LAUGHED OUT OF COURT

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123...

Call me dense but I'm still not getting the origin of two different absolute velocities for two parallel light beams projeced in the same vector.

What is the cause for the affect?


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Well, if the speed of the light beams were source velocity dependent, that would result in two different absolute velocities,
if one beam was emitted from a moving source. Or it could be that the gravitational field is varying differently for the paths of the two light beams (the earth is not a perfect homogeneous sphere). Or the two light beams could be traveling in two different mediums. We have empirical evidence that at least two of these "forces" can cause light to accelerate, changing its average "absolute speed", so it was very premature, imo, for MM, Einstein, et al to formulate a theory based on the constancy of the speed of light.

Hope that makes sense.

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In other words, there can be no mechanism for motion in pluralistic space but it can exist for discrete space if and only if, time-space is considered to evolve with motion. This is what in a sense Eistein did. Motion is possible because although the arrow does not change, space-time curves around it and the system arrow/space-time is different at every instant.





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I disagree on all points. If I am finitely sized and I can move, it doesn't matter if space is discrete or smooth if we assumed that I have to move a discrete and finite amount of space proportional to a quantum of, let's call it "moving energy". This would make motion a little bumpy but I don't see a logical problem with this.

The mechanism in either case can be identical. Let's say we were to bring a couple pigs down from the top of two 100 meter tall buildings using an elevator. In one builiding, there are no floors on the way down to the ground; the other building is separated into 10 floors. Imagine those floors represented smooth and discrete space, respectively. Now, Zeno may not be able to bring those pigs down on those elevators, but I'm sure you, Einstein, or any of us would be able to.

Why? Because our elevator's movement is dependent not on the space but on the juice required to run its motor. And if this "juice" is finite and discrete-sized, say only coming in packages of 10 meters of elevator movement, our elevator then must move 10 meters at a time. So, in either case, as long as we have paid our electric bills, space being smooth or divided in to 10 cubic meter parts, our pigs are going down.

As for Einstein, I don't think his space time curving resolves Zeno's paradoxes of motion. If I understand you correctly, you are saying it is the space that moves the arrow and not the arrow moving through space? There are many problems with that. First, as I type these words from my keyboard, I tend to think that I am moving my fingers to the keyboard and not that the space below my keyboard is pushing it to my fingers. Second, if this were possible, space contraction and expansion would imply that space is not discrete but smooth, and therefore, unable to move, since as you say, "motion is impossible in pluralistic space". Third, whether it's matter moving or space moving, if we are to be consistent with Zeno's paradoxes, we would hereby decree that space, in order to contract
a distance, must contract half of that distance, ad infinitum. Or in the case of the arrow paradox, this would be equivalent to saying that in each instant that space is contracting, it is not contracting, so that it cannot contract.

As you can see, Zeno's paradoxes are only complicated by space-time curving. No, as long as we agree with Zeno's two faulty premises: 1. That if space is continuous, motion has to be continuous, and 2. That if space was discrete, an arrow cannot possess potential "moving energy" at an instant in time", Zeno's logic will prevail.

"Let's say we were to bring a couple pigs down from the top of two 100 meter tall buildings using an elevator..."

By introducing an elevator to resolve the motion paradox for pigs, the paradox now becomes relevant to the elevator motion. So this is a circular argument involving a by-passing of original premises.

No, as long as we agree with Zeno's two faulty premises: 1. That if space is continuous, motion has to be continuous, and 2. That if space was discrete, an arrow cannot possess potential "moving energy" at an instant in time", Zeno's logic will prevail."

To say premises are faulty, one must prove why they are faulty. It is very different to claim that premises result in a self-contradiction and to say that premises are faulty. Zeno does not care how motion is accomplished. The paradoxes deal with the motion of objects. If one assumes a specific notion of space-time, like Einstein, the paradox is resolved in the sense that the its original premises result in a contradiction in the context of the said theory. But this is very different from claiming the premise are faulty. It is just that an addition to the origical premises is made in such a way as for the paradox to prove false.

If space is continuous, then motion is coninuous is not one of Zeno's premises. You see, you introduce an operation on this premise yourself to solve the paradox. But in doing that you implicitely subscribe to some notion of space-time. The same holds for the other premise you stated.

In does not matter how many bigs of how many floors your building has, Zeno will just look at the elevator and tell you its motion is impossible unless you adhere to a specific structure of space-time. This is the essence of Zeno's paradox. Static space models either continuous or discrete fail to explain motion. For you elevator to be moving you supplying energy is not enough. Unless there is something to cause motion, even if you spent 1 billion dollars in electric bills your bigs will never get to the ground, Zeno says.

Another way to look at Zeno paradox is to say that Pythagorean space -time concept fails to explain motion. There is a need for higher dimensions and interactions to consider. The naive view is that Zeno objected motion. He did not, he only objected motion in the sense of a infinitely divisible or discrete space. Again, if space is pluralistic there seems to be no hope for motion explanation in realistic terms but only mathmatically abstract but if it is discrete there can be possibilities for solution.

