I am reading Kip Thorne's book on Time Warps.

I have long heard the tale about an astronaut who goes for a journey
in a ship travelling close to the speed of light, and when the trip is
over, the Earth has aged millions of years into the future, while our
traveller is not much older.

But an example in Thorne's book says that time dilation is seen the
same by both parties, thus viewers on Earth see clocks on my ship as
ticking more slowly, and I also see Earth's clocks as ticking slowly.

At what point, then, do Earth's clocks speed up so quickly as to have
the planet age millions of years relative to my few?

I had always thought that Earth would see my clock tick slowly, and I
would see Earth's clocks tick very very fast in order to explain the
aging process.

But reading about this relative time dilation throws off this idea,
and I am stuck in my visualization of this phenomenon.

Jaxon

Subject: Relative Time Dilation != Future Time Travel
From: (Jaxon Bridge)
Date: 10/5/03 11:59 PM US Mountain Standard Time
Message-id:

I am reading Kip Thorne's book on Time Warps.

I have long heard the tale about an astronaut who goes for a journey
in a ship travelling close to the speed of light, and when the trip is
over, the Earth has aged millions of years into the future, while our
traveller is not much older.

But an example in Thorne's book says that time dilation is seen the
same by both parties, thus viewers on Earth see clocks on my ship as
ticking more slowly, and I also see Earth's clocks as ticking slowly.

At what point, then, do Earth's clocks speed up so quickly as to have
the planet age millions of years relative to my few?


They are reckoned by the accelerated observer to do this durring acceleration
due to the g_0_0 term in the metric according to the accelerated frame becoming
significantly larger than 1 at large distances in the direction of
acceleration. seepart c of problem 5.4.4 at
http://www.geocities.com/zcphysicsms/chap5.htm#BM65

"Jaxon Bridge" skrev i melding om...
I am reading Kip Thorne's book on Time Warps.

I have long heard the tale about an astronaut who goes for a journey
in a ship travelling close to the speed of light, and when the trip is
over, the Earth has aged millions of years into the future, while our
traveller is not much older.

But an example in Thorne's book says that time dilation is seen the
same by both parties, thus viewers on Earth see clocks on my ship as
ticking more slowly, and I also see Earth's clocks as ticking slowly.

At what point, then, do Earth's clocks speed up so quickly as to have
the planet age millions of years relative to my few?

I had always thought that Earth would see my clock tick slowly, and I
would see Earth's clocks tick very very fast in order to explain the
aging process.

But reading about this relative time dilation throws off this idea,
and I am stuck in my visualization of this phenomenon.

Some time ago I posted a scenario which may answer some
of your questions.
Here it is again:

OK. I will make a scenario where we see it from the travelling
twin's point of view.

But first:
Acceleration isn't the cause of time dilation, as exemplified in
another posting. That is, acceleration doesn't affect the rate of
a clock. If you have two clocks instantly at rest to each other,
and one clock is accelerating and the other not, they will run
at the same rate.
But:
Acceleration of the observer will affect the rate he will
measure distant clocks to have. You may well call
this gravitational frequency shift, but it isn't really necessary
to invoke the equivalence principle to arrive at this result,
it follows from SR (and a little calculus):
Like this:
An instantly stationary clock, accelerating at a, is at a distance d.
At the time dt, the speed of the distant clock will be a*dt.
Using the LT : t' = gamma*(t - v*x/c^2), we get:
dt' = 1*(dt - a*dt*d/c^2)
dt'/dt = (1 + a*d/c^2)
So:
An observer accelerating at a will measure the rate of
an instantly stationary clock at a distance d in the direction
of the acceleration to be: (1 + a*d/c^2)
(A clock higher up in the gravitational field runs fast.)

Now to the promised scenario.

Let us first describe it from the point of view of the "home twin" A.
============================================

A B- v
|-----------------------------------------|

B goes away at a speed v = 0.5c
When B has travelled a distance 100 LY,
he starts his rocket engine.
At that time A's clock shows 200 years,
and B's clock show 200*sqrt(1 - v^2/c^2) = 173.2 years.

