The traveling twin starts and travels for 4 years at speed v = 0.866c
and then brakes, as seen in the animation
https://www.geogebra.org/m/jzc4amud
Calculate the Earth-spaceship distance, before and after braking (in
the spaceship reference).
Calculate how many turns the Earth has made around the sun, before and
after braking (in the spaceship reference).
The traveling twin starts and travels for 4 years at speed v = 0.866c
and then brakes, as seen in the animation
https://www.geogebra.org/m/jzc4amud
Calculate the Earth-spaceship distance, before and after braking (in
the spaceship reference).
Calculate how many turns the Earth has made around the sun, before and
after braking (in the spaceship reference).
Suppose the two twins have just been born when the traveling twin starts
his trip. So they are each zero years old then. If the traveling twin
(he) travels for 4 years of his time, he will be 4 yours old when he
stops. (His age when he stops is an EVENT that all observers must agree about, and so she also agrees that he is 4 years old when he stops. He
says he has traveled (0.866)(4) = 3.464 lightyears away from his twin
(her) then. She says he traveled 8 years of her time ... i.e., she says
she is 8 years old when he stops. She says he is (0.866)(8) = 6.928 lightyears away when he stops.
After he stops, she says that he remains 6.928 lightyears away from her
after that. And she says they age at the same rate after he stops. He
says that, during his essentially instantaneous stopping time, his age essentially doesn't change during his stopping. She agrees with that.
But he says that during his essentially instantaneous stopping, SHE essentially instantaneously gets older by 4 years ... i.e., he says that
she essentially instantaneously goes from being 4 years old to being 8
years old during the essentially instantaneous time in his life it takes
him to stop. And he also says that their distance apart essentially instantaneously increases from 3.464 lightyears to 6.928 lightyears
while he is doing his essentially instantaneous stopping.
On 3/14/22 1:08 PM, Luigi Fortunati wrote:
The traveling twin starts and travels for 4 years at speed v = 0.866c
and then brakes, as seen in the animation https://www.geogebra.org/m/jzc4amud
Calculate the Earth-spaceship distance, before and after braking (in
the spaceship reference).
Calculate how many turns the Earth has made around the sun, before and after braking (in the spaceship reference).
Suppose the two twins have just been born when the traveling twin starts
his trip. So they are each zero years old then. If the traveling twin
(he) travels for 4 years of his time, he will be 4 yours old when he
stops. (His age when he stops is an EVENT that all observers must agree about, and so she also agrees that he is 4 years old when he stops. He
says he has traveled (0.866)(4) = 3.464 lightyears away from his twin
(her) then. She says he traveled 8 years of her time ... i.e., she says
she is 8 years old when he stops. She says he is (0.866)(8) = 6.928 lightyears away when he stops.
After he stops, she says that he remains 6.928 lightyears away from her
after that. And she says they age at the same rate after he stops. He
says that, during his essentially instantaneous stopping time, his age essentially doesn't change during his stopping. She agrees with that.
But he says that during his essentially instantaneous stopping, SHE essentially instantaneously gets older by 4 years ... i.e., he says that
she essentially instantaneously goes from being 4 years old to being 8
years old during the essentially instantaneous time in his life it takes
him to stop. And he also says that their distance apart essentially instantaneously increases from 3.464 lightyears to 6.928 lightyears
while he is doing his essentially instantaneous stopping.
Suppose the two twins have just been born when the traveling twin starts
his trip. So they are each zero years old then. If the traveling twin
(he) travels for 4 years of his time, he will be 4 yours old when he
stops. (His age when he stops is an EVENT that all observers must agree about, and so she also agrees that he is 4 years old when he stops. He
says he has traveled (0.866)(4) = 3.464 lightyears away from his twin
(her) then. She says he traveled 8 years of her time ... i.e., she says
she is 8 years old when he stops. She says he is (0.866)(8) = 6.928 lightyears away when he stops.
After he stops, she says that he remains 6.928 lightyears away from her
after that. And she says they age at the same rate after he stops. He
says that, during his essentially instantaneous stopping time, his age essentially doesn't change during his stopping. She agrees with that.
But he says that during his essentially instantaneous stopping, SHE essentially instantaneously gets older by 4 years ... i.e., he says that
she essentially instantaneously goes from being 4 years old to being 8
years old during the essentially instantaneous time in his life it takes
him to stop.
I made a careless mistake in my previous post. Here is that post, down to where my mistake occurred:his essentially instantaneous stopping, not by 4 years as I stated in my previous post.
