Experiments on the validity of Relativity

[Luigi Fortunati]

When there is an experiment that proves Einstein right, the whole world
is ready to praise him and his theories (and rightly so).

However, it is not right that, when an experiment proves Einstein wrong,
no one admits it and no one talks about it.

Einstein says that bodies in free fall are at rest and that the man
inside the falling elevator experiences no forces or accelerations.

I have demonstrated in every possible way (with well-illustrated thought
experiments via Geogebra) that it is a huge mistake, because two massive
bodies (which fall gravitationally and freely towards each other)
*accelerate* both in the reference of one and both in that of the other.

Therefore, they are accelerated reference systems and not at rest.

Both!

This is regarding acceleration.

It is even easier for the forces to demonstrate the error.

Is the elevator plummeting towards a black hole in free fall? Of course
yes: it is in free fall.

In such conditions, Einstein says that the man inside this free-falling
elevator does not suffer any force while (we all know!) the force is
there and (even) tears him to pieces together with the elevator!

No one has ever been able to dispute this colossal error (that bodies in
free fall are at rest) because it is indisputable.

And then, rather than admit the correctness of my statement, you all
preferred not to talk about it at all, because the flaws of Relativity
are better kept hidden.

It is not very courageous to boast about the successes of a theory and
systematically hide the failures.

Luigi Fortunati

[Luigi Fortunati]

Post by Luigi Fortunati
When there is an experiment that proves Einstein right, the whole world
is ready to praise him and his theories (and rightly so).
However, it is not right that, when an experiment proves Einstein wrong,
no one admits it and no one talks about it.
Einstein says that bodies in free fall are at rest and that the man
inside the falling elevator experiences no forces or accelerations.
I have demonstrated in every possible way (with well-illustrated thought
experiments via Geogebra) that it is a huge mistake, because two massive
bodies (which fall gravitationally and freely towards each other)
*accelerate* both in the reference of one and both in that of the other.
Therefore, they are accelerated reference systems and not at rest.
Both!
This is regarding acceleration.
It is even easier for the forces to demonstrate the error.
Is the elevator plummeting towards a black hole in free fall? Of course
yes: it is in free fall.
In such conditions, Einstein says that the man inside this free-falling
elevator does not suffer any force while (we all know!) the force is
there and (even) tears him to pieces together with the elevator!
No one has ever been able to dispute this colossal error (that bodies in
free fall are at rest) because it is indisputable.
And then, rather than admit the correctness of my statement, you all
preferred not to talk about it at all, because the flaws of Relativity
are better kept hidden.
It is not very courageous to boast about the successes of a theory and
systematically hide the failures.

Einstein always speaks of a body in free fall and a lift in free fall in
the singular, as if there could be a body that falls alone, without
there being another body that (simultaneously) falls in the opposite
direction.

But this never happens.

If body A falls towards body B, body B also falls towards body A.

If body A accelerates towards body B, body B also accelerates towards
body A.

And these two mutual accelerations never disappear, whatever the
reference from which we measure them! They are real accelerations
generated by real forces.

Luigi Fortunati

[Tom Roberts]

Post by Luigi Fortunati
When there is an experiment that proves Einstein right, the whole
world is ready to praise him and his theories (and rightly so).
However, it is not right that, when an experiment proves Einstein
wrong, no one admits it and no one talks about it.

This last is just plain wrong. Any REAL experiment that refuted either
SR or GR would be GREAT NEWS and the experimenters would win praise and
accolades. But they must be real experiments within the domain of
applicability of the theory, and statistically inconsistent with its
predictions. To date no such experiments have ever been published --
your allegations here are just drivel: they are not real experiments,
and they indicate that YOU do not understand General Relativity, because
your claims are based upon a PUN on the word "acceleration".

Post by Luigi Fortunati
Einstein says that bodies in free fall are at rest and that the man
inside the falling elevator experiences no forces or accelerations.

No. This is A LOT more subtle. So much so that this claim is just plain
wrong. You MUST learn about the actual theory before you can have any
hope of refuting it. All you have done here is shown that your personal
misconceptions are inconsistent with each other -- useless.

Post by Luigi Fortunati
[...] two massive bodies (which fall gravitationally and freely
towards each other) *accelerate* both in the reference of one and
both in that of the other.

Sure. This does not refute GR, because of your confusion between
coordinate acceleration and proper acceleration. These two bodies have
zero proper acceleration, and nonzero coordinate acceleration. The
equations (and predictions) of GR are necessarily coordinate
independent, and basically say nothing at all about coordinate
acceleration, because one can choose any coordinate system. In the
absence of forces on an object, GR predicts it has zero proper
acceleration (while its coordinate acceleration can be anything,
depending on the coordinates used). In GR, gravitation is an aspect of
the geometry of spacetime, not a force.