B accelerates at 1 (light year per year) per year for one year (c/year),
thus changing his speed by c and going at 0.5c in the other direction.
(This acceleration is in the order of 1g.)
A's clock is now showing 201 years.
B is again 100 LY away, heading home.
B's clock is showing 174.2 years.

When B is back, A's clock shows 401 years,
B's clock shows 2*173.2+1 = 347.4 years.

From "travelling twin" B's point of view:
==========================
A goes away at a speed v = 0.5c.
When B's clock shows 173.2 years, he starts his rocket.
At that time B will observe A's clock to show
173.2*sqrt(1 - v^2/c^2) = 150 years.

B accelerates for one year at c/year.
While he is doing so, he will observe A's clock to run at the rate:
(1 + a*d/c^2) = (1 + (c/year)*(100 light year)/c^2) = 101.
Thus will B observe that A's clock advances 101 years during
the year he is accelerating.
So when the acceleration is done, B's clock shows 174.2 years,
and he will observe A's clock to show 150+101 = 251 years.

A is approaching at 0.5 c.
When they meet, B's clock will show 347.4 years.
A's clock will show 251+150 = 401 years.

None of the twins are surprised when they see the other
twin's clock.

Important notice:
Note that it is B's acceleration that causes B to _observe_
(measure) A's clock to run fast.
But nothing ever happened to clock A, it ticked
along at its normal rate the whole time. The acceleration
of B can obviously not affect A in any way.
It can however affect B's measurements of A.

Paul

"Jaxon Bridge" wrote in message
om...
I am reading Kip Thorne's book on Time Warps.

I have long heard the tale about an astronaut who goes for a journey
in a ship travelling close to the speed of light, and when the trip is
over, the Earth has aged millions of years into the future, while our
traveller is not much older.

But an example in Thorne's book says that time dilation is seen the
same by both parties, thus viewers on Earth see clocks on my ship as
ticking more slowly, and I also see Earth's clocks as ticking slowly.

At what point, then, do Earth's clocks speed up so quickly as to have
the planet age millions of years relative to my few?

I had always thought that Earth would see my clock tick slowly, and I
would see Earth's clocks tick very very fast in order to explain the
aging process.

But reading about this relative time dilation throws off this idea,
and I am stuck in my visualization of this phenomenon.

Jaxon

Hi Jaxon

The question you put has indeed puzzled many who are unschooled in Special
Relativity theory.
Much of the confusion arises from non-careful use of terms -- even simple
every-day terms like "see." If by "see" you mean, literally, observing the
moving clock with your eyes (say with the aid of a powerful telescope), then
you should understand that the moving clock will present you with a clock
image that appears to move either slower or faster than your own
(non-moving) clock. Which it turns out to be depends on whether the moving
clock is moving away (making it appear slower) or toward you (making it
appear faster). This is the phenomenon called "Doppler shift" and occurs
both in SR and in Newtonian theory.

So its best not to use the word "see" in the context of your question. A
better way (though surely not the only way) to phrase it is to say "...thus
viewers on Earth rightfully claim that clocks on my ship tick more
slowly..." This "rightful claim" can be made by the "Earth-viewers" because
they have invoked a method of computation (using SR theory) that has widely
demonstrated its successful predictive ability.

Now as to the crux of your question: How, in the face of the stated
symmetry between observers, the fact that each observer can rightfully claim
that the other observer's clock ticks slower than his own, can we
nevertheless end up with such a non-symmetric result? The answer comes from
a consideration of the symmetry issue. Is there really full symmetry? The
answer is "No."

If the two observers both do nothing but coast (say in departure from each
other), then full symmetry exists; and though each can rightfully claim
(from the theory) that the other clock runs slower, there is no chance to
again directly compare the clocks side by side. To make such a comparison
of the clocks at least one observer has to do something to change the
scenario from "coasting away" to "coasting toward."

If one observer takes that initiative, then the symmetry is broken and there
is no longer any logical reason to expect the clocks to show the same number
of ticks between departure and return. What the difference in ticks is,
depends on the theory.

Interestingly, if both observers behave symmetrically (that is, turn around
in the same way after the same elapsed departure time on their respective
clocks), then their clocks will show the same number of ticks when they
again meet.

