Re: A relativity time dilation information paradox?
- From: xxein <xxein1@xxxxxxxxxxxxx>
- Date: Thu, 29 May 2008 17:37:22 -0700 (PDT)
On May 29, 8:03 am, "john.engelh...@xxxxxxxxx"
<john.engelh...@xxxxxxxxx> wrote:
I couldn't find any references regarding what I'm about to describe.
I'd appreciate it if someone could point out where I "took a wrong
turn", so to speak.
Taking the standard "astronaut traveling at relativistic speeds takes
a journey to Alpha Centari and back finds that while only 'some period
of time' has elapsed according to the spaceships clock, more time has
passed on an identical clock left on earth that was originally
synchronized at the start of the journey."
For simplicity and convenience, it is assumed that there is a solution
to the various acceleration parameters such that the ships clock
experiences 2 years of elapsed time and the earth bound clock
experiences 4 years of elapsed time. Again for simplicity, it is
assumed that a quarter of the acceleration time dilation effects
accumulates by the mid point transitions for acceleration /
deceleration going each way. Additionally, at the half way point (ie,
Alpha Centari, which we'll consider to be exactly one light year
away), the two clocks are assumed to be exactly stationary relative to
each other. All instruments are 'ideal' and all (hopefully!) 'non
essential' effects are sufficiently accounted for that only the effect
being discussed is measured, etc etc.
One of the obvious instruments on board is our ideally precise
clocks. I'm going to make the assumption that the particular time
keeping technology isn't relevant, and that all clocks in their
respective references (ie earth and ship) do not drift relative to
each other.
I'm obviously not an expert in relativity, but I believe that the
above scenario is plausible within the framework of relativity. I
don't think the particular values for acceleration to achieve the
above effects are important with regard to my question, and thus the
time dilation values are chosen largely for my convenience (nice 2:1
ratio).
Assume that there are two identical preciscion high frequency sources
(ie, a laser, etc) with one on earth and one on the ship. If I
understand things correctly then at the half way point at Alpha
Centari, when the ship and earth are stationary relative to each
other, these two frequency sources will be identical. Again, this is
ideally stationary relative to each other, so things like accounting
for doppler shift for the earths rotation don't factor in to things.
If these two sources were such that they were 180 degrees out of phase
with each other, they would exactly cancel each other. If one were to
count the cycles for each source, the counts would remain identical as
long as the two sources were exactly stationary relative to each
other, despite the great distance between the two.
Lets assume that on the ship, one of our 'clock measurements' is the
cycle count of this frequency source. If there was no time dilation
effect, one would assume that only doppler shift would effect the
count. From the ships perspective, the earth reference would shift
down relative to our own time source, and continue to shift down as we
continue to accelerate. During deceleration, the earths frequency
source would begin to shift up again. Once we've reach the
destination and the two sources are no longer moving relative to each
other, the frequencies of the two sources would again be identical.
The cycle counts of the two sources are obviously going to be
different, with the local source having the larger count. However, on
the return leg of the trip, the effects frequency shift effects are
reversed. If one does not include time dilation effects, the cycle
counts of the two sources should be identical once they are brought
back together.
My question is: What happens once one begins to account for
relativistic time dilation effects? This is where I've obviously done
something wrong because the conclusion I've come to simply can't be
correct.
Lets assume that the ship does experience time dilation and that at
the end of the round trip journey there is exactly a 2:1 ratio of
earth time relative to ship time with four years passing on earth
relative to the two years on the ship. To pass the time, our
astronaut watches TV. The astronaut experiences two years of time,
but obviously four years worth of TV is beamed to the ship. For
simplicity, if one assumes that the time dilation effect is averaged
over the duration of the journey, one can't help but conclude that
watching TV for the astronaut must be like someone has their finger
permanently on the fast forward button.
Temporarily dodging the details of 'when' this time / information
compression occurs (to, from, relative velocities, acceleration, etc),
it seems that one must be able to account for four years worth of TV
arriving at the ship over its two years of experienced time. I'm
using TV as a proxy for information as it makes things easier to
visualize: at some point the astronaut must experience the TV
information at twice the rate that he/she perceives time to be
passing.
