Relativity of Count – Spin Counter

Huh? I am saying that the station would see the train’s spinner moving in parallel to its own. When the train sped up, the spinner has no impetus to slow down rotation from the station’s perspective. that would be creating momentum in the y-axis.

I don’t know what you are thinking. The pictorial displays what I am talking about. The x-axis is the train’s motion. Of course the station would see the train’s spinner moving with the train along the x-axis, but the y and z axes do not change between the train and the station nor the spinners. They are only rotating in the y and z axes.

Look at the case for a real number line. If you count the points along the line, it will count to infinity. But now if you had 2 lines side by side, and you were counting both, your count will always be twice as much as the first time, even out near infinitely. So at no point will 2 * inf ever equal inf.

The limit as n reaches infinity is that 2*n is twice as great as n.

The y and z axes don’t need to change. The distance around the helix has a component of x. If x=0, the path is shorter than if x=v. Because the station knows the spinner to be moving, it must factor in that motion when calculating the distance traveled by a point on the edge of the spinner. The illustration you provided illustrates the difference in arc length.

I got this wrong when I said they were “countable”, but PhysBang corrected me (obliged, Phys). The infinity of points between any two points is uncountable, and is equal to the infinity of points between any other pair of points, no matter how far apart they are. From wiki:

So?? :-k

Wiki is probably talking about Cantor there. Cantor had issues. The Cardinality concerns are a different type of error that the old Europeans couldn’t figure out (or refused). The Greeks had it right.

You figure out any infinite series sum by watching it as it approaches infinity to see where it is headed. You know that if you count the whole numbers (to make them “countable”) along one line and also count along two lines, as n approaches infinity, the two line count will be steadily twice the one line count. That is how all “real” mathematics works throughout all calculus and infinite series issues. But I am not going to go through that on this thread. I’ll deal with Cantor some other time.

Why again are we worshiping a bunch of old Europeans? :-k

So the distance traveled by a point on the edge of the spinner is the arc length. Since the arc length differs for the two observers, but the speed is the same (it’s c for both observers), the time it takes the point to travel that distance differs for the two observers.

While I agree with PhysBang that these infinities aren’t countable, I think the idea is the same: There’s an isomorphism that maps each entity in a single number line onto each entity in two number lines, so the two infinite sets contain the same number of entities.

That’s fine, it’s a complex issue. But if you don’t go through it, you can’t use it as an assumption in the argument that “distance doesn’t dilate because what causes distance is the number of points between one affect and another.” I dispute that distance dilation requires that there be a different number of points between two events in different frames, and I will not accept it as a premise in an argument.

Don’t be facetious, Physbang. We measure each other as 2m long when at rest with respect to one another.

But that’s a different situation than when two things are in motion relative to one another. Either you accept SR or you do not.

Farsight, in relativity the consideration of a body’s attributes at rest is arbitrary. To say that the rest frame is the “real” frame is to prioritize one frame over others, which directly contradicts a central tenet of relativity.

Still, what’s the point? Are you saying that the train will see its light spinner turning slower because it is moving?

Whole number lines ARE “countable”.

An “isomorphism”??? :unamused:

The counts do not converge. They stay exactly different by a factor of 2 from zero up to infinity. What rationale do you have for proposing that magically at infinity they suddenly become the same?

I wasn’t “arguing” using the point. I mentioned that such was how I knew.

No, he is saying that in any reference frame in which we describe the train as moving, the spinner will be turning slower.

But we don’t use whole numbers in physics, we use at least rational numbers, if not real numbers.

You once claimed that you took mathematics in university. You obviously did not go very far. Isomorphisms are the means by which we compare the size, in a sense, of sets with infinite members.

Are there as many even whole numbers as odd whole numbers? Comparing these numbers is always different, too.

That’s arguing. It seems that you don’t want us to trust the claims of anyone who actually studied and published in mathematics or physics, but you want us to trust your pronouncements like you were some kind of religious leader.

