Twin Paradox: Simplifying Physics for Age Difference Explanation

[rqr]

Primary Goals of Thread:
(1) Eliminate all unnecessary concepts
(2) Focus solely on the physics

Tom and Bill are floating in space (that is, they are
moving inertially). Let Bill meet Tom as they pass
each other. They notice that they are both about
the same age. After Bill and Tom have separated, Bill
turns around and again passes Tom. However, during
this second meeting, they notice that Bill is much
older than Tom.

No clocks = no definition of simultaneity
No rulers = no definition of measurement
No need to mention coordinate systems

The only physical difference between the two
people (Tom and Bill) are Bill's accelerations
during his turnaround.

However, this is a difference without a
distinction because accelerations have no
effect upon either aging or clock rhythms.

[Reference:
http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html
(sighted words from cited site:
"... it has been verified experimentally up
to extraordinarily high accelerations, as
much as 10^18 g in fact ...")]

Therefore, current physics has no absolutely
no physical explanation for the age difference.

But there is a very good reason for this major
sin of omission, namely, the simple fact that
current theory incredibly denies all meaning to
the notion of motion through space, and yet such
motion is the only possible cause of the given
age difference.

I said "incredibly" because there has always
existed a simple and effective absolute frame
in the form of any light ray.

Despite the utter failure of the Michelson-Morley
experiment, the fact remains that all light rays
always move at the known speed c through space.
And all that is required of an absolute frame is
for it to have a constant and known speed through
space.
Why, then was the Michelson-Morley experiment utterly
unable to utilize the given absolute frame? The answer
is simple, and Lorentz gave it long ago - one ruler
contracted during the experiment. And if a clock is
added, then it will physically run slow during the
experiment. Given distorted instruments, one must
obtain a distorted result, namely, a null result,
despite the given absolute reference frame.

Had Michelson & Morley used an uncontracted ruler
(and/or an unslowed clock), then they would have
obtained a positive result.

Even though we have no means of finding an unslowed
clock or an unshrunken ruler, we need not despair
because we still have the one-way experiment.

As of today, no one has yet performed the one-way
version of the Michelson-Morley experiment. That
is, no one has measured light's speed between two
fixed points, despite special relativity theory's
strong-but-wrong implication that the result should
or would or could be null.

I said "implication" because, surprisingly to most,
special relativity does not scientifically predict
what will happen if we measure light's one-way
speed between two fixed clocks. ("Fixed" means
nonrotated and nontransported.)

This is because special relativity does not believe
in absolute simultaneity (absolute synchronization).

But not believing in something does not prove that
it cannot exist.

And given correctly related clocks (or absolutely
synchronous clocks), and given our absolute frame
(aka light), we must obtain a nonnull or positive
result in the one-way light speed case.

rqr

 

[JesseM]

No clocks = no definition of simultaneity
No rulers = no definition of measurement
No need to mention coordinate systems

The only physical difference between the two
people (Tom and Bill) are Bill's accelerations
during his turnaround.

However, this is a difference without a
distinction because accelerations have no
effect upon either aging or clock rhythms.

[Reference:
http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html
(sighted words from cited site:
"... it has been verified experimentally up
to extraordinarily high accelerations, as
much as 10^18 g in fact ...")]

Sorry, but saying "accelerations have no effect upon either aging or clock rhythms" is a statement that is only meant to apply within the context of the coordinate systems which you want to do away with...the page is pointing out that the instantaneous rate a clock ticks in a given coordinate system is solely a function of its instantaneous velocity in that system. Accelerations certainly do affect the amount a clock ticks over an extended period, as the page explains:

So the clock postulate says that the rate of an accelerated clock doesn't depend on its acceleration. But note: the clock postulate does not say that the rate of timing of a moving clock is unaffected by its acceleration. The timing rate will certainly be affected if the acceleration changes the clock's speed of movement, because its speed determines how fast it counts out its time (i.e. by the factor $$\gamma$$). (The clock rate won't be affected by circular motion at constant speed.) If that all seems confusing, think of an everyday analogy. If you ride your bicycle on an icy morning, you get very cold due to the wind chill factor. The faster you go, the colder your hands get. This wind chill is a function of your speed, but not your acceleration. Nevertheless, it is affected by your acceleration when your acceleration changes your speed. But regardless of whether you have a low or a high acceleration, the only thing that matters as far as your cold hands are concerned is what your current speed is. And for circular motion, two cyclists who follow different-diameter circles at the same speed will feel the same wind chill, even though they have different accelerations. So the wind chill factor does not depend on your acceleration, but it certainly can be affected by your acceleration.

Therefore, current physics has no absolutely
no physical explanation for the age difference.

The explanation is that one accelerated. Your attempt to deny this is nothing more than a word-game, conflating two quite different meanings of the phrase "accelerations have no effect".

I said "implication" because, surprisingly to most,
special relativity does not scientifically predict
what will happen if we measure light's one-way
speed between two fixed clocks. ("Fixed" means
nonrotated and nontransported.)

Yes it does, it just says it will depend on what physical process you use to synchronize the clocks. If you use the Einstein synchronization convention, then the one-way speed will be c (this is almost a tautology, since the Einstein synchronization convention is based on the assumption that clocks a distance of x apart as measured by rulers in their rest frame should be synchronized in such a way that a light signal takes a time of x/c to pass from one to the other). If you use some different convention, the measured speed can be different (although everyone should agree the two-way speed is c since this only requires a single clock so synchronization is not an issue)--this doesn't contradict relativity.

This is because special relativity does not believe
in absolute simultaneity (absolute synchronization).

Relativity makes predictions about any well-defined physical scenario. If you can't define a physical procedure for synchronizing two clocks so that they read the same time "simultaneously" according to absolute simultaneity, then you don't have a well-defined physical scenario--absolute simultaneity would be a purely metaphysical postulate with no relevance to the outcome of any specific experiment, and we'd have absolutely no way of testing whether two clocks were in fact "synchronized" in the absolute sense.

 

[Dale]

The answer is simple, and Lorentz gave it long ago - one ruler contracted during the experiment. And if a clock is added, then it will physically run slow during the experiment.

There is no experimental difference between Lorentz's theory and Einstein's special relativity. If you like the Lorentz story better than the Einstein one that is fine by me, but the ending is the same regardless of which one you choose.

 

[pervect]

I think the simplest approach is to accept, as a fundamental fact, the principle of maximal aging.

From the above link:

Principle of Extremal Aging: The path a free object takes between two events
in spacetime is the path for which the time lapse between these events, recorded
on the object’s wristwatch, is an extremum.

For most purposes, one can replace "extremum" with "maximum" (at least in SR), hence "principle of maximal aging".

This principle directly says that the "natural motion" (i.e. with no acceleration) of a body is the motion that maximizes the proper time - so if you fly in some roundabout path with a spaceship, you'll have a lower age than the maximal age you'll get by traveling along "a natural straight line". Which is the "twin paradox" in a nutshell.

The one bit of fine print needed in GR: you can have multiple extremal paths between two points in a general curved space-time. (This is not an issue in the flat space-time of SR). Only one of these multiple paths is a true maximum. This is the main technical reason for using the more general "extremal" than the more specific "maximal". I believe you'll see Taylor et al using the principle of maximal aging in other works where they talk about only SR and do not include GR.

The simplest approach (though not necessarily the most elementary approach) is to recognize the principle of maximal aging as a given, and to explore the consequences for physics. The approach is simple conceptually and philosophically, but requires knowledge of the calculus of variations, which is why it is not the most elementary.

 

[rqr]

JesseM, you misread the cited site.
It said that only speed affects clock rates,
not accelerations. This is readily apparent
from the following single sentence from the cite:

"(The clock rate won't be affected by circular motion
at constant speed.)"

(This is constant acceleration with no speed change.)

And a good little hint was the part about the 10^18 g's; why
mention that if acceleration in fact does affect clock rates?

Sure, a _change_ in acceleration will change a clock's
rate, but this is because of the different speed, not
the acceleration per se.

Also, take a look at this from Tom Roberts:

-------
NewsGroup: sci.physics.relativity
Thread: Acceleration should cause Time Dilation
Date: October 15, 2007

gu...@hotmail.com wrote:
> A person pulling Hi G's in a plane can barely move,
> likewise a clock should also have a hard time moving,
> which would cause time dilation?

