First collisions at the LHC with unprecedented Energy! (Ask a particle physisicist)

[Iroscato]

That gave me a fuckin' nosebleed.

[pocaracas]

How cool! The integral of x^n * exp(x), from 0 to infinity, is n!
Thanks Alex!

[Alex K]

@poca
You mean x^n * exp(-x), surely, otherwise it's not finite.

Look up the Gamma function which is directly related to n!, the above is more or less its definition.

But I'll tell you a secret (the most useful trick in the book when working with moments of exponentials): such identities and similar ones can for example be proven by introducing an auxiliary variable in the exponent:

exp(-a x)

and realizing that n times the derivative with respect to a and then setting a=1 gives you (-1)^n x^n exp(-x).
You can therefore simply calculate the integral

int_0^infty exp(-a x)

and *then* perform the derivatives. All you have to take care of is to put the appropriate minus sign to compensate for the (-1)^n.

But it turns out that simply,

int_0^infty exp(-a x)= a^-1

Taking the derivatives of that with respect to "a" the required number of times automatically gives you the combinatorial factor n! from the rule for calculating derivatives of monomials, and the alternating minus sign which cancels the extra (-1)^n above.

[pocaracas]

Right... I do tend to lose the minus sign...
Everything else... I'm more on the engineering side, so I'd resort to a table - Abramowitz & Stegun FTW! https://books.google.pt/books/about/Hand...MvoC&hl=en

[Alex K]

Table shmable. What if you're stranded on a desert island and really need to know the integral of x^n e^-x^2 to divert a sabre tooth tiger? What then, huh? Will the Russians come to the rescue? I think not!

[pocaracas]

Table shmable. What if you're stranded on a desert island and really need to know the integral of x^n e^-x^2 to divert a sabre tooth tiger? What then, huh? Will the Russians come to the rescue? I think not!

I build a power station to power my computer and, since it is known that all desert islands have satellite internet access, I'll have all the tables in the world at my disposal.

It's important knowing how to get there... but, for most practical uses, it's enough to know the result.

[Alex K]

Well, if you insist on doing it the hard way...

[Jackalope]

Here's something that kept me awake the other night.

You are no doubt familiar with some of the various experiments with quantum entanglement.  The experiments and their results are strange enough to be sure, but my question isn't really about that.

How are individual entangled (or non-entangled, for that matter) particles observed?  (Think back to the 1998 Caltech experiment where an individual photon was "teleported" about a meter.  What means is used to make the observations?

Often , a particular property of the particle is measured. For example, the polarization of a photon. The photon itself can be measured using a photo multiplier, and the polarization is decided by putting a polarizing surface or something in front of the photomultipliers. E.g. the decay of spin 0 positronium into two photons can be assumed to produce a quantum superposition of two photons with entangled opposite polarizations going off in opposite directions. One then catches them as far apart as possible with detectors  set up on opposite sides of the source. Does that answer the question a bit?

More or less, yeah, but I still wonder how an individual photon is isolated for observation like that. I mean that's kind of hard to wrap my brain around.

....wishing I had followed through on my intent to study physics beyond the two years I took in high school.

[Pyrrho]

Okay.  What questions should we be asking?  And what are the answers to those questions?

Seriously, if you can't come up with good questions, how do you expect non-physicists to come up with good questions?

What is it that we should know that we probably don't know about physics?  And why have you not told us these things before?

Although it wasn't clearly marked, I was specifically responding to JuliaL who mentioned that she had some more concrete questions, but after a round of googling didn't dare to ask them any more because they seemed too trivial. I was trying to encourage her to ask them anyway.

But to answer your question...

1. I kinda lost track of what I have mentioned before specifically, but I think what most people are not aware of, or underestimate, is: how well the theory describing the underlying rules for every process in our everyday lives is already known. Calling the scientific discipline "particle physics" is misleading - it actually is the study of the fundamental laws of nature. We have already come scary far, so for all practical intents and purposes, we already have the theory of everything. Everything you observe around you, and everything going on in your body, is based on laws that are well understood and tested to precision. No wiggle room.

Okay.  So what are the laws of nature?  Or can you recommend a short book?  Would something like this be a good choice?  If not, what do you recommend that is on that reading level?  Of course, you may feel free to just explain it all here.

This brings me to the second point: people should be more aware of what it means to know the fundamental laws of nature, and what one can do with them and where the limitations of interpretation are.

Okay.  So what does it mean to know the fundamental laws of nature, and what can one do with them and where are the limits of interpretation?

What Effective Theories are and what role they play in our understanding of nature. How the concept can loosely be applied universally beyond particle physics.

Okay.  So what are Effective Theories and what role do they play in our understanding of nature?  How can this be loosely applied beyond particle physics?

2. Then there are more specific questions: I think there are a lot of misconceptions and outdated notions about what the Big Bang is, what the scientific claims about it and evidence for it are, and what it is not. Where speculation begins

I am a bit less interested in the Big Bang, because unlike a lot of people, I am not obsessed with "knowing" the origins of the universe (I think it matters far less than many people seem to think; certainly, most people have lived their entire lives without knowing the answer to the question, and they still could have good lives that way).  But since you bring it up, what are the misconceptions that people have about the Big Bang?  What are the scientific claims about it?  What is the evidence for it?  And where does speculation begin on it?


That should be enough questions for the moment.

[popeyespappy]

But since you bring it up, what are the misconceptions that people have about the Big Bang?

You mean besides for goddidit about 6000 years ago?