My animation
https://www.geogebra.org/m/rfa2m4ys
correctly represents the relativistic contraction of lengths?
My animation
https://www.geogebra.org/m/rfa2m4ys
correctly represents the relativistic contraction of lengths?
My animation
https://www.geogebra.org/m/rfa2m4ys
correctly represents the relativistic contraction of lengths?
Sorry, no. It may correctly show the object C closer from the point
of view of B (I'm not going to try to check your math), but the object
would also be foreshortened by the same amount. That is, the
object would no longer appear as a circle but as an ellipse.
The tangent point, where the dotted lines are tangent to the circle,
would always be the same point on the object C, not shifted
towards the sub-observer point (where the dashed line enters
the circle C) as your animation shows.
Rich L.
Julio Di Egidio il 22/05/2023 09:07:46 ha scritto:
On Sunday, 21 May 2023 at 12:16:07 UTC+2, Luigi Fortunati wrote:
My animation
https://www.geogebra.org/m/rfa2m4ys
correctly represents the relativistic contraction of lengths?
Where are your *formulas*, the ones you use to build the graph?!
In my animation
<https://www.geogebra.org/m/rfa2m4ys>
I added the formulas I used (Beta e Gamma).
Distance is contracted in proportion to the gamma factor.
In my animation
<https://www.geogebra.org/m/rfa2m4ys>
I added the formulas I used (Beta e Gamma).
Distance is contracted in proportion to the gamma factor.
For constant (relative) motion, lengths only contract along
the direction of motion. That said, computing the distance
to C is easy, but each and every distance transforms in the
same way, so you don't just get semi-circles, that should be
an ellipse... Indeed, here is what I meant by "formulas": <https://www.desmos.com/calculator/e20mfh6ln0>
(I am not an expert: I hope I have not made any mistakes.)
But my objection to you is one of method and understanding
what is what: a simulation requires a (mathematical) model!
JulioLuigi
<https://www.geogebra.org/m/dzuyjaz6>
After this last correction of mine, is my animation still missing
something to conform to the "mathematical model" you are talking
about?
<https://www.geogebra.org/m/dzuyjaz6>
After this last correction of mine, is my animation still missing
something to conform to the "mathematical model" you are talking
about?
A meaningless statement, as already noted: I am talking about
"*your* *modelling* of the problem at hand", and the need thereof.
That said, yes, by "eye inspection", you still get the tangents wrong.
JulioLuigi
Julio Di Egidio il 23/05/2023 08:30:16 ha scritto:
In my animation
<https://www.geogebra.org/m/rfa2m4ys>
I added the formulas I used (Beta e Gamma).
Distance is contracted in proportion to the gamma factor.
For constant (relative) motion, lengths only contract along
the direction of motion. That said, computing the distance
to C is easy, but each and every distance transforms in the
same way, so you don't just get semi-circles, that should be
an ellipse... Indeed, here is what I meant by "formulas":
<https://www.desmos.com/calculator/e20mfh6ln0>
(I am not an expert: I hope I have not made any mistakes.)
You made no mistakes and your simulation is correct.
Thanks for the suggestion.
I corrected my animation which is now this: https://www.geogebra.org/m/dzuyjaz6
But my objection to you is one of method and understanding
what is what: a simulation requires a (mathematical) model!
After this last correction of mine, is my animation still missing
something to conform to the "mathematical model" you are talking about?
On Wednesday, 24 May 2023 at 19:33:38 UTC+2, Luigi Fortunati wrote:
<https://www.geogebra.org/m/dzuyjaz6>
After this last correction of mine, is my animation still missing
something to conform to the "mathematical model" you are talking
about?
A meaningless statement, as already noted: I am talking about
"*your* *modelling* of the problem at hand", and the need thereof.
That said, yes, by "eye inspection", you still get the tangents wrong. Indeed, a "model" concretely is a collection of "specific formulas",
ideally together with proofs of properties of those formulas/of that
model, that ensure that the model is *correct* re the underlying
(physical, in this case) theory in question: e.g. as to how to compute
the tangents and points of tangency, as well as prove (with some
mathematical derivation) that "[t]he tangent point[s], where the dotted
lines are tangent to the circle, would always be the same point[s] on the object C", as Richard Livingston has put it upthread (slightly adapted).