The decay of muons is a clock that is unaffected
by an acceleration of 10^18 g -- vastly larger
than any pilot could sustain.

> Yet none of the airplane time dilation tests seem to
> have taken this into account.

There is no such effect to take into account.

> As well Gravity generates a time dilation,

It is not "gravitational force" or "gravitational
acceleration" that is associated with gravitational
time dilation, it is a difference in gravitational
potential. Loosely speaking, that is a difference
in energy, not an acceleration.

Tom Roberts
-------

JesseM wrote:
"The explanation is that one accelerated."

No, accelerations do not affect clock rates;
therefore, current theory has no physical
explanation for the age difference.

The only possible physical cause is different
speeds through space or different absolute
speeds.

-------

Going back to the one-way light speed experiment,
you must cope with the fact that no one has
ever used two (fixed) clocks to experimentally
measure light's one-way speed.

In other words, the one-way Michelson-Morley
experiment has never been performed.

JesseM said:
"If you use some different convention, the measured
[one-way light] speed can be different ... --this
doesn't contradict relativity."

Wrong, relativity theory would certainly be contradicted
by a non-c measurement of light's speed.

JesseM said:
"Relativity makes predictions about any well-defined
physical scenario."

As I said, relativity theory makes no prediction in
the only open and the only post-SR case, the one-way
light speed case. To assume that clocks must be set
to get c is not a prediction of an experimental
result.

But you seemed to stretch relativity theory into
predicting an experimental outcome based upon the
use of that which the theory flatly denies, namely,
absolutely synchronous clocks.

Let's assume (and rightly so, because it's true) that
I have a specific method for absolutely synchronizing
two fixed clocks; if we then ask, as you apparently
did, What is relativity theory's prediction in the
case of using such synchronous clocks to actually
experimentally measure light's one-way speed?

I notice that your answer was 50% wrong and 50% right,
i.e., you said that the result would not be c, but
that this would not conflict with relativity.

If relativity's prediction is non-c, then it is
conflicting with itself by admitting that there is
certainly a way to detect absolute motion, and that
is by simply using absolutely synchronous clocks to
measure light's one-way speed.

This is also admitting that light is an absolute frame,
in contrast with relativity theory's constant claim
that no such frame exists.

Something is rotten in Denmark.

rqr

 

[Hurkyl]

rqr: do you recognize that there is a difference between

. the time dilation of an accelerating clock, as measured by an inertial frame
. the time dilation of an inertial clock, as measured by a noninertial frame

?



Incidentally..

Tom and Bill are floating in space (that is, they are
moving inertially). Let Bill meet Tom as they pass
each other. They notice that they are both about
the same age. After Bill and Tom have separated, Bill
turns around and again passes Tom. However, during
this second meeting, they notice that Bill is much
older than Tom.

You have that backwards. Bill is younger than Tom.

 

[jtbell]

Something is rotten in Denmark.

Please note the sticky thread at the top of this forum:

IMPORTANT! Read before posting

 

[JesseM]

JesseM, you misread the cited site.
It said that only speed affects clock rates,
not accelerations.

You ignore my point that the statement is only meant to apply to instantaneous "clock rates" and "speed" as measured in any given inertial frame. And of course, all acceleration results in a change in speed, so if you want to calculate the elapsed time on a clock over an extended period as opposed to just finding its instantaneous clock rate, you have to integrate the instantaneous clock rate over the whole period, so any changes in speed have an effect on this total time elapsed. It is possible to prove using calculations than in any given frame, if one traveler goes from one point in spacetime to another at constant speed, while another traveler goes between the same two points in spacetime at a non-constant speed, then the one with the non-constant speed will always have aged less.

If you want to drop all notions of "reference frames" from your scenario, and you want to talk about the elapsed time on the clock over an extended period as opposed to just its instantaneous rate of ticking at a single moment, then the statement "only speed affects clock rates" cannot be taken to imply that it's irrelevant which one accelerated--that is definitely not what the page you quoted was saying. Again, it had a specific meaning in terms of the instantaneous rate of ticking depending only on instantaneous speed in a particular frame, with the total time elapsed depending on integrating the instantaneous speed.

This is readily apparent
from the following single sentence from the cite:

"(The clock rate won't be affected by circular motion
at constant speed.)"

(This is constant acceleration with no speed change.)

Yes, in the particular inertial frame in which the clock is moving in a circle at constant speed, since its instantaneous speed is always the same its instantaneous rate of ticking will always be the same, that's what they mean by "the clock rate won't be affected". But the fact remains that if you have an object moving in a straight line which intersects the circle at two points, and the speeds are such that the object moving in a circle passes right next to the object moving in a straight line at both those points, then the object moving in the circle will have elapsed less time on its clock, and the reason for this is that it is accelerating. There is no contradiction between the two notions, it is only your word-games that make you think that since the instantaneous rate of ticking is affected only by the instantaneous speed, this somehow prevents us from explaining the fact that the total time on the clock moving in a circle is shorter in terms of the fact that it was accelerating.

And a good little hint was the part about the 10^18 g's; why
mention that if acceleration in fact does affect clock rates?

Acceleration doesn't affect instantaneous clock rates.

Sure, a _change_ in acceleration will change a clock's
rate, but this is because of the different speed, not
the acceleration per se.

Sure, I agree (although any comments about 'clock rate' and 'speed' only make sense relative to inertial coordinate systems, so your idea that we can dispense with coordinate systems and somehow still make sense of the statement 'clock rate only depends on speed' is nonsense). But like I said, it's possible to prove that if you have two paths between the same two points in spacetime, and one involves changing speed while the other involves constant speed, the clock with changing speed will always have less elapsed time.

JesseM wrote:
"The explanation is that one accelerated."

No, accelerations do not affect clock rates;
therefore, current theory has no physical
explanation for the age difference.

Once again, you're just playing word-games. Acceleration does not affect instantaneous clock rate at any given moment, but since the total time elapsed over an extended period depends on integrating the instantaneous clock rate, this is quite compatible with the notion that a path between two points with constant speed (and thus constant instaneour rate of ticking) will always have a greater elapsed time between a pathe between the same two points with non-constant speed (and thus non-constant instaneous rate of ticking).

It would really help if you looked at the geometric analogy I offered on a previous thread, which you never addressed there:

Here's an analogy--on a 2D sheet of paper, draw two points, a "starting point" A and a "finishing point" B, and then draw two paths between them, one a straight line and the other a bent line. Now draw x and y coordinate axes, with the y-axis parallel to the the straight line. To get some specific numbers, let's say the starting point A is at x=0, y=0 and the finishing point B is at x=0, y=8, and the bent path consists of two straight line segments at different angles, the first of which of which goes from A to a point C at x=3, y=4, while the second line segment goes from C to B. Note the y-coordinates of the two points A and B, in this case y=0 and y=8, and then for any y-coordinate in between these two values, like y=4, there will be a unique point on each path with this y-coordinate. So you can ask about the distance along each path that you'd need to travel to get to the point on the path that has that y-coordinate; let's invent a term for that distance, like "partial path length". For example, at coordinate y=4, the "partial path length" along the straight path would have to be 4, while the "partial path length" on the bent path would larger, in this case 5 (the distance from point A to point C). If you look at the y-coordinate of the finishing point B, y=8, then the "partial path length" at y=8 would just be equal to the total length of the path from the starting point to the finishing point. In this case the "partial path length" for the straight path at y=8 would be 8, while the "partial path length" for the bent path would be 10.

Now, keep the same two paths between the same two points, but redraw your x and y axes so the y-axis is no longer parallel to the straight path--for example, we might draw the y-axis so it's parallel to the line segment joining A and C. Now the coordinates of the starting point A and the finishing point B for each path won't be the same--if we place the origin so that A still has coordinatex x=0, y=0, then the finishing point B will now have coordinates x=0, y=5.12. It's still true that "partial path length" for each path at the y-coordinate of the finishing point, y=5.12, must just be the total length of each path, which won't have changed just because we picked a different coordinate system, so it'll still be 8 for the straight path and 10 for the bent path. But at some earlier y-coordinate, since the lines of constant y are now at different angles, they'll intersect the two paths at different points so the "partial path length" at this y-coordinate will be different--for example, at y-coordinate y=2.56 in this coordinate system, the "partial path length" on the straight path would be 4 (just like the partial path length at y=4 in the previous coordinate system), while the "partial path length" on the bent path would be 2.56. Notice that while in the previous coordinate system the "partial path length" of the straight path was always smaller than the bent path at a given y-coordinate, in this coordinate system the "partial path length" of the straight path can actually be larger for certain values of y, although both coordinate systems agree that the total path length between A and B is shorter for the straight path.

