Is 'time' time or is it not.
RHNL
If it is a 'constant' why is it applied differently
in QM and GR?
If it is a 'variable', why do we call it 'time'?
Igor Khavkine
You've put so many scare quotes around words in your post, I don't even
know what you mean by them. I do know what physicists mean by time, and
I can tell you what that is.
We live in a 4-dimensional space-time. This is a space (in the
mathematical sense of the word) where points are called events. We can
identify different events by what "happens" there. For example, a light
turns on, an abscent minded physicist bumps into a wall, an African
swallow drops a coconut, a radioactive atom decays, and a star going
supernova are all examples of events, each of wich helps us identify the
point in space-time where it occurs.
Time is a function on space-time. Given an event, an observer present at
it can look at her clock and read off a number. That's precisely the
definition of a function, an association of a number to a point of
space-time. Up to this point, the same description applies to any
physical theory.
In non-relativistic theories, once two clocks are synchronized, their
readings do not depend on the motion of the observers who carry them. If
these observers meet up again, their clock readings will agree.
In theories based on special relativity, the clock readings do depend on
the motion of the observers. So if two clocks are brought together after
an earlier synchronization, they will not necessarily give the same
readings. However, if we know details of the motion of the two observers
in between, special relativity gives us a recipe for translating between
the readings of different clocks.
In general relativity, the only alteration is now that the clock
readings depend not only on the motion of the observer that carries it,
but also on the gravitational fields that the observer encounters. GR
also suppies an improved recipe for translating between the clocks of
different observers.
For both non-relativistic and special relativistic theores, there exist
both classical and quantum formulations. In this sense, QM does not
treat time any different than we would expect. As to general relativity,
the main problems lie in the technical difficulties of constructing
quantum theories that take GR into account. Once these difficulties are
taken care of, at some point in the future, a quantum theory that takes
general relarivity into account (provided that gravitational fields
remain fixed and classical), would treat time in the same way as GR.
Hope this helps.
Igor
stefa...@yahoo.com
> We live in a 4-dimensional space-time.
It is quite strong statement ;o)
> In theories based on special relativity, the clock readings do depend on
> the motion of the observers. So if two clocks are brought together after
> an earlier synchronization, they will not necessarily give the same
> readings. However, if we know details of the motion of the two observers
> in between, special relativity gives us a recipe for translating between
> the readings of different clocks.
SR is applied only for inertial systems, so there is no way to consider
"brought together after an earlier synchronization" clocks. In GR
it is possible.
> For both non-relativistic and special relativistic theores, there exist
> both classical and quantum formulations. In this sense, QM does not
> treat time any different than we would expect.
Causality is the essence of time perception, in this sense, time in QM
and in GR looks different. Bell experiment is one of the profound
examples of that.
Regards,
Stefan
René Meyer
Neither. In QM, time is a parameter that describes the evolution of a
systems state. But it is not a "constant", it just takes values in the
Reals.
As GR is covariant, time looses its outstanding position at all. Its
just a coordinate choice.
One of the big problems in quantizing gravity is bringing together
these two different roles time plays.
René
J. Horta
"Constant" and "variable" tend to describe how one
is using a quantity in a calculation. Time can be viewed
as a parameter which is used the same way in GR as
in QM. In GR one parameterizes physics on charts or
coordinate regions using 4 somewhat arbitrarily chosen
real parameters, one of which locally acts like time
(which one depending on the metric). In QM, which
is usually applied in very small regions of space,
states and operators are parameterized in time. In
QFT this is even more evident in the Heisenberg picture
in which field operators are supplied as operator valued
distributions on a manifold (like in GR).
I.Vecchi
..
>
> We live in a 4-dimensional space-time. This is a space (in the
> mathematical sense of the word) where points are called events. We can
> identify different events by what "happens" there. For example, a light
> turns on, an abscent minded physicist bumps into a wall, an African
> swallow drops a coconut, a radioactive atom decays, and a star going
> supernova are all examples of events, each of wich helps us identify the
> point in space-time where it occurs.