I still fail to see how continuous or infinitely divisible space prevents motion. As near as I have been able to understand Zeno's position rests on the false belief that the sum of an infinite series must be infinite which we know is false. It seems to me that if his premise was not flawed then you could make a similar case for Calculus being a false idealogy even though it works quite well.

"It seems to me that if his premise was not flawed then you could make a similar case for Calculus being a false idealogy even though it works quite well."

G. Berkeley in 1734 offered a significant challenge to infinitesimals as soon as Newton postulated it. The subject is still ongoing and valid. Infinitesimals seem to work magically. Calculus, a product of Newton is not different from his laws in the sense that a total ignorance of cause and effect is clear. Newton and people who use infinitesimals in nowadays are not interested in causes of motion but only in practical results of motion effects, and that is ok. But many philophers and Physicists are interested in discovering the cause of motion and what space-time is made of and this is where Zeno's paradox apply. In this sense, your infinite series solution is hlf of the solution and half-solutions are hardly solutions for some people.

[Enrico]


By introducing an elevator to resolve the motion paradox for pigs, the paradox now becomes relevant to the elevator motion. So this is a circular argument involving a by-passing of original premises.

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[123] Right, because I disagree with Zeno's premise that motion is impossible in static space. Let's go over a couple of his premises
again, to show why it is flawed:

1. In the infinitely divided space paradox, he assumes that a finite object can travel infinitesmally small distances. Another flawed assumption is that the time it takes to travel smaller distances adds up to infinity, when it's actually an inverse relationship with the distance. Or that an object cannot even begin to move because of the way the space is divided. The list goes on and on, and if we changed but one of these premises, we can show a contradiction.

2. In his arrow paradox, he assumes that a moving object is the same as a non-moving object at each instant in time. Actually, this paradox is really a semantics trick: he defines each instant of the arrow's motion as at rest and then uses this definition to conclude that since an arrow is at rest at every instant, it is not moving. What's the word for this- tautology?

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[Enrico]
To say premises are faulty, one must prove why they are faulty. It is very different to claim that premises result in a self-contradiction and to say that premises are faulty. Zeno does not care how motion is accomplished. The paradoxes deal with the motion of objects. If one assumes a specific notion of space-time, like Einstein, the paradox is resolved in the sense that the its original premises result in a contradiction in the context of the said theory. But this is very different from claiming the premise are faulty. It is just that an addition to the origical premises is made in such a way as for the paradox to prove false.

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[123] The key here being that Zeno's premises led to a contradiction in Einstein's theory, and not to a self-contradiction in Zeno's arguments. He did not show that motion was possible under a static model of space-time, but that a static model of space-time was imossible. Nor did Einstein provide a mechanism for motion in his model or even dealt with the possibility that it wasn't possible under his own model so I can't see how Einstein refuted Zeno's claim of the impossibility of motion.

I can just as well claim then that since I can prove that there was no Achilles and that turtles don't talk, I have resolved Zeno's paradoxes of motion because if nothing else, Zeno must be a liar.

No, even if Zeno didn't "care about how motion is accomplished", we must care since the very subject of the paradoxes is motion.

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[Enrico]
If space is continuous, then motion is coninuous is not one of Zeno's premises. You see, you introduce an operation on this premise yourself to solve the paradox. But in doing that you implicitely subscribe to some notion of space-time. The same holds for the other premise you stated.

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[123] Well, if Einstein was allowed to rid of Zeno's premises entirely, why can't I change them just a little bit? Again, Einstein did not prove, nor was he trying to prove that motion under a static space-time was possible. Au Contraire, if we can interpret that the impossibility of a static space-time is equivalent to motion being impossible under this model, Einstein actually proved Zeno right- that motion is impossible!

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[Enrico]


In does not matter how many bigs of how many floors your building has, Zeno will just look at the elevator and tell you its motion is impossible unless you adhere to a specific structure of space-time. This is the essence of Zeno's paradox. Static space models either continuous or discrete fail to explain motion. For you elevator to be moving you supplying energy is not enough. Unless there is something to cause motion, even if you spent 1 billion dollars in electric bills your bigs will never get to the ground, Zeno says.

Another way to look at Zeno paradox is to say that Pythagorean space -time concept fails to explain motion. There is a need for higher dimensions and interactions to consider.

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[123] Well, you still haven't shown us how Einstein's non-Euclidean space-time doesn't fail to explain motion. Not that Zeno would've cared of course since apparently he was only interested in the consistency of his logic and not in the truth of it.

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[Enrico]
The naive view is that Zeno objected motion. He did not, he only objected motion in the sense of a infinitely divisible or discrete space. Again, if space is pluralistic there seems to be no hope for motion explanation in realistic terms but only mathmatically abstract but if it is discrete there can be possibilities for solution.

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[123] No, the Eleatic school of thought was that "The All is One"; that the universe was a unity, was constant and multiplicity, change , motion, etc. , merely an illusion. But the biggest clue is that he never argued for the existence of motion. Or in your own words, he didn't even care how motion was accomplished.