Discovery of evidence for cosmic inflation

First of all, I don't really understand it.  Haven't had time to read much about it yet, and was never that interested in the idea of cosmic inflation during the early part of the universe's existence, anyway.  But not understanding and not being that interested have never been good reasons for not discussing something.  If you understood something perfectly, I would think it would be the least interesting thing for you to discuss.  Which is how physics professors--with important exceptions that I have been fortunate to know--usually teach physics, as if they understand it perfectly.

Being on lunch break, however, makes it something I will discuss only briefly.  There are two important things involved in this discovery announced yesterday.  One is that it gives very good evidence for the idea of cosmic inflation, and the other is that it seems to be the first confirmation of the existence of gravitational waves.  Well, actually there's a third reason it's a great discovery, if it's not a "trick of light" deluding our radio antennas.  The inflation theory of Alan Guth and Andre Linde is based on quantum mechanics, so these gravitational wave signatures that have been detected were produced by a quantum process, implying a heretofore unknown but much sought connection between  quantum physics and the classical physics of general relativity .

See the New York Times article by Dennis Overbye for a more detailed discussion.

This discovery involves detecting and interpreting the polarization of very faint radio waves.  To get an idea of the meaning of polarization as it applies to electromagnetic waves, see my 11 June 2011 post.

Note added later: The next year, this discovery announcement was retracted. But, non-primordial gravitational waves were discovered that year (2015), coincident with the 100th anniversary of Einstein's publication of his general relativity theory of gravity. Gravitational wave detection has occurred several times since then.

The influence of symmetry in physics

The symmetery…

Is symmetry a force, like gravity or magnetism?  One of the books I quoted in my previous post is titled The Force of Symmetry.  A literal reading of the title implies that symmetry is a force, like the force of gravity.  But the title should be read impressionistically rather than literally, maybe as The Influence of Symmetry in Physics, for instance. The influence of symmetry in physics nowadays is huge, because symmetry in its mathematically most abstract form is considered to be the explanation for the existence of forces.

What is a force? That’s easy to answer. A force is a push or a pull.  Your body is being pulled toward the center of Earth by gravity right now, and the chair you’re sitting in is pushing up on you against the pull of gravity.  In terms of Newton’s third law, these aren’t the action-reaction forces, however.  The reaction force of the Earth’s gravity pulling on your body is your body’s gravity pulling back on Earth.  The action-reaction forces in the case of the chair you’re sitting in are the “contact forces” of the chair pushing up on you and your butt pushing back on it.  Well, partly your thighs pushing back also.

The contact forces are electromagnetic forces in the atoms of your body and of the chair.  The action-reaction pair in the case of you pulling up on Earth’s mass and Earth pulling down on your mass is due to the gravitational force.

What causes forces?  Physics has a pretty easy answer for that, too.  Forces are caused by fields. Even the contact forces of two objects in apparent direct contact with each other are caused by the interaction of the electromagnetic fields of the objects. But when you ask “what is a field?” well, now you’re getting into the land of abstraction. Now you’re getting closer to seeing the influence of symmetry in physics.  

Before getting into that, however, let’s not forget the simple symmetries we see all around us.  We see, for instance, numerous examples of squares, rectangles, circles and other such geometric figures.   We see the human body’s bilateral symmetry.  In all these examples, if you perform some transformation or operation such as rotating the object around a certain axis by a certain angle, you find that in some cases the object is unchanged by the transformation.

Draw a square on a piece of paper and then rotate the paper by 90°. The square looks just the same as it did before you rotated it.  Of course, there are things you can do to prevent the square from looking the same after you rotate it by 90°.  You can draw each side of the square in a different color.  Or if you use a rectangular sheet of paper, you will have an external reference that tells you your square has been rotated by 90° (but once you rotate it by 180° the external reference itself looks the same as it originally did). 

 

The square can be said to have a four-fold symmetry.  If you start rotating it around an axis through its center, you find there are four angles at which symmetry clicks in and the square looks like it originally did, no matter what the original position of the square was.  A hexagon has a six-fold symmetry, as its name implies.  Snowflakes also have sixfold symmetry.

How many “folds” of symmetry does a circle have?  We’re getting into the physicist’s idealized notion of symmetry here.  The circle has “perfect” two-dimensional symmetry, or an infinite number of choices of rotations about its center that leave it unchanged.  Squares, hexagons, etc. have discrete or countable degrees of symmetry.  The circle has continuous 2-dimensional symmetry.   

Likewise, a sphere has continuous or complete 3-dimensional symmetry.  Another way of putting this is that you can crawl around on the surface of a perfect sphere as much as you want, and no place on it will appear different from any other place. On a cube or any other polyhedron, you can crawl around and find its sides and corners. You won't be able to identify any corner or any side as being different from the others, but you can observe that corners are different from sides, and both of these are different from the "vertices" where more than two sides meet.