I realize that for the neophite in SR theory much of this is unsatisfying
because it still doesn't answer why the observers' behavior asymmetry
results in the elapsed time difference. The only correct and full answer
comes from understanding how the two postulates (form invariance and light
speed invariance) have this logical outcome. SR's successfull predictive
ability suggests that the postulates have a strong hand in defining the
structure of our spacetime.

A good tool in helping to "visualize" this phenomenon is to become familiar
with Minkowski diagrams, both 2-d (t, x) and 3-d (t, x, y).

Eli Botkin

"Paul B. Andersen" wrote in message
...

"Jaxon Bridge" skrev i melding
om...


Important notice:
Note that it is B's acceleration that causes B to _observe_
(measure) A's clock to run fast.
But nothing ever happened to clock A, it ticked
along at its normal rate the whole time. The acceleration
of B can obviously not affect A in any way.
It can however affect B's measurements of A.

This is the same as saying that B's clock rate is changed compared to A's
clock rate which remain unchanged. Acceleration will change the rate of B's
clock rate. Your assertion is designed to avoid the implication that
acceleration will affect the state of absolute motion of clock B and thus
the rate of clock B.

Ken Seto

"Jaxon Bridge" wrote in message
om...
I am reading Kip Thorne's book on Time Warps.

I have long heard the tale about an astronaut who goes for a journey
in a ship travelling close to the speed of light, and when the trip is
over, the Earth has aged millions of years into the future, while our
traveller is not much older.

But an example in Thorne's book says that time dilation is seen the
same by both parties, thus viewers on Earth see clocks on my ship as
ticking more slowly, and I also see Earth's clocks as ticking slowly.

At what point, then, do Earth's clocks speed up so quickly as to have
the planet age millions of years relative to my few?

I had always thought that Earth would see my clock tick slowly, and I
would see Earth's clocks tick very very fast in order to explain the
aging process.

But reading about this relative time dilation throws off this idea,
and I am stuck in my visualization of this phenomenon.

Jaxon

There are a lot of ways to answer this question. The FAQ is pretty good for
this (see under twin paradox), however it needs considerable thought to
understand - it took me two or three months but even I got it eventually.
g

The first problem some people have in understanding is they mix up what is
seen with what is measured. I'll use "measuring" technically to distinguish
it from seeing, some people use "observe" instead. Physics is about
describing what has happened and predicting what would/will happen under
certain circumstances. To do that it needs a framework. Movement is a
change in space at some point in time, and so the framework is that of space
and time. And if we want to describe an object moving through space we plot
where it is and when on our framework of space and time. We don't actually
need to see it. If a spaceship goes off to another planet we won't see it
arriving when it does. Eventually lightsignals would arrive back if we had
a powerful enough telescope, or a radio report would be received. But if we
know how fast the ship is moving we can predict it, and if we eventually
receive the reports we can use our knowledge of the speed of light to
calculate how long the signal took and therefore when the ship arrived.
Similarly we could use secondary evidence. We might turn up at the planet
some years later to find a crashed ship and use forensics to find out when
it arrived. It doesn't matter. If we have enough information and could
measure everything accurately, our measurements and our predictions of the
ship's arrival must all fit together if physics is to be consistent with
reality. The underlying understanding of what is happening/has
happened/will happen, plotted on our background of space and time is what I
mean by what we measure. By seeing, I mean the receipt of electromagnetic
signals, light or radio or some such.

Most physicists think that measurement is more important than seeing, but
your question was about seeing so that's what I'll try to answer.

Our ability to measure things against time is of course circumscribed by how
good our clocks are, but let's dismiss that and assume we have clocks as
good as they possibly could be. We want to discuss the physics of
spacetime, and limits to measurement are a red herring (at this point). Now
let's assume the spaceship and earth both have perfect clocks which are
capable of broadcasting a radio pulse every second. And each can pick up
the other's signal. If the ship moves away from Earth (or vice-versa) at
four fifths of the speed of light, two phenomena change the rate at which
the clocks pulses are received. The first is Doppler shift. This is the
same effect that changes the frequency of car engines and sirens as they go
past you. As the ship and the earth move away from each other the
increasing distance means that each successive radio pulse has further to
travel than its predecessor. So it takes longer to reach its destination
and the frequency the pulses are received is slowed down. The second
phenomenon is called time dilation, and that is what Thorne was talking
about. In order to keep everything consistent we have to change our
understanding of time, our measurements need to be altered as though time
were slowed down when measured on a quickly moving object. What we see is a
slowing down for both reasons, Doppler shift and time dilation. The pulses
are received less frequently than one per second. At 0.8c they come one
every three seconds. This is equally true both on the ship and on the
earth.

