Tom Mattson

I always thought that "law" and "theorem" are synonymous in mathematics, but according to Math World's Entry for "Law" there is a slight distinction. But "law of cosines", et al, still qualify as a "theorem".

What do you mean by "an absolute"? Do you mean independent of reference frame? If so' date=' then I can say that the distance is not an absolute because that statement is consistent with the best empirical data, and the negation of that statement is not. This is so vague that I can't even guess at what you mean.

Honestly' date=' I think that you would be ill-advised to attempt this. I taught physics out of Halliday and Resnick for 4 years, and you really should have a course in calculus if you are to really know what you are doing. There are questions such as, "The position of a particle as a function of time is given by [b']r[/b]=(4t-2t2)i+(-3+2t)j. What is the y-coordinate when the x-coordinate is a minimum?" To answer that question you need to understand differential calculus. Yes, you can be taught a quickie lesson wherein you learn to parrot the formal rules of differentiation so that you can "get the answer". But that's not the goal. The goal is understanding, and you aren't going to get that without having studied calculus.

v=s/t is not another model. In fact it isn't a model at all and it doesn't give results of any kind. It's a definition. It holds true in Galilean Relativity, Special Relativity, or General Relativity.

You have not answered my questions, and you are still not making any sense.

You're still talking as though you have proven something. I'm afraid that your website is unclear at best, as I have explained. Could you please answer my 2 questions?

You do get a new set of x-coordinates for the points of intersection after the transformation. They are precisely the old y-coordinates, which you already found.

If you can do better, then I'm all ears. So far all you've done is present arguments of incredulity, based on false statements made about relativity. Surely you don't expect anyone to be convinced by that.

Because you did. The others have already explained why. Great, now you've got "imaginary answers for FTL speeds" as yet another postulate! No, Saint, SR was designed to answer the question, "What type of universe is it that has the same speed of light for all inertial observers, and the same laws of physics for all inertial observers." As long as those two things hold true, then we are in the domain of applicability of SR. I wouldn't have said it if I didn't think it. It is only a misuse in your ill-informed opinion.

What's not to understand? It's a definition. You understood it when you read it here, so you certainly would have understood it if you had looked it up. Furthermore, if you really don't understand what open and closed intervals are then you shouldn't be taking calculus, because that is most definitely prerequisite knowledge. But I think you are perfectly capable of understanding it. You just didn't feel like cracking open the book. And the whole point of your education is to become self-sufficient. To learn how to think and to learn how to learn. Surely looking up a simple definition is not too taxing, eh? And for the record: ordinarily I don't believe in helping students with their questions unless it has been demonstrated that they have attempted it. If one of my own students in Calculus I or II asked me to explain what open and closed intervals are, I would say, "No. Look it up." The only reason I chimed in on this thread is that you had been given the wrong answer. But even if I hadn't corrected Crash, it is still your responsibility to check any answers you receive here for yourself.

That would indeed be "the other way around" from what Crash said. Sarah, I have seen you post calculus questions on this board. You really ought to look up this basic information for yourself.

The limits of integration will not change. Why would they? Instead of setting y^3-4y^2 +3y equal to y^2-y and solving, you are now setting x^3-4x^2 +3x equal to x^2-x and solving. It should be easy to see that you will get the same solutions.

No, it's the other way around. Crash is wrong.

You are onto something though. I made a tiny mistake in my first post. Switching x and y is not just a rotation. It is a rotation and a reflection. So say you have both curves plotted on coordinate system with the axes in "standard" position. If you rotate counterclockwise by 90 degrees, then reflect through the new x-axis (which is now vertical), then you get the same figure you would have gotten if you had just switched x and y in the first place. And the area is still the same, of course.

Made a mistake. Please delete.

He seems to know that he has to draw it out. What I think he's saying is that he doesn't know how to, because for both curves x is given as a function of y, and he learned his curve sketching techniques when the opposite was the case. That's why I say to interchange coordinates. He should then be able to easily plot the figure, and it will have the correct area.

Just interchange y and x. What this amounts to is a rotation of the figure, which does not change its area.

It was developed to provide answers for inertial frames when gravitational effects are negligible. It was not developed with the restriction that speeds must be less than c. It is a prediction of SR.

Yes' date=' it is a prediction of SR. He even cited the relevant equation! It would be difficult to make sense of it, even mathematically. But even so that in itself does not preclude its occurance. But that's not the point. The point is that the "imaginary time" prediction is regarded as a reason that faster-than-light travel is impossible. Why did you stop at those? Why? Yes, and you also need to have the fullest possible picture of reality before you. This includes what we know about electrodynamics and how it necessitates relativity. Once you've got the full picture, then you're in a position to start thinking about what must be true in reality. And even then, you cannot rule theories out on a priori grounds, unless the theory is self-contradictory. I, for one, have never met a physicist who does that.

OK, switching from Mozilla to IE did the trick. I can now see the images. Sadly, the website doesn't make any more sense than before. Some questions: 1. From the website, "Relative speed of bunch along the perpendiculat line is [imath]c^{\beta}=c\frac{sin\alpha}{sin\beta}[/imath]." "Relative speed"? "Relative" to what? And where does the formula come from? To get a relative speed you would have to use a rule for adding velocities. What did you use? 2. "In the theory of relativity this formula [imath]c^{\beta}=c\frac{sin\alpha}{sin\beta}[/imath] was represented only in case [imath]\beta = 90^o[/imath] when sin alpha has the following presentation [imath]\sqrt{1-(\frac{v_{90^o}}{c})^2}[/imath] and [imath]sin{\beta}=1: c=c\sqrt{1-(\frac{v_{90^o}}{c})^2}[/imath]." This is wrong. Relativity is not derived by a thought experiment that even remotely resembles the above. It is derived from the requirements that Maxwell's equations take on the same form in every inertial frame and that the speed of any light pulse is determined by any inertial observer is c. And the results do apply to a beam that is directed at any angle relative to the line of motion of the observer. The last equation (the one after the colon) does not follow from relativity at all. Since I do not think you've started the analysis correctly, I do not see any point going further until these two points have been cleared up.

What is it with you, Saint? Everyone knows that mathematical theories model the universe. But everyone also knows that overwhelming experimental confirmation makes for a strong case for the truth of a model. It is not unreasonable to answer a question about time with the predictions of SR, because there is no reason to think that SR should not apply. And besides, Mag qualified his question with the expression "in theory", so really what's the problem?

All the images on your site are broken. It is impossible to read it.