timo

To be pedantic: The majority of ideas I looked into never appeared in journals - they turned out to be wrong, useless, or just less promising than an alternative idea that I could spend my time working on. That said, I'm talking about humble solutions to "why do I get result X?" or hypotheses about "what happens if I toy around with Y?". Not mighty questions about Life, the Universe, and everything.

No.

I've solved it, not even looked it through. But the first step I'd try would be [math] \sum_{k=1}^{3} \sum_{j=1}^{k} \sum_{i=1}^{j+k} ( i + k -j ) = \sum_{k=1}^{3} \sum_{j=1}^{k} \left[ (j+k)(k-j) + \sum_{i=1}^{j+k} i \right][/math].This allows to get rid of the i, as according to a local (and long-dead) mathematician, [math] \sum_{i=1}^{j+k} i = \frac{(j+k)(j+k+1)}{2}[/math]. I don't quite understand what you tried to do.

Until recently my job involved spending a month of full-time work to write an 8-page article (not counting the time that went into getting the results described therein, of course). My opinion on "here's a link, I don't want to spend my time to add a proper explanation" should be obvious from this. I agree that in this respect a video link is even worse than a link to a text in the sense that it takes even more time to figure if you are actually interested. Consequently, I pretty much never followed a video link posted on sfn.

Not sure how to formulate a coherent text. There is a lot that could be said, but I'd prefer you put it into context yourself, so I'll use bullet points. If I understood you correctly you now agree that what your professor showed you is a proper proof. This should imply that you believe the statement. This is all a proof is for. You do not have to like the proof. You may prefer other forms to prove the same statement for whatever reason. You are, in principle, entitled to your own style preferences (though in practice the necessity for interaction with colleagues limits this). The WP proof could be straighforwardly modified to show that the function is O(x^13). Correctness of a statement does not imply usefulness. Needing to proof a particular statement/assumption occurs frequently. For example, a Monte Carlo algorithm properly scans the possible events if it is ergodic and obeys detailed balance (no need to understand what that means). So if I devise an MC algorithm, I have quite an interest to prove these two assumed properties. I recommend for talented young scientists to explore their own ideas. But don't let it get into your way. In practice, the whole big-O thing is simple handwaving stuff. The reason your prof deals with it with some rigor is because otherwise some smart-ass would try to correct him. Didn't really work out, since now he has a smart-ass trying to generalize him . Computational Science/Physics can apparently mean some variety of things. I've worked in the field of computational physics (with emphasis on physics) for the last four years. I have not met a single computer scientist, there (those were the times ... ).

My condolences. Until a few weeks ago I thought physicists were slightly socially awkward. Then I picked up a new job and met the computer scientists. I don't quite understand your issues with the proof given on Wikipedia (assuming you are referring to the four lines of inequality on the section you linked to). It is absolutely common that in a mathematical proof you make steps that help you (e.g. x^4 >= x^2 for all x>=1) instead of steps that don't help you (x^3 >= x^2 for x>=1). You need to convince yourself (and the juror of your proof) that the steps are correct. But a proof for a statement is not necessarily unique. And there is nothing wrong with trying to prove a statement that you made prior to the proof. EDIT: Perhaps I should at the following for clarification: The proof does not prove that the function is not O(x^3).

But at least it isn't just plain rude.

I wonder if the candidates at least read "their answers".

I don't see how this metric violates the triangle inequality and I particularly do not understand the rest of your post.

What's your own thoughts on it? What have you tried so far? Have you read the homework help rules of this forum?

You certainly should treat the case properly to arrive at the correct results. What I was trying to express is that I am not convinced that "photon in vacuum that is absorbed and re-emitted by electrons from time to time" is the proper treatment or point of view. Or with respect to what you said: I was wondering if the common folklore about "photons in media" is the proper way to go to calculate the "probabilities of all possible paths".

