Lorentz Jr

Actually, gravity doesn't create g-forces at all. None that can be felt, anyway. What we experience as the "force of gravity" is really the pressure force of the floor or whatever other object is supporting us. Taking the word "suddenly" literally, we would all be killed by the infinite force required to accelerate us instantaneously. Even a sharp gravitational pulse would rip us and Earth apart by accelerating some parts more than others. I'll assume you're asking why we don't feel the centripetal force of orbiting the sun at high speed. Speed itself doesn't require any force as long as it's constant and the motion is in a straight line. In Newtonian physics (i.e. old-fashioned Physics 101), the reason we don't directly feel the effects of gravity is that inertial mass is equal to gravitational mass. Inertial mass is the m in Isaac Newton's 2nd law, [math]F=ma[/math], and gravitational mass is the mass in his law of gravity, [math]\displaystyle{F_g = \frac{GmM}{r^2}}[/math]. They cancel out: If gravity is the only force acting on an object, then [math]\displaystyle{ma = \frac{GmM}{r^2}}[/math], so the object's acceleration is [math]\displaystyle{a = \frac{GM}{r^2}}[/math]. Gravity affects every molecule in your body exactly the same way, so your nerves don't sense any change in your body's configuration. This is why Albert Einstein was able to model gravity as the curvature of spacetime in his general theory of relativity. In that theory, gravity isn't even a force. It's just the curvature of spacetime, and objects with no (other) forces on them simply travel along "straight" lines. Not literally straight lines, because space itself is curved, but along curves called "geodesics", which are as straight as any path can be in the curved space.

That's right, it's not. When a car is "destroyed" in a junk yard, it ceases to "exist" in any usable or recognizable form, even though the parts and materials that it was made of are still there, buried somewhere in the junk heap. And that's why this thread has gone on for four pages in 24 hours: Regular posters took the word in scare quotes at face value and kept trying to explain the conservation of energy to the OP, because that's what physicists care about and it's one possible interpretation of the question. But the OP wasn't really asking about thermodynamics. Either intentionally or unintentionally, he was asking a question about semantics, or at least his question about physics was semantically ambiguous. So everyone kept talking past the OP, incorrectly assuming that the meaning of his question was well established. That's the problem with civility rules in public discussions: They fail to expose the uncivil motives of trolls and the incoherent thinking of beginners. The result is a waste of everyone's time.

It's an overstatement, Tom. Heat "disappears", but energy isn't "destroyed". It's a "general" rule for a certain class of situations that don't always occur, but not for other situations. So it's not "the" principle, it's only one specific principle that can be derived from the conservation of energy, which is "the" principle that physicists use in thermodynamics. Any more questions, Tom? I think all of your current ones have been answered.

You said the temperature of the fluid drops: That's the "rule" that you and swansont were debating, and it's the outcome I was referring to. Maybe you're the one who needs to be less disingenuous.

That's not enough. You must use the full Lorentz transformations. They're what Genady's diagrams represent.

Your calculations are incorrect. No relativity problem can be solved without taking the relativity of time into account. It's a problem because it's only true in A's reference frame. You were analyzing the problem in B's reference frame, where it's not true.

Your statement is correct if there's no heat source and no other source doing work on the fluid: The fluid will cool off if it's not heated and it does work on a net basis on its external environment. Yes, if there's no other heat source compensating for the work done. Not really. The principle is conservation of energy. The heat lost by the fluid is equal to the work it does, but the fluid's temperature is only guaranteed to drop in those specific situations where there's not enough external or internal heat input to compensate for the work done. It's not a general principle, it's just an outcome that occurs in certain circumstances.

Or steam engines. The working fluid may cool off temporarily, in the specific configuration you're describing now, because there's no input of heat at the moment it's doing work, but it has to be reheated in order to do more work on the next cycle, and that's not the general definition of a heat engine.

Your phrasing ("Period.") suggested that there are no exceptions to your rule. @swansont was pointing out that there are plenty of exceptions, because your rule only describes the class of situations where there's no other heat source. All re-usable heat engines have a source of heat, because that's the only way they can keep running. External combustion for steam engines, internal combustion for piston engines in automobiles.

"Prevented" or "avoided" would be a better word. The temperature of the system that's doing work won't drop if the outflow of energy is compensated for by inflow from some heat source (such as an exothermic chemical reaction, for instance).

