timo

It's not so awesome, actually: - For a start, it should be clear that assuming movement of the airplane is co-linear with the distance of the twins then the orientation of airplane movement determines the order of the events while the time-distance in the new frame is independent of orientation. - All the question is about is that you have two positions in spacetime P1=(0,0) and P2=(0,X) that get transformed to P1'=[math]\Lambda P_1[/math] = (p1t, p1x) and P2'=(p2t, p2x), respectively (1st entry is the time coordinate, 2nd is space coordinate, i.e. X=500 km, [math]\Lambda[/math] symbolizing a Lorentz-transformation). The time-distance is |p1t - p2t|, of course.

That kind of reasoning would straightforwardly lead to 1=2. @Gutz: There is no sensible reason to assume space as a discrete (countable) set of points as you seem to do (I might have misunderstood you, thugh). The real numbers and calculus were invented centuries ago and have been very successful.

The slow reaction of your eyes or brain, I guess. I first thought it is more likely to be the eyes but when thinking about how movies work (a set of static pictures appear like fluent movement) it might as well be the brain.

Substract the whole number before the dot then multiply by seven again. Not sure if that is really what you asked for, though. "145757 r 5" ist just a way to write "145757 + 5/7", after all.

We [physicists] call the stuff pseudo-norm and pseudo-metric when/if talking to mathematicians.

Well, does you brother have to find a common solution for the two equations in any way or by graphing? Sam's way leads to a solution but not by graphing. For finding a solution by graphing (whyever you'd want that) you would indeed rewrite both equations in the form y=..., plot them both (possibly by formally replacing y with f(x), depending on the notation you are used to) and look for the intersection point(s).

Parallel and anti-parallel to the external field.

I often see a capital phi ([math]\Phi[/math]) for physics. Not sure how "official" that is, though.

Let's name the variables in the moving system (referring to your nomenclature) with primes. As long as you do not change coordinate systems for the relation between distance d/d' , velocity v/v' with which the distance is crossed and time t/t' it takes to cross the distance there is no difference between SR and non-relativistic cases: (1): v = d/t (2): v' = d'/t' What you probably know is that the velocity v that the rocket moves in the rest frame is the same as the velocity v' of that the target approaches the rocket with in the moving frame. The time distances measured for the process and the space distances measured for the initial state for the two different frames are related to each other by (3): [math] t = \gamma t'[/math] and (4): [math]d = \gamma d'[/math]. Given is the time t' and the distance d' so you have calculate t via (3) (=my approach) and the plug into (1) or d' via (4) and plug into the equations for the moving frame (Tom's approach). I have to go now so no more details right now. Just as a comment: Tom's [math] \frac L\gamma [/math] (the whole fraction, not only nominator or denominator) is your x'; see eq. 4.

No. It is any space-distance and any time-distance that gets a Gamov-factor under changes of coordinate systems, not only the diameter of one object (you'd already run into problems for a scenario with 3 rockets) or the time of one clock*. Yes, see above. Comment: Rather than transforming the distance into the frame of the traveller you can (equivalently) just transform the time into the implicitly-assumed rest-frame (implicitly-assumed because the distance given must refer to some frame). The time it takes in the rest-frame is distance/velocity. The time in the traveller's frame is the time in the rest-frame with a suitable Gamov-factor => solve for v (might have to do that numerically). *: Despite having used the word: I strongly dislike this "clock runs slower" way of explaining relativity. I do not understand it. People trying to learn relativity have struggle with it (compared to how simple classical SR actually is). Crackpots use it as a starting point for spreading nonsense about "time does not go slower, only the clocks do".

There's rumors that IMM only became a moderator because they have the cut of the Star Trek TNG uniforms.

My guess is 1645 for Swansont. Reputations points can easily rank much higher (you even start at 10, I think) than the "Rep. power" number in the lower left, in case you mixed than up.

It's a logical continuation of Tesla's late work, after all.

[math]x^*[/math] ? Just use x^* or x^{*}.

I think you are simply answering a different question than me, namely "does a radioactive decay influence a chemical binding?". In that case: I would the first significant influence expect to be the recoil on the (formerly-)Uranium nucleus. In the case of an alpha decay that is MeV kinetic energy against a binding energy in the eV. I wouldn't be too surprised if the binding ripped. Whether decay products recombine later then depend on the environment and of course also on what was left of the uranium nucleus. EDIT: And I start to begin to understand why we did understand the OP differently. I think vedmecum did indeed ask what happens to the chemical binding, not whether the binding will influence the decay of the Uranium nucleus.

I was assuming the question was if the chemical binding of a radioactive atom has an influence on its radioactivity. The answer is basically "no". I might have misunderstood the question.

