Severian

The quenched approximation neglects the creation of quark-antiquark pairs, so you could still have gluonic vacuum fluctuations (since the gluon is colored).

I do too, but I don't think that is strange. A typical eight year old child doesn't really understand death. He probably just wanted his father to go away and leave him alone forever. Also children are a reflection of the environment they are brought up in - so the very fact that he is willing to shoot someone with a gun tells us that (most probably) his father was not a very good role model. I don't think it is fair to put all the blame on the kid. I am a strong believer that parents should be held responsible for their children's crimes, and in this case the punishment has already been meted out.

Are you sure? Hardly any serious calculations are done with the quenched approximation. The linked article mentions the calculation of the [math]B_c[/math] mass, and makes it sound like this is the next step (since it is for lighter quarks). That calculation (whose author sits in the office just across the hall from me) was not quenched and used a staggered action. I find it hard to believe they would get 2% accuracy with a quenched approximation.

It is so annoying when papers are published in Science rather than a more respectable journal, because I can never read them! Does anyone know what lattice action they used? The staggered action?

I should point out that (if quantum mechanics is correct) while the universe is not deterministic, it is stochastically deterministic. That is, the path down which the universe travels is decided by a set of random numbers and given the set of random number required for each measurement, the outcomes are fixed. Since the numbers are random, you have no control over them, so quantum mechanics is also not compatible with the classical notion of free will.

My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair!

How many times do we need to have this discussion?

What rubbish. The USA was founded on democratic principles. It doesn't matter one bit whether that is direct or representative democracy. The fact of the matter remains that the question under discussion was put to the vote and the electorate made its opinion clear. If you do not want to follow the decision of a democratic vote, then your representative democracy should not ask the electorate to vote on the issue. Would you still be saying that this is too important a decision to place before the electorate if your opinion had been reflected by the majority vote?

That is the price you have to pay for democracy. Banning slavery even though the majority want it is undemocratic. I would argue that the majority is "wrong" if they want slavery, but who am I to enforce my will on the majority. I would rather persuade them to my point of view with reasoned argument.

Democracy is by definition the oppression of the minority by the majority. But if you try and circumvent democracy by legislation (rather than persuasion) I think you are on a very slippery slope.

You forgot one of the pros supporting proposition 8: it was agreed by a democratic vote. You may be of the opinion that democracy doesn't work (fine, up to you), but you must recognize that active opposition to it (i.e. more than just stating your opinion) is fundamentally undemocratic.

What's wrong with saying "Where in line are you?", or alternatively. "Excuse me, Sir. May I inquire as to your position in this queue?"

Wouldn't you be better just buying some commercially available solar panels?

In my view, the most worrying thing about that clip is how stupid the politician is. I know nothing about guns, but just the words "barrel shroud" tell me rather explicitly what a barrel shroud is.

I am very open minded I think. If you come up with a theory that makes a new (non-trivial) prediction about the world, and we test the prediction and find out that it is true, let me be the first to shake your hand.

Hey, I didn't know that Einstein and Newton posted on these forums. Cool!