All of this is pretty closely analogous to the situation in relativity, with different coordinate systems on the paper being analogous to different inertial reference frames in relativity, the y-coordinate being analogous to the coordinate time t in a given frame, and the "partial path length" at a given y-coordinate being analogous to the proper time T accumulated by a particular clock at a given coordinate time t. Just as both coordinate systems agreed on the value of the "partial path length" at the y-coordinate of point B where the two paths reunite, so different frames in relativity will always agree on the value of the proper time read by each twin's clock at the t-coordinate where they reunite at a single point in space. But hopefully you would agree that there is no single true answer to the question of which path is accumulating "partial path length" faster before they reach point B--this is entirely coordinate-dependent, you can get different answers depending on how you orient your y-axis and none is more "objectively true" than any other. In the same way, I'd say there's no single true answer to the question of which twin is accumulating proper time faster (or 'aging faster') before they reunite at a single point in space.

To spell out the analogy:

1. a given set of xy axes on the paper = a given inertial coordinate system in SR

2. y-coordinate on xy axes = time-coordinate in inertial coordinate system

3. two paths on paper = two worldlines in SR

4. "partial path length" of a given path as a function of y = elapsed time on clock moving along a given worldline as a function of time-coordinate in inertial coordinate system

5. the fact that the rate at which the partial path length is growing at a given y-coordinate depends only on the slope of the line at that y-coordinate = the fact that the rate a clock's elapsed time is growing (i.e. its instantaneous rate of ticking) as a function of the coordinate's system time-coordinate depends only on its speed in that coordinate system

6. The fact that the length of a path between two points that has a non-constant slope will always end up being greater than the length of a path between the same two points with a constant slope = the fact that the elapsed time on a clock that goes between two points in space time with a non-constant speed will always end up being less than the the elapsed time on a clock that goes between the same two points with a constant speed

7. The fact that the statement about geometry (6) can be restated without reference to a particular set of xy axes, and without reference any notion of "slope" or "instantaneous rate that partial path length is growing" in that coordinate system, just by saying "a straight line is always the shortest path between two points" = the fact that the statement about SR in (6) can be restated without reference to a particular inertial frame, and without reference to any notion of "speed" or "instantaneous rate that a clock is ticking" in that frame, just by saying "an inertial worldline always gives the greatest elapsed time between two points".

So, do you think that since (5) says the rate at which partial path length is increasing at a given y-coordinate depends only on the slope, not the rate the slope is changing, this is incompatible with the statement in (7) that a straight path (with no change in slope) is always the shortest distance between two points? If not, then why should the statement in (5) that the instantaneous rate a clock accumulates time at a given t-coordinate depends only on its speed, not the rate the speed is changing, be incompatible with the statement in (7) that a clock moving between two points in spacetime with constant speed will always have the maximum time?

Going back to the one-way light speed experiment,
you must cope with the fact that no one has
ever used two (fixed) clocks to experimentally
measure light's one-way speed.

In other words, the one-way Michelson-Morley
experiment has never been performed.

Do you fail to understand that the very nature of the Einstein synchronization convention guarantees that the one-way speed is c? You're using a light signal between two clocks to "synchronize" them using the assumption that the one-way speed must be c, so of course any subsequent measurement of a light beam using the same two clocks will give a speed of c.

JesseM said:
"If you use some different convention, the measured
[one-way light] speed can be different ... --this
doesn't contradict relativity."

Wrong, relativity theory would certainly be contradicted
by a non-c measurement of light's speed.

Nonsense, relativity only says that the one-way speed is c when measured by clocks that are "synchronized" in their inertial rest frame, using Einstein's synchronization convention. Of course if you are allowed to define "synchronization" any way you want you can get pretty much any value for distance/time...for example, I could set a clock at the right end of my hallway to read a date of midnight, Jan. 1, 2000, while a clock at the left end of my hallway was set to read a date of midnight. Jan. 1, 1850 (say that in the clocks' relativistic inertial rest frame, these two readings are simultaneous). In this case a light beam moving from left to right will be measured to take over 150 years to complete the journey according to these clocks, even if my hallway is just a few meters long! Does this somehow invalidate relativity?

JesseM said:
"Relativity makes predictions about any well-defined
physical scenario."

As I said, relativity theory makes no prediction in
the only open and the only post-SR case, the one-way
light speed case. To assume that clocks must be set
to get c is not a prediction of an experimental
result.

You don't have to set them to get c...for example, you could use relativity to predict the times on the two clocks in my above example as the light passes them, using an inertial frame where the two clocks are 150 years out-of-sync. In this case relativity would give an accurate answer.

But you seemed to stretch relativity theory into
predicting an experimental outcome based upon the
use of that which the theory flatly denies, namely,
absolutely synchronous clocks.

Relativity does not say there cannot be something like "absolute simultaneity" in a metaphysical sense, it just says that the measured laws of physics look the same in all the inertial rest frames defined by relativity, which means it's impossible to find any actual experimental evidence of absolute simultaneity, or any experimental procedure for synchronizing clocks in an absolute sense.

Let's assume (and rightly so, because it's true) that
I have a specific method for absolutely synchronizing
two fixed clocks

This is the part that's incompatible with relativity. If relativity is true, then even if there is a single "correct" definition of simultaneity, it is unknowable by us, because any experiments we do will look the same in all the different inertial coordinate systems given by SR with all their different definitions of simultaneity. So, if SR is correct, the only way to ensure your clocks were synchronized in an absolute sense (assuming there is some truth about this question, which of course the philosophical view known as 'four-dimensionalism' or 'eternalism' would deny, as I explained on the previous thread) would be to obtain the knowledge in some "supernatural" way, like praying to God to give you the answer.

if we then ask, as you apparently
did, What is relativity theory's prediction in the
case of using such synchronous clocks to actually
experimentally measure light's one-way speed?

Relativity doesn't have a prediction about this, because if you have an experimental method for picking out a preferred definition of simultaneity, then relativity has already been falsified. But note that I mean "preferred" relative to the laws of physics, not relative to external physical landmarks like the galaxy or the CMBR...I'm talking about an experimental method that would allow different observers in closed windowless boxes in relative motion to all arrive at the same definition of simultaneity.

 

[robphy]

Let me offer my approach
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/
which, I feel, addresses your goals

Primary Goals of Thread:
(1) Eliminate all unnecessary concepts
(2) Focus solely on the physics

Once the light clock is established as a instrument measuring proper time along a worldline, the clock effect is demonstrated visually... essentially by following the paths of light rays in a light clock on a spacetime diagram.

 

[yogi]

Based on the way the rqr framed the problem, and after correcting the error noted by Hurkyl as to who is older, the straightforward treatment given by pervect in post 4, IMO hits the nail on the head. The cited material is from Taylor's book on "Black Holes" ... I found chapters I and II complete - does anyone know if the rest of the book on line for free??

 

[JesseM]

hey there can be no twin paradox..time dilation is only for light as per SR..it cannot be used for aging process...

No, that's very wrong. Time dilation is for all physical clocks in SR, I'm not sure what it would even mean to say it's "for light" (unless you mean a light clock). I recommend reading the twin paradox page from John Baez's site.

 

[journeytospace]

No, that's very wrong. Time dilation is for all physical clocks in SR, I'm not sure what it would even mean to say it's "for light" (unless you mean a light clock). I recommend reading the twin paradox page from John Baez's site.

Even in the website u given for reference to twin paradox, both twins are using the light clocks to measure their times ...from this it is obvious that only the time in their light clocks changes but not their age...Biological clocks are different from light clocks..

Moreover,can you give one real life evidence or proof for this twin paradox...

 

[JesseM]

Even in the website u given for reference to twin paradox, both twins are using the light clocks to measure their times

The light clock link was specifically about light clocks. But the twin paradox page doesn't say the twins use a light clock, it just says "Stella ages less than Terence between the departure and the reunion."

