Recent content by FactChecker

Honestly, I am having a hard time simply understanding the statement of your theorem, let alone know where it can be referenced as stated and proven. It's too tough for me. I think you should include your proof in your paper, showing the existence of U. Maybe in an appendix or footnote?

If their "pronouncements" are just relaying the best knowledge of experts in the field, is that OK? If so, they should just make it clear where their statements are coming from (and not misquote). Unfortunately, experts are trained to use accurate terms like "theory", "indicates", etc., which...

I disagree. Mathematics is based on logic derived solidly from the axioms and stated assumptions. The logic is not "bent" to fit observations. Neither are the axioms. Math is intentionally made agnostic of the applications, so that it is abstract enough to apply to anything that fits the stated...

If you have any counterexamples to the accepted mathematical axioms, please let us know. Pure math is pure until it is used; then it is suddenly appreciated. A lot of math was motivated by the need to understand physics. These days, a lot of modern physics theories are motivated by the mathematics.

Any IRF can be considered to be "stationary". So either one of the clocks in their respective IRF can be "stationary". It is not about which one is moving (both can be moving). It is about the difference in clock synchronization within the two IRFs.

The clocks are traveling long distances in opposite relative directions to each other. The ticking rate of a traveling clock is most simply measured by recording it here and down the line later and comparing it to my clocks at each location, which are "synchronized" within my inertial reference...

At what time, by whose set of synchronized clocks, at which carriage location? When A carriage 1 reads 2 sec, A carriage 2 also reads 2 sec. When B carriage 1 reads 2 sec, B carriage 2 also reads 2 sec.

"Understand" at what depth? There is a big difference between developing an intuitive acceptance and being able to do all the calculations. GR is an extreme example of that. Even Einstein had trouble doing specific calculations for examples to support GR. SR is much easier. Intuitive acceptance...

Yes.

Thanks. The terminology is tricky. That is the expected value for a single sample from that distribution. That is not the same as the average of several results, which would be expected to have a much smaller variance. I will assume that in all the posts, "average" meant what you say, and...

"do statistics" is vague. If you determine the variance of the single random momentum value of a single sample (possibly using a large sample to estimate the distribution), that is one thing. But if you "average" several sample momentum results and talk about the variance of that average, that...

Do you mean the sample variance of the sample distribution of a large number of measurement data, or the variance of the sample average? Wouldn't the Central Limit Theorem apply to the average and give it a small variance as the sample size grows?

That sounds wrong or unclear. The average of many may have a very small uncertainty, while the uncertainty (variance/spread) of the individuals that make up the average is large. I am only a casual amateur on this subject, but the latter is how I interpret the uncertainty principle.

Correct simplification includes keeping track of where the original function was undefined.

Good catch! You did very well to check the final answers in the original formula. As you go through a simplification, you should keep track of any values of x where the original function was undefined. That can become difficult and tricky. It is wise to check your results in the original formula.