OT: Movement of mass vs speed of light

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JF Mezei

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Dec 23, 2021, 2:10:16 AM12/23/21
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Saw an issue in a flat Earther video that caused me to wonder.

Say you have a long pole that spans the distance from Earth to the Sun
but floating somewhere in space. This pole is not compressible and
cannot bend. (built from unobtainium for sake of discussion).


If I push the pole at one end to move it say 5cm. I am not asking the
pole to move anywhere near speed of light. However, doesn't the force
of acceleration I put in at one end propagate to the whole pole
instantly instead of taking 8 minutes to travel ?

In other words, when I push the pole from one end, don't I feel the full
mass of it? If I apply 1 Newton of force, won't the resulting
acceleration at my end be based on 1 Newton being applied to the full
mass of the pole?

"For every action, there is an equal and opposite reaction"

So when I impart 1 newton onto the pole, don't I feel the equal and
opposite reaction from the full mass of the pole? If I get equal and
opposite reaction from full mass of pole, doesn't that mean that my 1
Newton is instantly propagated instead of taking 8 minutes to propagate
at speed of light?

If my 1 Newton does indeed take 8 minutes to propagage, how much of the
pole's mass do I feel when I push it (which would imply atoms are
compressed near me as I give my side of pole greater acceleration that
full mass would allow ad this then spread out over time through the pole
so eventually the whole pole behaves as if 1 Newton was evenly applied
to i).

When an atom pushes the atom next to it, does it know how many other
atoms are waiting in line to resist being pushed? Curious on what scale
between pushing a chopstick vs pushing a pole that is 147 million km
long atoms start behaving differently.

Niklas Holsti

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Dec 23, 2021, 3:37:54 AM12/23/21
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On 2021-12-23 9:10, JF Mezei wrote:
> Saw an issue in a flat Earther video that caused me to wonder.
>
> Say you have a long pole that spans the distance from Earth to the Sun
> but floating somewhere in space. This pole is not compressible and
> cannot bend. (built from unobtainium for sake of discussion).


Such unrealistic assumptions can make for wrong conclusions, so beware.


> If I push the pole at one end to move it say 5cm. I am not asking the
> pole to move anywhere near speed of light. However, doesn't the force
> of acceleration I put in at one end propagate to the whole pole
> instantly instead of taking 8 minutes to travel ?


No. Your "push" is a compression wave, or sound wave, that propagates at
the speed of sound in the pole. Of course, if you assume unobtainium,
you can assume or deduce a very high sound speed. But as the forces
between the atoms of the pole are mainly electromagnetic, the sound
speed will never exceed the speed of light, and is /much/ lower in real
materials.

JF Mezei

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Dec 23, 2021, 5:13:22 AM12/23/21
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On 2021-12-23 03:37, Niklas Holsti wrote:

> No. Your "push" is a compression wave, or sound wave, that propagates at
> the speed of sound in the pole.

Why the speed of sound? Isn't "speed of sound" the speed at which a
accoustic wave propagages through atmosphere at 1atm? (and would thus be
quite different from one trype of material to another?

If I get a vibrator to the pole, the vibrations are perpendicular to the
pole, and that accelerartion is "local" to where the vibrator touches,
but may spread along portion of the pole at their own leasurely speed.
But as thet are vibration, the back and forth cancels itself overall so
0 net acceleration.

But when I push the pole linearly, it is expected the whole pole will
move and accelerate in one direction. And this is what bugs me. When I
push it, how is acceleration calculated if the total mass is not
accelerated at the time I impart the force?

If, instead of a pole, we have a "compact" ball that I push with same
force, how come it will behave as if the full mass is accelerated as I
push it, but a very long pole of same mass would behave differently?

Niklas Holsti

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Dec 23, 2021, 6:49:40 AM12/23/21
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On 2021-12-23 12:13, JF Mezei wrote:
> On 2021-12-23 03:37, Niklas Holsti wrote:
>
>> No. Your "push" is a compression wave, or sound wave, that propagates at
>> the speed of sound in the pole.
>
> Why the speed of sound?


Because "sound" is compression-rarefaction waves, which is what your
"push" is.

If you then /keep/ pushing with a constant force for enough time, the
waves will eventually dampen out (after being reflected back and forth
in the pole) and average to a static compression profile, decreasing
smoothly from the pushed end to the far end of the pole, in proportion
to the pressure needed at each point to accelerate the section of the
pole beyond that point. (This pressure profile is equivalent to the
increase of pressure with depth in the oceans, or in the atmosphere, due
to the "force" of gravity.)

For a short pole of a stiff material -- say, a broomstick or a tent pole
-- that averaging happens quickly enough that it is not noticeable to
the person pushing on the pole, and the delay can be ignored for
practical purposes. But you are talking about a /very/ long pole.


> Isn't "speed of sound" the speed at which a
> accoustic wave propagages through atmosphere at 1atm?


That is the speed of sound in air at 1 atm (and some known temperature
and humidity).


> (and would thus be quite different from one trype of material to
> another?


I did say, the "speed of sound IN THE POLE". Yes, it is different for
different materials, increasing with stiffness.


> If I get a vibrator to the pole, the vibrations are perpendicular to the
> pole, and that accelerartion is "local" to where the vibrator touches,
> but may spread along portion of the pole at their own leasurely speed.
> But as thet are vibration, the back and forth cancels itself overall so
> 0 net acceleration.


