Saint

How about this for starters - authors are responsible for writing papers, responses, etc... in terms that can be understood by their target audience. Period. This is a skill that many people, not just physicists, are lacking. It's one of the reasons that skilled teachers are so few a far between. It's tough to do.

What?? On what is your curiosity based? Is it based on your research? I have a brain and an opinion. Pretty much the same as everyone else here. What level of study do you require to have an opinion, Tom?

Easy there killer - all I'm saying is that someone can, in fact, understand a given physical phenomena without ever using mathematics as his/her modelling tool. The problem that person might encounter when talking to someone who uses mathematics as his/her basis for understanding reality is that they would expect to get mathematically-based answers to questions. That bias toward mathematics does not discount the ability of someone to understand physical phenomena without mathematics. Does the physics world as a whole use mathematics - yes. Is it difficult to separate mathematics from physical reality once you've learned to look at it through a mathematical lense - yes. Is it possible to understand the physical world without mathematics - yes. The experiment used to validate a mathematical model can just as easliy be used as the basis for understanding. Trial, error and inspection, while time consuming, is a valid method for developing an understanding of a given phenomena.

What do physicists normally do to validate mathematical models?

On a related note, since we are talking about time dilation (Lorentz factor), does length contraction (Lorentz) work for the entire distance along the direction of travel? I mean, as you approach the speed of light, does the distance to an object you are leaving shrink as well? If you left Earth and accelerated to .9c, would the Earth appear to get closer? That's one that's always puzzled me.

Tom and Locrian, I should appologize for that one. I didn't mean to imply that physicists are incompetent. They're a whole lot smarter than I am, and I know they're doing their best to understand what's going on. I just don't buy relativity. I shouldn't make broad accusations like that.

You mean it's mathematically impossible, don't you? And causality isn't violated by travelling faster than c, unless you have to deal with time dilation, correct? I mean, velocity alone doesn't change causality, right? It's the relativistic time dilation/length contraction stuff that does it.

Really? Nothing else works with Maxwell's equation, AND fits experimental data for GPS, muons etc...? And I never said it was pulled out of someone's rear. I just said it had no mechanism. And it doesn't. It is a curve fit, because, even though no one understands a mechanism, they will stand up and say that evidence has been found for relativity because relativity's equations fit this data curve from such and such an experiment. Unless you can provide a mechanism for a theory, it is a curve fit. You're building equations to model results, not looking for the mechanisms that drive the results.

I'm talking about receivers and satellites, not about the cancellation of the frequency shift on the geiod. What I'm saying is that the GPS system is composed of a number of clocks, all moving wrt each other (at least the satellites are). So you have a bunch of clocks moving around, and relativity would suggest that they should all be running at different rates relative to one another. If you took a GPS satellite and a GPS receiver and put them in the same orbit, but travelling in opposite directions, the GPS system would conclude that there is no frequency shift between the two (same relative velocity wrt the ECI frame). Relativity would conclude that they are running at different rates wrt one another (approaching each other at 2X orbital velocity). Both can't be true. The fact is that the receiver would not see a frequency shift even though it was approaching the satellite at twice orbital velocity. Because they are both moving at the same velocity wrt the ECU frame.

What is the mechanism that drives radioactive decay? I assume you know what the mechanism is, and that that mechanism could never be influenced by acceleration or velocity. I assume that based on the fact that you jumped all the way to "time dilation" in order to show why muons reach the Earth. Or, by "time" do you simply mean the physical mechanism internal to the muon? If "time" is simply based on physical rates of vibration, then wouldn't it be more accurate, and less confusing to simply call it that?

Thanks Severian - I appreciate the time. One more question. WRT what are you moving in order to observe a doppler shift in a beam of light.

And I guess that ultimately where our disagreement comes from here. I don't see how you can approach the the wave peaks faster without approaching the beam of light faster. I mean, you have a beam of light, and the you have yourself. The only thing that changes the frequency in this case is your velocity wrt to the light beam. But that velocity is supposed to remain constant. It seems like you're saying that the relative speed will influence how often you encounter the wave peaks without inlfuencing your speed relative to the wave peaks. I don't see how that can be the case.