Tom Mattson

Sorry this has gone on so long without a response, but here goes. No, that means that V is a constant, which isn't true. You are supposed to make V(x) such that V(0)=0. That means that V(x)=mgx. The canonical way to start these problems is to begin by writing down the Lagrangian: [imath]L(x,\dot{x},t)=T-V=(1/2)m\dot{x}^2-mgx[/imath]. Note that our Lagrangian does not actually have an explicit time dependence. Now the Hamiltonian is a function of the momenta and the coordinates, not the velocities and the coordinates. So we find the momentum as follows: [imath]p=\frac{\partial L}{\partial \dot{x}}[/imath] [imath]p=m\dot{x}[/imath] [imath]\dot{x}=p/m[/imath]. I solved for [imath]\dot{x}[/imath] in the last step because when we write down the Hamiltonian we will use that relation to eliminate [imath]\dot{x}[/imath]. How we get the Hamiltonian. [imath]H=p\dot{x}-L[/imath] [imath]H=p\dot{x}-(1/2)m\dot{x}^2+mgx[/imath]. Make the substitution [imath]\dot{x}=p/m[/imath] and simplify.

Once again: That is not an ad hominem statement. Go look the term up if you don't know what it means. Well' date=' that's what I've been saying all along! Try reading it as a guest, without logging in. And if you can't do that then try reading it from another computer. Even so, you were a participant in the discussion and you read the posts in question. I did address your points, and at no point did I ever engage in ad hominem argumentation. There's no "may be" about it. You're mistaken. It's all well and good that you are eager to discuss Pulsoid Theory, but the way you are going about it is positively obnoxious. You hijacked this thread, and for the last several posts you have been baiting me to discuss it with you, when all I did in this thread was address your comment about Einstein. How about checking with the Staff of a forum to see if they host non-peer-reviewed work? How about heeding the warnings that are issued to you when you by the people who own and/or run the site? How about waking up and moving on once it becomes painfully obvious that your posts are not welcome at a particular site? How about sticking to the sites that do welcome your ideas? I did advise you, via a link. Don't assume too much. Just because I have no opinion on Pulsoid Theory, it doesn't mean that I consider it viable. And yes, I do fall in the category of a theoretical physicist, in training at least. Then why did you attempt to engage in it just there? It's also a serious offense, so you would be well advised to stop doing it. But you did make the call, when you unjustifiably dubbed my comments ad hominem. If all you really wanted was for the readers to look at the evidence and make up their minds on it, then you would simply have highlighted my comments without coloring them with your personal judgment (which is obviously wrong). It's a state of affairs created by you. Correction: You did your best to turn this thread into a discussion about Pulsoid Theory when you began. Again: This is argumentum ad populum, an informal fallacy. People are also more likely to view a fatal car wreck than someone changing a flat tire. It doesn't mean that fatal car wrecks are a good thing. Since you are so keen on talking about Einstein, maybe you can finally address my initial point in this thread, which was about Einstein's work. Is it too much to hope for that your next post will actually say something about that? Again: You are baiting me into a discussion of Pulsoid Theory, which is something I could not care less about. Hey, you're the one who's grandstanding. You can end this any time you want.

I did present the evidence. I posted a link to the thread. Do you need me to click the link and read it to you, too? Sorry, but no you didn't. As a Staff member of PF I can see deleted posts and all replies made by you to that thread are still there. The point is that the thread in question was pure nonsense. It isn't up to the readers to chase down your material on Pulsoid Theory to make sense of what you posted at PF. It's up to you to make yourself clear. No, I don't. You simply do not understand what ad hominem argumentation is, and you are simply ignoring the arguments that I have made against your posts. Again: You are imagining things. I have never expressed any opinion whatsoever about Pulsoid Theory. In fact I don't even give a damn about Pulsoid Theory. I am talking about the discussion that we did have. Funny, I thought you didn't approve of ad hominem argumentation. What a joke. You say that you are willing to put aside our differences, after a long tirade of lying about me and the non-existent ad hominems you say that I have leveled against you. And as far as dragging the thread off topic, you are more responsible for that than anyone. You hijacked a thread made by some curious kid asking a question, and you completely ignored the point that I initially made when I entered this thread, which was about how Einstein built relativity on the existing edifice of scientific knowledge. Rather than actually discuss the topic, you would turn this into a discussion of how you've been mistreated at Physics Forums. Get a clue. If there's anyone here who resorts to ad hominem attacks and who avoids debating the topic at hand, it's you.