I corrected my animation which is now this:
https://www.geogebra.org/m/dzuyjaz6
Your simulation may be more or less correct, but it doesn't help much in one's understanding it correctly, it even may induce erroneous
understanding.
First, it should be made clear in which direction the moving observer is supposed to move. My first impression was that he should move vertically which didn't make sense.
Furthermore, it doesn't help to superpose both 'circles' in a same
graph, which suggests a same reference frame, where in fact different reference frames are superposed. Now it gives the impression that "there
are two circles in space", one for each observer.
The fact is that there is only one object, but that both observers "fill
in" the space towards it, and the time values, differently! In order to respect the singleness of the object, your method is not a very proper
one. There are better alternatives. One is, to make two graphs, each
with its reference frame. Another one, to display only one object, say
in the rest system, and superpose the different reference frame of the
moving observer upon that, showing the length contraction, and possibly,
time dilation effects.
Lastly, this is not what the observers are going to *see*! Einstein's
Lorentz equations don't describe objects *as seen*, they describe
*measured*, backcalculated, positions of simultaneity. What the
observers are going to see, is what the light photons are telling them,
as they arrive at each observer, come from the different parts of the
distant object. In other words, they include Doppler distortions!
Julio Di Egidio il 23/05/2023 08:30:16 ha scritto:It is not showing the true 'embedding' of both 'circles' in spacetime,
In my animation
<https://www.geogebra.org/m/rfa2m4ys>
I added the formulas I used (Beta e Gamma).
Distance is contracted in proportion to the gamma factor.
For constant (relative) motion, lengths only contract along
the direction of motion. That said, computing the distance
to C is easy, but each and every distance transforms in the
same way, so you don't just get semi-circles, that should be
an ellipse... Indeed, here is what I meant by "formulas":
<https://www.desmos.com/calculator/e20mfh6ln0>
(I am not an expert: I hope I have not made any mistakes.)
You made no mistakes and your simulation is correct.
Thanks for the suggestion.
I corrected my animation which is now this: https://www.geogebra.org/m/dzuyjaz6
But my objection to you is one of method and understanding
what is what: a simulation requires a (mathematical) model!
After this last correction of mine, is my animation still missing
something to conform to the "mathematical model" you are talking about?
wugi il 29/05/2023 22:36:39 ha scritto:
I corrected my animation which is now this:
https://www.geogebra.org/m/dzuyjaz6
Your simulation may be more or less correct, but it doesn't help much in
one's understanding it correctly, it even may induce erroneous
understanding.
First, it should be made clear in which direction the moving observer is
supposed to move. My first impression was that he should move vertically
which didn't make sense.
In my simulation:
- observer B moves (instantaneously) to the right, i.e. towards body C
- observer A is stationary with respect to body C
- Observers A and B, at time t=0 of both, share the same space and the same time
- The time of C in the reference of A is different from the time of C in the reference of B.
Furthermore, it doesn't help to superpose both 'circles' in a same
graph, which suggests a same reference frame, where in fact different
reference frames are superposed. Now it gives the impression that "there
are two circles in space", one for each observer.
The fact is that there is only one object, but that both observers "fill
in" the space towards it, and the time values, differently! In order to
respect the singleness of the object, your method is not a very proper
one. There are better alternatives. One is, to make two graphs, each
with its reference frame. Another one, to display only one object, say
in the rest system, and superpose the different reference frame of the
moving observer upon that, showing the length contraction, and possibly,
time dilation effects.
Lastly, this is not what the observers are going to *see*! Einstein's
Lorentz equations don't describe objects *as seen*, they describe
*measured*, backcalculated, positions of simultaneity. What the
observers are going to see, is what the light photons are telling them,
as they arrive at each observer, come from the different parts of the
distant object. In other words, they include Doppler distortions!
Ok, let's talk about what happens when photons of light arrive on the photographic film (the observer) and form the image.
Are Einstein's Lorentz equations able to predict whether the body C will appear perfectly spherical or whether it will be squashed in the
direction of motion?
[[Mod. note -- Yes.