That's a very popular picture. I believe it's wrong: You inherently assume that the vacuum solution of the electromagnetic field is a proper Ansatz for the electromagnetic field in a medium, even for cases where the photon wavelength far exceeds the interatomic distance. In a medium, I wouldn't even speak of "photons" at all (as photons, by the physics I learned, are excitations around a vaccuum state of the electromagnetic field).

You're right. But being faster than light in any medium is just not what is meant by saying that you cannot exceed the speed of light. There, "speed of light" refers to the speed of light in vacuum. You did discover an instance of inaccurate/incomplete/ambiguous use of language.

For "please explain scientific topic X", Wikipedia is usually a good first place to turn to. Or Google. Or, if you are serious about your question, a textbook.

But that of course is still very vague, given that engineers routinely work with objects way above the Planck mass and still get along nicely without a theory of quantum gravity.

And in the context of R^n it's called the taxicab metric or L1 metric (though I am not 100% certain that the captial letter is an L - but somewhat sure), or -according to the German Wikipedia- Manhattan metric (never heard or used that term myself, though). If you plan on posting more mathematical expressions on sfn in the future (you already have 44 posts here, after all), then I recommend looking into the Latex capabilities of this forum (just search for "latex" on this forum).

1) It's not an equation at all, owing to the lack of an "=" sign. It's a "term" or "expression". 2) Of course I know what it is: The graphical representation of the term is directly above it. 3) There are no Mandelstamm variables in the expression. It is a t-channel diagramm, though. 4) I'm not a nuclear physicist. But I am a particle physicist in some sense, which is probably what you actually meant by "nuclear physicist".

Absolutely. It's a pitty that all those smart people outside there are so lazy. We, in our plot, avoid lazyness problems by only chosing the most reliable people as moderators, since that job involves things like removing the automatically generated link to the new location by hand. Nothing. It's not needed for my role in our plot.

No way are we going to tell you where your post went (we were actually hoping that you wouldn't realize that "has been moved to speculations" was a lie). We'd all be unemployed if you uncovered our dark matter plot.

If "instantaneous data transfer" means the sending of information and the receiving of information at different locations happening at the same time (in a Minkowski spacetime), then this violates causality in the sense that it is defined in special relativity. I think it's actually only fundamental for our mainstream ideas of how the universe works. If it was fundamental to how the universe works then we already knew that causality is not violated. I call this an urban myth. It's not more related to causality than switching on a lightbulb is (though admittedly switching on a lightbulb could have been what you meant with "etc"). The common statement heard in this context is that faster-than-light effects do not allow to carry information faster than light. To me that sounds like a cheap excuse for a problem of theory assumptions not holding true in reality. But I acknowledge that a) "do not allow for FTL information transport" is probably just the laymens' version and about as accurate as "LHC tries to recreate the Big Bang", and b) I lack the competence to form a proper opinion on the matter.

I don't think that single-proton bunches pose an unsolvable problem. But I don't see why one would want to do that. Main effect should be that you significantly reduce the number of collisions, and therefore amount of data you can collect, per time unit.

The line of thought is not that bad, in my opinion. Of course, it relies on the analogy with the slowing down to also be a good analogy for this aspect. As you correctly say yourself (in the part I didn't quote), that may or may not be the case. But I don't want to go into this question at the moment, because saying "the analogy breaks down here" would be a cheap excuse for an answer, and I cannot offer a better one at the moment. What I personally find more interesting or fruitful (and you are invited to disagree) is still considering the question I asked above: You have explained your thought a bit more now. But I still don't see how they warrant the conclusion that "mass is very similar to kinetic energy".

I don't see how "the Higgs field gives mass to the elementary particles" suggests the statement "mass is very similar to kinetic energy".

Sure. In the economists' perspective.

A lot of the apparently obvious problems with relativity mentioned in the OP could probably be resolved by actually knowing a bit about the topic. Didn't read the "Fresnel lens theory" part, so I cannot comment on that.