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December 25th Marks the Birthday of Isaac Newton

 

December 20, 2014
According to the Julian calendar used in England at the time, Isaac Newton was born on December 25, 1642, the day Christmas is celebrated.  Isaac Newton was considered a natural philosopher and one of the most original and influential theorists in the history of science. 

He is often noted for his three laws of motion:

1)  A body at rest will remain at rest, or a body in motion will remain in motion,
     unless acted upon by an external force.

2)  The force on a body will be equal to the mass of the body multiplied by its
      acceleration, or F = ma.  The direction of the force is in the same direction
      as the accelerating body.

3)  For every action there is an equal and opposite reaction.

These three fundamental laws of motion form the basis of mechanics.  They are referred to in just about every application of static or dynamical situations, including building structures, bodies in motion, analysis of earthquakes, aircraft in flight, design of boat hulls, space ships to the moon, and even the string of a kite.  The real question is: When are Newton’s laws not referred to ?   Almost never.  They are thought to always prevail somehow throughout our physical world.  By “always prevail somehow” is meant that any observation or measurement one makes within their own “frame-of- reference” will always be true.  This is always the case for any type of system on earth (sometimes called an “inertial coordinate system”), such as how an automobile operates or a bridge is designed, but is also true in outer space such as for studying the planets, stars, and even galaxies.  To the observer who is making the observations or taking measurements within his own reference frame (e.g., the earth), Newton’s laws of motion will always hold true.  Always.

It is only under certain circumstances which allow us to peer into more than one frame-of-reference, moving relative to one another at speeds near the speed of light, where another “set of rules” need be considered.  These other “set of rules”, or physical laws, are mostly credited to Albert Einstein due to his work on the subject of relativity.  However, regardless of whatever relativity effects there may be, Newton’s laws will always hold true for the observer described above.  This is a nice convenience.  Nothing will ever “distort” or “warp” to the observer.

.. Newton’s laws will always hold true for the observer ..  

Under special circumstances of high speed travel nearing the speed of light, or perhaps when dealing with sub-atomic particles, or even the electromagnetic radiation near large massive bodies – there will begin to pose a “different set of rules” and can involve more than one frame-of-reference, or if you will, point of view.

Relative motion is not difficult to understand.  We have all observed relative motion at one time or another.  Take for instance the flatbed of a moving train boxcar, which is in motion at 80 mph.  An Olympic sprinter is on the flatbed of the boxcar and decides to run to the other end.  The boxcar is long enough for the sprinter to reach a speed of 25 mph.  To the sprinter, all he knows is that he is running at 25 mph.  But you are an observer outside the train, and see the sprinter running at a speed of 25 + 80 = 105 mph, the sum of speed of the sprinter plus the speed of the train.  Your point of view records a different speed compared to the sprinter who observes only his motion relative to flatbed of the boxcar.


Now this time, a person standing stationary on the boxcar which is still moving at 80 mph, is shining a flashlight in the direction of the train’s motion.  The speed of light from the flashlight is given as 186,000 miles per second, or the speed of light.  The speed of light appears amazingly fast, but if you were to shine a light at a mirror on the Moon, it would reflect back into your eyes in just over 2 seconds - enough time for you to realize that light must take its course through space at a speed which is finite.  Now, as the light is travelling in the direction of motion of the train, and you are the outside observer, would you expect the speed of light to travel at 186,000 + 80/3600 miles per second ?  Although you might expect the speeds to add together, as in the previous example, they don’t.  The speed of the light beam to an observer outside the train is the same for the person holding the flashlight, or 186,000 mi/s.  For some reason, this is the nature of light, and the speed of the light beam will always be constant regardless of what relative motion is imposed on the source of the light beam.  In fact, this is the universal speed limit for any object, particle, or electromagnetic radiation.  Nothing can go faster than the speed of light.



The question is, what gives ?  Why won’t the speeds add up mathematically the way you would expect ? 1  After all, the speed of light is finite.  Again, it is because this is simply the nature of light, but also a glimpse into what could be a “truer perspective” of physical reality.  Going back to the question: “What gives ? Why won’t the speeds add up ?”  The answer could be that time “gives”- since it dilates or slows down - but also length contracts, as shown by the equations of special relativity. 

It is not so easy to measure the length contraction in examples of special relativity, but certain accurate atomic clocks, called cesium clocks (e.g., the HP 5061A cesium clock) which keep very accurate time, can measure the difference due to time dilation when placed aboard fast-moving commercial jetliners and comparing to a similar clock at rest on earth. The time difference measured is only on the order of nanoseconds (billionths of a second) but Einstein’s prediction that moving clocks slow down – or dilate - was proven, and the measured results agreed with the equations of special relativity.  Since the time difference even at speeds of the fastest jets is quite small, this will not introduce any real error for applications on earth which assume a Newtonian frame-of-reference only.  Ask any engineering student about the accuracy of significant digits needed to design an automobile or even a supersonic jet – it will not matter.  The main point is that time, and even distance, are not absolute like you may have thought.  The passing of time actually depends on the relative motion of bodies, and only appears absolute to the observer within their own frame-of-reference.  Sometimes the term ‘space-time’ is used to remind us of this aspect of relativity, and is used when discussing certain topics of astronomy.  Our viewpoint on how to view physical reality was revolutionized by Einstein’s accomplishments on relativity. 

Finding the difference of time passing on high speed jets is just one example of how time “dilates”, or slows down.  But what is a more real significance of special relativity’s claim to slow down time in moving clocks ?  One example, and often a favorite to some, is called the “twin paradox” in space travel.   Two identical twins are situated on earth, but one decides to take a high speed voyage on a space ship, travelling through space near the speed of light.  After some time he returns to earth, but when he sees his once-identical twin, he has aged beyond recognition.  The earthling-twin has grown a white beard, and is bent over and holding a cane.  He states his age as 85 years old, yet the twin on the spaceship has an age of only 30.  It’s as if the twin on the spaceship has “travelled into the future”.


Our physical laws provide for only a forward movement in the realm of time.

  

The above example implies we can take long journeys into space, travelling at high velocities near light speed, without hardly ever aging.  Projecting from this idea, it could allow us to seek out other habitable planets that could be far away, if for some reason we are faced with the circumstance of leaving earth one day.  But leaving our solar system because our Sun may one day expire (which, by the way, is at least six billion years plus or minus another billion or so) is not the only reason to take up interstellar travel.  We might someday become adventurous and just want to travel to another solar system or another galaxy, just like the starship Enterprise in Star Trek. 

One final mention regarding “time travel”.  Some contend that if we are able travel into the future, demonstrated by the twin paradox, is it also possible to travel back in time (to an earlier time in history) ?  Sorry to say, there is no formula nor basis for travelling back in time.  It may even be unethical to consider this type of reverse time travel.  Our physical laws provide for only a forward movement in the realm of time.

1.  When viewed as a wave model (wave-particle duality) a moving light source will exhibit an increase or decrease in wavelength to a stationary observer causing a detectable red shift or blue shift in the visible light spectrum, depending on if the light source is moving away or toward the observer.  Due to this, the properties of a moving light source can be considered to “add” or “subtract”, but only in the sense of a change in length of the light wave.  (see Doppler effect of light waves).