On 3/15/22 2:36 AM, Mike Fontenot wrote:
Suppose the two twins have just been born when the traveling twin starts
his trip. So they are each zero years old then. If the traveling twin
(he) travels for 4 years of his time, he will be 4 yours old when he
stops. (His age when he stops is an EVENT that all observers must agree
about, and so she also agrees that he is 4 years old when he stops. He
says he has traveled (0.866)(4) = 3.464 lightyears away from his twin
(her) then. She says he traveled 8 years of her time ... i.e., she says
she is 8 years old when he stops. She says he is (0.866)(8) = 6.928
lightyears away when he stops.
After he stops, she says that he remains 6.928 lightyears away from her
after that. And she says they age at the same rate after he stops. He
says that, during his essentially instantaneous stopping time, his age
essentially doesn't change during his stopping. She agrees with that.
The above is all correct. But here is the sentence where I made the careless error:
But he says that during his essentially instantaneous stopping, SHE
essentially instantaneously gets older by 4 years ... i.e., he says that
she essentially instantaneously goes from being 4 years old to being 8
years old during the essentially instantaneous time in his life it takes
him to stop.
According to him, her age right before he stops is 2 years old, not 4 years old as I said above. Immediately after he stops, they both agree about their respective ages. He says she is now 8 years old, so he says her age increases by 6 years during
I should also have pointed out that each of the twins, during his outbound trip, are entitled to use the famous time dilation equation for inertial observers: That equation says that any inertial observer will conclude that a person moving at speed "v"with respect to them is ageing at a rate gamma times slower than they are, where
gamma = 1 / sqrt { 1 / (1 - v * v) },he is 4 and she is 2. And immediately after he stops, they both agree that he is 4 and she is 8. So he says she essentially instantaneously gets 6 years older during his essentially instantaneous stopping.
where the asterisk indicates multiplication. For v = 0.866, gamma = 2.0. So on the outbound trip, each twin says the other twin is ageing half as fast as their own rate of ageing. So right before he stops, she says he is 4 and she is 8, but he says
Keep in mind that when the moving twin stops, both twins will agree
on how far apart they are. During the deceleration the moving twin
will observe the apparent expansion of the universe along the axis
of travel, and what while moving appeared to be 3.464 light years
will expand to 6.928 light years.
Something to keep in mind is that neither twin can see the other at
what each considers "now". They only see the other on their own
past light cone. So while the moving twin is stopping, he will NOT
see his twin back on earth suddenly aging. This is because what
he sees is not the instantaneous state of the earth, but an image
conveyed by light. Instead he will see her as she was about 6.928
years earlier. Thus what he sees is a much younger twin, only
about a year older than when he left earth. It is on the trip back
to earth that he sees her age rapidly as he passes the light
traveling outbound from earth.
The traveling twin starts and travels for 4 years at speed v = 0.866c
and then brakes, as seen in the animation
https://www.geogebra.org/m/jzc4amud
Calculate the Earth-spaceship distance, before and after braking (in
the spaceship reference).
Calculate how many turns the Earth has made around the sun, before and
after braking (in the spaceship reference).
That's all true. But I am not interested in what TV images he receives
from her ... those just tell him what she looked like in the past, and
how old she was in the past. Instead, I am interested in what he
DEDUCES about her CURRENT age at any given instant in his life, using
the laws of special relativity. I.e., I'm interested in his "NOW"
instant ... what does he say her age is "RIGHT NOW", at some instant in
his life. I'm purely interested in what he says about "simultaneity at
a distance".
This is why I ask: is it possible to calculate how many turns the
traveler twin will have * seen * make from the Earth around the Sun on
the spacecraft's telescope, after its 4-year journey, before starting to brake?
That's all true. But I am not interested in what TV images he receives
from her ... those just tell him what she looked like in the past, and
how old she was in the past. Instead, I am interested in what he
DEDUCES about her CURRENT age at any given instant in his life, using
the laws of special relativity. I.e., I'm interested in his "NOW"
instant ... what does he say her age is "RIGHT NOW", at some instant in
his life. I'm purely interested in what he says about "simultaneity at
a distance".
Simultaneity at a distance is not observable.
Simultaneity at a distance is not observable.
In our everyday experience
we actually experience the world on our past light cone and think of that
as "now". This a misconception.
I suggest that the only reality is on the
past light cone. That is something that all observers can agree on.
This is why I think it is a mistake in quantum mechanics to talk about the >instantaneous collapse of the wave function CAUSED BY a measurement
event. There cannot be a consistent causal explanation directly linking
two events that are outside the light cone.
Richard Livingston <richalivingston@gmail.com> writes:
Simultaneity at a distance is not observable.
In an inertial system: Place a detector D midway between A and B
(using a yardstick). I assume that A, B and D are at rest. Generate
two signals at A and B. If they arrive at D at the same time, they
were sent at A and B at the same time. This would be a kind of
observation, albeit delayed.
