Hi John,
Thank you very much for this explanation, I found it very "explicative".
What I am not able to grasp is the sense of the phrase " That second
part was what really baked peoples' noodles". I think that is some
colloquial but not being English my native language I can't figure out
its meaning.
Thank you,
Ignacio
El 27/11/2015 a las 21:54, John Miles wrote:
So, here's how I finally grokked this stuff. c, the speed of light in a vacuum, is often
spoken of as a "speed limit" that nothing can ever exceed. That's a bad way to
put it, and people who have expressed it that way in popular science writing for 100
years should feel bad.
Instead, the way to visualize relativity is to realize that c is the *only*
speed at which anything can travel. You are always moving at 300,000,000
meters per second, whether you want to or not. But you're doing it through all
four dimensions including time. If you choose to remain stationary in (x,y,z),
then all of your velocity is in the t direction. If you move through space at
100,000,000 meters per second in space, then your velocity in the t direction
is 283,000,000 meters per second (because sqrt(100E6^2 + 283E6^2) = 300E6.)
It doesn't make sense to speak of moving a certain number of "meters" through time, so
your location in time itself is what has to change. You won't perceive any drift in your personal
timebase when you move in space, any more than you will perceive a change in your location relative
to yourself. ("No matter where you go, there you are.") But an independent observer
will see a person who's moving at 100,000,000 meters per second in x,y,z and 283,000,000 meters per
second in t. They see you moving in space, in the form of a location change, and they also see
you moving in time, in the form of a disagreement between their perception of elapsed time and your
own.
Likewise, if you spend all of your velocity allowance in (x,y,z), your t
component is necessarily zero. Among other inconvenient effects that occur at
dt/dt=0, you won't get any closer to your destination, even though your own
watch is still ticking normally. Particles moving near c experience this
effect from their point of view, even while we watch them smash into their
targets at unimaginable speeds.
This is special relativity in action. The insight behind general relativity is
twofold: 1) movement caused by the acceleration of gravity is
indistinguishable from movement caused by anything else; and 2) you don't even
have to move, just feel the acceleration. That second part was what really
baked peoples' noodles. It is what's responsible for the disagreement between
the two 5071As.
-- john, KE5FX
Miles Design LLC
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