Severian

Darkmatter is, but antimatter has been generated and detected at labs many many years ago.

I would say that Dark Matter has been pretty solidly confirmed too. We just don't know what it is, but it is definitely there.

Harmony breeds complacency and mediocrity. Conflict breeds progress and innovation. The important thing is to channel conflict into productive avenues.

In Quantum Field Theory, the principle of least action is nicely explained by the path integral formalism. Basically, the system follows all the possible paths at once, but each is weighted by a complex phase (depending on the action). Adding up all the contributions, they almost all cancel one another out except for the path of least action (because it is an extremum).

I find this hard to believe. Can someone confirm or deny?

Sometimes true, but not in general. The energy has to go somewhere so there needs to be another particle to carry it off. For example, if an electron and positron meet, they do indeed annihilate, but convert into a photon which carries the energy away. A photon and another photon can't do this, since there is no 3-photon vertex (because photons are neutral). A gluon though could annihilate with another gluon to turn into a third gluon (the third gluon would need to be virtual though).

What is the mass of a billion photons travelling at C? The momentum is a billion times higher than one...

As juanrga said, zero, but this is in part because photons don't interact with each other. If these were gluons instead, then they would have a mass (from their interaction).

Since one traditionally regards a God as omnipotent, the question is really a little silly since we are still limited by our finite intellects, so really have no idea what we would do if we suddenly became God. A better question may be, what would you do if you were set up as absolute dictator over the entire world with absolute power?

Do you mean, are the generators of the group represented by symmetric matrices? If so, then no. The generators obey [math]T_a^\dagger=T_a[/math] so you need to transpose and take the complex conjugate. Orthogonal group generators are symmetric because the relation is [math]T_a^T=T_a[/math].

Surely this is trivially easy? Take a full plastic bottle of water, make a small hole in the cap, then clamp the bottle in a vice with the cap pointing up. Twist the vice handle a few times (this is the initial "kick" of energy) and the pressure will shoot water out the top for a while. The smaller the hole the longer it takes to equalise pressure, so the longer it lasts.

Alternatively place two sheets of glass together, and put them end-up in a bath of water. Capillary action will make the water rise between the sheets.

In what sense is this Marxism? This is already how most of the European democracies function. (Except for the last sentence which seems to have no link to the rest of the post.)

My first act would be to send all non-believes (atheists etc) to a hell of unimaginable suffering. Then I would demand absolute obedience from the rest. Those that pleased me would be free to live with only minor inconvenience (such as worshipping me for at least 4 hours a day) while I would inflict horrors and torments on those who were not so faithful.

It is probably a good thing that I am not God...

The strongest theoretical limit on the photon mass is from the galactic magnetic field (Chibisov et al), which implies that [math]m_\gamma < 3 \times 10^{-27}\;{\rm eV}[/math] though this relies on some assumptions.

From a theoretical point of view, the Standard Model predicts a photon with exactly zero mass. To have a non-zero mass one would have to break the U(1) symmetry of QED.

My current solution, though not perfect is to run windows, with a virtual Ubuntu install via Oracle VirtualBox.

It's hardly silly. Many relativity textbooks us it. Percentage wise about 67% of textbooks published between 1970 and now use it. I see no valid reason to think it silly when that many physicists use it.

 

[snip]

 

Plus I have several relativity texts which prove otherwise. The list inlcludes such texts by such authors as Misner Thorne and Wheeler (page 141), Mould, Rindler, D'Inverno, Schutz. Stephani.

 

You can see a short list here with the relevant quotes

http://home.comcast....vistic_mass.htm

Do you have any source to back up your 67%? I find that hard to believe. The link you include has a handful of texts. Also, the very fact that this thread exists proves that it is silly to use relativistic mass in text books, because it confuses the students.

That's incorrect. I was speaking to a well-known cosmologist/particle physicist yesterday and he told me that in cosmology physicists use the term "mass" to refer to E/c². H'e's very very well-known in his field so I trust him.

