danshawen:
A much better response than I have ever received here JamesR I do appreciate being treated as a genuine crank rather than one in the "crazy" category, although that remains to be seen. And you seem to understand the issues I have raised better too.
Thanks. Are you going to go through what I wrote and answer the questions I asked you, or do you think you are done after posting a response that is largely a
non sequitur?
Not a "real rotation"? My physics instructor did not hesitate for a moment to roll out Minkowski's "relativistic Cadillac tail lights" scenario, in which apparent 3D rotations were substituted for ones that were 4D by the math. Seen that one?
You mean Torrell rotation? You're not confusing the two, are you?
The invariant interval CONTAINS the INVARIANT SPEED OF LIGHT. That's what makes it invariant.
No. Lots of expressions include the speed of light, but most of them aren't Lorentz invariants. In other words, merely having a "c" in an equation somewhere doesn't create an invariant.
The geometry doesn't make it invariant in a relativistic universe. It makes it BOGUS. It makes up for the fact that geometry is not capable of setting a hard limit on a load of geometric nonsense the way the invariant speed of light can.
I have no idea what this is supposed to mean.
You cannot stipulate that two phase angles I used in connection with the single dimension of light travel time must follow the rules of Euclidean geometry if ithey simply do not.
Fine. Which rules of geometry do they follow? What are these angles, anyway? Please show me how you define and use them mathematically.
All that is necessary to notice here is that no matter which way you rotate it, light travel time in any direction makes more sense than designating them all as static dimensions that may not move without invalidating any geometry that is based on then.
Again, you've lost me. Please explain what you're talking about.
It is impossible to "prove" Minkowski used the wrong math. There is never anything that is "provably wrong" about using more dimensions without limit, complex math for quantities other than potential energy, etc. it isn't the math itself that is wrong. It's about resorting to more complex math when it is not necessary, and what that does to an understanding of a more complex conceptualization with relativity.
Fine. So show me your simple math that works better. You can use TeX, right?
All math ever does is to set up a problem and turn the crank until a number or an expression drops out in reduced form ONE number, or ONE reduced form or expression. NEVER two, which relativity uniquely requires.
You lost me again. Please explain what you're talking about.
You can't do trigonometry without three vertices, and you can't justify the basis of a coordinate system without an origin that is fixed.
This is an assertion that you have not supported. Show me why your claim is true. Show me the maths.
Relativity always has at least two frames of reference that are being compared, and I assert that it is impossible to relate both frames of reference to a common origin for more than one reason.
Two frames in relativity don't have a common origin. The whole point is that the origin of one frame moves with respect to the other one.
There is no preferred reference frame is one.
Yay! We agree on something.
The Uncertainty principle makes two.
I don't see the relevance of the uncertainty principle to Einstein's theory of relativity. Please explain.
Can YOU answer my classmate's question about whether something contracts with respect to the leading, trailing edge or its center? YOU show US the math.
Consider a straight ruler, which I will call Ruler A. In frame 1, the ruler's rest frame, it is 1 metre long. You can imagine that the centimetres are also marked on it.
In frame 2, the ruler A is seen to travel parallel to its length at a speed sufficient to give it a Lorentz factor of $$\gamma = 2$$, let's say. In frame 2, when we hold up a second, identical ruler (stationary in frame 2) which I will call Ruler B and use it to measure the length of Ruler A as it flies past, we see that Ruler A is 0.5 metres long in frame 2.
Suppose we measure the moving ruler at the single instant of time when the "zero" centimetre marks on our two rulers happen to be adjacent to one another, with the two rulers parallel of course. Then we see that the "100 cm" mark of ruler A coincides with the "50 cm" mark of ruler B. Similarly, we see that the "20 cm" mark of ruler A coincides to the "10 cm" mark of ruler B. And the "66 cm" mark of ruler A coincides with the "33 cm" mark on ruler B. And so on for any point you wish to consider.
Now, you ask whether Ruler A contracted "with respect to the leading, trailing edge or its centre". Can you see that it didn't contract from any one point, but rather that its
entire length contracted uniformly?
Do you understand this point?