>
> Time is a function on space-time. Given an event, an observer present at
> it can look at her clock and read off a number. That's precisely the
> definition of a function, an association of a number to a point of
> space-time. Up to this point, the same description applies to any
> physical theory.
>
> In non-relativistic theories, once two clocks are synchronized, their
> readings do not depend on the motion of the observers who carry them. If
> these observers meet up again, their clock readings will agree.
>
> In theories based on special relativity, the clock readings do depend on
> the motion of the observers. So if two clocks are brought together after
> an earlier synchronization, they will not necessarily give the same
> readings. However, if we know details of the motion of the two observers
> in between, special relativity gives us a recipe for translating between
> the readings of different clocks.
>
> In general relativity, the only alteration is now that the clock
> readings depend not only on the motion of the observer that carries it,
> but also on the gravitational fields that the observer encounters. GR
> also suppies an improved recipe for translating between the clocks of
> different observers.
>
> For both non-relativistic and special relativistic theores, there exist
> both classical and quantum formulations. In this sense, QM does not
> treat time any different than we would expect. As to general relativity,
> the main problems lie in the technical difficulties of constructing
> quantum theories that take GR into account. Once these difficulties are
> taken care of, at some point in the future, a quantum theory that takes
> general relarivity into account (provided that gravitational fields
> remain fixed and classical), would treat time in the same way as GR.
>
> Hope this helps.
>
It sure does, but I would surmise that not any function provides
credible time. Shouldn't clock readings be monotonously increasing?
What about the result by Unruh & Wald showing that any physical clock
has a non-null probability of running backwards ([1], cf. [2])?
Can you briefly elaborate on why a quantum gravity theory where
"gravitational fields remain fixed and classical" is a realistic
perspective?
IV
[1] Unruh & Wald "Time and the interpretation of quantum gravity" Phys.
Rev. D40, 2598--2614 (1989)
[2] http://math.ucr.edu/home/baez/week167.html
Ralph E. Frost
..
> We live in a 4-dimensional space-time.
Are you referring to
distance in the x direction
distance in the y direction
distance in the z direction
time
as the four dimensions?
Ralph
Igor Khavkine
>
> Igor Khavkine wrote:
>> On 2005-08-28, RHNL <rh...@exoptica.com> wrote:
>
>> We live in a 4-dimensional space-time.
>
> It is quite strong statement ;o)
It's an assumption, but it's served us exceptionally well for the past
300 years.
>> In theories based on special relativity, the clock readings do depend on
>> the motion of the observers. So if two clocks are brought together after
>> an earlier synchronization, they will not necessarily give the same
>> readings. However, if we know details of the motion of the two observers
>> in between, special relativity gives us a recipe for translating between
>> the readings of different clocks.
>
> SR is applied only for inertial systems, so there is no way to consider
> "brought together after an earlier synchronization" clocks. In GR
> it is possible.
That's a common misconception. SR applies whenever gravity (read
space-time curvature) can be neglected. See for example the explanation
of the Twin Paradox in the Physics FAQ:
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
>> For both non-relativistic and special relativistic theores, there exist
>> both classical and quantum formulations. In this sense, QM does not
>> treat time any different than we would expect.
>
> Causality is the essence of time perception, in this sense, time in QM
> and in GR looks different. Bell experiment is one of the profound
> examples of that.
Causality is built into both GR and quantum mechanics. I presume you
refer to EPR-type entanglement experiments. They do not violate
causality, so I don't see what you mean.
Igor
Marcel LeBel
The word "Time" has many meanings.If it is used without specifying
the meaning, it will effectively have all the meanings and none in
particular. In order to go around the problem of using such a rich word,
one has to add a specifying word to it, or explain it.
At the beginning of important theories/ body of work in fundamental
physics, since nobody knows exactly what Time is, this is one of the
things one has to a) declare/recognize his ignorance about and b)
explain what meaning he chooses to give or accept for the said word. For
that reason, "Time" was and should still be part of the fundamental
assumptions of any theory of physics. You should be able to find what
meaning of Time was chosen in the foundational statements of GR and QM.