...from this it is obvious that only the time in their light clocks changes but not their age...Biological clocks are different from light clocks..

No, they aren't. All the known fundamental laws of physics (which govern any type of physical clock) are Lorentz-symmetric, meaning they work the same in any inertial reference frame (and the first postulate of relativity says that all the laws of physics must work the same in any inertial reference frame, so if this wasn't true the theory of relativity would have to be thrown out). So, if a given type of physical clock runs at the same rate as a light clock that's at rest relative to it in one frame, then this must be true in all frames--any physical clock will run at the same rate as a light clock that's at rest relative to it.

Moreover,can you give one real life evidence or proof for this twin paradox...

Sure, many types of physical processes have been found to obey the time dilation equation, like how the decay time of various particles in particle accelerators is slowed down by just the right amount when they are traveling at relativistic speeds (see here), or how atomic clocks placed on the space shuttle, which were initially synchronized with atomic clocks on Earth, are slightly behind clocks on Earth when they return, by just the amount predicted by relativity (see the last paragraph of this article).

 

[Hurkyl]

I cannot consider atomic clocks as valid evidence since the difference is very small almost negligible which can also be accounted for experimental error...

Where did you get that idea?

http://en.wikipedia.org/wiki/Hafele-Keating_experiment

 

[journeytospace]

Where did you get that idea?

http://en.wikipedia.org/wiki/Hafele-Keating_experiment

There can also be effects of gravitational field which could have caused the minimal time difference... SR is applicable for only inertial frames...What are the two inertial frames in that experiment...

 

[russ_watters]

Please be advised that you are now looking clear evidence in the face and refusing to accept it. That is an unscientific posture and one that we do not accept here. That experiment (and there are others, such as GPS clocks, which perform the experiment continuously and at several orders of magnitude better accuracy) does test what it is intended to test. Look at the numbers! What is the SR effect? What is the GR effect? What is the accuracy of the clock?

 

[jtbell]

Biological clocks are different from light clocks..

Set up a light-clock that "ticks" once every second, when it is stationary. Find a person whose heart beats once every second. Synchronize the light-clock so that it "ticks" at the same time as the person's heart, when they are standing right next to each other. Connect the light-clock and the person to a coincidence detector that prints a mark on a piece of paper if and only if the light-clock and the person's heart "tick" simultaneously. In the inertial reference frame in which the light-clock and the person are stationary, marks appear on the paper at the rate of one per second.

Clearly all inertial observers must agree on the presence or absence of marks on the paper. Therefore, in another inertial reference frame, in which the same light-clock, the person and the coincidence detector are moving, marks must also be printed on the paper, although at a slower rate because of time dilation.

http://en.wikipedia.org/wiki/Hafele-Keating_experiment[/quote]
There can also be effects of gravitational field which could have caused the minimal time difference...

There are indeed effects due to gravity which are taken into account in the analysis of the experiment. Similarly, the GPS system must take into account (with greater precision) the effects of both gravity and speed on the orbiting satellite clocks.

 

[rqr]

2 jessem

JesseM concluded his analogy with the following:
"... I'd say there's no single true answer to the question of which twin is accumulating proper time faster (or 'aging faster') before they reunite at a single point in space."

Absolutely synchronous clocks could tell us the truth
about time in any multiple-event case. (See more about
such clocks below.)

rqr wrote:
Wrong, relativity theory would certainly be
contradicted by a non-c measurement of light's
speed.

JesseM replied:
"Nonsense, relativity only says that the one-way speed is c when measured by clocks that are 'synchronized' in their inertial rest frame, using Einstein's synchronization convention. Of course if you are allowed to define 'synchronization' any way you want you can get pretty much any value for distance/time...for example, I could set a clock at the right end of my hallway to read a date of midnight, Jan. 1, 2000, while a clock at the left end of my hallway was set to read a date of midnight. Jan. 1, 1850 (say that in the clocks' relativistic inertial rest frame, these two readings are simultaneous). In this case a light beam moving from left to right will be measured to take over 150 years to complete the journey according to these clocks, even if my hallway is just a few meters long! Does this somehow invalidate relativity?"

Of course not, because light's one-way speed
still wouldn't vary with frame velocity.

In other words, my above is not nonsense.
I was saying simply that a non-invariant
light speed would conflict with relativity.

JesseM wrote:
" Relativity does not say there cannot be something like 'absolute simultaneity' in a metaphysical sense, it just says that the measured laws of physics look the same in all the inertial rest frames defined by relativity, which means it's impossible to find any actual experimental evidence of absolute simultaneity, or any experimental procedure for synchronizing clocks in an absolute sense."

The same-laws rule does not preclude absolute
synchronization. For example, in the case of
light's experimentally-measured one-way speed,
the absolute synchronization result would be
w = c±v, and since this law would have the
same form in all frames, this would not be
a violation of the principle of relativity.

Further, since it is not possible to prove
a negative, no rule, including the principle
of relativity, could really say that it is
impossible to absolutely synchronize clocks.

JesseM wrote:
"So, if SR is correct, the only way to ensure your clocks were synchronized in an absolute sense (assuming there is some truth about this question, which of course the philosophical view known as 'four-dimensionalism' or 'eternalism' would deny, as I explained on the previous thread) would be to obtain the knowledge in some 'supernatural' way, like praying to God to give you the answer."

JesseM continued:
"I'm talking about an experimental method that would allow different observers in closed windowless boxes in relative motion to all arrive at the same definition of simultaneity."

That's precisely the method about which I am talking.
My method must be and is a closed-lab method.
It can also be independently verified.
The key notion behind this method is the simple fact
that we need not actually measure each clock-starting
entity's speed, but we need only to assure that these
speeds (relative to the clocks to be started) are equal.

JesseM wrote:
"... any comments about 'clock rate' and 'speed' only make sense relative to inertial coordinate systems, so your idea that we can dispense with coordinate systems and somehow still make sense of the statement 'clock rate only depends on speed' is nonsense)."

It is not nonsense, but is based on the
simple fact that no passing coordinate system
can possibly physically affect anyone's aging
process or any clocks atomic rate.

Returning to the twins, let's put it another way,
as follows:

Suppose we let Bill's turnaround be a very small
part of his overall trip. Then we cryogenically
stop Bill's aging process during the turnaround.
Then, if he and Bob have different ages when they
meet the second time, no one can use or pretend
to use, acceleration as the cause.

rqr

 

[JesseM]

rqr wrote:
Wrong, relativity theory would certainly be
contradicted by a non-c measurement of light's
speed.

JesseM replied:
"Nonsense, relativity only says that the one-way speed is c when measured by clocks that are 'synchronized' in their inertial rest frame, using Einstein's synchronization convention. Of course if you are allowed to define 'synchronization' any way you want you can get pretty much any value for distance/time...for example, I could set a clock at the right end of my hallway to read a date of midnight, Jan. 1, 2000, while a clock at the left end of my hallway was set to read a date of midnight. Jan. 1, 1850 (say that in the clocks' relativistic inertial rest frame, these two readings are simultaneous). In this case a light beam moving from left to right will be measured to take over 150 years to complete the journey according to these clocks, even if my hallway is just a few meters long! Does this somehow invalidate relativity?"

Of course not, because light's one-way speed
still wouldn't vary with frame velocity.