As wugi noted, (1) and (2) below are very different questions, with
very different answers:
(1) What are the coordinate positions of the objects measured (i.e.,
"backcalculated", as wugi quite correctly terms it) in different
(inertial) reference frames, as determined by the Lorenz transformation? (2) What image(s) would taken by a (ideal) camera located at a certain
point given (1) together with differential light-travel-time effects
(i.e., the Lampa-Penrose-Terrell effect, often just called the Terrell
effect or Terrell rotation)?
(1) is what's usually meant when we ask what an observer "measures" in special relativity. (2) is what you (Luigi) have now asked about.
See
https://en.wikipedia.org/wiki/Terrell_rotation
for a nice introduction to (2). Reference 4 in that Wikipedia article (written by Victor Weisskopf!) is a very clear exposition of the effect, explicitly working out the Terrell rotation for a moving cube and then generalizing it to an arbitrary-shaped body. The original 1960 paper is (still) behind a paywall :(, but as of a few minutes ago google scholar
finds a free copy.
-- jt]]
Initially I was asking about the contraction of the distances betweenPerhaps, but again (and again) your picture is not a complete one, in
the observers and body C, then the discussion shifted to the
contraction of body C.
I return to the initial question with my simulation https://www.geogebra.org/m/ujwjmgt8
Is it correct to say that for the alien flying disk the Earth-Sun
distance is 4.15 light-minutes?
Initially I was asking about the contraction of the distances betweenPerhaps, but again (and again) your picture is not a complete one, in
the observers and body C, then the discussion shifted to the
contraction of body C.
I return to the initial question with my simulation
https://www.geogebra.org/m/ujwjmgt8
Is it correct to say that for the alien flying disk the Earth-Sun
distance is 4.15 light-minutes?
that the Sun's image is not representative for both reference systems.
Look at my own desmos file: both observers, Earth and alien, are "at the
same event" in O.
But to Earth, the simultaneous position of the Sun is determined by
events AB. To the alien, it is determined by other (later ones, in
Earth's system) events A'B'.
Your single picture of the Sun has to represent these two
non-simultaneous event cases.
Also, while Earth's x-axis can be laid out as such in your picture,
alien's x'-axis must be understood as covering events that are non-simultaneous in Earth's system.
I return to the initial question with my simulation...
https://www.geogebra.org/m/ujwjmgt8
[[Mod. note -- The complications are inherent to the physical situation.
The phrase "at the moment in which it [the spaceship] passes close to
the Earth" specifies an event, and (if we treat the Earth as a point,
and idealise "close to the Earth" as passing through the Earth-point)
all observers can agree on this event.
But simultaneity is only local in special relativity, not global.
That is, different observers *disagree* about which event on the Sun's worldline is at the same time as the spaceship-passing-through-the-Earth-point event. To put it another way, if we imagine an ideal clock at (and moving with) the Sun, then different observers will compute different answers to the question
At the time when the spacecraft passes through the
Earth-point, what is the Sun-point's clock reading?
And this is the other question: how do moving spherical bodies appeares?,
in monitors and photographs?
In my animation
https://www.geogebra.org/m/kh38nfpd
where there is the body C in motion and the body D stationary in the reference of the monitor, I tried to give an answer.
Is it true that on the monitor (and in the photos) body D appears
spherical and body C appears squashed in the direction of motion?
[[Mod. note -- I can't tell from your your wording whether you are
asking about
(1) What are the coordinate positions of the objects measured (i.e.,
"backcalculated", as wugi quite correctly termed it) by special-relativity observers in different (inertial) reference fram=
or (2) What image(s) would taken by (ideal) cameras located at some positions,
[[Mod. note -- I'm sorry, I still don't know what you're asking. That
is, I don't know if your "monitor" is supposed to show (1) or (2).
Your animation has the monitor showing C squeezed in the direction of
motion, which would be correct for (1).
But in your message you refer to a "camera", which makes me suspect you
are asking about (2), in which case the monitor (showing the image formed
by an ideal camera placed at position B) will show C as a sphere, rotated
in a somewhat unobvious (that's why the effect is often called Terrell *rotation*). See
https://en.wikipedia.org/wiki/Terrell_rotation
for an explanation.
-- jt]]
So I repeat the question rigorously and clearly: how does the (moving)
body C appear on B's monitor, does it appear squashed or not squashed?