Let's assume there is a marker buoy in space at one light year out. When it
reaches the buoy the ship turns around. It now sees the earth coming toward
it at four fifths of the speed of light. The radio pulses received from the
earth are speeded up because the Doppler effect now works in reverse, but
the time dilation effect is due to speed not direction, so the pulses are
still slowed down for that reason. The Doppler effect predominates and
radio pulses are received on the ship more frequently than once a second -
three times a second at 0.8c. Not so on Earth! The ship may have turned
around but the pulses being received are still those sent a year before.
Nothing the ship does affects the pulses it has already broadcast which are
winging their way to earth at the speed of light. Earth still receives
pulses at the slowed down rate of one every three seconds and will continue
to do so for another year.

Meanwhile the ship speeds toward the earth all the time getting far more
pulses per second than the earth does.

After a year earth time, the earth too gets the pulses at the faster rate.
The earth sees the ship turn around and the received pulse rates become the
same. Nevertheless the earth can't catch up. When the ship arrives at the
earth it will have received far more pulses from the earth than the earth
did from it. The ship will have seen the earth age second by second, more
than the earth will have seen the ship age. But the phenomenon of time
dilation, the measured slowing down of the clocks, will have been constant
and equal throughout.

While that sort of answers your question (I hope), about where the
discrepancy would be seen, it doesn't explain what is going on. The
bookkeeping of the time-dilation makes the numbers add up all right on the
earth side, an additional bookeeping adjustment made by the ship when it
turns around makes the numbers add up for the ship, but it doesn't answer
why the ship/spaceman ages differently to the earth.

The answer to that lies in the nature of space and time. It isn't what we
classically thought it was. Because pretty much the whole of physics boils
down to measurement of change in space against a background of time, what we
plot out on our coordinates if you like, a change in our understanding of
what space and time are ripples through the whole of physics. Time dilation
is just one of the devices we use to ensure that our measurements conform to
our new understanding of space and time(okay so the "new" understanding is
ninety eight years old). You have revise ideas on simultaneity too. The
question "when?" often has the answer "from whose viewpoint?", because
different people measure time differently when they move at different
speeds. Space also changes. Lengths contract while distances expand.
Space and time become interdependent and one end of a moving rod has a
different timerate to the other. Our single absolute measuring scheme
plotting things against our framework of space and time shatters.

It turns out that different observers moving at different speeds to each
other have different measuring frameworks of space and time, and they
disagree where and when anything needs to be plotted to give a consistent
physics, modelling the universe. But all of them do have a self-consistent
framework and as long as they use their own framework the laws of physics
describe everything just fine. It's only if they try to mix their
measurements with someone else's without making corrections that it all goes
wrong. It is a confusing oddity that two observers both need to correct for
the other's clocks running slower.

Which framework is ultimately right? Relativity simply says that all
frameworks are equally good and the same laws of physics work in all of
them.

You see why it takes effort to get to grips with? And I still haven't
answered *why* the spaceman ages less than the earth. But that's enough for
one post. If you want to dig further, the complications of the FAQ await
you. One place you can find it is
http://math.ucr.edu/home/baez/physics/faq.html.

See you in two months

Cheers,

Jon

Jaxon Bridge wrote:

I am reading Kip Thorne's book on Time Warps.

I have long heard the tale about an astronaut
who goes for a journey in a ship travelling
close to the speed of light, and when the trip
is over, the Earth has aged millions of years
into the future, while our traveller is not
much older.

But an example in Thorne's book says that time
dilation is seen the same by both parties, thus
viewers on Earth see clocks on my ship as
ticking more slowly, and I also see Earth's
clocks as ticking slowly.