The difference in the force profile of the "push" -- whether it is
unidirectional, or oscillating -- is irrelevant to the propagation speed.

Even your vibrator /starts/ by pushing (or pulling) in one direction,
which (by the faulty reasoning) should instantly accelerate the whole
pole in that direction, which does not happen.


> But when I push the pole linearly, it is expected the whole pole will
> move and accelerate in one direction.


Eventually it will, but initially the acceleration propagates at the
speed of sound in the pole. The far end does not move until the
compression wave reaches that end.


> And this is what bugs me. When I
> push it, how is acceleration calculated if the total mass is not
> accelerated at the time I impart the force?


Stop assuming that the pole is "incompressible", which is an unreal
assumption.

Better imagine that the pole is sliced like a salami into a series of
flat thin disks with short and light helical springs in between adjacent
disks. You push on the disk closest to you; that accelerates this disk
and compresses the spring between this disk and the next disk; the
spring then pushes and accelerates that next disk, and so on to the far
end of the pole.

Given the masses and other properties of the disks and springs, the
acceleration of each element can be calculated, and also the speed with
which the acceleration propagates from disk to disk. In reality, the
disks correspond to the atoms or molecules of the pole, and the springs
correspond to the inter-atom/inter-molecule forces.

JF Mezei

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Dec 23, 2021, 4:32:24 PM12/23/21
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On 2021-12-23 06:49, Niklas Holsti wrote:

> Eventually it will, but initially the acceleration propagates at the
> speed of sound in the pole. The far end does not move until the
> compression wave reaches that end.

Thanks for explanation.

Is the compression happening at the atomic level, or at the material
level (like a sponge/spring)?


So when I push that 147 million km long pole, does science know how much
mass I will feel pushing back? I assume at that scale, I won't see any
difference whether the pole is 147 million km long or 300 million km long?

If I impart 1 Newton at one end, I take it I get an immediate 1 newton
"equal reaction" and the pole will figure out the push propagates within
itself?

(I assume that if I impart 1 Newton onto the space station, I get the
same reaction against me as uf I imparted 1 newton against that 147
million km long pole?

Niklas Holsti

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Dec 23, 2021, 5:48:13 PM12/23/21
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On 2021-12-23 23:32, JF Mezei wrote:
> On 2021-12-23 06:49, Niklas Holsti wrote:
>
>> Eventually it will, but initially the acceleration propagates at the
>> speed of sound in the pole. The far end does not move until the
>> compression wave reaches that end.
>
> Thanks for explanation.
>
> Is the compression happening at the atomic level, or at the material
> level (like a sponge/spring)?


Could be either or both, depending on the structure of the pole. If the
pole is compact steel, for example, the compression is at the atomic
level, but if you build a series of disks and springs as I described, it
would be at both levels, with most of the compression (measured by
change in length) in the springs.


> So when I push that 147 million km long pole, does science know how much
> mass I will feel pushing back?


If by "mass .. pushing back" you mean how much a given push force will
accelerate the pushed end of the pole, you have to consider separately
the dynamic case (when the force is first applied and shortly
thereafter) and the static case (constant force for a long time).


> I assume at that scale, I won't see any difference whether the pole
> is 147 million km long or 300 million km long?

In the static case (constant push for a long time) you will certainly
feel the full 300 million km of pole, and it will feel over twice as
massive as the 147 million km pole.

In the dynamic case, if you suddenly apply a push to one end of the
pole, the first acceleration will occur just at the surface where the
push is applied, thus it will feel like a very small mass. But that will
last a very short time because the push will quickly propagate along the
pole, and as quickly the acceleration will decrease as more and more of
the mass of the pole is involved.

Comparing the 147 million km pole and the 300 million km pole, you
should not see any difference until the compression wave has reached the
147 million km point. The situation after that becomes more complex as
the wave in the shorter pole is reflected back from its far end, while
the wave in the longer pole continues to propagate.


> If I impart 1 Newton at one end, I take it I get an immediate 1 newton
> "equal reaction"


Of course. That is more or less how "force" is defined... However, if
you want to measure the applied force with some kind of dynamometer, you
can do that easily in the static case, but in the dynamic case you would
have to include the compressibility and sound speed of the dynamometer
itself as corrections to the measurement (in fact, you must consider the
whole dynamic frequency response function of the dynamometer).


> and the pole will figure out the push propagates within
> itself?


Yes. Poles are very intelligent and can certainly figure out such things.


> (I assume that if I impart 1 Newton onto the space station, I get the
> same reaction against me as uf I imparted 1 newton against that 147
> million km long pole?


Theoretically yes. But in the dynamic case, any real "piston" or other
mechanism that you could use to apply the push would not be able to
maintain a constant 1 Newton force when the compression waves (and
flexures, for the space station) in the pushed object return to the push
point and accelerate it (move it about). If that acceleration is towards
the pushing mechanism, the force will increase; if it is away from the
pushing mechanism, the force will decrease; before the mechanism can
react and restore the 1 Newton force (until the next wave comes in). The
pushing mechanism would be able to sense these accelerations and force
disturbances quickly in the space station case, because the station is
small, while for the long pole they would happen much later.
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