[[Mod. note -- I'm sorry, I still don't know what you're asking. That
is, I don't know if your "monitor" is supposed to show (1) or (2).
Your animation has the monitor showing C squeezed in the direction of motion, which would be correct for (1).
But in your message you refer to a "camera", which makes me suspect youHis confusion remains...
are asking about (2), in which case the monitor (showing the image formed
by an ideal camera placed at position B) will show C as a sphere, rotated
in a somewhat unobvious (that's why the effect is often called Terrell *rotation*). See
https://en.wikipedia.org/wiki/Terrell_rotation
for an explanation.
-- jt]]
...
FWIW, Luigi, your animation is about Lorentz contraction, not about what cameras will record.
If you want a related example (I'm not going to redo your simulation),
look again at my picture of watching the approach, passing by, and regression, of a squadron of squares:
https://wugi.be/paratwin.htm =>
https://wugi.be/MySRT/Squad.gif
The squares are Lorentz contracted (see "actual position" dots at the
right).
They are *seen* as quadrangles, ie distorted rectangles.
At approach there is blueshift, at regression redshift (my colors are inverted, for a white background;).
At approach the speed seen is greater than the motion velocity v (it
becomes infinite for v=c), at regression it is less than v (it becomes
c/2 for v=c).
At approach there is a seen length expansion(! it becomes infinite for
v=c), at regression an extra length contraction(! it becomes L/2gamma
for v=c IIRC).
Now if you want to visualise spheres, or circles, fill in any of the quadrangles with a corresponding ellipse-like figure, that's how the distorted circles are going to be seen. If you want a symmetrical
circle, take 2*2 adjoining squares, 2 along either side of the axis of symmetry through the observer (the small black circle).
--
guido wugi
You want to talk about times and not about spaces.jt]]
Okay.
In the position of my drawing, will the spacecraft arrive at the Sun=20
after 9.58 minutes of *its* time (8.3/0.866) or after 4.79 minutes=20 (4.15/0.866)?
I ask about the time of the spaceship, other times are of no interest.
[[Mod. note -- If I'm understanding things correctly, 4.79 minutes. -- =
In the position of my drawing, will the spacecraft arrive at the Sun=20jt]]
after 9.58 minutes of *its* time (8.3/0.866) or after 4.79 minutes=20
(4.15/0.866)?
I ask about the time of the spaceship, other times are of no interest.
[[Mod. note -- If I'm understanding things correctly, 4.79 minutes. -- =
Exact.
If the spacecraft (which is next to Earth) travels at a speed of 0.866c
and takes 4.79 minutes to reach the Sun, then the spacecraft's distance
from the Sun is d=v*t=0.866*4.79=4.15 light-minutes, half the distance
to Earth-Sun (8.3 minutes-light).
Here's how you can *see* (with the eyes, with the camera or with the
monitor) the contraction of distances: observing the size of the image
of the Sun, as in my animation
https://www.geogebra.org/m/cux34wvb
where the ray of the Sun on the spaceship's monitor (4.15 light-minutes
away) is twice as large as it appears on the Earth's monitor (8.3 light-minutes away).
From my calculations, these light rays that arrive at the spaceshiphave traveled for an enormously longer time than the 8.3 minutes of the rays that arrive on Earth: they arrive after almost 31 minutes!
FWIW, Luigi, your animation is about Lorentz contraction, not about what cameras will record.
If you want a related example (I'm not going to redo your simulation),
look again at my picture of watching the approach, passing by, and regression, of a squadron of squares:
https://wugi.be/paratwin.htm =>
https://wugi.be/MySRT/Squad.gif
The squares are Lorentz contracted (see "actual position" dots at the
right).
They are *seen* as quadrangles, ie distorted rectangles.
At approach there is blueshift, at regression redshift (my colors are inverted, for a white background;).
At approach the speed seen is greater than the motion velocity v (it
becomes infinite for v=c), at regression it is less than v (it becomes
c/2 for v=c).
At approach there is a seen length expansion(! it becomes infinite for
v=c), at regression an extra length contraction(! it becomes L/2gamma
for v=c IIRC).
