devolve into personal attacks. This only weakens the position of  science in wider society.

String does  have many attractive features and seems to be our best hope at understanding the Universe.  The best response to  the critics is come up with an alternative!

CERN to announce glimpse of the Higgs.

Today at CERN scientists will present reports on the progress of the hunt for the Higgs boson.

I await the news…

For now read the BBC report here.

CERN’s public website can be found here.

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Update

Both the Atlas and CMS experiments at CERN independently suggest that the Higgs has been observed and has a mass of about 125 GeV.  However, the statistical uncertainly in the data means that the Higgs has not truly been discovered.

There will be further experiments and lots of data analysis before the claim of discovery will be made.

Optimistically,  some time next year we may have confirmation of the Higgs.

Find out about the press release  here.

Read the BBC News report here.

 

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Now we await news of supersymmetry.

 

Bridging mathematics and art

We all know that art,  symmetry,  beauty and mathematics are well intertwined.  Since 1998 the Bridges Organization organised an annual conference bringing together mathematicians and artists. All very interesting stuff and shows that mathematics can be appreciated by those who are not traditional mathematicians.

The next conference is July 25-29, 2012 at Towson University, located in the Baltimore Metropolitan Area.

I guess I will now have to go away and create some interesting computer graphics or something! (Not that I think I will be attending this conference)

2015, The International Year of Light

The European  Physical Society has initiated a drive to get the United Nations to proclaim 2015 as the International Year of Light.

 

Light plays a central role in human activities in science, technology and culture. Light itself underpins the existence of life, and light-based technologies will guide and drive the future development of human society. Light and optics have revolutionized medicine, have opened up international communication via the Internet, and continue to be central to linking cultural, economic and political aspects of the global society. Advances in lighting and solar energy are considered crucial for future sustainable development.

Follow this link to the full statement.

 

I think making 2015 the International Year of Light is a great idea. Of all the physics, understanding light and more generally electromagnetic radiation,  has had a huge impact on society as well as all branches of  science and engineering.

2005 was the International Year of Physics, 2009 was the International Year of Astronomy and 2011 is the International Year of Chemistry. It seems fitting that 2015 be the year of light, lets see why…

  • 1815  Fresnel published his first works on light as a wave.
  • 1865 Maxwell mathematically described electromagnetic phenomena via his now famous equations.
  • 1915 Einstein developed general relativity, which shows that light is fundamental in understanding space-time and gravity.
  • 1965  Penzias and Wilson discover the Cosmic Microwave Background Radiation (CMBR).

 

Let us hope the United Nations agree on the importance of  light in all our lives and declare 2015 The International Year of Light.

Random thoughts on mathematics, physics and more…