In my opinion, it is important to distinguish between our experience of
Time and what can said about Time from these experiences. The following
properties can be inferred; dynamic nature, spontaneous evolution,
universal in presence and local in value, affects the rate of evolution
of events including clocks, .. etc.
If you believe this point of view is worth exploring,
my website is www.angelfire.com/ak/mlebel (old)
mar...@muontailpig.com remove particle
Marcel LeBel
Eight short reflections on the nature of time as may be deduced from
known physics, assuming that time duration is the integrated measure of
the passage of time.
1- Spontaneous: Time runs by itself. Nobody makes time run. Time is
spontaneous. We know we can't rush time. This is why our time measuring
instruments are based on spontaneous processes; sand falling in the
hourglass, mechanical relaxation of quartz crystal, spontaneous
electronic transition in atoms.. etc. In this, we trust a that
spontaneous process does represent the nature of the passage of time.
2- Universality: It is safe to assume time runs everywhere in the
universe. Its pace or rate may differ in different location and
circumstances. (see Necessity below)
3- Rate: Time passes at a certain pace or rate. The passage of time
being a dynamical concept, it is required that it passes at a certain rate.
4- Complexity: The passage of time passes at a certain rate, and this
rate can vary in various location and/or circumstances as can be deduced
from General Relativity. For example, for a successively accelerated
and decelerated body, this rate of passage of time is decreasing and
then increasing back. We may suspect the existence of other derivatives
of variations in the rate of passage of time corresponding to a jerk ? A
Snap? a Crackle ? A Pop?
5- Relative: Relativity tells us that time is relative. This means that
measuring time consists in making a relative comparison between the
duration of two events; one is the observation and the other is the
clock. The meaning of Relative also suggests that there is no causal
connection between the clock and the event i.e. one is not driving or
causing the other in any way. They are rather assumed as sharing the
same local rate of passage of time, hence the use of one clock for two
locations (comparison)
6- Locality: The logical conclusion of the relativity of the passage of
time is its next property; locality. To a specific location corresponds
a specific set of properties of time.
7- Size: Now, if the passage of time is local, how big is the size of
the passage of time? What is the size of a moment in time? In other
words, what is the natural set of joint locations that has no time
between any of its parts? The concept of space-time tells us that a
moment in time is infinitesimally small. Any distance in space
corresponds to a distance in time as well.
8- Necessity: Is time a requirement for this universe? Is ti necessary
for what exists and happens around us? Or can we do without time? The
answer could be in the following questions. Can we say that something
exists without understanding that it does so with a minimum (non
virtual) persistence in time? Can we say something happens without
understanding that it does so at a certain rate?, hence, in a certain
amount of time? No. The passage of time appears to be an intricate
dimension of what exists and happens.
I had other properties that were rated by the moderator as overlay
speculative. I hope to work them out in order to increase their rating
at least to the - defensible- level. Thanks
le...@muontailpig.com remove particle
Nick Maclaren
In article <slrndh7hmu....@corum.multiverse.ca>,
Grrk. Causality seems a simple concept but, as statisticians and
quantum mechanics know, gets harder when you study it more deeply.
Those experiments do violate some of the stronger formulations of
causality, which is where the confusion arises.
And extrapolating general relativity beyond singularities violates
all forms of causality (see Tipler et al.), which is why many
physicists regard the people who publish such results as mere
fantasists.
Time and causality are terribly slippery concepts.
Regards,
Nick Maclaren.
Christopher Fortin
<le...@muontailpig.com>, wrote:
>
> 3- Rate: Time passes at a certain pace or rate. The passage of time
> being a dynamical concept, it is required that it passes at a certain rate.
Please forgive a question I've wondered about, but what units would
be used to measure this rate? Seconds/second seams redundant.
