A free-falling brick is an inertial frame?
Are a pair of free-falling half-bricks an inertial frame or are they
two distinct inertial frame?
rA free-falling brick is an inertial frame?=20
A free-falling brick is *in* "an" inertial frame. Which more precisely
means that we can find an inertial frame in which the brick is in
uniform motion, then just a special case is an inertial frame in=20
which the brick is at rest, and and even more special case is the
frame in which the brick is at rest at the origin of space. And we
might call that last one "the brick's own frame", because there is
indeed something "privileged" about it as far as that brick is
concerned: OTOH, though, notice that the fact that the brick is in *free-fall* requires no frame to state or verify at all, it's altogethe=
a *true* physical property that can be verified *locally*.
Julio Di Egidio sabato 07/05/2022 alle ore 15:00:52 ha scritto:
A free-falling brick is an inertial frame?
A free-falling brick is *in* "an" inertial frame. Which more precisely means that we can find an inertial frame in which the brick is in
uniform motion, then just a special case is an inertial frame in
which the brick is at rest, and and even more special case is the
frame in which the brick is at rest at the origin of space. And we
might call that last one "the brick's own frame", because there is
indeed something "privileged" about it as far as that brick is
concerned: OTOH, though, notice that the fact that the brick is in *free-fall* requires no frame to state or verify at all, it's altogether
a *true* physical property that can be verified *locally*.
How small must this be "locally"?
As small as a brick? A half brick? A tenth of a brick?
Julio Di Egidio sabato 07/05/2022 alle ore 15:00:52 ha scritto:
A free-falling brick is an inertial frame?
A free-falling brick is *in* "an" inertial frame. Which more precisely means that we can find an inertial frame in which the brick is in
uniform motion, then just a special case is an inertial frame in
which the brick is at rest, and and even more special case is the
frame in which the brick is at rest at the origin of space. And we
might call that last one "the brick's own frame", because there is
indeed something "privileged" about it as far as that brick is
concerned: OTOH, though, notice that the fact that the brick is in *free-fall* requires no frame to state or verify at all, it's altogether
a *true* physical property that can be verified *locally*.
How small must this be "locally"?
As small as a brick? A half brick? A tenth of a brick?
On Sunday, 8 May 2022 at 09:41:41 UTC+2, Luigi Fortunati wrote:
How small must this be "locally"? As small as a brick? A half[... verbiage that does not answer the question]
brick? A tenth of a brick?
[I] invite you to [...] reconsider [...] what it even means for a
property to be a *true physical property* vs e.g. an artefact of the coordinate system.
A free-falling brick is an inertial frame?
Are a pair of free-falling half-bricks an inertial frame or are they
two distinct inertial frame?
On 5/8/22 9:21 AM, Julio Di Egidio wrote:
On Sunday, 8 May 2022 at 09:41:41 UTC+2, Luigi Fortunati wrote:
How small must this be "locally"? As small as a brick? A half[... verbiage that does not answer the question]
brick? A tenth of a brick?
You both miss the key concept about locally inertial frames: they are
only APPROXIMATELY inertial, and the maximum size they can be is
determined by your measurement resolution; better resolution puts a
smaller limit on the size of the region in which they can be considered inertial.
Here's a simple example.
Suppose you start with a 4-meter-wide elevator in freefall near the
surface of the earth, and you release two small ball bearings 3 meters
apart horizontally, at rest relative to the inside of the elevator. They
will APPROXIMATELY remain at rest relative to the elevator, but we know
that they are each falling toward the center of the earth, so they will slowly approach each other as the elevator continues to fall.
Imagine you can measure the distance between them with a resolution of 1 millimeter. Since the earth radius is 6.371E6 meters, the elevator can
fall 1,460 meters until they are 2.999 meters apart, which will take
17.2 seconds.
Suppose, instead, that you can measure the distance between them with a resolution of 1 micron. The elevator can fall 1.46 meters until they are 2.999999 meters apart, which will take 0.54 seconds.
Clearly the limited region of spacetime over which this locally inertial frame is approximately inertial depends on how well you can measure.
Other types of measurements will put different constraints on the size
of the region. For instance, recent measurements of optical clocks at
NIST will put a limit of a few centimeters tall before such clocks at
rest in the elevator at its ceiling and floor will cease to remain in
sync.
Julio Di Egidio continued with an unrelated quest:
[I] invite you to [...] reconsider [...] what it even means for aModern physics has a simple and very general requirement: "true physical properties" must be invariant under changes of coordinates. This is why modern physical theories are all expressed in terms of tensors, which
property to be a *true physical property* vs e.g. an artefact of the
coordinate system.
are completely independent of coordinates, and therefore invariant under changes of coordinates.
Tom Roberts
On Sunday, 15 May 2022 at 11:10:45 UTC+1, Tom Roberts wrote:
the key concept [is that] locally inertial frames [...] are
only APPROXIMATELY inertial [...]
An interesting point you make.
It follows that there is no such
thing as an inertial frame
So an inertial frame cannot actually
exist in 3D space.
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 343 |
Nodes: | 16 (2 / 14) |
Uptime: | 29:28:07 |
Calls: | 7,516 |
Calls today: | 13 |
Files: | 12,713 |
Messages: | 5,642,042 |
Posted today: | 2 |