At what point, then, do Earth's clocks speed up
so quickly as to have the planet age millions
of years relative to my few?

I had always thought that Earth would see my
clock tick slowly, and I would see Earth's
clocks tick very very fast in order to explain
the aging process.

But reading about this relative time dilation
throws off this idea, and I am stuck in my
visualization of this phenomenon.


Mutual time dilation is *Bull***** and Kip Thorne
is a time trevalling crackpot.

Time does not exist, so how can you "travel" in it ?

Time is a mathematical artefact derived from
motion, and a sensory illusion caused by our memory.

Relativity theory is an *ABSOLUTE* theory, the
absolute reference being the mass distribution of
the universe. The clock that does not move wrt to
this background runs fastest.

Here I give you my "Full Absolute Monty" :
hope you enjoy it.

And one personal note : imo the absolute
background is a 100% determined by "the
distribution of meterial objects".

Hayek.



***** The Full Absolute Monty **********

http://www.mathpages.com/home/albro/albro2.htm
"
I must say, this entire discussion has a strong
ironic element, because in the age-old debate
between absolute and relational theories of space,
time, and motion, the theory of relativity
represents the absolute side. It's well known
(outside of internet discussions) that the theory
of relativity is most definitely NOT a relational
theory of motion, i.e., it does not attribute all
physical effects to the relations between material
bodies.
The effects are ultimately determined by the
absolute background metric, which is affected by,
but is not determined by, the distribution of
material objects (except arguably in some specific
cosmological models that are not currently in
favor among cosmologists). Thus, relativity, no
less than Newtonian mechanics, relies on
space(time) as an absolute entity in itself,
exerting influence on material bodies. (This is
typically introduced to relativistic treatments by
a set of boundary conditions necessary to
determine a solution of the field equations.)

There actually have been attempts to create true
*relational* theories of motion, notably the
interesting work of Barbour and Bertotti in the
1970's. It's just an unfortunate historical
accident that the name "relativity" was given to
Einstein's theory. The word actually refers to
the covariance of spatial and temporal intervals,
not to any Leibnizian notion that only the
relations between material objects are
physically significant. Admittedly Einstein was
sympathetic to this philosophy, especially early
in his career, and entertained hopes of banishing
absolute space from physics, but like Newton
before him he was forced to abandon this hope in
order to produce a theory
that satisfactorily represents our observations.
It is therefore doubly ironic to see Einstein
daily excoriated in this newsgroup for foisting a
relational theory of motion on the world."

http://www.mathpages.com/rr/s4-07/4-07.htm
4.7 The Inertia of Twins
"
The puzzling asymmetry of the spinning globes is
essentially just another form of the twins
paradox, where the twins separate and reconverge
(one accelerates away and back while the other
remains stationary), and they end up with
asymmetric lapses of proper time. How can the
asymmetry be explained? According to Einstein:

"The only satisfactory answer must be that the
physical system consisting of S1 and S2 reveals
within itself no imaginable cause to which the
differing behavior of S1 and S2 can be referred.
The cause must therefore lie outside the system.
We have to take it that the general laws of
motion...must be such that the mechanical behavior
of S1 and S2 is partly conditioned, in quite
essential respects, by distant masses which we
have not included in the system under consideration."
"

http://www.mathpages.com/rr/s7-01/7-01.htm
7.1 Is the Universe Closed?
"
Nevertheless, the idea of a closed finite universe
is still of interest, partly because of the
historical role it played in Einstein's thought,
but also because it remains (arguably) the model
most compatible with the spirit of general
relativity. In an address to the Berlin Academy of
Sciences in 1921, Einstein said :
"I must not fail to mention that a theoretical
argument can be adduced in favor of the hypothesis
of a finite universe. The general theory of
relativity teaches that the inertia of a given
body is greater as there are more ponderable
masses in proximity to it; thus it seems very
natural to reduce the total effect of inertia of a
body to action and reaction between it and the
other bodies in the universe... From the general
theory of relativity it can be deduced that this
total reduction of inertia to reciprocal action
between masses - as required by E. Mach, for
example - is possible only if the universe is
spatially finite. On many physicists and
astronomers this argument makes no impression... "
"