Chris
--
Christopher Fortin, Ph.D. EE, Senior_Scientist@BBN <ch...@fortins.org>
The boss stops by to see if anyone's up for lunch, but the
PFY tells him, without a word of a lie, that I'm supervising
some emergency downloads.
stefa...@yahoo.com
> > "brought together after an earlier synchronization" clocks. In GR
> > it is possible.
> That's a common misconception. SR applies whenever gravity (read
> space-time curvature) can be neglected. See for example the explanation
> of the Twin Paradox in the Physics FAQ:
>http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
Thanks for the link, it is quite entertaining. The Doppler explanation
from your link is a good illustration that acceleration does not make
observations asymmetric.
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html
Following to logic of mutual clock observation through telescope
illustrates it very well. It is essential to take into account
curvature of space-time to solve twin paradox and the acceleration
indeed makes systems asymmetric.
Twin paradox remains paradox within SR frame and it is not a paradox in
GR. The reason is evident; SR is based on thought experiments for
inertial systems and only for inertial systems it can be applyed.
It's a common misconception that TP can be solved in SR.
Regards,
Stefan
Igor Khavkine wrote:
> On 2005-08-29, stefa...@yahoo.com <stefa...@yahoo.com> wrote:
> >
> > Igor Khavkine wrote:
> >> On 2005-08-28, RHNL <rh...@exoptica.com> wrote:
> >
> >> We live in a 4-dimensional space-time.
> >
> > It is quite strong statement ;o)
>
> It's an assumption, but it's served us exceptionally well for the past
> 300 years.
>
> >> In theories based on special relativity, the clock readings do depend on
> >> the motion of the observers. So if two clocks are brought together after
> >> an earlier synchronization, they will not necessarily give the same
> >> readings. However, if we know details of the motion of the two observers
> >> in between, special relativity gives us a recipe for translating between
> >> the readings of different clocks.
> >
> > SR is applied only for inertial systems, so there is no way to consider
> > "brought together after an earlier synchronization" clocks. In GR
> > it is possible.
>
> That's a common misconception. SR applies whenever gravity (read
> space-time curvature) can be neglected. See for example the explanation
> of the Twin Paradox in the Physics FAQ:
>
> http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
>
> >> For both non-relativistic and special relativistic theores, there exist
> >> both classical and quantum formulations. In this sense, QM does not
> >> treat time any different than we would expect.
> >
> > Causality is the essence of time perception, in this sense, time in QM
> > and in GR looks different. Bell experiment is one of the profound
> > examples of that.
>
> Causality is built into both GR and quantum mechanics. I presume you
> refer to EPR-type entanglement experiments. They do not violate
> causality, so I don't see what you mean.
>
> Igor
Igor Khavkine
Yes.
Igor
Ralph E. Frost
> On 2005-08-29, stefa...@yahoo.com <stefa...@yahoo.com> wrote:
> >
> > Igor Khavkine wrote:
> >> On 2005-08-28, RHNL <rh...@exoptica.com> wrote:
> >
> >
>
> It's an assumption, but it's served us exceptionally well for the past
> 300 years.
To keep this discussion on the physical track, don't you mean the last
300 orbits?
Ralph Frost
Ralph E. Frost
> Hi RHNL,
>
> Neither. In QM, time is a parameter that describes the evolution of a
> systems state. But it is not a "constant", it just takes values in the
> Reals.
>
> As GR is covariant, time looses its outstanding position at all. Its
> just a coordinate choice.
>
> One of the big problems in quantizing gravity is bringing together
> these two different roles time plays.
>
> René
Isn't this a rather huge, fundamental misunderstanding?
Ralph Frost
RHNL
Experiment and calculate Newtonian angular momentum without
a concept of time: Look once, 'State 1', look twice, 'State 2', record
each state relative to any physical constant; and so on to
termination of the experiment.
Take it from there. Newton did, only he used an incremental
metric -- time -- but maybe he could have used any physical
constant, say, 'volume'?
RHNL
"Christopher Fortin" <ch...@fortins.org> wrote in message
news:wKmRe.8736$fP.2903@trndny08...