[...]
Observation implies a physical quantity is being observed. Simultaneity
at different spatial points is not any kind of physical quantity, it is
a CONVENTION based on the time coordinate of a particular inertial
frame
Richard Livingston <richali...@gmail.com> writes:
Simultaneity at a distance is not observable.In an inertial system: Place a detector D midway between A
and B (using a yardstick). I assume that A, B and D are at
rest. Generate two signals at A and B. If they arrive at D
at the same time, they were sent at A and B at the same time.
This would be a kind of observation, albeit delayed.
This is the highest degree of reality: Something is very
real when one can interact with it, i.e., observe it /and/
affect it. Causality implies:
Systems of the past only have a semi-reality:
You can sometimes observe them, but not affect them.
For example, the Boston Tea Party. Also, systems of
the past are only inferred from records, so it is never
completely sure whether they even existed at all.
The collapse of an imagined function can be imagined in an
inertial frame quite as "everywhere at the same time",
as long as no energy-impulse is transported with superluminal
speed by this collapse.
A major lesson of modern physics is to discuss only measurable
(observable) quantities
A major lesson of modern physics is to discuss only measurable
(observable) quantities [#]. Both "everyday lives" and "wavefunction collapse" violate that dictum (in very different ways).
[#] Interestingly, this applies to both QM and GR (for
very different reasons).
Tom Roberts
On 3/19/22 12:27 PM, Tom Roberts wrote:
Observation implies a physical quantity is being observed. Simultaneity
at different spatial points is not any kind of physical quantity, it is
a CONVENTION based on the time coordinate of a particular inertial
frame
Tom, what is your "take" on the use of an array of clocks, stationary in
some inertial frame, that have been synchronized using only the
assumption that the speed of light is equal to the universal constant
"c" in that frame. Each of those clocks is attended by a human "helper friend" (HF), who can observe his immediate local surroundings. Another particular observer (whom I'll refer to as "he"), also stationary in
that inertial frame, wants to know (when his watch shows time tau) the current reading on a particular distant clock which is NOT stationary
with respect to that array of clocks. It seems reasonable that he is entitled to say that the current reading on that distant clock is what
the HF, who happens to be colocated with that distant clock at the
instant when the HF's clock reads tau, directly observes it to be.
Doesn't that convey a sense of "meaningfulness", to the observers who
are stationary in that frame? I think Einstein thought it does.
On 3/20/22 4:44 AM, I (Mike Fontenot) wrote:
On 3/19/22 12:27 PM, Tom Roberts wrote:
Observation implies a physical quantity is being observed. Simultaneity
at different spatial points is not any kind of physical quantity, it is
a CONVENTION based on the time coordinate of a particular inertial
frame
Tom, what is your "take" on the use of an array of clocks, stationary in
some inertial frame, that have been synchronized using only the
assumption that the speed of light is equal to the universal constant
"c" in that frame. Each of those clocks is attended by a human "helper
friend" (HF), who can observe his immediate local surroundings. Another
particular observer (whom I'll refer to as "he"), also stationary in
that inertial frame, wants to know (when his watch shows time tau) the
current reading on a particular distant clock which is NOT stationary
with respect to that array of clocks. It seems reasonable that he is
entitled to say that the current reading on that distant clock is what
the HF, who happens to be colocated with that distant clock at the
instant when the HF's clock reads tau, directly observes it to be.
Doesn't that convey a sense of "meaningfulness", to the observers who
are stationary in that frame? I think Einstein thought it does.
Tom hasn't responded yet. Maybe he will shortly. But while waiting,
I'd like to add a bit to my above argument.
I think a sizeable number of physicists DO believe that simultaneity at
a distance is a meaningless concept, and I've even noticed a trend of
trying to de-emphasize talking about simultaneity-at-a-distance in introductory special relativity courses. But I think that is a big
mistake. It certainly wasn't Einstein's view, at least for inertial observers. (I've seen a quote from Einstein somewhere where he said he hardly recognizes his theory when he reads some modern descriptions of
it.)
My above question of Tom Roberts was prompted mostly by his use of the
word "Convention" in describing simultaneity at a distance for an
inertial observer. To me, the term "Convention" implies that there is
more than one possible answer to the question "How old is that distant
person (she), right now", when asked and answered by a particular
inertial observer. "Convention" implies that one can pick from among multiple alternatives, all equally good.