1) Don't worry: It's not so many people familiar with nuclear reactions, certainly not all (I am not, for example). 2) Nuclear reactions, like the radioactive decay of uranium you mentioned, are a process happening in the nucleus, not in the electron shell. Chemistry is concerned with the electron shell of atoms (and the complex structures these shells can form). 3) As a rule of thumb the nucleus cares pretty little for the electron shell. An Uranium-Oxygen binding is a structure formed by the electron shell. So you can assume that at least as long you do not consider any form of complex interplay of a radioactive substance with its surrounding (like mediators in nuclear reactors) the radioactivity of Uranium is the same as the radioactivity of uranium oxide.

I'm afraid the food the journals' staff eats does.

Not sure what "x2" is but in any case you have to integrate. For example for getting the mass you add up the masses of small pieces of the rod which in the limit of very small pieces is an integration over the density. For the center of mass (what is what CM means?) you should have a suitable formula (if not, then think of one) that you can also take the limit of super small pieces of.

The charge degree of freedom is fixed with giving the reaction partners. The kinetics (strictly speaking also the reaction mechanism) is not fixed. There are kinetic configurations for the process (say all for which the muon gets 3 GeV kinetic energy) which would violate energy conservation and hence do not occur in nature. You implicitly claimed that if the sum of the masses of the reactants and their kinetic energies is at least as high as the sum of the masses of the products then the reaction can occur. This assumption is true in the cms system and only in the cms system. I am not sure to what extent this frame-dependence is obvious to everyone. In short: I thought I should give a hint that a reaction of course also must conserve momentum.

The assumptions that nature's laws are the same everywhere in the universe is one of the most fundamental assumptions for cosmology (they even go a step further and for practical purposes often assume that the universe looks the same everywhere). I am not sure if I would call it arbitrary. It is a choice and there is no proof that the choice is correct, yes. But that is true for other common choices in science, too. Some assumptions are simply an integral part of a scientific field. Not exactly what you talk about but related (assuming identity in time rather than space): One of the most basic assumptions in science, particularly physics, is that one you (experimentally) found some rule to apply to some situation you assume that it will also apply next time. Like: For the last 1000 years apples fell to the ground, therefore apples will fall to the ground in the future. This assumptions seems obvious (I claim that is because it is how human learning works) but that is no reason for correctness - in fact "seems obvious" is often an "erroneous content here"-sign. The approach also has lead to great successes in the past - but taking this as an argument is self-referencing. I do not know what the philosophers' answer to the problem is but afaik there is a whole branch of philosophy ("Epistemology", according to Wikipedia-translation) dedicated to the question what you can really know. At least in physics at some point you simply have to assume things to come to conclusions. For me that is also a strong argument to consider science as something that should ultimately lead to applications - an attitude that most of my colleagues do not share, as far as I know.

I think you should add a plan or at least a few comments how you plan to keep posts in this thread legal, i.e. without copyright violations.

Being pedantic one should say "can conserve", not "conserves" (for energy).

I would rather assume that most experts would argue that light traveling through some medium with a high refractive index will not suddenly emit light that is not slowed down. Hence, you do not see a "ball of bright" moving through the high-refraction medium. Seeing light from a source that no longer emits is an old hat - it is commonly believed that some stars that we see on the night sky do no longer exist. Putting in obstacles with a high refractive index does not qualitatively change anything. It might quantitatively change something; namely put time and distance in a different relation.

All below applies to de.wikipedia.org, not en.wikipedia.org. To answer the last question first: I used to edit a bit. Started with smaller mistakes, then rewrote paragraphs, then moved on to rewriting whole (but relatively small) articles. Now I almost completely stopped due to not having (read: wanting to take) enough free time for WP (why spend time editing WP when I can instead spend the time on my work?) and due to a dislike for the community there. My biggest problem is the people who want to be helpful, who simply have no competence but want to contribute. Not those who want to vandalize (barely seen any of those, in fact). And I really lost any interest discussing with those people, particularly the "I attended a [quantum mechanics/electrodynamics/whatever] lecture this semester so I know everything about modern physics"-idiots. My current interest in discussions on WP is so low that I leave such contributions -even when obviously wrong- uncommented. If a physics topic is over the head of a physics student then in the end it probably doesn't matter if the WP article on the topic is correct or not. The majority of people will only read the introduction paragraph, professionals do not get information from WP when accuracy counts. My feeling, also from discussions within WP, is that vandalism is a serious non-existing problem. Do I understand you correctly that people do not edit WP because they are afraid of vandals? I imagined the other way round to be a bigger problem: If I am an expert in a certain field, do I want to correct an error or rewrite a section if a teenager then just resets everything with a single click and the message "no improvement on the existing article"? I am not sure if I understand that statement: The frequent use of WP as a reference certainly is a sign that many people get their online information (I assume by references you talk about an online environment) from it. For me that is a sign that information about a topic is easy to find there. So you think that when you present good information there you can educate many people? I am not convinced that looking up terms in an encyclopedia really contributes to education.