Relavistic Contraction

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Mac</i>
<br />Can you remember the string you discussed this?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

It's easier to repeat it than to find it again among our 380 discussion topics.

SR – Canoe & Stream Analogy

Consider a canoe in a stream. Let the stream speed be s, and assume we paddle the canoe always at speed c ("c" for canoe). We will take a trip upstream a distance x (measured along the shore), then turn around and paddle back to our starting point. Consider two cases:

** If the stream speed s = 0, then the upstream trip time is t_u = x / c. The downstream time t_d is the same. So the total trip time is 2 x / c to travel a total distance of 2 x. Easy physics, right? We need only one change to make this general.

** If the stream speed s &gt; 0, then the upstream trip time is t_u = x / (c-s). The downstream time t_d = x / (c+s). So the total trip time is t_u + t_d = x / (c-s) + x / (c+s) = 2 x / [c (1 - s^2/c^2)]. To simplify writing this expression, I will introduce the shorthand dimensionless parameter gamma = 1 / sqrt (1 – s^2/c^2)). Then this last result becomes t_u + t_d = 2 gamma^2 x / c.

To make the example closer to SR, let's decide to use a meter stick shrunk by a factor gamma so that we will measure the total shore distance as 2 gamma x. And let's use a clock that ticks slower by a factor gamma so that we will measure a round-trip time as 2 gamma x / c. Then we will conclude that our average canoe speed was distance/time = c. So c will be invariant for us regardless of stream speed, given our choice of distance and time units.

Now as s approaches c, the trip becomes more and more difficult to complete. If s &gt; c, we can never complete the upstream leg of the trip because the current is faster than our paddling. So this math breaks down. But that does not inhibit us from changing mode of transportation and going upstream faster than speed c. We will still get to our destination, even though we discover that our canoe-based clocks and meter sticks are no longer useable.

The analogy is not perfect; but it does show the natural origin of the Lorentz transformations. Moreover, using the Lorentz transformations one-way (as in the canoe & stream example, or in LR) does not imply a speed limit for the universe, but only a limiting wave speed in that particular light-carrying medium. -|Tom|-

Tom,

Thanks for the effort. I will have to digest this a bit in that at first glance I still don't see the justifiction for the gamma function not being linear. We are not moving in a pythagorean path.


Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe can make you a genius.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Mac</i>
<br />I still don't see the justifiction for the gamma function not being linear.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Short descriptive answer: As you paddle against a slow current, the time you lose going upstream is roughly compensated by the time you gain coming downstream. But as the stream flows faster, you start to lose much more going upstream than you gain coming downstream.

In the end, when the stream speed equals your paddling speed, it takes an infinite time to go upstream. So if the round trip time is the tick of a "clock", the clock will slow in a very non-linear way as the stream speed increases. The mathematical function that describes the clock rate is the Lorentz gamma factor. -|Tom|-

Tom,

Thanks. I think I see where stream speed approaching paddle speed also approaches infinity.

Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe can make you a genius.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Mac</i>
<br />123....,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><b>Well, if light is being observed by humans, Einstein was correct:
objects moving away from an observer at any velocity will appear smaller,
and smaller, and smaller until the object disappears from sight! Since this
affects all objects moving away from us, one can then claim that space has
contracted (and hence time dilated) due to relative velocities.</b><hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I'm not sure but it appears you have linked depth perception to time dilation. The affect you seem to be referring to doesn't require velocity at all but mere spatial seperation and affects simultaneity but not dilation.


Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe can make you a genius.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

If distance between two objects are shorter, it also takes less
time to travel between two points in that space; i.e. space contraction implies time contraction.

My analogy was in reference to the paradoxical nature of SR observers; in this context, depth perception results in
an identical paradox. I.e., A observes B&lt; A and B observes
A&lt; B, resulting in the contradiction, A&lt;B&lt;A.

In both, symmetry exists, and in the latter case at least, it is easily demonstrated to be a real phenomena. And if we were to stop
here, we could rightly conclude that Nature is absurd since
it allows for contradictions.

Upon closer inspection however, in both cases, there is no paradox.
In both cases, the observers both observe identical effects for
events in the other frame and a different identical effect for
things in their own frame. That is, A observing B in A is not symmetrical with A observing B in B and vice versa.

To conclude, SR doesn't have a logical contradiction if time dilation/length contraction is an observed effect (due to the instruments used and the limited speed of light), but it becomes one if these visual effects were interpreted as real changes in space-time structure.

SR should have made a clear distinction, imo, between effects due to observation and effects due to real changes in physical structures.
Instead, it tries to have it both ways. If QM concludes Nature is absurd, SR's statement is that Nature is a complete moron.

123....,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><b>SR should have made a distinction, imo, between effects due to observation and effects due to real changes in physical structures.
Instead, it tries to have it both ways. If QM concludes Nature is absurd, SR's statement is that Nature is a complete moron.</b><hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Thanks for clarifying. I have made this same general arguement for some time. So I think we agree. Relativity is for the most part "Perception" vs "Physical Reality".

Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe can make you a genius.