But I don't believe that is true, given my above description of how an
array of synchronized clocks (all permanently stationary with respect to
the given inertial observer) can be set up, creating a common "NOW"
instant for him and for all of the HF's ("helper friends") co-located
and co-stationary with the clocks. At any given instant "tau" in the
life of the given inertial observer, it's clear that there is just a
single answer to the question "How old is that particular distant person (she) right now (at the given time "tau" in the life of the inertial observer): it is what the particular HF (he) who happens to be
momentarily co-located with the distant person (she), says it is, at the instant when he is age "tau". The only way there could be any other allowable answer is if the synchronization of the clocks isn't valid,
and that is impossible if the velocity of light in that inertial
reference frame is equal to the universal constant "c".
I think a sizeable number of physicists DO believe that simultaneity at
a distance is a meaningless concept, and I've even noticed a trend of
trying to de-emphasize talking about simultaneity-at-a-distance in introductory special relativity courses. But I think that is a big
mistake. It certainly wasn't Einstein's view, at least for inertial observers. (I've seen a quote from Einstein somewhere where he said he
hardly recognizes his theory when he reads some modern descriptions of
it.)
My above question of Tom Roberts was prompted mostly by his use of the
word "Convention" in describing simultaneity at a distance for an
inertial observer. To me, the term "Convention" implies that there is
more than one possible answer to the question "How old is that distant
person (she), right now", when asked and answered by a particular
inertial observer. "Convention" implies that one can pick from among
multiple alternatives, all equally good.
But I don't believe that is true, given my above description of how an
array of synchronized clocks (all permanently stationary with respect to
the given inertial observer) can be set up, creating a common "NOW"
instant for him and for all of the HF's ("helper friends") co-located
and co-stationary with the clocks. At any given instant "tau" in the
life of the given inertial observer, it's clear that there is just a
single answer to the question "How old is that particular distant person (she) right now (at the given time "tau" in the life of the inertial observer): it is what the particular HF (he) who happens to be
momentarily co-located with the distant person (she), says it is, at the instant when he is age "tau". The only way there could be any other
allowable answer is if the synchronization of the clocks isn't valid,
and that is impossible if the velocity of light in that inertial
reference frame is equal to the universal constant "c".
What if the twins (or clocks) were quantum-entangled?
On Friday, March 25, 2022 at 5:57:18 AM UTC-5, Mike Fontenot wrote:
[...] At any given instant "tau" in the
life of the given inertial observer, it's clear that there is just a
single answer to the question "How old is that particular distant person
(she) right now (at the given time "tau" in the life of the inertial
observer): it is what the particular HF (he) who happens to be
momentarily co-located with the distant person (she), says it is, at the
instant when he is age "tau". The only way there could be any other
allowable answer is if the synchronization of the clocks isn't valid,
and that is impossible if the velocity of light in that inertial
reference frame is equal to the universal constant "c".
I think I mostly agree with you, but still think that the problem with
"now" at a distant location is that people take it as something
real and meaningful, and I think an argument can be made that it
is not very meaningful.
On 3/19/22 12:27 PM, Tom Roberts wrote:
Observation implies a physical quantity is being observed.
Simultaneity at different spatial points is not any kind of
physical quantity, it is a CONVENTION based on the time coordinate
of a particular inertial frame
Tom, what is your "take" on the use of an array of clocks,
stationary in some inertial frame, that have been synchronized using
only the assumption that the speed of light is equal to the universal constant "c" in that frame. Each of those clocks is attended by a
human "helper friend" (HF), who can observe his immediate local
surroundings. Another particular observer (whom I'll refer to as
"he"), also stationary in that inertial frame, wants to know (when
his watch shows time tau) the current reading on a particular
distant clock which is NOT stationary with respect to that array of
clocks. It seems reasonable that he is entitled to say that the
current reading on that distant clock is what the HF, who happens to
be colocated with that distant clock at the instant when the HF's
clock reads tau, directly observes it to be.
Doesn't that convey a sense of "meaningfulness", to the observers who
are stationary in that frame? I think Einstein thought it does.
On Saturday, March 19, 2022 at 1:27:38 PM UTC-5, Tom Roberts wrote:
A major lesson of modern physics is to discuss only measurable
(observable) quantities [#]. Both "everyday lives" and
"wavefunction collapse" violate that dictum (in very different
ways).
[#] Interestingly, this applies to both QM and GR (for very
different reasons).
Tom, I would be very interested in your expanding a bit on how this
all applies to GR. -Rich L.
Mod. note -- I too would be interested in what Tom says.
My take would be that in GR, there is no preferred coordinate system
and all physical quantities (= those that are measurable, at least in
a gedanken sense) should be independent of the coordinate system in
use.
Notably:Yes to all. The Moderator and I agree, except for details in wording.
