Six Not-So-Easy Pieces: Einstein’s Relativity, Symmetry, And Space-Time

This sequel to Richard Feynamn’s Six Easy Pieces grabs six more additional lectures from his famous three-volume series, Lectures on Physics.  In this book, Feynman unfolds the complexity of Relativity, Symmetry and Space-Time.   As is typical for his style, he makes these very complex subjects approachable, but then drives deeper to reveal the mathematics behind the mysteries.   The narrative and related equations are definitely geared toward math and science students. 

As is his genius, Richard Feynman often unpacks complex concepts through the use of practical analogies.  His description of curved space in Chapter 6 was one of my favorite sections (p. 112). 

Curved Space

In order to understand this idea of curved space in two dimensions you really have to appreciate the limited point of view of the character who lives in such a space.  Suppose we imagine a bug with no eyes who lives on a plane, as show in Figure 6-1.  He can move only on the plane, and he has no way of knowing that there is any way to discover any “outside world.” (He hasn’t got your imagination.)  We are, of course, going to argue by analogy.  We live in a three-dimensional world, and we don’t have any imagination about going off our three-dimensional world in a new direction; so we have to think the thing out by analogy.  It is as though we were bugs living on a plane, and there was a space in another direction.  That’s way we will first work with the bug, remembering that he must live on his surface and can’t get out.

As another example of a bug living in two dimensions, let’s imagine one who lives on a sphere.  We imagine that he can walk around on the surface of the sphere, as in Figure 6-2, but that he can’t look “up,” or “down,” or “out.”

Now we want to consider still a third kind of creature.  He is also a bug like the others, and also lives on a plane, as our first bug did, but this time the plane is peculiar.  The temperature is different at different places.  Also, the bug and any rules he uses are all made of the same material which expands when it is heated.  Whenever he puts a ruler somewhere to measure something the ruler expands immediately to the proper length for the temperature at that place.  Whenever he puts any object–himself, a ruler, a triangle, or anything–the thing stretches itself because of the thermal expansion. 

Feynman uses this constructed analogy to explain how the bug would get different measurements in each of these “worlds.”  The bug is able to determine what type of world it lives in based on the measurements.  It is interesting to see through his example that the bug on the sphere experiences the same measurements as the bug on the temperature varying hotplate (both can measure a triangle with an angle-sum of 270 degrees where the bug in the plane would see a maximum sum of 180 degrees).  Scientist speculate on the “space” curvature of the universe by conducting experiments.  So far, it is inconclusive.

In this book, Feynman also covers a refresher course on Vectors (Ch. 1), discusses the Symmetry in Physical Laws (Ch. 2), does a detailed analysis of The Special Theory of Relativity (Ch. 3), Relativistic Energy and Momentum (Ch. 4), Space-Time (Ch. 5), and Curved Space (Ch. 6).

Realativity

The Special Theory of Realativity (p. 49) is a facinating approach to motion that for over 200 years was ruled by equations developed by Isaac Newton.   In Newton’s Second Law, 

which is the same as F=ma (where a is acceleration or the time derivative of velocity, dv/dt), the assumption is that mass (m) is a constant.  Einstein corrected this formula with his theory by saying that mass has the changing value,

where mo is the “rest mass” of a body when it is not moving and c is the speed of light (186,000 mi/s or 3×10^5 km/s).�

Faster than the Speed of Light

Dr. João Magueijo presents a theory that allows for variable speed of light (VSL).   This is a rather controversial subject as it deals with a value in physics that has traditionally been constant (c, the value of the speed of light, 186,000 mps or 300,000 kps).  The speed of light is the underpinnings of Einstein’s theories of special relativity, as seen in the famous E=mc² equation.

The Book

While dealing very little with the science of theory itself, João does provide a very entertaining look at the often painful, slow and bureaucratic scientific process.  He spends considerable time presenting the histories and struggles of scientist like Einstein as well as his colleagues.  These narrative backdrops are used to provide contrast and similarities to his own scientific speculation.  These also provide the basis for the bipolar challanges against and support for VSL.

The Theory

João proposes that the speed of light is dependant upon energy or space-time.  He postulates that during the moment of creation, the high energy big bang of those intial moments could well increase the speed at which light travels by sixty orders of magnitude (that is 1 with 60 zeros).  This could explain the horizon problem of cosmology and propose an alternative to cosmic inflation.  This would reveal itself near black holes or cosmic strings.

The Scientist

Dr. João Magueijo received his doctorate from Cambridge, has been a faculty member at Princeton and Cambridge, and is currently a professor at Imperial College, London.   A lecture from João can be found here: http://forum.wgbh.org/wgbh/forum.php?lecture_id=3195

João writes, “we do not notice energy, but only variations in energy.”  He concludes the book by saying, “It’s difficult to sum up where VSL stands, as I finish this book… VSL is now an umbrella for many different theories.”

Links

VSL: http://en.wikipedia.org/wiki/Variable_speed_of_light
Speed of LIght: http://en.wikipedia.org/wiki/Speed_of_light

 

Robotics

The LEGO mindstorm robotics kit is a popular programmable controller that can allow kids and adults alike to enter the world of robotics.  I am currently playing with a few free software programs that my friend found that let you simulate virtual robots, including the mindstorm.

LEGO Mindstorm

LEGO Digital Designer – Just for fun, build something!

Microsoft Robotics Developer Studio – This allows you to model a virtual robot and world, complete with controls to maneuver your robo-friend.

