J.C.MacSwell

The ball will reach 3.1 metres

An atom of hydrogen would not have a defined temperature. If you heat something up the mass increases and that mass would be considered in any gravitational effect calculation.

...well for having a cup of tea, you have your fluid dynamics, your heat transfer... ...and of course some finite suffering and pain if it is too hot... ...so for the OP, more of that and for longer...

The simplest formula generally is that the buoyant force is equal to the displacement (weight of volume of water displaced) It means it could be anywhere in the fluid. Unless a change in pressure changes the density of the object it will tend to stay where it is, or continue on it's path. It has neutral buoyancy.

regular old water is 10 lb per regular old gallon What do you need it for?

http://en.wikipedia.org/wiki/Cyclic_model

I think... therefore I sweet potato.

Luxury! I used to live in a paper bag...

That's it. Not that the clocks are right. Essentially they are reading the signallers time, not there own. So the clocks tend to agree, even if they accumulate an increasing error for their location (+ or - depending on location) That's it. Not that the clocks are right. Essentially they are reading the signallers time, not there own. So the clocks tend to agree, even if they accumulate an increasing error for their location (+ or - depending on location) I guess the GPS gets tuned to "Earth time" (lapse) not it's own.

Statistically speaking, that's probably the most likely scenario: http://www.nytimes.com/2008/01/15/science/15brain.html?em&ex=1200718800&en=0aad49ca807c848f&ei=5087%0A

I don't see the difference. The incoming signal is received at different frequencies but the time elapsed at each location compensates. So the clocks are kept in synch. After 10 (or 10,000,000) signals/cycles only the signal lag of the last signal, including any relativistic effects, will effect the difference in the clocks. Once received, each will have received 10 (or 10,000,000) signals/cycles

My interpretation of the proposed scenario: The remote driver of the signal is driving the two clocks.Their time can vary but the difference cannot accumulate. If the two clocks were proper time clocks for their respective locations the difference would accumulate, but they are constantly adjusted ("incorrected") to match within signal time and 1 cycle time differences by the remote driver.

These effects should cancel with that of the proper time elapse of each location.They would both be constantly "incorrected" to match each other, and never get far out of synch with each other.

At some point the gravitational attraction of the Earth becomes insignificant to the extended column of water. So the question is closer to "what is the pressure of an infinite column of water 10 X 10 meters?" and adjust locally for the Earth as it may still be highest at the "bottom". Without doing the math I would hazard a guess that it converges to a limit, and does not create a black hole.

With sound you have a preferred reference frame, that of the rest frame of the air.

Long live the King!

Negentropy http://en.wikipedia.org/wiki/Negentropy

So you are describing a frame in uniform motion as inside a vehicle in uniform motion. But not everything inside a vehicle is necessarily going the same speed or direction...things can be in motion, both uniform or otherwise with respect to this frame. So is everything inside the vehicle still in this frame? The driver? The wheels? The passenger in the back that is switching seats?

It got a little OT, but it was to do with what can be considered "in a frame". The accelerations discussed were more with respect to the frame, not due to the frame itself accelerating. If you have a link to a definition of being "in a frame" that would be helpful. I do not believe a definitive one exists, leaving it somewhat ambiguous and depending on context.

Physics is not the problem. It is the definition of what can be considered to be in a frame.

I understand what you mean, but to me (present interpretation) they are in each others frames, but do not share the same rest frame. The two observers still exist in each others time and space. I think sometimes people learning SR get some mysterious sense that they are separate, and it is reinforced when they are told they are not in the same frame as each other and misinterpret the context. The frame is not accelerating. The object at rest (zero velocity) with respect to it's coordinates is. An inertial frame is said to be one in which physics takes it's simplest form. Obviously this does not just refer to the physics of fixed objects so context is everything. I think I misinterpreted this (bolded). So you are saying an accelerating object is not in an inertial frame, not even one that it has zero velocity in. I'm OK with your interpretation, though I don't think it is universal in physics and do not see where it is taught or defined (prior to here) It seems unnecessarily non intuitive to say my arm is not in the frame of my body, or something inside a rocket is not in the frame of the rocket. At other times it makes more sense, though using phrases like "at rest in or "with respect to" makes the context more clear.

"However, a frame of reference can always be chosen in which it remains stationary" Choice implies that there are others in which it does not remain stationary Too me that example just states that you can choose an inertial rest frame for an object that is at rest (no external forces) Not sure how that summarizes what you quoted, but in any case this contradicts your definition for an accelerating object not being in any inertial frame... ...since you can always choose an inertial frame that it would be stationary with respect to the coordinates of (zero velocity, regardless of the acceleration) Sorry if this seems picky, that is not my intention, but to me "not in a frame" needs context, and I don't believe everyone automatically realizes you mean "not fixed in the coordinates of" or even "not at rest in". At times in can be inferred from the discussion (easier with your peers) but at times it seems misleading or implies something has somehow moved outside of a frame.

I've seen that. I don't see where it would support your definition of what is in or not in.

So "not in that frame" simply means not at rest and not accelerating in that frame? Even while accelerating, there exists an inertial frame with respect to which I am at rest, though only instantaneously. So from your definition I am not in that frame? "In that frame" means fixed in that frame? Can you provide a link or source for that definition? Is it just the context you and your peers always use or is it strictly defined in physics?

To me this seems more than a little ambiguous and a source of confusion (it can't be just me) Is there a link or source for that definition? Can you explain why something that is clearly there is said or implied not to be there? My use of of the phrase "in the frame", would include everything of interest, including any Mack Truck in my vicinity accelerating or not. Can you tell me why this is wrong? I know that "in the frame of the truck" would imply something different but that is true whether the truck is accelerating or not. Inertial frames are generally chosen as they simplify the physics, and not just linear transformations. Others are chosen because they simplify the math, at the price of adding pseudo forces to the physics. If your definition is correct for physics there must be a reason for it. What is the use of it? Why is something that is accelerating said to be not in the frame?