* the coordinate "time" of an event, or the difference between the
coordinate times of two events) is merely a coordinate; it has no
inherent physical meaning and can be changed arbitrarily by changing
our coordinate system
* *proper* time along some (timelike) worldline is measurable (it's
what an (ideal) clock moving along that worldline would measure),
can be said to have an inherent physical meaning (as the observable
result of that measurement), and *doesn't* change when we change
coordinates
* similarly, the coordinate position of an object, or the (coordinate)
distance between two objects, is also a coordinate, has no inherent
physical meaning, and can be changed arbitrarily by changing our
coordinate system
* the *proper* distance along a given path is measurable (at least in
a gedanken sense: one can imagine laying down a sequence of standard
rulers end-to-end along the path), and doesn't change when we change
coordinates;
* coordinate singularities (and the set of events where they occur)
have no inherent physical meaning, and a change in coordinates can
change the set of events where there is a coordinate singularity;
only singularities in observable quantities like curvature invariants,
proper times/distances, etc, are physically meaningful
On 3/20/22 5:44 AM, Mike Fontenot wrote:
Doesn't that convey a sense of "meaningfulness", to the observers who
are stationary in that frame? I think Einstein thought it does.
You simply implemented the CONVENTION of Einstein synchronization. If
you synchronized the clocks differently you would get a different
result.
But what about a non-inertial observer? In particular, what about a
given observer who is undergoing a constant acceleration? What does HE
say the current age of a distant person is? It turns out to be possible
for such an accelerating observer to rely on an array of clocks and associated "helper friends" (HF's) to give him the answer. Unlike in
the inertial case, those clocks DON'T run at the same rate. But the
ratio of the rates of those clocks can be CALCULATED by the given
observer. And if he (and the HF's) are initially stationary and unaccelerated, they can start out with synchronized clocks (and ages).
Then, if they all fire their identical rockets at the same instant, they
can each CALCULATE the current reading of each of the other clocks, at
each instant in their lives. The calculations of each of the HF's all
agree. So, at any instant in their lives during that acceleration, they
each share the same "NOW" instant with all of the other HF's. That
means that the given observer (he), at any instant "tau" in his life,
can obtain the current age "T" of some distant person (her), by asking
the HF, who happens to be momentarily co-located with her at that NOW instant, what her age is then.
So there you have it. That's the calculation that defines "NOW" for the
AO and all of the HF's, and makes simultaneity at a distance a
meaningful concept for them. Simultaneity at a distance is not a choice.
On 4/2/22 12:22 AM, Tom Roberts wrote:
You simply implemented the CONVENTION of Einstein synchronization.
If you synchronized the clocks differently you would get a
different result.
If you synchronized those clocks differently, you would be ignoring
the fundamental assumption that special relativity is based on: that
the speed of light in any inertial frame is always equal to the
universal constant "c".
On Saturday, March 19, 2022 at 1:27:38 PM UTC-5, Tom Roberts wrote:
A major lesson of modern physics is to discuss only measurable
(observable) quantities [#]. Both "everyday lives" and
"wavefunction collapse" violate that dictum (in very different
ways).
[#] Interestingly, this applies to both QM and GR (for very
different reasons).
Tom, I would be very interested in your expanding a bit on how this
all applies to GR. -Rich L.
Mod. note -- I too would be interested in what Tom says.
My take would be that in GR, there is no preferred coordinate system
and all physical quantities (= those that are measurable, at least in
a gedanken sense) should be independent of the coordinate system in
use.
Notably:Yes to all. The Moderator and I agree, except for details in wording.
* the coordinate "time" of an event, or the difference between the
coordinate times of two events) is merely a coordinate; it has no
inherent physical meaning and can be changed arbitrarily by changing
our coordinate system
* *proper* time along some (timelike) worldline is measurable (it's
what an (ideal) clock moving along that worldline would measure),
can be said to have an inherent physical meaning (as the observable
result of that measurement), and *doesn't* change when we change
coordinates
* similarly, the coordinate position of an object, or the (coordinate)
distance between two objects, is also a coordinate, has no inherent
physical meaning, and can be changed arbitrarily by changing our
coordinate system
* the *proper* distance along a given path is measurable (at least in
a gedanken sense: one can imagine laying down a sequence of standard
rulers end-to-end along the path), and doesn't change when we change
coordinates;
* coordinate singularities (and the set of events where they occur)
have no inherent physical meaning, and a change in coordinates can
change the set of events where there is a coordinate singularity;
only singularities in observable quantities like curvature invariants,
proper times/distances, etc, are physically meaningful
On 4/2/22 11:36 AM, (I) Mike Fontenot wrote:
So there you have it. That's the calculation that defines "NOW"
for the AO and all of the HF's, and makes simultaneity at a
distance a meaningful concept for them. Simultaneity at a
distance is not a choice.