http://www.mathpages.com/home/albro/albro16.htm
"
To put this in more familiar terms, Einstein would
say to all the people who claim that special
relativity is adequate to "handle" the twins
paradox: We can say that the twin who followed
the unaccelerated worldline will have aged the
most, but if we are asked which twin had the
unaccelerated worldline we can only answer: the
one who aged the most! Accelerometers can't
rescue us from this circle, because the
Equivalence Principle implies that the lapse of
proper time along a given worldline cannot be
inferred from the locally "felt" accelerations.
For example, both twins could spend the entire
interval from A to B experiencing 1g of local
acceleration, and yet the lapses of proper time
could be vastly different.

Thus, as soon as the Equivalence Principle is
adopted, it's clear that special relativity is
epistemologically unsatisfactory, and can only be
salvaged by a suitable theory of gravitation
(e.g., general relativity), within which SR may
serve as a useful approximate simplification in
appropriate limiting cases. However, we can only
assess the appropiateness of SR in a given
circumstance by evaluating it in the context of
GR. In other words, SR can serve as a set of
convenient computational recipes for technicians
who don't want or need to understand what they are
doing, but from an epistemological standpoint
there is only one modern theory of relativity, and
that is GENERAL relativity. Special relativity had
already been discarded as a viable theory of
knowledge by 1911. I think it's also worth
mentioning that when ordinary non-physicists ask
about relativity, they aren't hoping to become
technicians or computational experts, they are
asking from a broad philosophical and
epistemological standpoint, i.e.,
they are curious to know, in broad terms, the
basis of relativity as a theory of knowledge.

From this perspective, the custom of telling such
people that special relativity is "the answer" to
the twin's paradox is particularly unfortunate.
(I say this in spite of the undeniable fact that
most people who worry about the twins paradox have
actually failed to understand special relativity,
and aren't even close to the level of
comprehension on which the actual inadequacy of
special relativity appears. On the other hand,
most of the people who DON'T worry about the twins
paradox are equally far from understanding the
real issues involved.)
"

But first:
Acceleration isn't the cause of time dilation, as exemplified in
another posting. That is, acceleration doesn't affect the rate of
a clock. If you have two clocks instantly at rest to each other,
and one clock is accelerating and the other not, they will run
at the same rate.

How can two objects be at rest with each other, yet one is
accelerating and the other is not?

curious,
jaxon

Jaxon Bridge wrote:

But first:
Acceleration isn't the cause of time dilation, as exemplified in
another posting. That is, acceleration doesn't affect the rate of
a clock. If you have two clocks instantly at rest to each other,
and one clock is accelerating and the other not, they will run
at the same rate.


How can two objects be at rest with each other, yet one is
accelerating and the other is not?

For a single instant, when their speeds are
exactly the same, they are "at rest" wrt to
eachother, same speed in same direction, implies
being "at rest" wrt eo.


Hayek.

Hayek wrote in message ll.nl...
Jaxon Bridge wrote:

But first:
Acceleration isn't the cause of time dilation, as exemplified in
another posting. That is, acceleration doesn't affect the rate of
a clock. If you have two clocks instantly at rest to each other,
and one clock is accelerating and the other not, they will run
at the same rate.


How can two objects be at rest with each other, yet one is
accelerating and the other is not?

For a single instant, when their speeds are
exactly the same, they are "at rest" wrt to
eachother, same speed in same direction, implies
being "at rest" wrt eo.

You have got to be kidding. Theyr'e never at rest.
Sounds like yur a nut.
At this instant there would be no time passing. You are speaking
of instantaneous velocity at a single point!
If you eliminate time by shrinking the space interval to zero
everything would be at rest. Of course you could recognize no motion!

What about the continuity of all the other points where the speed is
changing?

This also would apply to uniform motion where any body passes the
other
shouldn't it? You would have to say these were at rest relative to
each other
wouldn't you? You have no understanding of gamma in relativity.
It changes by acceleration.
The change in time rate by acceleration is absolute and this is the
reason there is no Twin Paradox.

Mitch Raemsch