"readings"

Yes, it's wrong. [math]\theta<\kappa[/math] means "theta is less than kappa". Or something like that, given the context. Definitely not equivalence.

Maybe the word is a bit overdramatic. It doesn't mean the energy ceases to exist.

Heat in matter is energy in the form of random (i.e. uncorrelated) motions of molecules, atoms, and the subatomic particles inside them. That energy can be converted to other forms, for instance the kinetic energy of an automobile powered by an internal combustion engine.

GMT-3

It's Newton's 3rd law, the action-reaction law. A force is required to slow down the air, and therefore the air must exert an equal and opposite force on the wall. Pressure is force per unit area. @studiot's comment about the air's direction changing is partially right: Air can't just slow down and not go anywhere, because it already occupies all the volume in the region in front of the wall. So it curves upward (and doesn't slow down as much overall) before becoming turbulent around the top of the wall (at least if the wall is free-standing). Other way around: For solid objects, F causes the m to a. In the case of air being redirected by the wall, F = dp/dt = d(mv)/dt = v (dm/dt), i.e. the force from the wall keeps slowing down the horizontal velocity component of more and more incoming air, while the ground increases its vertical component. The wall and the ground can't do work on the air because they're not moving, so the overall effect is redirection. Generally speaking, there will usually be an ma for the air but not much for the wall. A brick wall won't go much of anywhere (i.e. not more than a few millimeters) until the force on it creates a torque that snaps it in two near the base. The force on the wall is caused by a combination of things: A distant(-ish) source of static high pressure, loss of momentum by a temporary gust of wind (that's the ma), and the net force can be further increased by a decrease in the pressure on the other side. You can think of the incoming air as riding up a sort of curved "ramp" that's made of pressurized air already in place near the lower regions of the wall. The microscopic picture is more complicated, but this is a reasonable macroscopic approximation. It's the same reason the nose of an ideal aerodynamic shape is rounded instead of pointy: At subsonic speeds, there's always a small amount of fluid that's already accelerated to the object's speed and repels incoming fluid more or less smoothly. Pressure is transmitted through air at the speed of sound, so this doesn't happen above that speed. That's why the noses of supersonic jets are pointy.

The air definitely experiences an acceleration, that's at least part of what causes the pressure on the wall, but calculating the amount of force is complicated. It's a problem in fluid dynamics, and where you have to start analyzing it will depend on what the source of the wind is. Air will slow down and be pushed upward, and there will be a chaotic vortex pattern that flows over the wall. High pressure on the wind side, low pressure on the other side, and the wall may be toppled by the torque of the wind acting in a region near the top of the wall and above the base.

I think it was. The only thing I don't see any discussion of is how the observers are supposed to know where the "midpoint" is when B and C receive their signals.

That's only true in B's reference frame. In C's reference frame, B begins to age earlier than twin C does. In the midpoint's reference frame, B and C begin to age at the same time. You need to start and end B and C at the same point if you want to make fair comparisons, and that means they have to accelerate.

... in B's reference frame. (I know you already said that, but sometimes it helps for beginners to see it again.) What were B and C doing before they received their signals?

3a. Another signal reaches B. B starts his clock. At this moment, neither B nor C is moving relative to the midpoint (because they've been waiting for the signal), so B's clock shows 0 and B calculates that C's clock also shows 0. 3b. B accelerates back toward the midpoint, and B also assumes that C has done the same. At this moment in the B frame, B's clock shows 0 and B calculates that C's clock already shows 5. Yes, but this is a problem with your example. B and C should really start at the midpoint (i.e. at the same point) if you want to make direct comparisons.

It's just the relativity of time, which depends on relative velocities. When the spaceships are moving away from each other, the Lorentz transformations indicate that each astronaut perceives or calculates the other astronaut's clock to be behind by [math]\gamma v D / c^2[/math], where v is their speed relative to each other and D is the distance between them. Then, as soon as they both turn around, each perceives/calculates the other's clock to be ahead by that amount (i.e. to have jumped forward by twice that amount).

"each twin sees the other twin as moving, and so, as a consequence of an incorrect and naive application of time dilation and the principle of relativity, [i.e. the Lorentz transformation for times] each should paradoxically find the other to have aged less." Surely not by anyone but trolls or clueless amateurs.

You're mangling the associativity of the operator (it's right-associative). We've proved A -> (A -> B), not (A -> A) -> B. In English, it's "if A, then if A then B", not "if (if A then A) then B".

+1! 😋