But what does the above say about the current age of the home twin
(she), according to the traveling twin (he), for each instant in his
life on his trip? The answer is that the above equations give the
same results as the Co-Moving-Inertial-Frames (CMIF) simultaneity
method. That is very fortuitous, because the CMIF method is
relatively easy to use. The value of the array of clocks discussed
above (which establish a "NOW" moment for the accelerating observer
that extends throughout all space) is that they GUARANTEE that the
CMIF results are fully meaningful to the traveler, and that the CMIF
method is the ONLY correct simultaneity method for him.
He has no other choice.
So, for the idealization of an essentially instantaneous velocity
change, the change of the reading on the leading clock is INFINITE
during the infinitesimal change of the rear clock. That means that,
when the traveling twin instantaneously changes his speed from zero to
0.866 (toward the home twin), the exponential version of the R equation
says that the home twin's age becomes infinite. But we know that's not
true, because the home twin is entitled to use the time dilation
equation for a perpetually-inertial observer, and that equation tells
her that for a speed of 0.866 ls/s, the traveler's age is always
increasing half as fast as her age is increasing. So when they are
reunited, she is twice as old he is, NOT infinitely older than he is, as
the exponential form of the gravitational time dilation equation claims.
The time dilation equation for a perpetually-inertial observer is the
gold standard in special relativity. Therefore the exponential form of
the gravitational time dilation equation is incorrect.
The correct gravitational time dilation equation turns out to
approximately agree with what Einstein used in his "small acceleration" analysis, for very small accelerations, but differs substantially for
larger accelerations. And the correct gravitational time dilation
equation agrees with the ages of the twins when they are reunited. It
also exactly agrees with the CMIF simultaneity method for the traveler's conclusions about the sudden increase in the home twin's age when the traveler suddenly changes his velocity. The CMIF method provides a
practical way to compute the change in the home twin's age when the
traveler instantaneously changes his velocity. But it is the new gravitational time dilation equation, and its array of clocks with a
common "NOW" moment, that guarantees that the CMIF result is fully
meaningful to the traveling twin, and that the CMIF method is the ONLY correct simultaneity method for the traveling twin.
Your calculations are all related to the Ehrenfest Paradox and Rindler Coordinates.I looked up Ehrenfest Paradox on Wiki, and it says it's about a rotating
On 4/6/22 12:22 PM, Richard Livingston wrote:
Your calculations are all related to the Ehrenfest Paradox and Rindler Coordinates.I looked up Ehrenfest Paradox on Wiki, and it says it's about a rotating disk. The work I've been doing has nothing to do with a rotating disk.
What myself and others have been trying to get you (Mike Fontenot)
to understand is that the acceleration of the observer does not actually change anything about the distant twin.
What is really new, though, in my latest results, is the fact that the accelerating observer can assemble an array of clocks (and attending
"helper friends" (HF's)), which give him a "NOW" that extends throughout
all space (analogous to what Einstein did for inertial observers). And
THAT guarantees that the accelerating observer's conclusions about the
home twin's age are fully MEANINGFUL to him. His conclusions agree with
the CMIF simultaneity method, which means that the CMIF simultaneity
method is the only correct simultaneity method.
[[Mod. note -- I think you're mistaken in a couple of places [...]:
On 4/8/22 1:05 AM, Mike Fontenot wrote:
What is really new, though, in my latest results, is the fact that the accelerating observer can assemble an array of clocks (and attending "helper friends" (HF's)), which give him a "NOW" that extends throughout all space (analogous to what Einstein did for inertial observers). And
THAT guarantees that the accelerating observer's conclusions about the
home twin's age are fully MEANINGFUL to him. His conclusions agree with
the CMIF simultaneity method, which means that the CMIF simultaneity
method is the only correct simultaneity method.
[[Mod. note -- I think you're mistaken in a couple of places [...]:
I WOULD like to hear your "take" on my arguments here:
I and you synchronize our clocks, and as long as thethat's only true if we follow the same worldline, i.e., if our positions
clocks keep working, forever and ever I and you will be reading the
same exact time at at the same exact moment
What do you mean by the word "meaningful"?
So basically you're saying that what you observe is
meaningful to you, regardless of whether anything else in the universe
is affected.
if I'm mutually stationary wrt the array of clocks that I have
previously described, which provides a "NOW" for me extending
throughout space, [...]
If I am an accelerating observer, and if I OBSERVE a TV image of the
distant person, that tells me what that distant person looked like a
long time ago. That's not meaningful to me, because I don't know how to determine how much she aged while the message was in transit.
But if I'm mutually stationary wrt the array of clocks that I have
previously described, which provides a "NOW" for me extending throughout space, that DOES give me a meaningful answer to the question of how old
she currently is. And by "meaningful", I mean that I REALLY believe
that she is currently that age. The only way I can be wrong about her current age is if my equation for the rate ratio of the two clocks is
wrong. I'm confident that it is correct. I think it IS experimentally testable.