Patently false. The one and only extendend conversation you and I have had was at Physics Forums in the thread' date=' The fundamental concepts of physics are all based upon metaphysics. Anyone with at least a pair of brain cells to rub together can see that I was debating the topic and that I did not resort to ad hominem argumentation. And while we're at it, let's also review one of Gokul's beastly personal attacks that you've bemoaned in this thread. From An elliptical constant at Physics Forums.

It's a right pity that you see an honest, valid criticism, based solely on what you have written, as an ad hominem attack. It seems clear enough to me that you really don't understand what "ad hominem" really means. I don't employ those arguments. To the contrary, it was brunardot's nonsense that does not belong at a serious forum. Furthermore, when Forum Staff enforce policies, it is not a personal attack against anyone. *yawn* Like I haven't heard that before. Don't the warnings that are issued to you tell you anything at all about how the Administration here at SFN regards your posts? Does not the slightest clue sink in when you are told by Staff members that you are doing something that is not appreciated here? This is nothing other than argumentum ad populum, an informal fallacy. I don't recall ever addressing the ideas of Pulsoid Theory at all, let alone with hostility. I think you're imagining things. Yes, and I don't think that my actions at PF or at SFN (especially in this thread) are inconsistent with what I said there.

Swansont's answer is the right one. At the turn of the (20th) century one of the big questions in physics was how to reconcile Newton's mechanics, Galileo's relativity, and Maxwell's electrodynamics. Galilean relativity leaves the form of the equations Newtonian mechanics unchanged for all inertial frames, but not those of EM theory. Physicists were trying to decide between a number of options: 1.) Are Galileo and Newton correct, and Maxwell wrong? 2.) Are Galileo and Newton correct, and Maxwell correct only in a single preferred inertial frame? 3.) Are there two different correct theories of relativity, one that maintains the form of Newton's laws and another that maintains the form of Maxwell's equations? 4.) Are Newton and Galileo wrong, and Maxwell correct? 5.) Is Galileo wrong, and Newton and Maxwell correct? The experimental evidence in favor of Maxwell--especially in moving frames--did not warrant #1 or #2. #3 can be rejected out of hand once it is understood that electrodynamics really is the mechanics of charged particles, so the distinction between mechanics and EM theory is really just a matter of whether or not the moving bodies are charged. The experimental evidence of the day also did not warrant #4, since Newton's laws worked spectacularly well (violations of Newton's laws at the quantum level are not being considered here). So we were left with #5: Galilean relativity is just plain wrong. This is the option that Einstein settled on. From there he postulated a new relativity, one that leaves Maxwell's electrodynamics invariant for all inertial frames. It turned out to force some changes on mechanics, but Newton's laws survived the revision. His view of space and time, however, did not.

You can describe distances in that way. Consider the distance between the two ends of a rod of length L that is moving with speed v along the positive x-axis in some frame S, and let frame S' be the rest frame of the rod. Let Event 1 be the measurement of the x-coordinate x1 of the left end of the rod, and Event 2 be the measurement of the x-coordinate x2 of the right end of the rod. If the measurements are made simultaneously in S (that is, t1=t2) then the difference x2-x1 is the length of the rod (aka: the distance between the endpoints of the rod) in S. And this distance is relative. From the Lorentz transformation: [imath]\Delta x'=\gamma (\Delta x -v\Delta t)[/imath]. If [imath]\Delta t=0[/imath] (simultaneous measurements) then we have: [imath]\Delta x'=\gamma\Delta x[/imath]. We understand [imath]\Delta x'[/imath] to be [imath]L_0[/imath], the "proper length" of the rod, and [imath]\Delta x[/imath] to be [imath]L[/imath], the length of the rod in Frame S. They aren't the same. Unfortunately this is too vague to be meaningful. In some sense the measurements of the length of the rod is "connected" to time inasmuch as the two frames are at two different velocities, and velocity is the derivative of position with respect to time. But I really have no idea of what you are trying to say here.

Viewing requires light. Light doesn't travel to us from the future. The only thing we can do as far as "time viewing" is concerned is look into the past, which is indeed what you do every time you look at anything.