Yes it would, if you define clocks as "synchronized" when they are actually out-of-sync in their SR rest frame. In the above example, the light would take a little over 150 years to travel from the left end of the hallway to the right, but it would take a little over -150 years (a trip back in time) to travel from right to left. To pick an example that doesn't involve time travel, suppose I take a hallway 5 light-seconds long, at the left end I put a clock that reads 0 seconds, at the right end end I put a clock that reads 2 seconds "simultaneously" in their mutual SR rest frame, but then I throw away the SR rest frame's definition of simultaneity and define simultaneity in terms of these two clocks (so an event that happens next to the left clock when it reads 3 seconds is defined to happen at the 'same time' as an event that happens next to the right clock when it reads 3 seconds, for example). If I send a light signal from left to right when the left clock reads 0 seconds, analyzed from the SR frame it takes 5 seconds to get to the right clock, but since the right clock clock was already 2 seconds ahead in the SR frame it'll read 7 seconds when the light reaches it. So, if I am defining these clocks as "synchronized", I'll say that the one-way speed of the beam=distance/time = 5 light-seconds/7 seconds = 0.71c. Now if I send a beam back to the right at 7 seconds, then in SR terms it again takes 5 seconds to travel back, but since the left clock is 2 seconds behind the right one in their SR frame, the left clock only reads 7+5-2=10 seconds when the beam reaches it. So, if I'm defining these clocks as "synchronized", the beam departed from the right clock at 7 seconds and arrived at the left one at 10 seconds, so speed = distance/time = 5 light-seconds/3 seconds = 1.67c. So clearly, because I have arbitrarily chosen to define these clocks as "synchronized" even though they are out-of-sync by 2 seconds in their SR rest frame, then the one-way speed of light will be different in different directions in any coordinate system where the two clocks actually are synchronized. Do you think this simple trick of setting clocks to be out-of-sync in their SR rest frame is a falsfication of relativity, even though I actually used the SR rest frame to calculate what the time would be on each clock as the light beam passed them?

In other words, my above is not nonsense.
I was saying simply that a non-invariant
light speed would conflict with relativity.

If their was some physical method for picking out a preferred definition of simultaneity for two clocks that did not necessarily agree with the definition of their SR rest frame, then using this alternate definition you could get different one-way speeds. But in this case the thing that contradicts relativity is the physically preferred definition of simultaneity, the fact that the one-way speed can vary is just a consequence of that. On the other hand, it's quite easy to arbitrarily define two clocks to be "synchronized" even when they're out-of-sync in their SR rest frame with no physical motivation for this altered definition of simultaneity, as I did in the above example, and in this case you'll also get a varying one-way-speed, but that doesn't contradict SR.

JesseM wrote:
" Relativity does not say there cannot be something like 'absolute simultaneity' in a metaphysical sense, it just says that the measured laws of physics look the same in all the inertial rest frames defined by relativity, which means it's impossible to find any actual experimental evidence of absolute simultaneity, or any experimental procedure for synchronizing clocks in an absolute sense."

The same-laws rule does not preclude absolute
synchronization. For example, in the case of
light's experimentally-measured one-way speed,
the absolute synchronization result would be
w = c±v, and since this law would have the
same form in all frames, this would not be
a violation of the principle of relativity.

Yes it would be, because each frame would have a different numerical value for v (which is presumably their velocity relative to a preferred frame whose SR definition of simultaneity is the "correct" one in absolute terms). Lorentz-invariance means the equations for all fundamental laws must be identical when written in the coordinate systems of different inertial frames, there can't even be a difference in numerical constants.

Further, since it is not possible to prove
a negative, no rule, including the principle
of relativity, could really say that it is
impossible to absolutely synchronize clocks.

But relativity doesn't "prove" that the first postulate is true, it postulates that as a fundamental principle. It's up to experimentalists to decide whether the real-world laws of physics respect this postulate. The point is that if experimentalists find that the laws of physics are not identical in every inertial frame in flat spacetime, then this proves that the theory of relativity itself is incorrect. My argument is just that absolute synchronization would be totally incompatible with the theory of relativity, not that I can "prove" that the theory of relativity is actually correct (although all evidence found by physicists so far suggests it is).

JesseM wrote:
"So, if SR is correct, the only way to ensure your clocks were synchronized in an absolute sense (assuming there is some truth about this question, which of course the philosophical view known as 'four-dimensionalism' or 'eternalism' would deny, as I explained on the previous thread) would be to obtain the knowledge in some 'supernatural' way, like praying to God to give you the answer."

JesseM continued:
"I'm talking about an experimental method that would allow different observers in closed windowless boxes in relative motion to all arrive at the same definition of simultaneity."

That's precisely the method about which I am talking.
My method must be and is a closed-lab method.
It can also be independently verified.
The key notion behind this method is the simple fact
that we need not actually measure each clock-starting
entity's speed, but we need only to assure that these
speeds (relative to the clocks to be started) are equal.

Maybe instead of being mysterious about your new method you could give the details, so if there's a flaw in your reasoning we could point it out?

JesseM wrote:
"... any comments about 'clock rate' and 'speed' only make sense relative to inertial coordinate systems, so your idea that we can dispense with coordinate systems and somehow still make sense of the statement 'clock rate only depends on speed' is nonsense)."

It is not nonsense, but is based on the
simple fact that no passing coordinate system
can possibly physically affect anyone's aging
process or any clocks atomic rate.

Relativity simply says there is no coordinate-independent truth about one's "rate of aging", at least not one that can be experimentally tested (there could be an 'metaphysical' truth just like there could be an 'metaphysical' truth about simultaneity). Did you read my geometric analogy? Do you understand that in the block spacetime view, "rate of aging" (i.e. the rate that a clock's total time is increasing) is analogous to the notion of "the rate that the partial path length is increasing" for a path drawn on a piece of paper, which just depends on the slope of a line at a given point? Do you agree that by rotating our xy axes, we can change the slope of the same line at any given point? Would you argue that this is problematic since "no rotated coordinate system can possibly physically affect the slope of a physical line drawn on a piece of paper", or would you acknowledge that "slope" is itself a coordinate-dependent concept with no absolute physical reality, so this isn't a problem?

Perhaps the difference between these situations is that "the rate partial path length increases" is defined relative to the y-coordinate, and you don't assume there is any such thing as an "absolute y-axis" on a piece of paper, whereas "the rate that a clock's elapsed time increases" is defined relative to a given frame's t-coordinate, and you assume there is such a thing as absolute time so that it makes sense to ask what rate a clock's elapsed time is increasing relative to absolute time. But unless you can come up with an experimental way of figuring out which SR frame's t-coordinate corresponds to absolute time, this is a purely metaphysical belief with no empirical basis, and I think the geometric analogy shows that there is nothing illogical about dispensing with the idea of absolute time altogether.

Returning to the twins, let's put it another way,
as follows:

Suppose we let Bill's turnaround be a very small
part of his overall trip. Then we cryogenically
stop Bill's aging process during the turnaround.
Then, if he and Bob have different ages when they
meet the second time, no one can use or pretend
to use, acceleration as the cause.

First of all, relativity is talking about time passed in terms of fundamental physical processes, if the time elapsed for a given traveler is 40 years then this isn't changed by freezing him so he doesn't look 40 years older, an atomic clock placed next to him would still show that 40 years had passed and the number of oscillations in the atoms in his frozen body would still be the number that the laws of physics would predict for a 40-year period, and the same would go for any other 'clock' based on fundamental laws like the decay of isotopes in his body.

Second, I don't understand why it was Bill who you imagined freezing, and why you specified that he only be frozen in the turnaround...I think you may still be confused about how the twin paradox works in SR. First of all, if Bill is the one who accelerates during the turnaround while Bob moves inertially, SR already less time will have elapsed for Bill, so freezing Bill won't make their ages equal, it'll just make him appear even younger when they meet...wouldn't it have made more sense to suggest freezing Bob? Second, relativity doesn't predict that anything special happens during the turnaround phase...you can make Bill's turnaround instantaneous and the time on his clocks will still be significantly less than Bob's when they reunite.

 

[Dale]

Hi Pervect, JesseM, et al.,

I think it is pointless to debate people who insist that Lorentz was right and Einstein was wrong. Since special relativity is just a simpler way to derive the Lorentz transform the two theories are experimentally indistinguishable. Whenever you are talking with someone who thinks that they have actually said something meaningful by asserting Lorentz over Einstein then you know that you are not dealing with someone who is really interested in science.

 

[pervect]

Hi Pervect, JesseM, et al.,

I think it is pointless to debate people who insist that Lorentz was right and Einstein was wrong. Since special relativity is just a simpler way to derive the Lorentz transform the two theories are experimentally indistinguishable. Whenever you are talking with someone who thinks that they have actually said something meaningful by asserting Lorentz over Einstein then you know that you are not dealing with someone who is really interested in science.

Personally, I'm not really interested in "debating" relativity. It's well established, it doesn't need to be "debated". What I am interested in doing is explaining it, but only to people who are interested (i.e. to people who are not already convinced it's wrong for whatever misguided reason).