If you are an astronaut in a spaceship that can travel at an appreciable fraction of c, and which you maneuver, then such an array of clocks is impossible -- each such clock must vary its acceleration in concert with yours [...]
If I am an accelerating observer, and if I OBSERVE a TV > image ofthe distant person, that tells me what that distant > person looked like
But if I'm mutually stationary wrt the array of clocks that I > havepreviously described, which provides a "NOW" for >me extending
she currently is. And by "meaningful", I mean that I >REALLY believethat she is currently that age. The only >way I can be wrong about her
On 4/11/22 1:19 PM, Tom Roberts wrote:
If you are an astronaut in a spaceship that can travel at an
appreciable fraction of c, and which you maneuver, then such an
array of clocks is impossible -- each such clock must vary its
acceleration in concert with yours [...]
No, that's not correct.
According to the accelerating observer (the AO), whose conclusions
we seek, he and each of his "helper friends" (HF's) undergo EXACTLY
the same (constant) acceleration, as recorded on their
accelerometers.
This is clear by looking at the equivalent scenario in the case of a
constant gravitational field with no accelerations (via the
equivalence principle) ... all of those people are motionless,
unaccelerated, and mutually stationary. And according to them, the
distance between each of them is also constant.
In the acceleration scenario (in the infinite flat spacetime of
special relativity), perpetually-inertial observers, who are
initially stationary with respect to the AO and the HF's, WILL
conclude that the accelerations of the AO and the various HF's, and
their distances apart, DO vary with time.
But it is not their conclusions that I am interested in.
On Saturday, 9 April 2022 at 04:03:57 UTC+2, Mike Fontenot wrote:
On 4/8/22 1:05 AM, Mike Fontenot wrote:
What is really new, though, in my latest results, is the fact that the accelerating observer can assemble an array of clocks (and attending "helper friends" (HF's)), which give him a "NOW" that extends throughout all space (analogous to what Einstein did for inertial observers). And THAT guarantees that the accelerating observer's conclusions about the home twin's age are fully MEANINGFUL to him. His conclusions agree with the CMIF simultaneity method, which means that the CMIF simultaneity method is the only correct simultaneity method.
[[Mod. note -- I think you're mistaken in a couple of places [...]:
I WOULD like to hear your "take" on my arguments here:(IMO) You are perfectly right: relativity as it is usually presented
and interpreted is simply inconsistent and arbitrary nonsense unless
one does fix the notion of *proper time* and what that even means.
Indeed yes, if I and you synchronize our clocks, and as long as the
clocks keep working, forever and ever I and you will be reading the
same exact time at at the same exact moment, aka we age the same
just like clocks tick the same (amd I think this is already some
postulate, and if not it should be). The fact that we on the other
hand move in space-time entails we are not anymore on the same plane
of simultaneity, it does not and cannot change the synchronization
of our clocks any more than it does in Galilean physics, just we
here drift in space-time instead of just space. Proper time is
just not coordinate time which has rather to do with coordinate
systems. And if we drop that postulate I am saying, physics indeed
becomes "disconnected" and plain arbitrary...
Please look at this diagram to begin with: isn't there already, in it's elementarity indeed, the unescapable answer to all above questions?
<https://jp-diegidio.github.io/STUDY.Physics.SpecialRelativity/InertialFrames/App/index.html>
[[Mod. note -- When you write
I and you synchronize our clocks, and as long as thethat's only true if we follow the same worldline, i.e., if our positions
clocks keep working, forever and ever I and you will be reading the
same exact time at at the same exact moment
are the same at all times.
If our positions differ then in general we'll
see different clock readings when we get back together again
experimentally tested by (among others) the Hafele-Keating experiment
(1972)
https://paulba.no/paper/Hafele_Keating.pdf
...
But at some instant (say, t = 0), there suddenly appears a constant and uniform gravitational field, of strength "g", directed downwards, and
acting over the entire length of the building. Each person suddenly
feels exactly the same force per unit mass, trying to pull them
downwards against the floor. (But they don't move, because they were
already tethered in that position). They could be constantly standing
on a bathroom scale, displaying their weight.
Tom, you've misunderstood what I'm doing.
[... completely new scenario involving clocks at different floors of
a high-rise building]
Bottom line: the POE applies ONLY in regions of spacetime that are small enough that any curvature is negligible (compared to measurement
accuracies). For the case you have in mind, with helper friends
("people") near a distant friend while the accelerated observer ("AO")
roams the universe, those people span an enormous spatial region, over a
very long time.