Modeling Programs we are investigating to see if they can be used to construct virtual robots or the worlds they live in:  Wings3d, Silo3d, Blender3d

Mindstorm blog:
http://thenxtstep.blogspot.com/

 

Richard Feynman

Richard Feynman is Nobel prize winning physicist and famous communicator.  I put together a collection of YouTube Feynman videos: 

The Pleasure of Finding Things Out

Part 1
 

Part 2

Part 3

Part 4

Part 5

 

Beyond AI: Creating the Conscience of the Machine

I have always been fascinated with the study of Artificial Intelligence.  I began my interest as many computer science majors by simulating intelligence through maze solving LISP automated mice.  These are brute force methods that appear to be intelligent by recursively exploring every possible solution.  This is not intelligence.  It is merely programmatic problem solving.

What is Artificial Intelligence?  How do we copy the creation that is the human mind and intellect, and impress that upon silicon and wires?  Is it even possible? 

BookBeyond AI: Creating the Conscience of the Machine
by J. Storrs Hall

Artificial intelligence (AI) is now advancing at such a rapid clip that it has the potential to transform our world in ways both exciting and disturbing. Computers have already been designed that are capable of driving cars, playing soccer, and finding and organizing information on the Web in ways that no human could. With each new gain in processing power, will scientists soon be able to create supercomputers that can read a newspaper with understanding, or write a news story, or create novels, or even formulate laws? And if machine intelligence advances beyond human intelligence, will we need to start talking about a computer’s intentions?

This book contemplates several interesting topics related to artificial intelligence, including the consequences of actually creating a systems that is intelligent.  A lot of what is intelligence appears to be search and pattern matching.  It seems that we build complex associations that help us grapple with our environment and interact with others in an intelligent fashion. 

What is intelligence?  I believe that we will continue to see progress in developing artificial minds.  Predictive expert systems already provide a sense of “smarts” but they are not creating anything new.  Attempts to build systems that take inputs, learn and even postulate solutions (as in mathematical proofs) have been limited in their success.  It seems that these intelligent systems hit a “glass ceiling” beyond which they are unable to produce anything new.  

Tools, Programs and Links

SHRDLU is a program for understanding natural language, written by Terry Winograd at the M.I.T. Artificial Intelligence Laboratory in 1968-70. – http://hci.stanford.edu/~winograd/shrdlu/

The Spiritual Brain

The study of neuroscience continues to expand.  As the name would suggest, the foundational science is the study of the nervous system which of course, includes the study of the brain.  As the study expands beyond the pure biological investigation, it branches to include the cognitive studies and modeling within computer science, including the study of artificial intelligence (AI).

I recently stumbled across this interesting book:

BookThe Spiritual Brain
A Neuroscientist’s Case for the Existence of the Soul
By Mario Beauregard, Denyse O’Leary

In this book, the authors discuss the various claims and studies that attempt to locate the “region” of the brain or “God gene” that is responsible for spiritual experiences (the emotion of faith, the sense of the presence of an outside intelligence, the connection to God).  In this they attempt to investigate and answer the question, has God created the mind or does the mind create God. 

Is the brain synonymous with “the mind”?   The brain appears to be the physical fabric in which the mind lives.  Instead of some special area of the brain that is predisposed to invent spiritual experiences, the mind has the ability to “wander” around within the brain, perceiving and communing with the eternal realities.�

Quantum Physics

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated.

I find this to be a fascinating topic.  The best way to describe these two “entities” is to think of them as being part of the same function.  

The strangeness of the quantum world is that these functions (often thought of as waves) exist within a domain.  Within this domain, the quantum “particle” is said to existing only in terms of probability rather than in definitive terms.  In the Cartesian world of modeling, we expect to see a particle exist at location x,y,z at time t.  In the world of the very small, those quantum particles have a probability of existing at that location.  In reality there could be multiple location at which a particle can exist (having the same probability). The quantum weirdness says that the particle exists in all of those location at the same time.  In entanglement, the distant particle is a superposition of the other (I am using distance as relative to the observer). The act of observing a quantum system causes it to collapse into a finite particle/state.

Matter as Particles and Waves

Quantum Physics says that matter exists as particles and waves.  A particle, much like a marble, can be observed as being in a single location (x,y,z) at a certain time (t).  The de Broglie hypothesis states that all matter has a wave-like nature.  At the quantum world of the very small, this can be seen through the famous “double split experiment”.

Double Split Experiment

With Quantum Physics, the mechanics of the physical word that Newtonian Physics model define are suddenly redefined.  

The Newtonian model is deterministic, that is to say that everything can be determined if we understand all the variables that are in play.  In a real sense, Newton’s system of equations can be used to define everything that will happen in the Universe in a predetermined sense.  The very actions that we take are a result of physical systems responding to a biochemical process involving synaptic electrical network engaging biological responses (though a series of predictable pathways).  In this sense, everything that we experience, do or observe is predetermined by an elaborate matrix of equations.  

Quantum mechanics throws a wrench into this non-volitional cosmos by introducing a truly random nature at the very fundamental building blocks of all Creation.  The attributes of these quantum elements, these tiny sub-atomic particles that make up all of matter and transfer energy, are ultimately unpredictable.  The attributes of these particles are said to exist as probabilities.  There is a probability that a electron surrounding the nucleus of an atom would exist at a particular orbit (atomic orbitals).  The Heisenberg uncertainty principle says that even when we know one attribute of a quantum particle (e.g. the location of an electron) one of the other attributes will remain completely uncertain (e.g. the momentum). 

 

Science

I love science.  My degree and career is in computer science (applied in various capacities including my current systems engineering role).   However, I love all sciences. My latest adventures have been in quantum physics and neuroscience.
 

 
[God] alone spreadeth out the heavens, and treadeth upon the waves of the sea…maketh Arcturus, Orion, and Pleiades, and the chambers of the south…doeth great things past finding out; yea, and wonders without numbers.

Book of Job 9:8-10