Motor Daddy:
Changing the radius of a gear in one direction and not the others means the circumference changed. If the circumference changed the ratio changed. But how could that be, because you can count the rotations of the crank, and count the rotations of the wheel, and the math doesn't add up. EVERYTHING needs to add up, and by claiming one direction is length contracted you are F'n up the math!
Like I said, rotation is almost certainly too hard for you to cope with, given that you can't understand the basics of length contraction in a straight line. I'm going to skip your stuff about rotating gears until we have sorted you out on straight-line motion. Otherwise, I'll just be wasting my time.
I can lay two same length sticks perpendicular from each other on the side of a gear and prove the diameter of the gear is THE SAME each way.
When the gear is stationary, you mean? Yes.
You fly past and claim it is NOT the SAME each way. You are just flat out WRONG!
You're still trying to argue by assertion. Skip it. It's not getting you anywhere.
An imbalance of the wheel. A (theoretical) wheel that is 10" tall and 9" wide will not roll even, it will "jump up and down" as it rotates along the road, because the circumference is not a circle.
More about rotating objects. You don't seem to realise that the elliptical shape of the wheel doesn't rotate along with the wheel in this example. There's no point in my going into further detail, so I won't.
What do you mean "the measured distance will be different? There is one distance between the Earth and the Sun.
No. You must specify which frame of reference you are using to measure the distance. This is a basic mistake. I talked you through this 10 years ago in some detail, trying to educate you about reference frames.
Why have you done no work on understanding this stuff in the 10 years you have been away from sciforums?
What are you comparing to to make the statement that it's "different?" For anyone, there is 93,000,000 Blue sticks between the Earth and the Sun!
Try to keep up. Everybody has already agreed with that.
What you are claiming is that the Moon is only 6" wide because at night when there is a full moon I can hold my 6" hand up and compare it to the Moon, and it fits perfect! So the Moon is 6" in diameter!!! LOL
That is a useful example in showing you how the
apparent size of an object can differ from its
actual size. In that example, the reason the apparent size is different from the actual size is due to your making the mistake of assuming that the moon is at the same distance as your hand, which it isn't.
When it comes to relativity, the mistake you keep making is in assuming that observers in relative motion all perceive a "blue ruler" to have the same length, regardless of their velocity with respect to the ruler. They do not. Your error, again, is in ignoring differences in perspective. In fact, I sometimes think that you believe there's really only one "god-like" observer in the universe.
If I travel past the Earth and Sun at .866c how many miles are between the Earth and the Sun, according to you? 46,500,000?
Why don't you learn the relativistic length contraction formula? Then you'll be able to work out answers to simple questions for yourself.
Look, I'll provide it for here, just this once, with instructions on its use.
1. Measure the length of an object (or set of objects) when it is at rest relative to an observer, whom we will call A. If you want the distance between Earth and the Sun, imagine 93 million mile-long rulers placed end-to-end between the Earth and the Sun by A, who does this in such a way that the Earth and the Sun and the rulers are not moving with respect to A. (We can assume A does this at a given instant in time, so we don't have to worry about the Earth's revolution around the Sun etc.)
2. Assume that observer B is moving at speed v in a straight line, relative to observer A (whom we assumed to be "at rest" relative to the distance we measured in item 1, above).
3. Calculate the Lorentz factor using the following formula:
$$\gamma=\frac{1}{\sqrt{1-(v/c)^2}}$$
where c=299792458 m/s (a constant equal to the speed of light in vacuum). Be careful to convert the v value to units of metres per second first.
4. Calculate the length of the object or objects, as measured by observer B, using the following formula (use your result for the Lorentz factor from step 3, above):
$$L_B=L_A/\gamma$$
Easy!
Now, let's have a quick test to see if you can do this yourself. Here's the problem:
Observer A measures the distance between Earth and the Sun to be 150,000,000,000 metres. At a given instant in time, Observer B is travelling in a straight line that is parallel to a line drawn between Earth and the Sun, at a speed of v=0.866 c, where the value of c is given in step 3, above.
Question: What is the distance from Earth to the Sun, according to observer B?
---
In case you're confused, this question is
not asking you what
you think the distance should be. This is solely a test to see whether you can use the method above to calculate what distance the theory of relativity would predict. I don't care whether you think this is the wrong distance; I already know you think that. What I want to see is that you're capable of following a simple set of instructions to apply a theory with which you disagree. If it turns out you're incapable of doing that, then future discussion with you on this topic is likely to be a complete waste of time.
I'll wait for your answer.