[Note to experts: there are missing caveats and conditions
here, but they are irrelevant to Fortunati's basic problem.]

Post by Luigi Fortunati
[... other claims showing further ignorance of GR]

As I have repeatedly told you, you MUST get a good textbook and STUDY
physics. Start with classical mechanics, and be sure you have mastered
it before attempting GR. Better would be taking physics courses at a
local college or university. Posting dubious claims in a newsgroup is a
TERRIBLE approach and will never teach you much physics. There are no
shortcuts.

Post by Luigi Fortunati
If body A falls towards body B, body B also falls towards body A. If
body A accelerates towards body B, body B also accelerates towards
body A. And these two mutual accelerations never disappear, whatever
the reference from which we measure them! They are real accelerations
generated by real forces.

Not in GR. GO STUDY and stop wasting your time on nonsense. You do NOT
have enough knowledge to just "think this through" on your own.

Tom Roberts

[Luigi Fortunati]

Post by Tom Roberts

Post by Luigi Fortunati
[...] two massive bodies (which fall gravitationally and freely
towards each other) *accelerate* both in the reference of one and
both in that of the other.

Sure. This does not refute GR, because of your confusion between
coordinate acceleration and proper acceleration.

In my animation https://www.geogebra.org/m/ttgky8xu there are two small
planets (A and B) that accelerate gravitationally and simultaneously
towards the common center of mass P.

Is this acceleration what you call "coordinate acceleration"?

And what is your "proper acceleration"?

Is it, perhaps, the acceleration of planet A with respect to itself and
of planet B with respect to itself?

Or is it something else?

Luigi Fortunati


[[Mod. note --

For your specific questions, a careful reading of
https://en.wikipedia.org/wiki/Proper_acceleration
together with its references, would likely be useful.



In your animation, while A and B are initially stationary (before the
animation starts):
* in the coordinate system of your animation, A's center of mass
has zero coordinate acceleration
* in the coordinate system of your animation, B's center of mass
has zero coordinate acceleration
* A's center of mass has nonzero proper acceleration
* B's center of mass has nonzero proper acceleration

In your animation, while A and B are free-falling towards each other:
* in the coordinate system of your animation, A's center of mass
has a (time-dependent) nonzero coordinate acceleration
* in the coordinate system of your animation, B's center of mass
has a (time-dependent) nonzero coordinate acceleration
* A's center of mass has zero proper acceleration
* B's center of mass has zero proper acceleration

Notice that I've referred explicitly to A's and B's *center of mass*:
both coordinate and proper acceleration are properties of a *point*
or an *observer* (more precisely, in GR, a "worldline"). Applying
these concepts to an extended body may be ok if the body has negligable
self-gravity. But, it's tricky try to apply these concepts to extended
bodies with non-negligible self-gravity, precisely because the answer
to the question "what's the proper acceleration of this point on the
body?" differs from one point to another.



But more generally, as Tom Roberts has noted in this thread (and many
people have said in past threads in this newsgroup), to learn GR you
really need a more extensive treatment than newsgroup discussions. That
is, you really need a good textbook or textbooks, and/or a university
course or courses. For self-study, my suggestion would be to get copies
of several textbooks and work through them in parallel -- often seeing
multiple pedagogical treatments can help you better understand what's
going on.

A few book suggestions (in roughly increasing order of mathematical
difficulty):

Robert Geroch
"General Relativity from A to B"
University of Chicago Press, 1981

James B Hartle
"Gravity: An Introduction to Einstein's General Relatiity"
Cambridge University Press, 2021

Ian R Kenyon
"General Relativity"
Oxford University Press, 1990
(or you could go for the 2nd edition of this,
which includes some cosmology as well as GR)

Bernard F Schutz
"A First Course in General Relativity", 3rd edition
Cambridge University Press, 2022

Sean M Carroll,
"Spacetime and Geometry: An Introduction to General Relativity"
Addison-Wesley, 2004

Of these, the book by Geroch is notable for being almost completely
non-mathematical and for being very cheap. The other books all introduce
a certain amount of tensor calculus, because that's what's needed to
cleanly present GR.
-- jt]]

[Luigi Fortunati]

Post by Luigi Fortunati
[[Mod. note --
In your animation, while A and B are initially stationary (before the
* in the coordinate system of your animation, A's center of mass
has zero coordinate acceleration
* in the coordinate system of your animation, B's center of mass
has zero coordinate acceleration
* A's center of mass has nonzero proper acceleration
* B's center of mass has nonzero proper acceleration

These two latest statements are equivocal.

You say that the centers of mass A and B (which are stationary) have
their nonzero proper acceleration and this is in contrast with what I
have studied, that is, that acceleration is the variation of velocity.

