1) Message boards : LHC@home Science : If Neutrinos have no mass, can they escape a black hole? (Message 17459)
Posted 20 Jul 2007 by David C.
Post:
Millikan's oil drop experiment showed that charge is quantized. It had nothing to do with the mass of the electron.
Touché. You have proven that my memory of physics curriculum is rusty.

However, I do sense that you you believe that mass and energy are well separated concepts. That, I am still confident, is shaky ground. Consider wave-particle duality; it is clear that these concepts are NOT well separated. the Schrödinger equation, the de Broglie hypothesis, and the Heisenberg uncertainty principle all point to this idea.

But how does wave-particle duality relate to mass-energy duality? Notice that in modern physics, the terms "mass, velocity" and even "energy" are often replaced by the concept of momentum. Momentum allows us to side-step the problems of thinking about particle 'x' having mass, velocity, energy, or some combination of these. It's a handy theoretical (and for now, mathematical) shortcut. Your full energy-momentum relation in special relativity was certainly a shot in the arm for me, but is there a mass-momentum relation in special relativity? Enlighten me if you have the time; I'm eager to learn.


Your sense about him believing mass and energy are well separated is incorrect. He's simply stating one of the basic equations of special relativity, which is, again

E^2 - p^2c^2 = m^2c^4

where m denotes the invariant or rest mass. A photon has no rest mass, so the equation reduces to

E = pc

where p is the momentum of the photon. Even though the photon has no rest mass, that doesn't make it an exception to general relativity. In fact, because the photon has no invariant mass, it will travel along a perfect geodesic since it does not distort spacetime.

To answer your other question, yes, there is a mass-momentum relationship in special relativity, but it only applies to particles that actually have mass (read: invariant or rest mass).

It is:

p = mv/Sqrt[1-v^2/c^2]

I am unsure if you are familiar with the concept of a Taylor series, but it is a common technique used in physics to approximate an equation about some value by an infinite series. The idea is to find a polynomial whose derivatives all match a given function at a point of interest. The upshot is that the more terms you add, the better the approximation is, and for small perturbations, the approximation is extremely accurate. In this case, we can take the above expression and expand it into this series:

p = mv + mv^3/(2c^2) + 3mv^5/(8c^4) + O(v^6)

where the O term denotes whatever higher order terms I have left out in this expansion (the higher the order, typically the less important the term). The interesting point is that we see the first term (typically the most important) is mv, which is the classical expression for momentum, so we know then that the special relativity relation for momentum-rest mass reduces to what we classically expect in the small velocity regime v << c.
2) Message boards : Number crunching : Results of LHC@Home (Message 9097)
Posted 2 Aug 2005 by David C.
Post:
Well, what I really meant is not how many units of computation the project has done, but what the actual result is of that computation. i.e. what did it tell us? The article about picking up signals seems like something that doesn't really explicitly cite our computation efforts, and I'm wondering if there are any like formal papers that talk about what scientists can infer from the data we've computed.
3) Message boards : Number crunching : Results of LHC@Home (Message 9017)
Posted 29 Jul 2005 by David C.
Post:
It seems like the project has been going for quite some time now, albeit only recently has the number of accounts been allowed to increase quite a bit.

I'm wondering if there is anywhere we can see the results of our computations? I understand that we are simply calculating run throughs under different conditions to find the best condition for operation, but are there any research papers to read that talk about the results thus far? I know that every now and then, the project is paused while physicists analyze the results - is there any way we could read about the results of this analysis?

-David



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