PhysBang nailed everything. A few quick additions:

  1. I don’t know why you would roll your eyes at the term “isomorphism” in a discussion of infinite sets.
  2. I’m not saying they converge, I’m saying they have equal infinities of elements.
  3. There is no “at infinity”. For every number on two infinite number lines, there is a corresponding number on one infinite number line. There’s no value in the two number lines that doesn’t have a unique, corresponding element on the single number line. Contrast that with an uncountable infinity of elements, for which an infinite set of whole numbers cannot provide a unique corresponding element.

What’s more, there are as many even whole numbers as there are whole numbers. :open_mouth:

The clear fact that neither you nor Phys can handle infinities is an entirely different thread. I have a book of things to clear that issue up. Stick to the subject and question I asked’ “Still, what’s the point? Are you saying that the train will see its light spinner turning slower because it is moving?

-You brought up the infinities to justify your rejection of length contraction. Even if its just a personal reason, it’s relevant if it leads to you rejecting every argument we could possibly offer in support of length contraction. If that’s why you actually reject length contraction, why wouldn’t it be right at the heart of our discussion?
-What book do you have? Or is a book you wrote? What source would you accept, since you don’t seem willing to accept any argument for the idea that all countable infinities are equal? Are you unfamiliar with isomorphisms?

PhysBang answered that:

A stationary observer, for whom the spinner is moving, will measure a point on the edge of the spinner as moving farther, and thus spinning more slowly, than an observer who sees that spinner as stationary in her own frame.

As I said, I did NOT use it to justify anything. I merely mentioned that was how I personally knew, just in case you had enough sense to see it yourself.

So you are saying that the station will see the train’s light spinner turning more slowly?

What will the train see of the station’s light spinner? And why?

In the world outside of your head, doing that activity is what we can “justifying a claim”. I hope that you understand this but you are stalling for time until you can come up with a real response.

Welcome to the world of Special Relativity.

The train will see the station’s light spinner spin more slowly. The reason for this is a) the Lorentz transformations between frames, or, equivalently, b) because the train sees the station spinner operating just like the station sees the train spinner. However, because of the relativity of simultaneity, this doesn’t produce a contradiction.

That’s very relevant. If that’s your personal justification, it will continue to cause you reject length contraction until it is dealt with. Again, why don’t we discuss your real reasons for your positions, rather than some after-the-fact justification at the end of which you’ll still fall back and say “well, my real reason still stands”?

Because you are merely imagining that argument, possibly to avoid the fact that you have no defense for your own position other than as PhysBang’s, “well those smart guys told me that SR says…

So if you disagree with what I have proposed. SHOW me your logic/math for your disagreement. I need not show you my reason for why I believed it in the first place. All I have to do it show you the errors in yours.

“What will the train see of the station’s light spinner? And why?”

Carleas directly answered this question and gave you the explanation why that did not appeal to SR. He told you about the difference in arc length. You have not addressed this other than to be incredulous. Try working it out.

More of your BS. I and everyone acknowledged the arc. I even drew a pictorial of it. I am asking, repeatedly, “SO WHAT???”

What is the conclusion that is to be drawn from such a thought?

No one is arguing against the idea that there is an arc. But let’s get a move on. Why do we care? What is the next step in reasoning? What is the conclusion from such a thought? Then where does that lead us (relevant to the OP)?

If the arc length is different from one frame to another, and the speed is the same, the time is different. So the spinners read different times. So… I don’t understand what you’re looking for. SR accepts and accounts for what you’re calling “relativity of count”, but it calls it time dilation or relativity of simultaneity.

Those are VERY different concepts. You can have time dilation without any trace of “relativity of simultaneity”.

What does the train see of the station’s spinner? - That is the next step of concern. I don’t accept PhysBang’s answers as yours. He’ll just repeat rhetoric spins (“the repeated meme”).