Igor Khavkine
> On Wed, 31 Aug 2005 04:27:23 +0000 (UTC), Marcel LeBel
> <le...@muontailpig.com>, wrote:
>>
>> 3- Rate: Time passes at a certain pace or rate. The passage of time
>> being a dynamical concept, it is required that it passes at a certain rate.
>
> Please forgive a question I've wondered about, but what units would
> be used to measure this rate? Seconds/second seams redundant.
Something like that, i.e. dimensionless. Time dilations and contractions
can be measured relative to other observers (other clocks), cf. the Twin
Paradox.
Igor
Igor Khavkine
>> > SR is applied only for inertial systems, so there is no way to consider
>> > "brought together after an earlier synchronization" clocks. In GR
>> > it is possible.
>> That's a common misconception. SR applies whenever gravity (read
>> space-time curvature) can be neglected. See for example the explanation
>> of the Twin Paradox in the Physics FAQ:
>>http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
>
> Thanks for the link, it is quite entertaining. The Doppler explanation
> from your link is a good illustration that acceleration does not make
> observations asymmetric.
> http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html
I think you either meant "acceleration *does* make observations
asymmetric" or you are mistaken.
> Following to logic of mutual clock observation through telescope
> illustrates it very well. It is essential to take into account
> curvature of space-time to solve twin paradox and the acceleration
> indeed makes systems asymmetric.
There is no gravity in that example. There is no space-time curvature,
only flat Minkowski space-time.
> Twin paradox remains paradox within SR frame and it is not a paradox in
> GR. The reason is evident; SR is based on thought experiments for
> inertial systems and only for inertial systems it can be applyed.
> It's a common misconception that TP can be solved in SR.
The "Twin Paradox" is not a paradox in SR either. Modern formulations of
special relativity allow for accelerated frames (it's just a choice of
coordinates) and accelerated observers (the proper time element along
the world line is also known). GR comes into the picture only if gravity
is taken into account.
The reason I pointed to the FAQ is that it gives a treatment of
acceleration purely in the confines of the SR. Did this point not come
across?
Igor
the softrat
<ref...@isp.com> wrote:
>Ren=E9 Meyer wrote:
>> Hi RHNL,
>>
>> Neither. In QM, time is a parameter that describes the evolution of a
>> systems state. But it is not a "constant", it just takes values in the
>> Reals.
>>
>> As GR is covariant, time looses its outstanding position at all. Its
>> just a coordinate choice.
>>
>> One of the big problems in quantizing gravity is bringing together
>> these two different roles time plays.
>>
>> Ren=E9
>
>Isn't this a rather huge, fundamental misunderstanding?
>
No. It is a huge stumbling block to the unification of the two
theories.
the softrat
Sometimes I get so tired of the taste of my own toes.=20
mailto:sof...@pobox.com
--
Turn on, tune in, drop out. Do not attempt while in an aeroplane.
Igor Khavkine
> Igor Khavkine ha scritto:
>> For both non-relativistic and special relativistic theores, there exist
>> both classical and quantum formulations. In this sense, QM does not
>> treat time any different than we would expect. As to general relativity,
>> the main problems lie in the technical difficulties of constructing
>> quantum theories that take GR into account. Once these difficulties are
>> taken care of, at some point in the future, a quantum theory that takes
>> general relarivity into account (provided that gravitational fields
>> remain fixed and classical), would treat time in the same way as GR.
>>
>> Hope this helps.
>
> It sure does, but I would surmise that not any function provides
> credible time. Shouldn't clock readings be monotonously increasing?
> What about the result by Unruh & Wald showing that any physical clock
> has a non-null probability of running backwards ([1], cf. [2])?
> Can you briefly elaborate on why a quantum gravity theory where
> "gravitational fields remain fixed and classical" is a realistic
> perspective?
> [1] Unruh & Wald "Time and the interpretation of quantum gravity" Phys.
