[time-nuts] A different way to think about time dilation?
Bill Byrom
time at radio.sent.com
Mon Jul 11 00:30:23 EDT 2016
I think you are on the wrong track with assuming that every object has a
velocity c. What you need to consider is relativity. Velocity is a local
measurement (local reference frame distance and local reference frame
time). Light (and other electromagnetic radiation) always travels at a
local velocity c (local distance divided by local time). Time dilation
is a way of describing the effect of the relativity of simultaneity.
Events which are not local (adjacent) to each other can't be
unambiguously described as simultaneous. There is no universal clock
which allows us to determine which of two separated events occurred
"before" the other.
There are two causes of time dilation:
(1) Relative uniform motion. If two spacecraft are passing each other
in uniform motion (not accelerating), from the point of view of
each spacecraft the clocks on the other vessel will be slow
compared to the local clocks. Due to the relativity of
simultaneity, the seeming contradiction of a lack of symmetry (each
of the remote clocks appears slow compared to the local clock)
isn't a problem if you consider the two spacecraft starting with no
motion at the same location, then moving relative to each other,
then coming together again.
(2) Gravitational fields (or - by the principle of equivalence -
acceleration). As the Pound-Rebka experiment verified, clocks at
different gravitational potentials appear to run at different rates
from each other. This also causes the gravitational redshift. This
is a symmetric effect, and observers at both gravitational fields
will agree that the clocks at one are slower than the other.
For an explanation of why relative motion causes time dilation, see:
https://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity
If you want to understand why the relativity of simultaneity is so
important, research the "ladder paradox" or the "train and platform
light flash" thought experiment:
https://en.wikipedia.org/wiki/Ladder_paradox
https://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform_thought_experiment
Consider this last example as the velocity of the train approaches c.
Inside the train car, the observer at the center of the car will view
the experiment as very simple. If there are mirrors at each end of the
car, from the point of view of the observer at the center of the car the
light flash reaches the two end mirrors at exactly the same time, and
the reflected light pulses arrive back at the center simultaneously. But
from the point of view of the observer on the platform, the light
reaches the "back" mirror long before it reaches the "front" mirror, due
to the rapid motion of the train.
--
Bill Byrom N5BB
On Sun, Jul 10, 2016, at 11:01 AM, Chris Albertson wrote:
> Is this a valid TN subject? It's about time but a little off of the
> usual
> subject of 10Mhz oscillators.
>
> I heard of an alternate way to describe time dilation caused by
> velocity.
> I think this makes it easier to understand but I've not been able to
> verify the math. This alternate explanation also makes it easy to see
> why
> we can never go faster than light. But I've not seen a mathematical
> derivation so it could be wrong or just an approximation.
>
> Here goes:
>
> 1) We assume a 4 dimensional universe with four orthogonal axis, x,
> y, z,
> and time (t)
> 2) assume that at all times EVERY object always has a velocity vector
> who's
> magnitude is "c", the speed of light. The magnitude of this vector
> (speed)
> never changes and is the same for every particle in the universe.
>
> This at first seems a radical statement but how is moving at c much
> different from assuming every partial is at rest in t's own reference
> frame? I've just said it is moving at c in it's own reference frame.
> Both
> c and zero are arbitrary speeds selected for connivance.
>
> How can this be? I know I'm sitting in front of my computer and
> have not
> moved an inch in the last four hours. c is faster than that. Yes
> you
> are
> stationary in (x,y,z) but along the t axis you are moving one
> second per
> second and I define one second per second as c. Now you get smart and
> try
> to move faster than c by pushing your chair backward in the Y
> direction
> at
> 4 inches per second. So you THINK your velocity magnitude is
> the vector
> sum of c and 4 inch/sec which is greater than c. BUT NO. Your speed
> along Y axis causes time dilation such that your speed along T is now
> slower than 1 second/second. In fact if you push your chair backward
> along Y real fast at exactly c your speed along t axis is zero, time
> stops. Try pushing your chair at 0.7071 * c and you find
> yourself moving
> through t at 0.7071 sec/sec and the vector sum is c. You can
> NOT change
> you speed from c all you can do to change the direction of the
> velocity
> vector and your speed through time is determined by the angle between
> that
> vector and the t axis.
>
> It works ok to just use one of the three spacial axis because we can
> always
> define them such that (say) the Y axis points in the direction
> of motion.
> So a plot of your speed in the dy,t plane covers the general case and
> looks
> like an arc of radius c.
>
> If this works out then I have some work to do, like defining
> momentum as
> a
> function of the area between the velocity vector and the t axis
>
>
> --
>
> Chris Albertson
> Redondo Beach, California
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