J.C.MacSwell

I'm pretty sure GDG had it right for a hot air balloon. Your right that it doesn't or shouldn't leak out, but it certainly is free to get out, as it is open at the bottom. http://www.inhabitat.com/wp-content/uploads/hotairbal-ed01.jpg

101%! I think we are assuming the majority are liquid hippos.

So...how does that differentiate time dilation due to expansion displacement vs movement displacement? Not disagreeing or agreeing there's a difference, but I don't see it in those paragraphs.

Ouch.

Moist air is heavier though, when it has liquid water suspended in the air. I think a lot of people consider that moist air.

Nice Link, but can you direct us to where it makes the time dilation distinction between expansion recession and recession due to movement otherwise? If we are both on the CMB rest frame but very far apart and I send a probe that accelerates toward you, closes the gap, decelerates less than it accelerated originally to come to a halt in your lap, is it then in the same time frame it started? I don't know, and saw nothing in that link that would indicate either way when I scanned it. Edit: I hadn't read NTWK's latest post. I will re-check and try and see if it makes sense to me. Re-edit: Checked it rather quickly but not sure that's the key. Isn't the expansion of the Lorentz interval not equal in all directions if you are not at rest wrt the CMB? How can it be invariant for GR if that is the case? (I can see how it is invariant for SR)

How about a mole of moles?The furry kind that can't see very well. That must be closer to the moon's size.

Fair enough, you have used pretty much the same definition of weight in each case. However, if you used a scale, 10 kg of lead would weigh more than 10 kg of feathers due to the greater buoyant force of the atmosphere on the feathers. That is more or less the definition some others have used in this thread. They have allowed buoyancy to be factored into the terms heavier or lighter. Still valid, but they are weighing things differently. OTOH, mass is always defined the same way. So on the moon, with no buoyant forces from the atmosphere 10 kg of lead or feathers weigh the same, even on a scale. The difference might be subtle, but become quite significant with respect to something as "light as air".

Not if while and when are defined in the same frame.

Which has more weight, 10 kg of lead or 10 kg of feathers? What about if you weighed them on the moon? Which has more mass, 10 lb of lead or 10 lb of feathers? A lot depends on how you define your terms. Does a boat weigh nothing when floating in water - or just enough to displace an equal weight of water?

Assuming the same mass of air they would weigh the same on the moon. Assuming the same volume the denser air would weigh more due to the additional mass in the same volume. No atmosphere means no buoyant forces to complicate matters. Most would say less dense air is lighter generally, but it depends on what you are comparing and what you mean by lighter.

Just to be clear, any time I referred to this ,it was with regard to a mass outside the sphere. I know I mentioned it with regard to a mass inside a hoop.

I think it was obvious to Newton, no calculation required, that the closer half sphere contributed more to the gravitational force on an external mass, than the further half. Every point on the closer half has a symmetrically opposite point. Each of those on the closer half contributes more gravitational force than the corresponding point on the further half. Not sure if Newton would have needed to give it even that much thought, to draw the above conclusion. Was it not obvious to you, or did you have to think about it? (I assume you didn't have to calculate it). Edit: Adding after seeing your last post: Geistke, there exists a point closer than the COM where half of the force contribution lies further away and half lies closer. However, for the purposes of modeling the gravitational force using the inverse square law the COM is exactly where to place a point mass for a sphere, not closer.

I thought your post #11 was in part replying to my post #10. Sorry about that.

The distortion is the natural shape of the object viewed from a chosen frame at significant relative velocity. Any lack of distortion, would be cause for alarm. That could lead to the spaceman's death. Beware the spaceman speeding by at relativistic speeds yet apparently undistorted. He is considerably "stressed".

When you integrate for a hoop though, say for a test mass inside the hoop, you would get a resultant force towards the nearest point on the hoop, where inside a spherical shell you would have no net force at all. A single hoop could be modeled as a point mass at the COM only as an approximation at a distance. It is the geometry of a sphere that conspires with the inverse square law to get the shell theorem. It doesn't work with any other shapes or groups of masses unless you carefully "tune" them. It is amazing that with everything else he did, Newton practically invented calculus to do this.

If you take the master clock with you on a trip it seizes to be a master clock...unless it worked on something outside of known physics. So you do the math based on distance, the speed of light and speed of sound and happily are confident that they were simultaneous. Do the same based on the distance and speed of light between the twins...and they each still think the other has slurred speech.

The gravitational net force towards a hoop does not act as if the mass was concentrated at the COM. In this particular case what Geistke describes makes sense (it would act as if the mass was closer to the object than the COM when outside the hoop but in the plane of the hoop) and I think he is confused with regard to the sphere being similar to that or to a group of masses. Edit: I thought Geistke's point was that the closer half of the sphere contributed to the gravitational force more than the further half, which is true and of course obvious to Newton. The resultant force acting as if at the COM is pretty much unique to the sphere, or shell of the sphere. It is exact and not a close approximation.

Let's say they stopped accelerating in a symmetrical predetermined way and started signaling each other as planned. They would both agree that the master clock had slowed the same amount relative to their own. But even after accounting for the time for transmission of the signals they would each think the other twin's clock had slowed, by more in fact than the master clock had slowed.

I think this is a great question. I don't know. I think it would depend on how you define "time frame". At rest with the CMB, or on the Big Bang Track is reference frame I like to use, but can it be considered an inertial frame? A continuum of inertial frames? Can a standard SR inertial frame extend cosmic distances and still give valid predictions? Earth would judge them to be in the same time frame. They each would each consider the Earth's time frame to have slowed the same amount, relative to their own, but they would not agree at all that they were in the same time frame. At the same time (so to speak), wouldn't each be at rest with respect to some distant point on the Big Bang Track, at rest in an inertial frame that included a Big Bang Track "rest point"? I don't, I have more questions than answers, but I think when you extrapolate local physics to cosmic distances and times, you must lose some degree of certainty. Someone with a better understanding of Astronomy, Cosmology and General Relativity like Martin may be able to give you a more definitive answer.

What Mokele said. In particular what you are describing sounds like a paraglider heading (and falling relative to the flow) upwind in a rising air current. Gravity has a slight forward component relative to the flow. Lift, a force perpendicular to the flow, has a slight forward component relative to the ground. The drag, a force parallel to the flow, has a slight upward component. It can all balance out so that the paraglider is stationary.

If you know the total net force and direction you have the resultant force. It effectively acts through the center of mass (assuming a homogenous sphere), not from that point. If you want to say the resultant acts through your CMF described that is fine, it is in the same direction, but it is not acting from that point either, the resultant simply is in that direction. The COM is simply an easier point to describe, can be used as the masses change in position, and is the point from which the inverse square is measured. Why complicate something that is being simplified? - the summing of gravitational forces into a resultant force that consistently acts through the COM. Do you think Newton didn't realize what you just described?

You are in an infinite number of reference frames at near lightspeed. How ya feelin'? No need to reply if you're dead.

The CMB frame is only an inertial frame locally, or more of a continuum of frames. There's lot's of fun to be had with this. If you go strictly by SR anything moving faster than light should be going backwards in time, so in our time frame some of the oldest things we are viewing should be much younger by now!

Yes Yes. If you know the mass, and acceleration due to gravity you can calculate the force. If the train hits the wall and slows down from 30mph to 10 mph over 2 seconds that would be the average force during that time, but you have to be careful not to mix metric and english units. Technically it is right, if you mean 50,000 kg miles/hr second, but you should convert this to standard units in one system so that it is recognizable. Before contact is made, how do you know how long the collision will last and the final speed?