As far as Lorentz ether theory goes, I find that most people who take that approach wind up with misconceptions about relativity (there are exceptions, for instance John Bell comes to mind, as per his essay on relativity in what has come to be called the "Bell spaceship paradox").

So while it's possible to believe in a version of LET that is equivalent to relativity, unfortunately it's rarer than one would think.

 

[journeytospace]

Set up a light-clock that "ticks" once every second, when it is stationary. Find a person whose heart beats once every second. Synchronize the light-clock so that it "ticks" at the same time as the person's heart, when they are standing right next to each other. Connect the light-clock and the person to a coincidence detector that prints a mark on a piece of paper if and only if the light-clock and the person's heart "tick" simultaneously. In the inertial reference frame in which the light-clock and the person are stationary, marks appear on the paper at the rate of one per second.

Clearly all inertial observers must agree on the presence or absence of marks on the paper. Therefore, in another inertial reference frame, in which the same light-clock, the person and the coincidence detector are moving, marks must also be printed on the paper, although at a slower rate because of time dilation.



There are indeed effects due to gravity which are taken into account in the analysis of the experiment. Similarly, the GPS system must take into account (with greater precision) the effects of both gravity and speed on the orbiting satellite clocks.

Just because you connected a light clock with heart beat, will the heart beats slow down when we move in constant velocity..only the light clock will slow down and that too only to a stationary observer... if moving at a constant velocity slows down our aging process then that would be the best medicine ever found to remain young ... why we have to care for all these wordly things...why no one has moved at a constant velocity and remained young in the past 100 years...

Whenever time dilation relation has to be derived, they all use the light clock in which light is set to move in the perpendicular direction to the moving frame...and they get the time dilation relation using pythagoras theorem and then use it to derive the contraction relation by setting the object to move in the same direction as the moving frame...why there is change in the direction?

why they are using the relation which they get in the perpendicular direction and use it to the same direction as the moving frame?

can anyone derive the time dilation relation by setting the light to move in the same direction as the moving frame? They can derive the time dilation relation only using pythagoras theorem and for this, they are setting the light to move in the perpendicular direction to the moving frame..what a nice trick is used to get the time dilation relation?
and then they use this to the object moving in the same direction as the moving frame..again this is also a nice trick... All these are my opinion ...am not opposing anything...

 

[JesseM]

Just because you connected a light clock with heart beat, will the heart beats slow down when we move in constant velocity..only the light clock will slow down and that too only to a stationary observer...

But as mentioned already, it's been proven that other types of clocks slow down too, including atomic clocks and the "clocks" defined by the decay time of various particles. What's more, all the fundamental laws of physics known have equations which respect Lorentz-invariance, which means that if these equations are correct they will work the same way in all inertial frames (meaning that any clock constructed out of objects which obey these equations will keep time with a comoving light clock).

if moving at a constant velocity slows down our aging process then that would be the best medicine ever found to remain young ... why we have to care for all these wordly things...why no one has moved at a constant velocity and remained young in the past 100 years...

What do you mean by "moving at constant velocity"? There's no such thing as an absolute notion of velocity, only velocity relative to something else...if an object moved at constant velocity relative to the Earth, then their clocks would run slow in the Earth's frame of reference. But the time dilation is only noticeable when you travel at a significant fraction of the speed of light (or when you use ultra-precise clocks which can notice differences of just nanoseconds)...do you think we have the technology to accelerate someone to a large fraction of light speed relative to Earth?

Whenever time dilation relation has to be derived, they all use the light clock in which light is set to move in the perpendicular direction to the moving frame...

They are deriving it using the assumption that the two postulates of relativity are correct:

1. The laws of physics are the same in all inertial reference frames
2. The speed of light is c in all inertial reference frames

We can use #2 to show that if a light clock is moving in your frame, the time between ticks will be longer in your frame since the light has a bigger distance to travel than it does in the clock's rest frame (that's where the pythagorean theorem comes in). But #1 also means that if you have a certain light clock which ticks at the same rate as some other physical clock (like an atomic clock) when both are at rest in your frame, then if you have an identical light clock and an identical version of the other clock which are moving in your frame, then since the laws of physics must work the same in the frame where they are at rest, the two clocks must be ticking at the same rate just like the ones in your own rest frame.

why they are using the relation which they get in the perpendicular direction and use it to the same direction as the moving frame?

They have the line between the two mirrors of the light clock be perpendicular to the clock's direction of motion so that there's no need to worry about Lorentz contraction.

can anyone derive the time dilation relation by setting the light to move in the same direction as the moving frame?

You could do this, but then you'd have to take into account the Lorentz contraction, so the distance between the mirrors in your frame would be shrunk from the distance between the mirrors in the clock's own rest frame. Would you like to see the derivation?

Also, if you want to see some derivations for the Lorentz transformation (from which it's easy to derive the formula for time dilation) which don't use a light clock at all, you can see a few on this thread...I'm sure people could provide you with additional links if you asked.

 

[pervect]

A quick comment: it's a mistake to think that one can just edit time dilation out of special relativity via fiat because "one doesn't like it" and have a self-consistent theory. If time dilation were to be disproven, one would have to throw out the entire theory of SR and start from scratch, time dilation is a necessary part of SR.

As Jesse notes, there are experiments other than the Haefele-Keating experiment that confirm SR's prediction of time dilation. Muon lifetimes are one frequently quoted example, see for instance http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html.

Without taking a strong position on one particular experiment(Haefele-Keating), there is plenty of evidence that SR is a correct theory, and some of these experiments do test for time dilation. I'd suggest

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

for a list.

 

[bernhard.rothenstein]

the principle of maximal aging

Please explain me what is the difference between time dilation and the principle of maximal aging?
Thanks

 

[Hurkyl]

That's like asking the difference beween the slope and the principle that a line is the shortest distance between two points.


Well, to be precise, I should say "derivative of arclength with respect to a coordinate" instead of "slope". (e.g. in one particular case, if m = slope, I should have said $\sqrt{1 + m^2}$)

 

[bernhard.rothenstein]

maximal aging

That's like asking the difference beween the slope and the principle that a line is the shortest distance between two points.


Well, to be precise, I should say "derivative of arclength with respect to a coordinate" instead of "slope". (e.g. in one particular case, if m = slope, I should have said $\sqrt{1 + m^2}$)

Thanks. Please express all that in equations.

 

[rqr]

Note: My reply's (3) relatively brief sections
are in order of increasing importance (to me)

quoting JesseM:
"Yes it would be, because each frame would have a different numerical value for v (which is presumably their velocity relative to a preferred frame whose SR definition of simultaneity is the "correct" one in absolute terms). Lorentz-invariance means the equations for all fundamental laws must be identical when written in the coordinate systems of different inertial frames, there can't even be a difference in numerical constants."

Your self-contradiction here lies in your final phrase
"numerical constants"; each frame's velocity v through
space is not supposed to be a constant. It is the _form_
of the equation that must be the same in each frame, not
the variables.

Of course, it doesn't help that Einstein misconstrued
the PR (the principle of relativity) by claiming that
it meant "all null results." He should have seen that
all frames getting a positive result (e.g., had the MMx
"gone good") is compatible with the PR, but is _not_
compatible with SR theory.

But Einstein was still careful enough to use the phrase
"same form":
http://www.bartleby.com/173/18.html

And here's a simple analogy for you:
The general law for the area of rectangles is A=LW; note
that this law has the same form for all rectangles even
though both L and W can vary all over the place.

quoting JesseM:
"First of all, relativity is talking about time passed in terms of fundamental physical processes, if the time elapsed for a given traveler is 40 years then this isn't changed by freezing him so he doesn't look 40 years older, an atomic clock placed next to him would still show that 40 years had passed and the number of oscillations in the atoms in his frozen body would still be the number that the laws of physics would predict for a 40-year period, and the same would go for any other 'clock' based on fundamental laws like the decay of isotopes in his body."
"Second, I don't understand why it was Bill who you imagined freezing, and why you specified that he only be frozen in the turnaround...I think you may still be confused about how the twin paradox works in SR. First of all, if Bill is the one who accelerates during the turnaround while Bob moves inertially, SR already less time will have elapsed for Bill, so freezing Bill won't make their ages equal, it'll just make him appear even younger when they meet...wouldn't it have made more sense to suggest freezing Bob? Second, relativity doesn't predict that anything special happens during the turnaround phase...you can make Bill's turnaround instantaneous and the time on his clocks will still be significantly less than Bob's when they reunite."

