3 ms·

Imagine going back to Kronecker and their contemporaries and telling them that a spinning top weighs more than a top at rest. They would have laughed you out o

Imagine going back to Kronecker and their contemporaries and telling them that a spinning top weighs more than a top at rest. They would have laughed you out of the room, but a few years later the arrogant scientific confidence of the 19th century was completely crushed by quantum mechanics and general relativity. Science is not a body of knowledge, it is a frontier of ignorance. I like to "feel" that complex numbers are part of the fabric of the universe, if only because it would be more beautiful. "Clouds are not spheres, Mountains are not cones" - Mandelbrot

EthanHeilman 6y ago
A spinning top weighs more than a top at rest? I get that mass increases with speed, but that works in a rotating system as well as a linear system?
- skzv 6y ago
  At any given instant, velocity is linear. That is, if you take a snapshot of the top, you can draw a straight vector for each particle of the top, indicating the direction of velocity. And, if the top suddenly flew apart, each piece would continue in a straight line, following its velocity at that instant.
  - EthanHeilman 6y ago
    Can velocity exist in a snapshot?
    - skzv 6y ago
      Or rephrased: is instantaneous velocity real? Are limits real, or just a mathematical invention? Well, I think instantaneous velocity is real, and I think I have a convincing argument. Imagine you have a piece of gum stuck to your bike tire. As your tire spins, the piece of gum spins with it, and its velocity is constantly changing. But when the piece of gum flies off your tire, it flies off in a straight line, following the instantaneous velocity at the moment of separation. Seeing as the gum can fly off in a straight line, its instantaneous velocity at that moment must be well-defined.
- selimthegrim 6y ago
  Relativistic mass is not a well defined abstraction.
- Ma8ee 6y ago
  Both phenomena are a consequence of the equivalence between mass and energy. So since a spinning top has a higher energy than one at rest, it will also have a higher mass. Another example is that an excited atom has a higher mass than the same atom in its ground state.
MeinBlutIstBlau 6y ago
My hot take is that this is why it doesn't matter if there are vaccine deniers or flat earthers. The facts speak for themselves and inevitably they'll be wrong again just as the people before them.

EthanHeilman 6y ago

A spinning top weighs more than a top at rest? I get that mass increases with speed, but that works in a rotating system as well as a linear system?

skzv 6y ago
At any given instant, velocity is linear. That is, if you take a snapshot of the top, you can draw a straight vector for each particle of the top, indicating the direction of velocity. And, if the top suddenly flew apart, each piece would continue in a straight line, following its velocity at that instant.
- EthanHeilman 6y ago
  Can velocity exist in a snapshot?
  - skzv 6y ago
    Or rephrased: is instantaneous velocity real? Are limits real, or just a mathematical invention? Well, I think instantaneous velocity is real, and I think I have a convincing argument. Imagine you have a piece of gum stuck to your bike tire. As your tire spins, the piece of gum spins with it, and its velocity is constantly changing. But when the piece of gum flies off your tire, it flies off in a straight line, following the instantaneous velocity at the moment of separation. Seeing as the gum can fly off in a straight line, its instantaneous velocity at that moment must be well-defined.
selimthegrim 6y ago
Relativistic mass is not a well defined abstraction.
Ma8ee 6y ago
Both phenomena are a consequence of the equivalence between mass and energy. So since a spinning top has a higher energy than one at rest, it will also have a higher mass. Another example is that an excited atom has a higher mass than the same atom in its ground state.

MeinBlutIstBlau 6y ago

My hot take is that this is why it doesn't matter if there are vaccine deniers or flat earthers. The facts speak for themselves and inevitably they'll be wrong again just as the people before them.