There is a space ship in an accelerated motion (to the above ; non-uniform accelerated motion). A body is hung with an elastic string from the ceiling. Motion of the body will not be the same as the motion caused by the change of gravity (if two bodies are hung with two strings [length is different], it will be more clear).
Newton's second law (F = Ma) will stand up on gravity also. And above formula will be meaningful not only on a falling body but also on a body on the ground (differently from a contact force). But in falling and on the ground, how about the value of F and a (g) ? Both will be the same. If so, M is the same. Therefore the sameness of gravitational mass and inertial mass will be natural.
There are two elevator cabins. Now one begins free fall. After a few seconds, the other begins free fall also. Motion of the both isn't a uniform motion. How does equivalence principle explain ?
In the air, an elevator cabin is in "free fall". Eventually, falling speed reaches the terminal speed (at the same time, inertial force fades). This "free fall" will be better (to ascertain the relation between gravity and inertial force) than Einstein's free fall (at least).
About the equivalence principle ; A little
《1》 Two small space ships are in free fall. But speed of one of them was decelerated (by jet emission ; downward), and then, was accelerated (by jet emission ; upward) for a while. During the deceleration and acceleration, a crewman (of the latter) would feel -a and a. Equivalence principle will be wrong.
《2》 Allow me to ask. Are there any error in the following passage (ignore rotary motion). There is a small body. It will be able to ascertain that no external force is acting (except for gravity) on it. So if there is some internal force, it's caused by gravity !! Equivalence principle will be wrong.
Are there any errors in the following passages (all occur in vacuum) ? There is a tall steel tower. Along this tower, an elevator cabin is in free fall. On this tower, light sources are set at intervals of ten meters. Lights are emitted from these and pass through horizontally a hole on the wall of this cabin (supposed to be the left wall ; timing is arranged). Light will reach somewhat upper point on the right wall. It will not be the same phenomenon occurs in non-gravitational field (even if steel tower is supposed to be accelerated upward).
An elevator cabin is at a standstill in non-gravitational field. On the side wall (supposed to be the left wall), there are ten holes (at regular intervals ; vertically). The sun light is coming from the just left and passing through the holes. Then, on the right wall, there are ten projections (spot-lights ; don't move). But, if this elevator cabin begins free fall (downward), projections will move upward.
On the ground, there are slanting rails (45 degrees). On this rails, an elevator cabin was accelerated upward at 1G and then at 2G. Can equivalence principle explain the change of resultant force (by inertial force and gravity) ?
In non-gravitational field, there is a space ship (mother ship). Now, two probes separate from the mother ship and begin an accelerated motion to opposite direction (at 2g and 1g. by gas jet). No gravitational field will occur on the mother ship.
A tall elevator cabin is in free fall. In this cabin, pressure of gaseous body is different (because value g is different). Equivalence principle will be wrong.
An elevator cabin is accelerating upward. With the roof, a small body collided (came vertically). And after 10 seconds, a second body (the same mass) collided (came vertically also). This situation will not be the same to an elevator in gravitational field (at a standstill).
- P.S.- Some books today say that accelerated motion is not relative.
"Accelerated motion is not relative". It’s a subheading of a book (in Japanese). Yes, time dilation in gravitational field is written to be real (one sided ; not relative). But in many books, it seems to be written that "accelerated motion is relative"