So can you explain to me how two points whose velocity is always the
same (i.e. zero) can have an acceleration (whether proper or not)?

Can there be non-zero acceleration if velocity is zero and remains zero?

Obviously not.

So, your "proper acceleration" is not a real acceleration.

Luigi Fortunati

[[Mod. note --
*Coordinate* acceleration is indeed "the variation of velocity".

But, *proper* acceleration is something different: An observer's
*proper* acceleration is defined as the acceleration measured by an
(ideal) accelerometer she carries with her. Another way to say this
is that an observer's proper acceleration is her acceleration
*relative* to a freely-falling inertial reference frame (IRF) at her
current location.

Another way to think of this is to imagine that the observer carries
a small rocket with her. The observer should let go of the rocket, so
that there are no forces acting on the rocket except for the rocket's
own thrust and any gravitational fields, and then adjust the rocket
thrust until the rocket matches the observer's motion (i.e., the rocket
remains stationary *relative to the observer*). If the rocket thrust
required to keep the rocket stationary *relative to the observer* is
$F$, then the observer's proper acceleration is $F/m$, where $m$ is the
(current) mass of the rocket.


Before considering your two planets, it might be useful to first
consider a few simpler situations.

#1. If you're in free-fall, what's your proper acceleration?
In this case you and the freely-falling IRF are both freely-falling
at the same location, so your acceleration with respect to that IRF
is zero, and your rocket doesn't need any thrust to match your motion
and stay stationary next to you. This means that your proper
acceleration is zero. This is important: the proper acceleration
of a freely-falling observer is *zero*.

#2. If you are on the Earth's surface, stationary with respect to the
Earth's surface), what is your proper acceleration? To answer this,
we need to think about what a freely-falling IRF's motion would be
at your location. That IRF would be accelerating downwards at (about)
9.8 m/s^2 relative to the Earth's surface. Therefore,
*relative to that freely-falling IRF*, you (stationary with respect
to the Earth's surface) are accelerating *upwards* at 9.8 m/s^2.
Equivalently, to hang stationary in mid-air next to you (not
accelerating with respect to you), your rocket needs to be thrusting
*upwards* so as to deliver an acceleration of 9.8 m/s^2 *upwards*
relative to free-fall. This last sentence is important, so let me
repeat it: in order to hang stationary in mid-air next to you, your
rocket needs to be thrusting *upwards* so as to deliver an acceleration
of 9.8 m/s^2 *upwards relative to free-fall* (at your location).
Therefore, your proper acceleration is 9.8 m/s^2 *upwards*.


Now let's consider your two planets A and B, in the initial condition
where they are held apart (stationary) by some external forces. (E.g.,
maybe there's a strut between them; the strut is in compression due to
mutual gravitational attraction of A and B.)

This situation is precisely analogous to my scenario #2 above. We've
said that A and B are being held apart by external forces, so they're
stationary with respect to each other. This means that A's center of
mass is *not* in free-fall.

If you are located at ("holding on to") A's center of mass, what does
your accompanying rocket need to do to stay stationary next to you?
(Remember, we've said that the only forces acting on the rocket are
it's own thrust and any gravitational fields.) In order to stay
stationary next to you, your accompanying rocket needs to thrust
directly *away from B* in order to counteract B's gravitational field.

Therefore, your proper acceleration (which is exactly the same as the
proper acceleration of A's center of mass) is nonzero. In fact, your
(and A's-center-of-mass's) proper acceleration points *away from B*,
and (assuming A and B are both spherical) has a magnitude $GM/R$ where
$G$ is the Newtonian gravitational constant, $M$ is the mass of planet B,
and $R$ is your distance from B's center of mass.
-- jt]]

[Luigi Fortunati]

Post by Luigi Fortunati
[[Mod. note --
*Coordinate* acceleration is indeed "the variation of velocity".
But, *proper* acceleration is something different: An observer's
*proper* acceleration is defined as the acceleration measured by an
(ideal) accelerometer she carries with her.
...
-- jt]]

Relativity is wrong to trust the accelerometer.

In my animation https://www.geogebra.org/m/r9zk9smz there are two
accelerometers that accelerate in the *same* way but the first one says
that the acceleration is present (the EK spring contracts and the LM
spring contracts lengthens) and the second says that it is not there
(the springs VR and SW keep their length unchanged at rest).

This shows that the accelerometer (despite its name) does not measure
acceleration at all but measures something else because only a *couple*
of non-concordant forces can compress or stretch the springs and not an
acceleration.

The difference between accelerometer 1 and 2 lies in the point of
application of the external force.

In accelerometer 1 the red external force F acts against a single
surface point (E) as happens in the push of a hand, while in
accelerometer 2 it is divided into an endless number of tiny equal
forces that act individually on each single particle (whether internal
or peripheral), as happens in the case of gravity and electromagnetism.

