Zeno's Paradoxes: Misunderstanding or Misconception?

[ahrkron]

Originally posted by Tom
[...]Zeno's reason for forwarding Premise 1 is that, at any instant, there is no physical difference between a stationary arrow and a moving arrow. I don't see the logical connection there, but we now know that there is a physical difference: the moving arrow would be length contracted as per Special Relativity.

If SR were known at the time, would Zeno have offered this argument?
Did Zeno forsee SR?

I don't see the connection either, but if there is one, we can also ask the question in a slightly different way: would motion be possible in a universe with no length contraction?

This reminds me of the fact that Poincare was extremely close to the gist of SR. He even mentioned that there is no experimental backup for the idea that simultaneity is absolute (which is closely related to length contraction).

Of course, Poincare had the context of Maxwell equations and the struggle to interpret the "Lorentz-Fitzgerald contraction", but anyway, it strikes me as impressive that he made the connection, and the sole idea that Zeno may have glanced at it so long ago is just mind-boggling.

 

[heusdens]

Originally posted by Tom
Incidentally, it is said that Zeno's reason for forwarding Premise 1 is that, at any instant, there is no physical difference between a stationary arrow and a moving arrow. I don't see the logical connection there, but we now know that there is a physical difference: the moving arrow would be length contracted as per Special Relativity.

If SR were known at the time, would Zeno have offered this argument?
Did Zeno forsee SR?

In SR we would just state that the arrow, in it's own space-time frame is at rest. It shows to be moving, according to a different space-time frame, and also is length contracted and has a little more mass. These are observational things though. As seen from the arrow itself, physical properties don't change.

 

[heusdens]

Originally posted by ahrkron
I don't see the connection either, but if there is one, we can also ask the question in a slightly different way: would motion be possible in a universe with no length contraction? [/b/]

This is a weird interpretation, you better focus on the causes of length contraction and other relativistic phenomena, which are of course a consequence of the speed of light.
We could state it differently, what if the speed of light were infinite? Then every measurement would be instantaniously, since no time elapse between the happening of the event and the observation of it from a distant. Hence, no length contraction or any other relativistic phenomena would occur.

I would reformulate this then as:

Suppose the light speed would be infinite, would there still be motion possible?

What would the universe look like if the speed of light were infinite?


But let us look at the problem again, the arrow in motion.
What is the difference between an arrow, that is in motion and one that is at rest (relative to some default intertial frame of reference that is).
Both arrows are at some point in time T at some point in space S.
Yet, the moving arrow is at a different point in space at a different time, and the arrow in rest, does not change it's point in space at a different time. So obviously, the arrows differ.

We have to be aware of the fact though that the moving arrow, did not start it's motion out of nothing, but it was accelerated due to some force. This force has transferred energy onto the arrow.
That makes the arrows physically different. The moving arrow carries kinetic energy, the arrow at rest not.

The speed of light in this experiment is of no theoretical consequence. Hence this would not be of any influence to the fact that one arrow is moving, and the other is at rest.

 

[heusdens]

Originally posted by Lifegazer
That just implies that nothing can exist unless it moves.

This is fairly true, there is no existence without motion or change.

But you cannot impose physical-law upon all existence

Since all existence is physical existence, it is obvious that all physical existence is subject to physical laws.

 

[Mentat]

Originally posted by Tom
OK, it goes something like this:

1. If the arrow occupies a space its own size, then it is at rest.
2. The arrow always occupies a space its own size.
3. Therefore, the arrow is always at rest.

As far as I can see, the error in this argument is that the first premise is false. It basically says that if you know the position of the arrow, you know its state of motion. But every student of Physics I knows that you have to specify both the initial position and the initial velocity to get the state, because motion is described by a 2nd order differential equation.

So, in order to conclude that motion is impossible, Zeno had to assume that motion is impossible!

Relativity also contradicts the first premise, doesn't it? In Relativistic reasoning, any frame of reference could be said to be "at rest".