I also find that hard to believe. Who was this person? The only reason I can think of for doing this would be if their energies are so large that rest mass becomes negligible, allowing them to use the term "mass" for something else. Still seems a bit daft though. If you use the term "mass" to refer to E/c^2, why not refer to it as "energy"? They are even identical in Planck units.

That relation doesn't always hold. On example is when the body is under stress. [math]p=\gamma m v[/math] is inlid under such a case but p = mv is still valid. Another example is an extended body which is emitting radiation. In such a case the mass per unit length of the rod can be uniformly decreasing. In an inertial frame moving parallel to the rod the mass per unit length is not uniform. The proper time in this case has no meaning so that

 

[math]p = m\frac{dt}{d/tau}[/math]

 

has no meaning. However p = mv still has meaning. For details please see

http://home.comcast....ariant_mass.htm

 

See last section entitled An Incorrect Application of Invariant Mass

Well, it also breaks down for something moving at the speed of light. My point was that having a definition of mass that provides no extra benefit is pointless. p=mv is not useful. Lev Okun agrees with me.

The Windows/Linux thing is a real problem for me. My research is much better done with Linux, since there are certain things I can't run in Windows. But Windows is much better for office related work, and I need to do quite a bit of admin too. OpenOffice in Linux is really rubbish, and I prefer Outlook to Thunderbird.

And please note that half the people earn less than the average.

That isn't true. Considerably more than half the people earn less than the average. Half the people earn less than the median (which is what is shown in the plot you link to).

Mass contributes to energy, but it is not equal to it. There are other forms of energy that are not mass. Your equation is even invalid for a moving object. You would need to augment it to [math]E^2=p^2c^2+m^2c^4[/math] where [math]p[/math] is momentum.

Also, your first and third sentences are contradictory; mass can be created and destroyed.

If our ancients worshiped the Sun as a star in the milkway, something which we can empirically verify then religion wouldn't be a problem to science but the problem is our ancients worshiped the Sun as a deity, as an anthropomorphic God with his own pantheon, God is a person who resides inside everyone, this is where the problem lies and challenges the accepted notions of science and becomes incompatible with it having its own epistemology and methodology. If scientists doesn't want to investigate it then its fine but why make statements like "God is dead".

If you are going to require god to be a "person" you are going to have to define what a person is first.

It is perfectly consistent to define mass as the frame dependent "relativistic mass" if you like. But it is a bit silly for 3 reasons:

1. All professional physicists mean "rest mass" when they say mass.

2. Rest mass is frame invariant, so a property of the particle, whereas relativistic mass is frame dependent, so dependent on the observer.

3. If m is used to denote relativistic mass, we have momentum p=mv. This is a waste of notation since p and v are now always proportional to one another. It is much more convenient to keep a non-linear relation between them, i.e. [math]p=\gamma m v[/math] with [math]\gamma = 1/\sqrt{1-v^2/c^2}.[/math]

It is fairly easy to prove that a god exists. Since religion is a personal matter I can choose to worship whatever I like. Therefore, I can choose a god that I can prove exists (for example, maybe the Sun). If you think the Sun doesn't exist, I won't try to convince you otherwise...

You make it sound as if the only reason to disagree with you is if one does not understand you.

Well, at least you understood some part of it.

That's better, but it is not what you wrote before. Now you correctly have the [math]\lambda[/math] in the Higgs mass, and since you don't know [math]\lambda[/math] you no longer have a Higgs mass prediction.

The wave is made up of water but the water itself did not cause the wave. But I confess, I don't see how this is relevant...

Since I entirely got that wrong, can you tell me what your point actually was?

You went wrong at the point where you said "I can easily come up with scenarios where killing someone is not only OK, but is the right thing to do." You seem to assume that an action is automatically "OK" because it is the "right thing to do". I disagree.

This article suggests its not the Higgs, but the top quark "super-particle" or stop squark. Seems a bit premature to announce it, but what do I know.

 

http://physicsworld...._on_what_h.html

I am restraining myself, so that I don't say something... unprofessional about these authors.

Glad to have you posting with us again, Severian. Have you been busy at CERN this whole time?

That Higgs boson wasn't going to find itself!