Saint

All I'm saying is that while the constant "c" may appear in many of our models, the physical connection between c and the interactions we're modeling may not physically exist. Since most of our models are based on validation through observation, we can use many terms that may not have any bearing on the physical reality of the interaction being modelled. I realize this is the best we can do in many cases, but we should be careful when making the statement that changing one of our "constants" would alter the physical reality of an interaction. That statement requires a deeper understanding of the physical reality, not just the model. You asked: "Does it matter if that's the way nature actually behaves?" Well, if you're just talking about a constant "c", unrelated to the physical reality of the speed of light in a vacuum, then no. But once you apply a physical meaning to that constant; pull it off the page and relate it to something real, then yes. I would think that it would be important to define models in such a way that they accurately portray the way nature behaves, not just an accurate curve fit for the observable outcomes. Again, I don't know one way or the other. Nuclear physics is not my forte. You may very well be correct. This is just something worth mentioning in the context of theoretical physics.

Do they truly depend on the value of c, or do the equations we've developed to model the interactions depend on c? I'm asking because I don't know. But you should realize that there is a difference.

OK - so the universe started out non-homogeneous. It would seem difficult for a singularity (the thing that got "banged"), to be non-homogeneous would it not? Wouldn't all the non-homogeneity have been "squeezed" out the singularity by definition? I guess the question is: where did the non-homogeneity come from? How would it arise from a homogeneous singularity?

Severian - thanks for the response. I guess my question then continues: if everything was flying away from everything else very early on - before galaxy formation could occur, and the galaxies, as they are currently understood, are in fact still flying away from each other (even accelerating?), what enabled them to form in the first place? It seems that they would have required a pretty solid chunk of mass to start with in order to attempt to pull together the particles that were expanding away from each other.

Just a quick question about the expansion of the universe. What is the largest unit of cosmic classification (solar system, galaxy etc...) for which the expansion does not apply? I mean, does the expansion of the universe only imply that galaxies are moving away from each other? Are the galaxies themselves expanding by some smaller factor as well?

It seems that this discussion really gets to the heart of the relativity debate. Velocity can only be defined wrt to something else. That is, we cannot describe an absolute velocity (according to relativity). With respect to what is acceleration defined? If velocity wrt something else is truly relative, and can lead to the "observed" conclusion that clock A is running faster than clock B from A's point of view, and vice versa from B's point of view, what is it that allows acceleration to make that "observed" clock rate difference a reality? If velocity is relative, how can changing the relative rate of movement between two bodies (acceleration) be an absolute? What makes acceleration real, while it's resulting velocity is simply relative.

Since when is a stationary clock, on earth, truly inertial? There is no inertial frame. We use that term wrt the earth with the understanding that's it not true, but is convenient. Everything is moving relative to something else. The claim of relativity seems to suggest that every moving frame (whether you want to approximate it as inertial or not) has a valid claim to the statment that every other moving object is aging slower.

Moving relative to what? When a satellite orbits the earth, they are both moving around the sun. And, the satellite is generally moving slower than the earth wrt the sun for half of it's orbit, and faster for the other half. So when you state that moving clocks run slower, you really have to be specific as to what you're using for comparison.

Why does the direction of force matter? It seems like you're coming close to recognizing absolute space. Force is force. Acceleration is acceleration. Accelerating one way and then the next does not changes the fact that you are accelerating the whole time. Accelerating in one direction to the speed of light (slowing down the clock) and then turning around and accelerating the other way to the speed of light doesn't reverse the slowing of the clock. If it does, then you enter into the absolute space realm. Relativity doesn't like absolutes.

Severian - When you talk about force are you neglecting the force of gravity on twin one? There has never been a clear difference between "force" through acceleration as opposed to "force" through gravitation. People get muddled quite a bit when this topic somes up. If twin one stays on earth, subject to 1g the entire time, and twin two rides a ship that accelerates at 1g up to the speed of light, decelerates at 1g, and turns around to head back under 1g acceleration, then they've both been subject to the same forces the entire time. How does force play into that scenario.