No' date=' it isn't. The relativity of length has nothing to do with the fact that lengths are defined between two points of reference. It comes from the metrical structure of the spacetime we inhabit. If the metric of Galilean relativity were descriptive of our actual universe, then lengths would not be relative, despite the fact that reference points define lengths. That depends on what you mean by "distance". If you mean a spatial "distance" between two points, then yes it is. If you mean "distance" in the more general sense (eg: that which is given by a metric in a metric space), then no it isn't.

On what basis? You said it yourself: We have no evidence of "quark parts".

That's true for Newton, too. I have no idea of how you get from A to B in this bit. Same thing here. If you could build a QED computer like this, it wouldn't imply that matter is reducible to math. It would imply that matter can be used to execute mathematical operations. Think about it, why wouldn't your argument also apply to more conventional computers?

Take the more general version cited by dave, and yes it has numerous practical applications, by virtue of the fact that exponential functions are easier to calculate with than trigonometric functions. One very important application of complex exponentials is in electric circuit analysis in the frequency domain.

The metric is well-defined mathematically. That means that it wouldn't be rejected out of hand by a theorist. I have no idea of how you got from 'A' to 'B' there, but I'll say that the point of discussion at hand here is that NRQM (a man-made mathematical construction used to describe reality) either does or does not make use of a spacetime, which is characterized by a metric (another man-made mathematical construction used to describe reality). So it only makes sense that I am talking mathematics here. It can't. It is just a diagram. I said that much myself in my next post. (Incidentally Galilean spacetime is not our current notion. Galileo has been supplanted by Einstein.) My view of time is that it is "that which is measured by a clock". The best link I can think of is this one: http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf

Yeah, I was just at PF and I noticed you looking up this thread when I clicked "Who's Online?" Ain't I clever? Yes, it is true that you can't define a Hermitian operator for time in NRQM. But doesn't the notion of a "spacetime" come from coordinates, intervals, boosts, rotations, etc...? Why should Hermitian operators come into the definition of what is and is not a spacetime? Galilean spacetime is the background for NRQM. All wavefunctions are defined on it. Also, the Schrodinger theory is covariant under Galilean boosts. In these respects Galileo's spacetime plays the exact same role in the Schrodinger theory that Minkowski's spacetime plays in the Dirac theory. The asymmetry of space and time with respect to operators in NRQM doesn't suggest to me NRQM isn't formulated on a spacetime. It suggests to me that NRQM is formulated on the wrong spacetime.

Why come? Galilean spacetime has a well-defined metric, and you can draw Galilean spacetime diagrams.

Actually by definition each train travels at 0c within its own reference frame.

Cool. I've just noticed that unless you are a member of their message board (which I am), all you get mostly is snippets. There is the complete recording of Blast the Message (title track from their 2nd album). If you join the message board then you can raid the archives for many live MP3s. I love the albums, but this is a band that really catches fire onstage, so I would definitely recommend joining up and snagging some of the live ones. My favorite ones are "Made Up Worlds", "Northern Girl", and "High Hopes", so I'd say start with those. edit: Ah, there are some complete live tracks there for the taking on the audio page, down at the bottom. High Hopes and Day Bye Day are originals, and they are two of my favorites. Be warned though: they are a little on the long side. This band likes to jam, but not in the lameass Grateful Dead kind of way. It's more like Zeppelin or the Allmans. Don't Burn, Baby is a great, quick rocker that is actually a remake of a Sly and the Family Stone song. And just about everyone knows Que Sera Sera (also redone by Sly), but Super 400 does it with a strong bluesy accent.

My favorite band is called Super 400 (see my avatar). They are local to Troy, NY but they play all over the northeast and they are freaking amazing. To the people who mentioned Zeppelin, Hendrix, Cream, AC/DC, and even Cake, you should check out http://www.super400.com and download some of the free MP3's. It's great stuff.

If you've got the math (through linear algebra and differential equations) then you could safely begin with either Brehm and Mullin or Eisberg and Resnick. They are both good introductions that don't require a lot of classical mechanics (like, say, Griffiths or Liboff).

ecoli is a foodborne pathogen.

This remark could be confusing, because neither the law of sines nor the law of cosines is assumed to be true. They are indeed theorems, and yet they are called "laws". The MathWorld definition seems to be consistent with that.

The value of the relative velocity determines the exact age difference. The faster the rocket travels, the greater the age disparity when it returns to Earth.