Let's "instant-replay" one key part here:
"Second, relativity doesn't predict that anything special happens
during the turnaround phase ..."

Hmmmm ... I could swear that someone here claimed
that the physical cause of the twins' age difference
was the one twin's acceleration during the turnaround.

That's why I decided to eliminate all possible
acceleration effects upon the turnaround twin's
aging by simply freezing him at that critical
stage. (There is no need to freeze Bob because
he doesn't acceleration.)

We could add a third person as a control, or use
atomic clocks, stopping one and keeping one running
during the acceleration periods. This would, as you
said, tell us the turnaround time for the traveling
frame, thereby allowing us to remove that from the
end result; thus, if the frozen dude and the stay-at-
home dude ages still differ, we know that this cannot
be due to acceleration.
quoting JesseM:
"Maybe instead of being mysterious about your new method you could
give the details, so if there's a flaw in your reasoning we could
point it out?"

Well, this falls within the tricky area
of homeland security - _my_ "homeland"
and _my_ security.

If you had a clearly certain way of absolutely
synchronizing clocks, would you blare it out
freely to all on the internet, or would you be
a little more circumspect? I cannot publish it
in any scientific journal because it would not
even be sent to the refs., much less ref'd.
(This is from personal experience.)

Maybe you have a good suggestion?

In the meantime, perhaps this will work as a
workaround:

Regardless of any possible physical length
contractions, it is easy to make sure that
the clock-starting entities travel truly
equal distances by simply starting them at
the midway point (between the two clocks).
The hard part is making sure that the two
entities travel at truly or absolutely
equal speeds relative to the clocks. If we
try to use propelled entities such as a
couple of bullets or baseballs, then we
face the problem of mass variance with
velocity. (If this problem did not exist,
then we could have used bullets to truly
or absolutely synchronize clocks long ago.)
Therefore, we must use self-propelled objects,
e.g., cars. I could go further, but I seem to
be running into homeland security problems.
(But trust me, it has all been worked out.)

rqr

 

[JesseM]

Note: My reply's (3) relatively brief sections
are in order of increasing importance (to me)

quoting JesseM:
"Yes it would be, because each frame would have a different numerical value for v (which is presumably their velocity relative to a preferred frame whose SR definition of simultaneity is the "correct" one in absolute terms). Lorentz-invariance means the equations for all fundamental laws must be identical when written in the coordinate systems of different inertial frames, there can't even be a difference in numerical constants."

Your self-contradiction here lies in your final phrase
"numerical constants"; each frame's velocity v through
space is not supposed to be a constant. It is the _form_
of the equation that must be the same in each frame, not
the variables.

I was talking about numerical constants that appear in the equations of the fundamental laws of physics as they're written in a particular frame. "Each frame's velocity v through space" is not a numerical constant that appears in these equations in current physics when they're written in one of the coordinate systems given by the Lorentz transformation, but the speed of light as measured in a given frame is, it can be derived directly from Maxwell's equations for example. This means that if you want the one-way speed of light to differ in different frames, the fundamental equations for the laws of electromagnetism will differ too, each frame's equations for electromagnetism will include a constant telling you that frame's velocity relative to some preferred frame where the speed of light is c in all directions (traditionally this preferred frame was conceived as the rest frame of the aether).

And here's a simple analogy for you:
The general law for the area of rectangles is A=LW; note
that this law has the same form for all rectangles even
though both L and W can vary all over the place.

The problem with this analogy is that it doesn't really feature a clear analogue of "dynamical laws" which are separate from the initial conditions of a particular situation you're analyzing. In physics this distinction is clear--for any given coordinate system, you will have a set of general equations expressing the dynamical laws, and then to analyze any specific physical situation (a particular collection of particles, for example), you plug in the appropriate initial conditions and evolve them forward using the dynamical laws. For example, in Newtonian physics the general equation for gravity is F=GmM/r^2 and the general equation for an object's motion is a = F/m, and using that you can plug in any initial conditions involving different masses with different starting positions and initial velocities and that will determine their future dynamics, with the numerical constant G appearing in the gravity equation being one of the constants of the fundamental laws of physics (so that Galilean relativity dictates this must be unchanged in different inertial coordinate systems given by the Galilei transformation), but the particular masses and positions and velocities described by the initial conditions not being part of the fundamental laws. And the situation is the same in SR, it's the equations for the dynamical laws which should be the same in every coordinate system given by the Lorentz transform in SR, any other features of a specific physical situation that relate to the specific choice of initial conditions can vary. There is no way you could have it so that the speed of light differed in different coordinate systems given by the Lorentz transformation, yet the fundamental dynamical equations for electromagnetism were the same in each of these coordinate systems.

Incidentally, this is not to say that dynamical laws acting on initial conditions is the only way to understand what is meant by the "form" of the laws of physics--in general relativity the "laws" are something more like a global constraint on allowable spacetimes, expressed in terms of a relationship between the stress-energy tensor and the curvature tensor that must be satisfied at every point on a given spacetime--but it's probably the simplest way conceptually.

Let's "instant-replay" one key part here:
"Second, relativity doesn't predict that anything special happens
during the turnaround phase ..."

Hmmmm ... I could swear that someone here claimed
that the physical cause of the twins' age difference
was the one twin's acceleration during the turnaround.

Yes, the two statements are compatible, you just have to understand that when I say SR doesn't say "anything special happens during the turnaround phase", I'm talking about the rate that each twin's clock is ticking as measured in any given inertial frame, there's no inertial frame where one twin's clock jumps forward by a huge amount during the turnaround or anything like that. Once again you can go back to my geometric analogy--the rate at which a non-straight path on a piece of paper accumulates "partial path length" as the y-coordinate increases does not do anything special during the section of the path that bends (regardless of where you draw your y-axis), yet the fact remains that any path with a bend in it will be longer than a straight path between the same two points on the paper, showing that the bend is critical in a different way.

That's why I decided to eliminate all possible
acceleration effects upon the turnaround twin's
aging by simply freezing him at that critical
stage. (There is no need to freeze Bob because
he doesn't acceleration.)

Again, nothing special happens to the twin's age during the acceleration itself. To go back to the geometric analogy, suppose we have a road on flat ground that's shaped like a "V" with a rounded bottom, i.e. two straight segments at different angles with a short non-straight section connecting them. And also suppose we have another perfectly straight road going between the two top ends of the V. I start off driving along the perfectly straight road and you start off on the V-shaped road (both starting at the same point in space), and then we reunite when we both reach the end of our respective roads (meeting at another common point in space). We each turn on our odometers when we start off, and compare them again when we reunite. Do you agree that of course my odometer will show less accumulated distance then yours when we reunite, since a straight line is always the shortest distance between two points on flat ground? And what if you turn off your odometer when you first enter the brief non-straight segment of the road at the bottom of the "V", and turn it on again once you're back on a straight segment (equivalent to stopping the twin's aging during the acceleration phase of his worldline)--do you agree that this will make virtually no difference to your odometer reading when we reunite, that you'll still have accumulated significantly more distance than I did since the length of the two straight segments of the "V" is significantly larger than the length of the single straight road connecting the two top ends of the "V"?

quoting JesseM:
"Maybe instead of being mysterious about your new method you could
give the details, so if there's a flaw in your reasoning we could
point it out?"

Well, this falls within the tricky area
of homeland security - _my_ "homeland"
and _my_ security.

If you had a clearly certain way of absolutely
synchronizing clocks, would you blare it out
freely to all on the internet, or would you be
a little more circumspect? I cannot publish it
in any scientific journal because it would not
even be sent to the refs., much less ref'd.
(This is from personal experience.)

Maybe you have a good suggestion?

