Quote:
Originally Posted by James Putnam
This is why I work from the fundamentals step by step.
|
This is not only a good approach, some might argue that it’s the
only approach that actually works. While “leaps of intuition” are commonly reported in math and science, after such experiences, the mathematician or scientist must be able to present proof of their theorem or the derivation of their theoretical prediction in a formal, step-by-step manner.
Quote:
|
Great leaps forward into complex theory and the terms that are born out of the theory do not address the question of: What have we learned about the operation of the universe that leads step by step toward fuller understanding.
|
True.
For this reason, effective instruction in Math and Physics needs to, and in nearly all ordinary academic setting do, follow a series of well-explained, orderly, step-by-step explanations.
Unfortunately, internet science forums - even one as esteemed as hypography
– aren’t like well-taught academic classes. People tend to discuss ideas assuming readers have about the same academic experience as they do, which is often not true. Being less formal and hierarchical than the usual class setting, we’re really not suited to ordinary academic communication – in short, science forums aren’t a substitute for science classes.
Nonetheless, I’ll try to give an overview of physics sufficient to put time dilation in a sensible context.
Quote:
|
If Einstein's theory is correct, then we should be able to see the development of that theory step by step from the fundamentals.
|
The theory of
special relativity is very succinct and straight-forward in proceeding from its assumptions (postulates) to its conclusions.
It begins with an earlier theory of relativity,
Galilean relativity. To understand Galilean relativity, it’s helpful to consider what it is not, the pre and early scientific ideas that preceded it. In short, these views held that the laws of physics were different for moving bodies than “stationary” ones. This made intuitive sense, based on everyday experience: actions performed in the interiors of jostling horse-drawn carriages or pitching ships at sea
seemed to obey different laws of motion than those done on solid ground. A natural conclusion of this view was geocentrism: if Earth was orbiting Sol at a great speed, surely we would
feel it. The eventual acceptance of Galilean relativity went along with that of heliocentism, and continued to be accepted when
Isaac Newton much improved its mathematical formalism.
By the late 19th century, however, with the great successes of
James Clerk Maxwell and others in describing electromagnetism and light as wave phenomena, the idea that Galilean relativity could be violated by such things as measurements of the speed of light from a moving body was widely entertained, culminating in the famous
Michelson–Morley experiment, which attempted, in essence, to do just that, and, along with subsequent experiments, wound up not only supporting Galilean relativity, but adding to its list of laws of physics that were the same regardless of motion a new, and to many unexpected, item: the constancy of the speed of light.
Hence, special relativity as described by Einstein has two postulates: the first, Galilean relativity; the second, that the speed of light in vacuum is constant.
Quote:
Originally Posted by James Putnam
Transform equations force a relationship without going through this step by step approach. Transform equations are not safe mathematics for helping to learn truth about the operation of the universe. That is my opinion.
|
Working from these two postulates, time dilation and the equation that describes it – usually called the
Lorentz factor – follow from very simple geometry.
The usual “though experiment” illustration of this is the
“light clock”, which simply notes the difference in the path of a reflected pulse of light observed by a person stationary with respect to the apparatus vs. a person moving with respect to it. The shape of this path is a triangle. In the simplest units (known as
Planck units) The Lorentz factor (or, precisely, its
reciprocal) is just the famous
Pythagorean formula for one side
of a right triangle with a diagonal of length 1 given the length of the other side
:
.
This series of small steps of explanation allows us to answer part of this thread’s original question:
Quote:
Originally Posted by James Putnam
What is the cause for this clock dilation? The clock's operation is a physical occurrence. Does empirical evidence indicate the reason for clock dilation?
|
According to relativity, clocks do
not run slower when in motion as perceived by an observer at rest relative to the clock. No sort of physical stress, shaking, etc. is involved – time dilation (it makes little sense, IMHO, to reject the most well known term for the effect for philosophical reasons) is simply a geometric effect due to differences in observers, somewhat analogous to effects such as
geometric perspective.
As is usually the case when that thorn-in-the-side of physics, gravity, is involved, things get more complicated - but no less explicable in a step-by-step manner - when one considers the
gravitational time dilation of the
general theory of relativity. It’s an educational tradition, therefore, for the student to become comfortable with special relativity before undertaking the study of general relativity.
How can a clock be dilated?
The step-by-step approach to relativity
