Re: The Nanometre Twin

Peri of Pera wrote:
Bertie is 1.8m tall and weighs 60kg. In 2110 when he is 30 years of
age, he leaves on a spaceship to destination xyz in our galaxy. On
board, Bertie is in suspended animation with his body positioned in
the direction of motion. The speed of the spaceship is of a magnitude
to affect time, length and mass by a factor of 10. The trip to xyz and
back lasts 100 earth clock years but on his return Bertie should be
only 40 years of age due to the time dilation he experienced in space.
He should be 18cm tall and have a mass of 600kg according to the
contraction and mass increase effects of special relativity.

No. You are confusing effects on INCREMENTAL MEASUREMENTS with accumulated values.

Note: you cannot use "suspended animation" (whatever that means), because it presumably affects Bertie's biological age, which is the center of your question. So I ignore that.

Age: Bertie will accumulate 10 years of proper time during his journey, and will be 40 years old when he returns. When he returns AND COMES TO REST in the earthbound inertial frame, he will age at the same rate as everyone else on earth. His elapsed proper time (age) is ACCUMULATED, but the RATE at which he ages is an INCREMENTAL measurement.

Length: during his trip, if Bertie lies down parallel to his direction of travel, he will BE MEASURED to be 18cm tall by an earthbound observer, using the usual co-moving assistants in the earthbound inertial frame to make the measurement. If he stands or lies perpendicular to his direction of travel, that earthbound observer and assistants will measure him to be 180 cm tall. But when he returns AND COMES TO REST in the earthbound inertial frame, that earthbound observer and assistants will measure him to be 180 cm tall regardless of his orientation. This is so because the height of an object is INTRINSIC, and is not an accumulated property (i.e. not accumulated over a trip like this).

Mass: you are confusing "relativistic mass" with mass. Bertie's mass never changes (strict diet, of course). Recognizing that "relativistic mass" is just m/sqrt(1-v^2/c^2), it's clear that this is simply a function of his speed, and when Bertie returns AND COMES TO REST in the earthbound inertial frame, v=0 so his "relativistic mass" equals his mass, 60 kg.


As I have remarked so often, precision in thought and word is ESSENTIAL to understanding modern physics, including relativity.


Tom Roberts
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