Sorry - I have just been a bit busy (with work and then family things over the weekend) so didn't get around to responding. The reason that I asked about the box, it because it is crucial to the discussion. If you simply have a collection of particles then the sum of their four-momenta is also a four-vector. Since the four-vector's inner product with itself is a constant, you can define that as being the total mass of the collection of particles with no problem, and there is no ambiguity. If you claim there is a problem with this, then you are claiming that the Lorentz symmetry is broken. However, you cannot define an energy density in this way, since not only do the "relativistic masses" change with a Lorentz transformation, but the volume of the space does too. Therefore, you need a rank 2 tensor (the stress-energy tensor) to describe the energy density. Although this is not a four vector, it transforms as a 2nd rank tensor under the Lorentz transformational. Clearly, it is fundamental whether you are regarding the box as a closed system, such as a "rigid" body (however we choose to define that!), in which case you need to calculate the energy of the entire body, not just the density. Or is the box a part of something more? Your claims seem to indicate the former - that you are calculating the energy and momentum of the entire object. But in that case, why do you have forces on the box. Where are they coming from and what is their point? What is pushing back against the force. And as I pointed out, if you do the sensible thing, and set [math]F^\prime_x=0[/math] then you do return to the usual energy and momentum satisfying [math]E^2-p^2c^2=m^2c^4[/math]. On the other hand, your calculation implies that you are only considering an element of a larger object. Indeed, Eq.(46.2) in Rindler (I had to walk to the Library to check this) is for this case. Rindler is very explicit in this (look at the discussion starting on page 146 about internal and external forces). Then you shouldn't be surprised that the energy and momentum don't transform as a four-vector since you need a 2nd rank tensor. In either case, your "proof" must retain its inverted commas. For an isolated box, your forces should be zero and you end up proving my assertion yourelf(!). For an element of a larger fluid, you are not proving what you claim to prove, and your proof is inappropriate.

Are you aware that there is no such thing as a rigid body in relativity? Since you like Rinder so much, let me quote him on page 36: "One consequence of the relativistic speed limit is the "rigid bodies" and "incompressible fluids" have become impossible objects, even as idealizations or limits." So are you sure your box is rigid?

You presumably don't mean that you want it published in a journal, since no journal will take anything as lengthy as a PhD thesis. I am assuming you want it published as a book. Is this correct? If so, you have to approach an academic publisher.

You should sue. As for the OP, I think this demonstrates that Obama's election success was partially based on race. He got a lot of votes from minorities because he is black, even from those who hold completely opposite political views.

OK - I'll be nice, tolerant and cuddly. Let's go through your "proof" at http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm one step at a time. "Consider a square box at rest" What do you mean by this? What is a "box"? Is it defined just as a volume of space? Is it a collection of interacting particles which just happen to fill a box? Is it a rigid body? What is this box?

You don't need an iterative method for this one - it can be solved exactly in a couple of lines of algebra.

How the theory was produced has absolutely no bearing on the question. Whether a theory is "wrong, complete or incomplete" is purely a matter of whether or not it makes predictions, and what the experimental outcome of testing these predictions is.

You made a claim that there was no way to define (proper) mass in all cases. I gave you a counter example. Everything is made up of elementary particles, so it seems a reasonable place to start. Of course, when you have composite systems, you then have to take into account the interactions within the system. The proton mass for example is not just the mass of the quarks summed up - you have a contribution from the strong force too. (Technically, the mass of the proton is the coefficient of the bilinear term in the effective Lagrangian.) However, I had made the reasonable assumption that we were talking about free bodies with no external forces. If you are present when a friend weighs themselves, do you put your foot on the scales? In your "proof", you apply an external force so it is not surprising you get different answer. If you set the external force to zero, then your own equations have [math]E=\gamma mc^2[/math] and [math]p=\gamma m \beta c[/math] (I have taken the liberty of rewriting the "m" in your equations in terms of the (what you would call the "proper") mass [math]m[/math]), so that (lo and behold!) [math]E^2-p^2c^2=m^2c^4[/math]. For the record, I have no objection to using the quantity [math]\gamma m[/math] in any calculations or physics discussions. My objection is to the name you use (mass) and the symbol [math]m[/math], because it causes no end of confusion. At the very least, you should quote the frame of reference in any name for [math]\gamma m[/math] since it is frame dependent, so I would even object to calling it "relativistic mass". Something like "the effective mass in frame S" would be OK though. (Also not that I never said Gilded post was wrong - I just said it was a horrible way of expressing it.)

Well, that is probably what I would look at too, but since Sven, Wolfgang and Georg are all good friends of mine, I might be a little biased. I seem to remember a nice review paper by Dominik Stoeckinger too - I will go look for it.