Relativity of Count – Spin Counter

[James S Saint]

So??

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.

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

the two line count will be steadily twice the one line count

While I agree with PhysBang that these infinities aren't countable,

Whole number lines ARE "countable".

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.

An "isomorphism"???

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 am not going to go through that on this thread.

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.

I wasn't "arguing" using the point. I mentioned that such was how I knew.

[PhysBang]

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

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

Whole number lines ARE "countable".

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

An "isomorphism"???

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.

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?

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

I wasn't "arguing" using the point. I mentioned that such was how I knew.

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.

[Carleas]

PhysBang nailed everything. A few quick additions:

An "isomorphism"???

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?

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.

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

What's more, there are as many even whole numbers as there are whole numbers.

[James S Saint]

PhysBang nailed everything. A few quick additions:

An "isomorphism"???

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?

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.

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

What's more, there are as many even whole numbers as there are whole numbers.

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?"

[Carleas]

The clear fact that neither you nor Phys can handle infinities is an entirely different thread.

-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?

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

PhysBang answered that:

he is saying that in any reference frame in which we describe the train as moving, the spinner will be turning slower.

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.

[James S Saint]

The clear fact that neither you nor Phys can handle infinities is an entirely different thread.

-You brought up the infinities to justify your rejection of length contraction.

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.

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

PhysBang answered that:

he is saying that in any reference frame in which we describe the train as moving, the spinner will be turning slower.

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.

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?

[PhysBang]

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.

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.

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

Welcome to the world of Special Relativity.

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

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.

[Carleas]

I merely mentioned that was how I personally knew

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"?

[James S Saint]

I merely mentioned that was how I personally knew

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?"

[PhysBang]

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.

[James S Saint]

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)?

[Carleas]

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.

[James S Saint]

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").

[Carleas]

Those are VERY different concepts.

You haven't fully expounded what you mean by "relativity of count," so I'm not sure which best captures it. But your objection seems to be that the clock read differently in different frames, which is involved in both time dilation and relativity of simultaneity.

You can have time dilation without any trace of "relativity of simultaneity".

In some sense yes, but in special relativity they are inextricably related.

What does the train see of the station's spinner?

I agree with PhysBang:

The train will see the station's light spinner spin more slowly.

Also,

Because you are merely imagining that argument...

I didn't imagine it. You said:

I know that distance doesn't dilate because what causes distance is the number of points between one affect and another.
There are an infinite number of points between any 2 affects. And even though 2 * inf and inf are infinite, they are not equally infinite. Thus merely by moving, you cannot alter the number of points between 2 other affects from infinite to 2 * infinite. You would have to move them relative to each other, not yourself.

If, for instance, the set of all whole numbers and the set of all even whole numbers have the same number of elements, then everything that follows from that (including your personal rejection of length contraction) is left unsupported. If this argument prevents you relenting on your assault on SR, it's something we'll have to deal with sooner or later. And if it's why you know, it's better that we deal with it sooner.

[James S Saint]

What does the train see of the station's spinner?

I agree with PhysBang:

The train will see the station's light spinner spin more slowly.

Then you run into the Twin Clocks Paradox.

Either twin A ages more than twin B or visa versa. It can't be both. Either time is dilated on the train or it is dilated at the station. If it were both, there would be no actual dilation at all. They would always agree in the end.

So try again.

[Carleas]

What is "the end" in which they would agree? Let's say "the end" is a flasher going off at a given time according to the train clock. They certainly wouldn't agree on what time it went off, since everyone agrees their clocks aren't synchronized.



Also, the "Twin Paradox" is easily resolved using Special Relativity.

Like all such paradoxes the paradox is only apparent.

[James S Saint]

What is "the end" in which they would agree? Let's say "the end" is a flasher going off at a given time according to the train clock. They certainly wouldn't agree on what time it went off, since everyone agrees their clocks aren't synchronized.

No that is not the end. The end is when the train stops. Or when the twins get back together.

If the train were to stop itself and its clock as soon as they read 4:00, the station would see them read 4:00 and see it's own clocks read perhaps 4:02. It is that simple. No magic.

Also, the "Twin Paradox" is easily resolved using Special Relativity.

Like all such paradoxes the paradox is only apparent.

Special Relativity misuse is what proposed the paradox in the first place. It is easily resolved using common sense. Resolve to the Twins Paradox

But now back to the question, what will the train see of the station's clock timing?

[Carleas]

But now back to the question, what will the train see of the station's clock timing?

You're getting a little ahead of yourself. We've answered that question, and your argument against it can be summed up as,

The Twins Paradox is not a problem for Special Relativity, so saying "then you run into the Twin Clocks Paradox" is not a reason to reject our answer.

[James S Saint]

But now back to the question, what will the train see of the station's clock timing?

You're getting a little ahead of yourself. We've answered that question, and your argument against it can be summed up as,

The Twins Paradox is not a problem for Special Relativity, so saying "then you run into the Twin Clocks Paradox" is not a reason to reject our answer.

What do you think the solution is???

Which twin aged more?

[Carleas]

I agree with the solution in the link I posted earlier. And this one and this one (both with nice animations).

[James S Saint]

I agree with the solution in the link I posted earlier. And this one and this one (both with nice animations).

I didn't ask what you agree to. I asked which twin aged more.

[Carleas]

The twin at home, as all three explanations indicate.

[James S Saint]

The twin at home, as all three explanations indicate.

So if the twin at home ages more, that means that the twin B's clock was moving slower and to the traveler, the Earth's clock was moving faster.

So I ask again, what does the train see of the station's clock?

[Farsight]

Take a look at some of Sardin's papers: http://arxiv.org/find/grp_physics/1/au: ... /0/all/0/1 and do read The Other Meaning of Special Relativity.

[Carleas]

In the twin paradox, symmetry is violated. That is not the case here. Both the station and the train see the other's clock as moving more slowly.