> Rev. D40, 2598--2614 (1989)
> [2] http://math.ucr.edu/home/baez/week167.html
Thanks for the interesting references. I finally had a chance to look at
them. However, I must clarify what I meant above. I was talking about
formulating quantum theory (which includes quantum field theory) on
curved backgrounds, where the background is considered fixed. From what
I understand, the greatest difficulty is the construction of non-linear
quantum fields on the curved space-times. However, the difficulties are
mostly of technical nature, due to the singularity of the field operator
valued distributions, and will most likely be worked out with time. I
wouldn't presume to say anything with as much confidence about a quantum
theory of the gravitational field itself. There, the difficulties are
more than technical, as illustrated in the references you provided.
Igor
Igor Khavkine
> Hi Igor,
>
>> There is no gravity in that example. There is no space-time curvature,
>> only flat Minkowski space-time.
>
> non negligible relativistic effect and should be treated by GR.
Ok, now you'd have to say what you mean by "flat". Here's what I mean.
Given any space-time metric, we can calculate its Riemann curvature
tensor. If it is zero, then we say that the space-time is flat. This
exactly what happens in Minkowski space.
Acceleration refers to the curvature of the world line of an observer.
One example is a space ship with a set of rocket engines. Acceleration
can also refer to a coordinate system defined by an observer that is
accelerating. None of which, changes the fact that we are still in
Minkowski space-time, which is flat.
> SR
> guaranties that observer's clock is the fastest one in the universe
> of the flat space time - in the universe of inertial systems. TP
> arrangement is possible only if acceleration is allowed and the
> acceleration is the only source of asymmetry so if time dilation in TP
> experiment is not negligible the space time curvature is not negligible
> as well and must be treated by GR.
Again, acceleration does not imply curvature. If the space ship has
small mass (or rather small density, since it's an extended object),
gravity and curvature can be very well neglected.
Igor
Igor Khavkine
>> >> There is no gravity in that example. There is no space-time curvature,
>> >> only flat Minkowski space-time.
>> >
>> > When acceleration is involved it is not flat any more especially for
>> > non negligible relativistic effect and should be treated by GR.
>>
>> Ok, now you'd have to say what you mean by "flat". Here's what I mean.
>> Given any space-time metric, we can calculate its Riemann curvature
>> tensor. If it is zero, then we say that the space-time is flat. This
>> exactly what happens in Minkowski space.
>
In either SR or GR space-time is described by 4D manifold with a
Lorentzian metric on it. If you say otherwise, then you say doesn't
pertain to either theory.
> there is only space time of
> observer which is formed by acceleration and by gravity.
If you were talking about SR or GR, I'd say that these are different
coordinate systems on the same space-time manifold. Otherwise, I don't
know what you mean. BTW, the equivalence between uniform gravity and
uniform acceleration hold only locally, in a small neighborhood around
the observer.
> The observer
> mass is irrelevant it only should be non zero. The microwave radiation
> mapping showed that our universe (I mean universe from point of view of
> observer) is quite flat - actually suspiciously flat it supports the
> inflationary prospect about casually separated domains (relatively
> observer) of enormously bigger structure and "flatness" of earth is
> a good analogy to describe "flatness" of universe.
You still haven't defined what you mean by "flat" nor have you given a
quantitative measure of it. Can you give a number and calculate it for
the reference frame of an accelerated observer in Minkowski space? I can
give you the Kretschmann scalar, which is roughly the square of the
Riemann tensor. It's zero for Minkowski space, which is independent of
the observer and implies that the space is flat.
>> One example is a space ship with a set of rocket engines. Acceleration
>> can also refer to a coordinate system defined by an observer that is
>> accelerating. None of which, changes the fact that we are still in
>> Minkowski space-time, which is flat.
>
> It is wrong, there is no undependable on observer space-time, there is
> no absolute scene, there is no absolute reference frame, so statement
> "the fact that we are still in Minkowski space-time, which is flat"
> makes no sense since the observer space time curvature establishes
> space-casual relation with another observers only in context of
> observer reference frame.
Here, you must not be talking about either SR or GR. Either theory
assume the present of a space-time manifold that may be covered by
different coordinate charts (which can correspond to inertial observers,
but are more general).