If one assumes that the time dilation occurs due to acceleration, and
that half of the total time dilation effect has accumulated by the
half way point at Alpha Centari, then the astronaut would have to have
'watched' two years worth of TV in just one year once he or she
arrives at Alpha Centari, which is just one light year away. Even
though it took one year to travel one light year by the astronauts
clock, the speed of light was not violated because of time dilation
effect: two years passed on earth.
If one switches back to our precision frequency sources, time dilation
would seem to have some curious, if not impossible, repercussions.
Assuming that the amount of time dilation experienced by the ship and
astronaut is governed by the Lorentz transformation, a zero order
approximation would seem to be something like the following: Lets
assume that our frequency source is a green laser. If one were to
"look back" at the laser from the space ship, the doppler effect would
initially be the dominating effect. The green laser would shift
further and further towards red the more we accelerated away from
earth. At some point, time dilation from the Lorentz transformation
is going to begin to have a measurable effect.
This is where I've done something wrong, but I can't figure out what.
The question is: From the perspective of the ship and astronaut, in
which direction will the Lorentz transformation / time dilation cause
the frequency of the laser to shift on the outbound leg? The answer
I've come up with is "higher".
On one hand, despite the odd and completely non-intuitive result, this
fits in many ways. Assuming that Alpha Centari is exactly one light
year away and the ship is completely stationary relative to earth once
it arrives at Alpha Centari, and the current time of the earth clock
is constantly beamed towards Alpha Centari, there should be some
amount of clock slip between the ships clock and the time encoded in
the reference time beamed from earth. While I'll happily concede that
"how much" and "when and where" are complicated answers that are easy
to get wrong, at some point in the journey the ships clock and the
encoded time beamed from earth and received by the ship must 'slip'
relative to each other in such a way that it is possible for there to
be two full years of accumulated slip once the ship and astronaut are
back at earth.
If one were to have a display of the ships clock and the decoded time
received from earth, at some point in the journey the decoded earth
time must equal the ships clock, and then exceed it. During the
initial part of the journey, it's obvious that the two clocks will
drift apart, with the earth clock being the slower one. In other
words, the decoded time from earth on the ship has 'red shifted'. But
if time literally slows down for the ship at relativistic speeds, then
at some point the clock we are traveling away from must 'tick' faster
than our clock. If time literally slows down, then once one accounts
for doppler shift differences, there literally must be 'two ticks' of
the clock that we are moving away from received for every 'one tick'
of our clock. Or, in other words, a frequency shift up in the
received signal. And if it doesn't happen on the outbound leg, a like
effect must take place on the return leg. Not only that, but it needs
to 'make up time' if the effect didn't happen on the outbound leg.
However, if time literally slows down for us compared to time on the
earth on the outbound leg, the earth clock must tick faster than our
own clock. If that's the case, it would seem that it's only a matter
of finessing the numbers to come up with a set of parameters of
distance traveled and velocity in which even on the outbound leg,
there must come a point where the time received from earth, decoded,
and displayed next to our own clock stops loosing time due to doppler
shift, and begins to gain time because of the effects of time
dilation: two ticks received from earth for every perceived tick of
our clock.
In other words, if one had perfect doppler frequency shift
compensation so that the compensated result was exactly the same
frequency / green color as our reference laser, the time dilation
effects experienced by the ship would cause the frequency of the
received earth laser to blue shift. More time passes on earth than
for us, which means that in the end we need to account for two years
of extra oscillations in the earths reference laser relative to the
oscillations of our reference laser. If laser frequencies are
constant with respect to a time source that is in the same reference
frame as the laser, then by definition the frequency of the laser
received by the ship from earth must be greater than the ships
reference laser. Simplified, if the frequency of the laser from earth
as received by the ship were averaged over the duration of time
experienced by the ship, the earths laser would be 'blue'.
On the other hand, this would appear to violate some fundamental
physical laws, and in fact
read more »...
xxein: Garbage. Who taught you these things?
You might be saved, but your teacher is not.
.
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- A relativity time dilation information paradox?
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