On 4/16/22 12:57 AM, Tom Roberts wrote:
Bottom line: the POE applies ONLY in regions of spacetime that are
small enough that any curvature is negligible (compared to
measurement accuracies). For the case you have in mind, with
helper friends ("people") near a distant friend while the
accelerated observer ("AO") roams the universe, those people span
an enormous spatial region, over a very long time.
The theory of special relativity places no limits AT ALL on the
extent of spacetime. THAT is the domain of my scenario with
acceleration.
Your argument is invalid because
the physical situations aren't actually equivalent -- the region
involved is too large for the Principle of Equivalence to apply
On 4/18/22 9:46 AM, Tom Roberts wrote:
Your argument is invalid because
the physical situations aren't actually equivalent -- the region
involved is too large for the Principle of Equivalence to apply
[[Mod. note -- The EP applies if and only if we neglect tidal effects,
i.e., if tidal effects are "small". But the size of tidal effects grows
with the distance, so saying that tidal effects should be "small" (so
that we can apply the EP) is essentially saying that the size of our
region should be "small". So, effectively, the EP only applies in "small" regions, where the precise definition of "small" depends on the curvature
of spacetime and your accuracy threshold for how small tidal effects need
to be before it's ok to neglect them.
The equivalence principle has no restrictions on the size of the
region in which it is valid.
There are NO "tidal effects" in my gravitational scenario (nor in my equivalent special relativity scenario, of course).
But a calculation shows that in SR, helper friends (HFs) with proper accelerations equal to that of the accelerated observer (AO), do NOT
remain at constant proper distance from the AO, contrary to your claim.
Look up Bell's spaceship paradox for an example calculation:
https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox
On 4/20/22 11:57 AM, Tom Roberts wrote:
But a calculation shows that in SR, helper friends (HFs) with
proper accelerations equal to that of the accelerated observer
(AO), do NOT remain at constant proper distance from the AO,
contrary to your claim. Look up Bell's spaceship paradox for an
example calculation:
https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox
I looked at that wiki page, [...] So that is a DIFFERENT scenario
than the one I have described.
In my scenario, the people who are accelerating conclude that their accelerations are exactly equal, and that their separations are
exactly equal.
On 4/20/22 11:57 AM, Tom Roberts wrote:
I, Mike Fontenot wrote:
But a calculation shows that in SR, helper friends (HFs) with proper
accelerations equal to that of the accelerated observer (AO), do NOT
remain at constant proper distance from the AO, contrary to your claim.
Look up Bell's spaceship paradox for an example calculation:
https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox
I looked at that wiki page, and here's what they say:
"A delicate thread hangs between two spaceships. They start accelerating simultaneously and equally as measured in the inertial frame S, thus
having the same velocity at all times as viewed from S."
So in the above scenario, according to the inertial frame "S", the two spaceships accelerate equally (and thus remain separated by a fixed distance). But in that scenario, the people in the spaceships would NOT agree that they were accelerating at the same rate, and they would NOT
agree that their separation was constant. So that is a DIFFERENT
scenario than the one I have described.
In my scenario, the people who are accelerating conclude that their accelerations are exactly equal, and that their separations are exactly equal. The inertial observers there disagree.
On 4/21/22 12:21 AM, Mike Fontenot wrote:
On 4/20/22 11:57 AM, Tom Roberts wrote:
But a calculation shows that in SR, helper friends (HFs) with
proper accelerations equal to that of the accelerated observer
(AO), do NOT remain at constant proper distance from the AO,
contrary to your claim.
In Tom Roberts' scenario (which is the "Bell Paradox" scenario), the perpetually-inertial observers correctly conclude that, according to
their inertial frame, the accelerating people are all accelerating at
the same constant rate (and therefore that their separations are all
equal and constant).
The accelerating people do NOT agree with them.
The perpetually-inertial observers are certainly entitled to set up
that scenario, but that is a scenario that I have NO interest in at
all.
The scenario that I am interested in, is the scenario where it is
the accelerated people who correctly conclude that their
accelerations are all equal, and that their separations are all
constant.
In that scenario, perpetually-inertial observers do NOT agree with
them.
[... further discussion based on the above error]
[...]
In a SINGLE SCENARIO:
(1): YOU (Tom Roberts) contend that the accelerating person (the AO) concludes that
the separation between himself and his helper friend ("HF") is CONSTANT.
(2): YOU (Tom Roberts) contend that the perpetually-inertial observer ALSO concludes
that the separation between the AO and the HF is CONSTANT.
The special theory of relativity does NOT allow item (1) and item (2) to
BOTH be true, in a SINGLE SCENARIO. In special relativity, a perpetually-inertial observer can NEVER agree with an accelerating
observer for longer than a single instant.
Michael Leon Fontenot
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