> My expertise in this area is just recall of my university time 20 years
> ago, so technical details now is out of my grasp but I did spent a lot
> time then trying to understand meaning of GR math.
Unfortunately, it seems you've kept some misconceptions along with what
you understood of the theory.
Igor
Harry
"Igor Khavkine" <igo...@gmail.com> wrote in message
news:slrndh7hmu....@corum.multiverse.ca...
> On 2005-08-29, stefa...@yahoo.com <stefa...@yahoo.com> wrote:
> >
> > Igor Khavkine wrote:
> >> On 2005-08-28, RHNL <rh...@exoptica.com> wrote:
> >
> >> We live in a 4-dimensional space-time.
> >
> > It is quite strong statement ;o)
>
> It's an assumption, but it's served us exceptionally well for the past
> 300 years.
Only in a mathematical sense. Unwittingly you adopted an expression that
originates from the philosophy according to which something called
space-time is *reality*. For over 200 of those past 300 years, the
philosophy that reality is made up of 3D space + time served us
exceptionally well, and it has never been disproved.
> >> In theories based on special relativity, the clock readings do
> >> depend on the motion of the observers. So if two clocks are brought
> >> together after an earlier synchronization, they will not
> >> necessarily give the same readings. However, if we know details of
> >> the motion of the two observers in between, special relativity
> >> gives us a recipe for translating between the readings of different
> >> clocks.
> >
> > SR is applied only for inertial systems, so there is no way to
> > consider "brought together after an earlier synchronization" clocks.
> > In GR it is possible.
>
> That's a common misconception. SR applies whenever gravity (read
> space-time curvature) can be neglected.
Indeed: eventhough the extension to accelerating frames was called GRT by
Einstein, it follows directly from SRT. Anyway, it doesn't matter since SRT
as defined by Einstein is valid as long as an inertial frame is used for the
description - the above example about clocks is even contained in his 1905
SRT paper:
http://www.fourmilab.ch/etexts/einstein/specrel/www/ (paragraph 3)
> See for example the explanation
> of the Twin Paradox in the Physics FAQ:
>
>
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
>
> >> For both non-relativistic and special relativistic theores, there exist
> >> both classical and quantum formulations. In this sense, QM does not
> >> treat time any different than we would expect.
> >
> > Causality is the essence of time perception, in this sense, time in QM
> > and in GR looks different. Bell experiment is one of the profound
> > examples of that.
>
> Causality is built into both GR and quantum mechanics. I presume you
> refer to EPR-type entanglement experiments. They do not violate
> causality, so I don't see what you mean.
It depends on certain interpretations - see Ilja Schmeltzer's comments in
"what is the history of relativity", his posting of 7 September.
Harald
Igor Khavkine
>
> "Igor Khavkine" <igo...@gmail.com> wrote in message
> news:slrndh7hmu....@corum.multiverse.ca...
>> On 2005-08-29, stefa...@yahoo.com <stefa...@yahoo.com> wrote:
>> >
>> > Igor Khavkine wrote:
>> >> On 2005-08-28, RHNL <rh...@exoptica.com> wrote:
>> >
>> >> We live in a 4-dimensional space-time.
>> >
>> > It is quite strong statement ;o)
>>
>> It's an assumption, but it's served us exceptionally well for the past
>> 300 years.
>
> Only in a mathematical sense. Unwittingly you adopted an expression that
> originates from the philosophy according to which something called
> space-time is *reality*. For over 200 of those past 300 years, the
> philosophy that reality is made up of 3D space + time served us
> exceptionally well, and it has never been disproved.
Mathematically, that hasn't really changed. 3 space dimensions plus 1
time dimension still make a 4-dimensional continuum (manifold). What has
changed in the last 100 years is how coordinates on this manifold are
interpreted. We've also learned how not to rely on coordinates by
introducing tensorial objects into the description.
As for reality, I only run into it when something I say gets tested by
experiment. At other times, I don't bother it, and it doesn't bother my
manifolds.
Igor