26  Light and the Twins Paradox                                  Table of Contents     Previous       Next

Resolving a Longstanding Problem:

Einstein’s postulate that the speed of light is constant for all observers (irrespective of their velocity) is troubling, not because it is not true, but because it violates our human sense of motion and how the velocities of normal objects are relative.

If I am on a moving train and throw a ball in the direction of travel.  Physics says that the ball’s velocity as seen by someone on the train platform is the addition of the velocity of the train and the velocity of the ball. 

Now instead of throwing a ball I emit a photon in the direction of the train.  Now physics says forget the principle of adding velocities because light is special and the observer on the platform sees the photon as moving at the speed of light and the velocity of the train makes no difference in its speed.

This conundrum has never felt good and is a basic thorn in the side of physics.  I will postulate that the speed of light is actually relative, but in a way that is unexpected. Read on.

Postulate Concerning the Special Relativity Law:  A photon of light has angular momentum (in the sense that a gyroscope has angular momentum).  When the source of a photon is given a linear acceleration, the photon instead of increasing its speed in a forward direction moves perpendicular to the direction of the acceleration (precession). This new direction of the photons will remain until further accelerations are given to the source. This “bending” (diffraction) of the light is caused by the acceleration of the light source and it is usually associated with the speed of the source. A vector relationship between the speed of the light and and the speed of the source v is shown below. 

1.    When both rocket ships have no velocity, the lasers project their photons straight ahead.
2.  As the rocket ships accelerate, the velocity vector “v” slowly increases at right angles to the rocket’s motion.  This type of motion resembles that of precession  in a spinning gyroscope.  When a force is impressed on the gyroscope instead of moving in the direction of the force, the gyroscope moves at right angles to the force.  This is generally known as precession.
3.   The above diagram has a single photon laser source.  When multiple photons are produced by the laser sources, the observer sees a widening circular interference pattern as velocity increases.  See below:
Note that the light produced by the incoming rocket has more interference rings because it is doppler shifted to shorter wavelengths.

What happens if we have the following situation where we swap lasers and telescopes?
In this situation the light source has not been accelerated and therefore both pilots see no diffraction.    A light source that accelerates is different than one that doesn’t accelerate.  This behavior of light highlights the asymmetry in the twins paradox, where the twin that accelerates ages less.

Is it still true that all clocks that are in moving frames of reference tic slower than the observers clock?  Yes, moving clocks tic slower to the observer, see youtube video of a excellent presentation of this by clicking here. We may be correct in saying that no matter the frame of reference, clocks slow with relative velocity, but the story is not complete until all accelerations from the past are accounted for.  This makes the twins paradox a bit more palatable.

Why is this rather strange behavior of light with acceleration important?
1. It clarifies the twins paradox.  Yes, acceleration breaks the symmetry, and the accelerating twin therefore ages less.  But what is it about acceleration that does this?  The answer: Acceleration effects space-time, which light and all physical phenomena are part of. 

In the twins paradox it is always the twin that experiences acceleration (the twin that sends out diffracted light) that has the shortening of dimension and a clock slowdown.

2. This unintuitive property of light (it diffracts when its source is accelerated) gives a physical basis to Lorentz’s insight that: “if it was assumed that moving bodies contracted very slightly in direction of their motion then the observed results of Michelson-Morley experiment could be accounted for”.  The work done here indicates that the measurement of accelerating bodies with light will yield a measurement that indicates a contraction in the direction of motion.  

Calculating the Lorentz Transform (the DWT way):
The Lorentz transform is usually calculated by examining how clocks slow when seen in moving frames of reference.  See the youtube video of a excellent presentation of this by clicking here.  DWT is in agreement with this analysis, but wants to give a big picture visualization of how the diffraction of light has a major role in what is going on.  In particular it will be postulated that the net slowing of time demonstrated in the video is due to the diffraction of light.

1.  Let us use the vector diagram developed at the beginning of this section:

2.  The three velocities are treated as distances.  However we need to handle the fact that the observer measures the speed of the laser light for both the upper and lower vector as the same value.  Yet the bottom vector is longer than the top vector. To compensate for this the observer assigns a conversion factor L to the top vector.  The new vector diagram looks as follows:

Since this is a right triangle we have c2 = (Lc)2 + v2 . Solving for L we get:  L = (1 - v2/c2)1/2
The observer concludes that distances are shorter in the space-time of the rocket when it accelerates to the speed v.

How come the velocity of the rocket is represented as a vector that is rotated 90 deg up and
down with respect to the velocity of light?
(click on the picture to see the video)

The reason light changes direction when it is accelerated is because it experiences precession.  This action is analogous to that of a gyroscope that has a force (acceleration) applied to it.   Click on image to see video explaining gyroscopic motion.

As soon as we apply a force intended to move the gyroscope to the right, we are surprised that the gyroscope does not move to the right, but precesses up and down instead.  We may interpret this as a break in the rules of adding velocities.  We apply a force that should push the wheel to the right and instead end up giving it a velocity that is up and down, very strange.  As the video indicates this wrongness we feel about precession lies in our predisposition that motion should be in the direction of the force that produces it.  This assumption is not true, particularly so for rotational motion (i.e. gyroscopes).        

I will postulate that this gyroscope precession action that causes right angle motions with acceleration (force) for a gyroscope, also applies to light.  I will further postulate that this right angle motion for light is something already known as diffraction.

The diffraction of light looks like magic. Plane waves coming in at the right are turned into a beam that has interference lobes.  The light that is coming straight in with a single velocity vector to the right (a plane wave) is transformed to light going out with the original velocity direction plus a light vector at up and down angles.  The insight is that light can be made to have velocity components that are at right angles to its motion.

This analogy of light acting like a gyroscope and developing a motion of precession (diffraction) when it is accelerated, is high speculation and will require some experimentation to verify.  If this postulate is wrong the fault is with your humble author Don Limuti 7/6/2014.

A Possible Experiment:
In this experiment a laser beam is reflected off a rotating mirror and directed to a target screen.  When the mirror is rotated slowly the trace on the target will be at its thinest value.  When the mirror is rotated rapidly (a fraction of the speed of light), the trace on the target will increase in width (if the diffraction with speed postulate is valid).  Note that this experiment should work for clockwise and counter clockwise rotation of the mirror.

Note that this experiment has some similarities to the experiment (space-time curvature) given in section 19. In that experiment we are looking for gravitons to bend light. In this experiment we are looking for an accelerating object to cause light to diffract.  The conjunction of gravity with acceleration and the behavior of light is tightly coupled. If we can understand this coupling better would enhance out understanding of how the universe operates.

This experiment is easy to outline, an actual implementation will require some careful design.  As usual making good experiments is more challenging than creating interesting theories.

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