Now if you want to visualise spheres, or circles, fill in any of the quadrangles with a corresponding ellipse-like figure, that's how the distorted circles are going to be seen. If you want a symmetrical
circle, take 2*2 adjoining squares, 2 along either side of the axis of symmetry through the observer (the small black circle).
Il giorno domenica 11 giugno 2023 alle 22:59:24 UTC+2 wugi ha scritto:
...
FWIW, Luigi, your animation is about Lorentz contraction, not about what
cameras will record.
If you want a related example (I'm not going to redo your simulation),
look again at my picture of watching the approach, passing by, and
regression, of a squadron of squares:
https://wugi.be/paratwin.htm =>
https://wugi.be/MySRT/Squad.gif
The squares are Lorentz contracted (see "actual position" dots at the
right).
They are *seen* as quadrangles, ie distorted rectangles.
At approach there is blueshift, at regression redshift (my colors are
inverted, for a white background;).
At approach the speed seen is greater than the motion velocity v (it
becomes infinite for v=c), at regression it is less than v (it becomes
c/2 for v=c).
At approach there is a seen length expansion(! it becomes infinite for
v=c), at regression an extra length contraction(! it becomes L/2gamma
for v=c IIRC).
Now if you want to visualise spheres, or circles, fill in any of the
quadrangles with a corresponding ellipse-like figure, that's how the
distorted circles are going to be seen. If you want a symmetrical
circle, take 2*2 adjoining squares, 2 along either side of the axis of
symmetry through the observer (the small black circle).
--
guido wugi
The monitors and photos capture the images present on the place and, therefore, show exactly what the eyes see.
I don't understand how they (monitors and cameras) can represent anything else.
I had believed that the contraction of a sphere could be "seen" and, instead, it is not so.
The moderator directed me to the right path which is the one represented by my last animation
https://www.geogebra.org/m/axxtdurx
where the moving body C is exactly equal to the stationary body D.
Here's the lesson: the contraction of a moving sphere is like the trick: it's there but you can't "see".
...
As for the Terell rotation,
https://en.wikipedia.org/wiki/Terrell_rotation
as I've said before,
that's just a special case of the distortions seen, valid only
perpendicular to the direction of motion, and far enough away, in my
picture: at the far end of the vertical through the observer.
wugi il 16/06/2023 07:35:50 ha scritto:d
...
As for the Terell rotation,
https://en.wikipedia.org/wiki/Terrell_rotation
as I've said before,
that's just a special case of the distortions seen, valid only
perpendicular to the direction of motion, and far enough away, in my
picture: at the far end of the vertical through the observer.
The discussions serve to improve the knowledge of the interlocutors an=
this discussion is very useful to me.
What you wrote seems correct to me: a spherical body in motion
maintains its sphericity visually (and on the monitor) only in one particular case and appears crushed in the other cases.
So, my two animations
https://www.geogebra.org/m/axxtdurx (The contraction is there but you
can't see it on the monitor)
https://www.geogebra.org/m/grq2shgx (The contraction is there andThis is the "measuring" process.
appears on the monitor)
are both correct, one in one case and the other in another.A last try, hoping to be clear:
Is that it?
....
Hope you'll understand at last that there can be no question of
*constant shape*, circle or not, to be *seen* passing by.
Il giorno lunedÄ— 19 giugno 2023 alle 01:53:05 UTC+2 wugi ha scritto:
....
Hope you'll understand at last that there can be no question of
*constant shape*, circle or not, to be *seen* passing by.
Yes, I understood that you can't see a body of constant shape passing
by throughout the movement.
And I agree with you.
But the photos don't show any movement, they are instantaneous and are
the ones you see in my 2 animations when we press the "Position:C=D"
button.
We can say that (based on the position of the camera) in one case the
photo will look like in the animation
https://www.geogebra.org/m/grq2shgx
in another as that of animation
https://www.geogebra.org/m/axxtdurx
and in another will it be even different?
But you inspired me to update my "relativistic squadron watching", so you can try it out here:
https://www.desmos.com/calculator/yey8cgrgat?lang=nl
Moreover you inspired me to modify it into "relativistic circle watching", precisely your thema here, with choices of radius and position, so you can try here, and find out that "perfect circles" are nowhere to be "seen":
https://www.desmos.com/calculator/yxmju4xjrd?lang=nl
So the animation should be disposed of?
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