The question was raised here whether, according to Special Relativity, a ball dropped off the top of the Empire State Building would loose mass due to the fall (as opposed to shattering at the bottom - let us say that it is an invincible ball).
Although the issue was debated rather fiercely for a couple of pages, we never really settled the issue. Rather than necro-posting a thread to discuss something that was off-topic, I figured that it would be a better idea to raise the issue in the Science and Technology Forum. Not only is it a more appropriate location, but it would allow input from those far more knowledgeable on the subject than I.
Basically, the reasoning is this: if a ball is atop the Empire State Building, it has a certain amount of potential energy. After it has been dropped off the building, once it reaches the ground, it will have a different amount of potential energy. Of, both values are arbitrary, but the difference between is not: it is work done on the ball done as it fell.
According to Special Relativity, energy and mass are related. Therefore, the non-arbitrary change in the ball's potential energy (due to the work done on it by gravity) should result in a change of mass. Although it was argued that the potential energy is arbitrary, the work done on the ball is not - and that is were Conservation of Mass comes in.
According to this link, relativistic mass is conserved in all inertial frames of reference and rest mass is not necessarily conserved. As the ball falls, mass dilation causes its relativistic mass in increase relative to its rest mass. Since there is no source of mass to increase the ball's relativistic mass (the new mass cannot come from the Earth, as the Earth would be accelerating ever-so-subtly up to meet the - meaning that it would be experiencing mass dilation as well), we have to assume that its rest mass decreases. In short, "rest mass" is converted into "kinetic energy mass" as the ball falls.
Once the ball hits the ground, it looses the kinetic energy in the form of sound and heat. This energy is dispersed outward into the Earth, not into the ball, so the mass that that energy carries must also be transferred into the Earth, away from the ball.
As for why we cannot take the ball as our frame of reference (as was suggested in the original topic), Special Relativity applies only in inertial (that is, non-accelerating) frames of reference. However, in the ball's frame of reference, the Earth is accelerating upwards at 32 feet per second per second (9.8 m/s^2) without any apparent cause.
As a side note, for those who think that Special Relativity is wrong, my reply is this post.
Furthermore, below is an amendment (copied from here) to the original post clarifying the issue of Emitter Theory:
Although the issue was debated rather fiercely for a couple of pages, we never really settled the issue. Rather than necro-posting a thread to discuss something that was off-topic, I figured that it would be a better idea to raise the issue in the Science and Technology Forum. Not only is it a more appropriate location, but it would allow input from those far more knowledgeable on the subject than I.
Basically, the reasoning is this: if a ball is atop the Empire State Building, it has a certain amount of potential energy. After it has been dropped off the building, once it reaches the ground, it will have a different amount of potential energy. Of, both values are arbitrary, but the difference between is not: it is work done on the ball done as it fell.
According to Special Relativity, energy and mass are related. Therefore, the non-arbitrary change in the ball's potential energy (due to the work done on it by gravity) should result in a change of mass. Although it was argued that the potential energy is arbitrary, the work done on the ball is not - and that is were Conservation of Mass comes in.
According to this link, relativistic mass is conserved in all inertial frames of reference and rest mass is not necessarily conserved. As the ball falls, mass dilation causes its relativistic mass in increase relative to its rest mass. Since there is no source of mass to increase the ball's relativistic mass (the new mass cannot come from the Earth, as the Earth would be accelerating ever-so-subtly up to meet the - meaning that it would be experiencing mass dilation as well), we have to assume that its rest mass decreases. In short, "rest mass" is converted into "kinetic energy mass" as the ball falls.
Once the ball hits the ground, it looses the kinetic energy in the form of sound and heat. This energy is dispersed outward into the Earth, not into the ball, so the mass that that energy carries must also be transferred into the Earth, away from the ball.
As for why we cannot take the ball as our frame of reference (as was suggested in the original topic), Special Relativity applies only in inertial (that is, non-accelerating) frames of reference. However, in the ball's frame of reference, the Earth is accelerating upwards at 32 feet per second per second (9.8 m/s^2) without any apparent cause.
As a side note, for those who think that Special Relativity is wrong, my reply is this post.
Furthermore, below is an amendment (copied from here) to the original post clarifying the issue of Emitter Theory:
Spoiler:
Comment