If you're just worried about establishing priority, there's no need to have it published in a scientific journal, you just need to establish some clear evidence that you alread had the idea by a certain date--you could simply post it on a usenet group like sci.physics.relativity since google keeps a permanent archive of all usenet postings along with their dates (see here for posts on sci.physics.relativity), or if you were really paranoid you could get it published through a professional self-publishing company which will have a record of when they received the manuscript (and some, like XLibris, will even get the book listed on amazon). This could cost some money, though, you could also just publish it as an ebook through some place like http://www.lulu.com/en/help/, they would also have a record of when they received it. But I really wouldn't worry too much about this, since I can pretty much guarantee that if you hold up your method to the scrutiny of people who know a lot about physics, they'll be able to point out flaws in it; the known laws of physics are all Lorentz-symmetric, so this guarantees mathematically that unless you are invoking totally new physical effects not described by existing laws, you won't be able to set up an experiment that picks out a preferred frame.

In the meantime, perhaps this will work as a
workaround:

Regardless of any possible physical length
contractions, it is easy to make sure that
the clock-starting entities travel truly
equal distances by simply starting them at
the midway point (between the two clocks).
The hard part is making sure that the two
entities travel at truly or absolutely
equal speeds relative to the clocks.

Yes, unless you have a method of measuring absolute speed, there's no way to guarantee that their absolute speeds are the same (if there even is a truth about absolute speed); any time their speeds are equal in one frame, they will be unequal in other frames.

If we
try to use propelled entities such as a
couple of bullets or baseballs, then we
face the problem of mass variance with
velocity. (If this problem did not exist,
then we could have used bullets to truly
or absolutely synchronize clocks long ago.)
Therefore, we must use self-propelled objects,
e.g., cars.

It's totally irrelevant whether they're self-propelled--cars showing a given speedometer reading are driving at that speed relative to the surface they're driving on, not relative to absolute space. If you have two ships moving at different velocities relative to one another (or relative to absolute space), and there are cars driving inside the ships showing the same speedometer reading, the speedometer reading will represent each car's speed relative to the floor of the ship, so of course the speed of the cars is completely different in any frame where the speed of the ships is different (including absolute space if such a thing exists). And remember, the whole point of this synchronization exercise is to find a way to synchronize clocks that would work even if you were inside a windowless ship whose speed relative to anything else you don't know in advance (although you're free to try to measure your speed relative to absolute space or the aether or whatever using experiments you do inside the ship--relativity predicts this won't work, though).

 

[rqr]

[JesseM noted:]
"It's totally irrelevant whether they're self-propelled
--cars showing a given speedometer reading are driving
at that speed relative to the surface they're driving on,
not relative to absolute space."

If it were that easy, then we would have had
absolute synchronization a long time ago.
(But such cars cannot be used to absolutely
synchronize clocks, as is evidenced by the
fact that special relativity theory is still
in vogue.)

I see that we need to start with a much better
example, namely, my single-rod proposal.

Please tell us whether the following single-rod
proposal for absolutely synchronizing clocks
will work or not:

In any inertial coordinate system, align a rod
with the frame's x axis. While the rod is at rest
in this frame, cut it so that it fits precisely
between two arbitrary points on this x axis. Then
remove the rod, and place it at some other location
along the x axis. Finally, slide the rod inertially
toward the two points. The claim here is that since
the rod formerly fit between the points, it should
still fit, so its end points could be used to truly
or absolutely synchronize clocks at the points.

rqr

 

[JesseM]

I see that we need to start with a much better
example, namely, my single-rod proposal.

Please tell us whether the following single-rod
proposal for absolutely synchronizing clocks
will work or not:

In any inertial coordinate system, align a rod
with the frame's x axis. While the rod is at rest
in this frame, cut it so that it fits precisely
between two arbitrary points on this x axis. Then
remove the rod, and place it at some other location
along the x axis. Finally, slide the rod inertially
toward the two points. The claim here is that since
the rod formerly fit between the points, it should
still fit, so its end points could be used to truly
or absolutely synchronize clocks at the points.

rqr

But to "move" it and then let it come to rest relative to this frame, you have to accelerate it. Changing its velocity will change its length in any frame, including this one, because of Lorentz contraction. And if in this frame both ends of the rod experience an acceleration simultaneously so the rod un-contracts and both ends touch the two points simultaneously, then in other frames the two ends began accelerating at different times, and hence touched the two points at different times too.

 

[rqr]

2 JesseM:
I am not really worried about other frames' opinions or views.

All I am worried about here is whether or not the sliding rod
will absolutely synchronize clocks in the single given frame.

What do you say?

YES _______ or NO_______

Thanks!

(And please remember that the rod is not accelerating
during the critical stage of the experiment. As I said,
it is moving merely inertially.)

rqr

 

[paw]

I am not really worried about other frames' opinions or views.

You have to be. The rod in your scenario is moving at constant velocity wrt the two marks. That is by definition a different inertial frame of reference.

You can only claim it isn't in a different inertial frame if you abandon the idea of frames of reference entirely. If you do that you abandon science in general and physics specifically.

All I am worried about here is whether or not the sliding rod
will absolutely synchronize clocks in the single given frame.

What do you say?

YES _______ or NO_______

NO.

Let's try it a slightly different way. Alice makes two marks 1 meter apart to the highest precision we can imagine, that is 1 meter +/- 1 Planck length. Bob, who is traveling toward Alice at some speed v<c, builds a meter rod to the same precision, that is 1 meter +/- 1 Planck length.

This is the same scenario as you postulated above without any explicit acceleration. Do you agree?

Now can Alice and Bob synchronize clocks with this apparatus? No! Bobs rod is shorter than the tick marks according to Alice (Bob is moving wrt Alice) and the tick marks are shorter than the rod according to Bob (Alice is moving wrt Bob).

 

[JesseM]

2 JesseM:
I am not really worried about other frames' opinions or views.

All I am worried about here is whether or not the sliding rod
will absolutely synchronize clocks in the single given frame.

What do you say?

YES _______ or NO_______

Thanks!

What do you mean by "absolutely" synchronize? Does this mean something different than just synchronizing the clocks according to that frame's definition of simultaneity? If it's supposed to be frame-independent, then you do have to worry about what happens when you repeat this experiment in different frames--an absolute method should yield the same definition of simultaneity regardless of the rest frame of the clocks or the rod (that was my point earlier about needing an experiment different physicists could perform in windowless rooms that would yield the same definition of simultaneity regardless of the different rooms' velocity relative to one another).

Anyway, this experiment doesn't even seem well-defined enough to clearly say whether it'll yield the same definition of simultaneity as the Einstein synchronization convention would in the clocks' rest frame. It really depends critically on the final acceleration which brings the rod at rest relative to the clocks.

(And please remember that the rod is not accelerating
during the critical stage of the experiment. As I said,
it is moving merely inertially.)

You mean, it's moving inertially past the two clocks? In this case it would be Lorentz-contracted relative to them. Or do you mean that it's moving inertially after being accelerated so it's at rest relative to them? In this case the moment that each end of the rod comes to rest next to a clock will depend on how the rod is accelerated.

 

[rqr]

Jeese, Jesse, youse guys are making this much too
complicated! ;-)

The rod is merely given a wee little starting shove
at the start of its wee little journey toward the
clocks, and after this wee little acceleration
period, it continues to travel inertially forever
and ever, amen!

As the rod passes the clocks, I want to know if its
wee little end points (speaking theoretically, not
Planck-length-perfect reality) will or will not hit
and start the clocks absolutely simultaneously.

[JesseM wrote:]
"You mean, it's moving inertially past the two clocks? In this
case it would be Lorentz-contracted relative to them."

Yes, yes, I mean that it's moving inertially past the
two clocks. That's the ticket!

Now we're getting somewhere, but where I don't know! ;-)

But do we really, really, really have to worry about
the rod's Lorentz contraction **relative** to the
clocks?

We do if this is a physical or intrinsic contraction,
but we do *not* if it's only an apparent or observer-
dependent "contraction."

Let me put this in "slow-motion" mode for a moment:

The rod's end points R1 and R2 exist continuously.
Therefore, whenever the left-hand end point R1 is at
the matching left-hand clock C1, we know that the
right-hand end point R2 must be somewhere, and I
would guess that it's within a few light-years of C2,
at least. ;-)

In fact, we know that R2 must be either to the
right or left of C2 or dead on C2.

Now all we have to do is to figure out where
"your" observed Lorentz contraction places R2.

CHOICE A _____To the right of C2_____

CHOICE B _____To the left of C2_____

CHOICE C _________Dead on C2_________

Vote now or forever hold your peace!
(Careful, Pee-Wee Herman!)

rqr