In both cases, the external force generates the *same* acceleration of
the accelerometer, however, in the first case the accelerometer 1
measures the acceleration, while in the second case the accelerometer 2
says that the acceleration is not present.

Why?

Luigi Fortunati


[[Mod. note --

Why would you expect accelerometer #2 to register any acceleration?

I referred to an "(ideal) accelerometer". "Ideal" includes that
non-gravitational external forces are applied only to the outer case,
not the inner "proof mass". Accelerometer #1 satisfies this condition,
but accelerometer #2 doesn't.

As you've described the situation, there are two possble cases for
what's going on with accelerometer $#2:
(a) The "external forces" are really a gravitational field. In this
case accelerometer #2 is in free-fall, and having it read
"zero acceleration" is just what we expect -- by virtue of the
equivalence principle, no local accelerometer can detect a
uniform gravitational field, so an accelerometer in free-fall
should indeed read "zero acceleration".
(b) There are no gravitational fields around, but there's an ambient
magnetic field and the accelerometer's intern "proof mass" is
magnetic (e.g., iron/steel) so that the magnetic field is applying
a force to the proof mass. In this case the accelerometer is being
misused (and we shouldn't pay any attention to its readings): it's
design is such that it doesn't properly measure accelerations when
there's an ambient magnetic field, and we're trying to use it in
an ambient magnetic magnetic field.
-- jt]]

[Luigi Fortunati]

Il 24/05/2024 01:02, Mod. note --

(a) The "external forces" are really a gravitational field. In this
case accelerometer #2 is in free-fall, and having it read
"zero acceleration"...

It's not zero acceleration, it seems zero to you because it's very small
but it's not zero.

This is what happens to accelerometer 1 in my animation
https://www.geogebra.org/classic/vtvnm8uv where you don't notice the
contraction and stretching of the springs just because the variations
are too small to be visible.

But just increase the force of gravity to realize that it doesn't show
zero acceleration at all.

Look what happens to accelerometer 2 which is also in free fall in a
gravitational field: does it seem to show zero acceleration?

Luigi Fortunati

[Jonathan Thornburg [remove -color to reply]]

Post by Luigi Fortunati
This is what happens to accelerometer 1 in my animation
https://www.geogebra.org/classic/vtvnm8uv where you don't notice the
contraction and stretching of the springs just because the variations
are too small to be visible.
But just increase the force of gravity to realize that it doesn't show
zero acceleration at all.
Look what happens to accelerometer 2 which is also in free fall in a
gravitational field: does it seem to show zero acceleration?

Your animation shows the accelerometers placed in an ambient gravitational
which varies significantly across the dimensions of the accelerometer.
We don't expect an accelerometer to work properly in such a situation.

The definition of an "ideal" accelerometer includes (among other
conditions) measuring acceleration-relative-to-free-fall at a *point*,
i.e., it assumes that tidal fields are negligable, i.e., it assumes that
the accelerometer is small compared to the scale of variation of any
ambient gravitatonal fields. Your accelerometer #2 violates this
assumption.

[Luigi Fortunati]

Post by Jonathan Thornburg [remove -color to reply]

Post by Luigi Fortunati
This is what happens to accelerometer 1 in my animation
https://www.geogebra.org/classic/vtvnm8uv where you don't notice the
contraction and stretching of the springs just because the variations
are too small to be visible.
But just increase the force of gravity to realize that it doesn't show
zero acceleration at all.
Look what happens to accelerometer 2 which is also in free fall in a
gravitational field: does it seem to show zero acceleration?

Your animation shows the accelerometers placed in an ambient gravitational
which varies significantly across the dimensions of the accelerometer.
We don't expect an accelerometer to work properly in such a situation.
The definition of an "ideal" accelerometer includes (among other
conditions) measuring acceleration-relative-to-free-fall at a *point*,
i.e., it assumes that tidal fields are negligable, i.e., it assumes that
the accelerometer is small compared to the scale of variation of any
ambient gravitatonal fields. Your accelerometer #2 violates this
assumption.

You judge the tidal forces during free fall to be negligible based only
on the dimensions of the accelerometer and do not consider the
gravitational mass: tree falling in the Earth's gravitational field is
not the same as free falling in that of a neutron star!

They are both free falls but the negligibility is not the same.

Consider an accelerometer made of a single diatomic molecule of hydrogen
H2, does it seem small enough to make the tidal forces negligible during
the fall towards the neutron star?

It seems not to me.

The tidal forces on this microscopic-sized accelerometer are so little
negligible that they manage to break the H2 molecule into two separate
and distinct H atoms: where is the negligibility in this free fall?

Luigi Fortunati