Why would God be interested in free lunches?

[QED]

Most of us are familiar with the saying "there's no such thing as a free lunch" and physics backs this up with the notion of conserved properties. The best known of these is probably energy which most schoolkids will tell us "can neither be created nor destroyed". Other example of conserved properties are electric charge and angular momentum. This jives with the idea of a provident God -- only he who has the power to break these universal rules and inject energy, charge and momentum into the unfolding universe. And what a lot of this we might imagine there to be!

But actually there isn't. All these laws of conservation hold within the universe, however they do not apply to the universe as a whole. The total mass-energy has a net sum indistinguishable from zero (when the negative contribution of gravitational potential energy is accounted for) and any imbalance in the numbers of electrons and protons would have a dramatic affect on structures of cosmic scale as the electric force is so much stronger than the force of gravity holding these structures together. If there was any net angular momentum to the universe then it would have shown as an increase in the microwave background radiation in the direction of its rotation axis. This radiation has now been measured to be the same in every direction to on part in a hundred thousand.

So why would a God with unlimited powers be so frugal? It's as though he's been down to the charity shop and blagged himself a universe for nothing. Perhaps it's the greatest testament to his ingenuity, but perhaps it's telling us something about the reason why we see the appearance of so much stuff when, with the proper accounting, it all sums to zero.

[Grumpy]

harvey1

Unfortunately most atheists won't accept metaphysical causation because deep, deep, deep down it is as if someone turned on the lights.

We don't accept metaphysical explanations because there is no evidence supporting such explanations, they have no explanitory power, nor can they be investigated by scientific methods. We consider "...and then a miracle occured!!!" to be a cop-out, cutting off any further investigation.

Deep, deep, deep down we consider anyone who uses these explanations not worthy of any respect in scientific discussions and of susspect intellectual quality, but we do try to hide it, really we do!!!

Grumpy

[wuntext]

Zeno was born over 2000 years before the introduction of calculus. Zeno's paradox is based on his ignorance, not some stunning metaphysical truth, and I cannot see the reason why this dead horse is still being flogged >2000 years later. But the fact that believers have to rely on such ludicrous non-evidence to support their position shows just how threadbare their arguments really are.

His paradox is based on the idea of infinitely divisible units, which can be described in mathematical terms as a geometric series with ratio r=1/2. A common ratio whose absolute value is less than 1 converges:

a/(1-r), where [a] is its initial term and [r] its ratio. In the case of Zeno's paradox, a=1/2 and r=1/2. The series converges, and its sum is a/(1-r) = (1/2)/(1-1/2) = (1/2)/(1/2) = 1.

The terms of such a series is obtained by multiplying the previous term by the common ratio, r = Σ(n=1, ∞, arn-1).

We can define the nth partial sum sn = Σ(i=1, n, ari-1) = a + ar + ar2 + ... + arn-1.

We know that when r=1, the series is a + a + a + ... + a. In this case, sn = na, which goes to infinity as n grows to infinity. In this case, the series diverges.

When r≠1, (i.e. the ratio is not equal to 1, such as in Zeno's paradox), then sn = a + ar + ar2 + ... + an-1. rsn = ar + ar2 + ... + arn-1 + arn. Subtracting these, sn-rsn = a - arn = sn(1-r). So sn = (a(1-rn))/(1-r).

when -1 < r < 1, rn, goes to 0 as n goes to infinity. This means that lim(n&#8594;&#8734;, sn) = lim(n&#8594;&#8734;,(a(1-rn)/(1-r)) = (a/(1-r))(1 - lim(n&#8594;&#8734;,rn)) = (a/(1-r))(1-0) = a/(1-r)

Simple my dear Watson, there is no paradox. This is basic calculus Harvey1, (or more correctly, infinitesimal calculus) you can find it in any high school math text book, it isn't rocket science. Sometimes I think theist's won't learn disciplines such as physics or math because, deep, deep, deep down they know their baseless superstitions will burn away if they are forced to turn on the lights of rational thought.

[harvey1]

Simple my dear Watson, there is no paradox. This is basic calculus Harvey1, (or more correctly, infinitesimal calculus) you can find it in any high school math text book, it isn't rocket science.

I'm tempted to not even respond to this demeaning post, but for the sake of others I'll just refer the reader to this published paper which discusses the real challenges that Zeno's paradoxes bring about:

``No one has ever touched Zeno without refuting him'' [A.N. Whitehead]. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science... One can superficially think that the resolutions of the paradoxes was provided by calculus centuries ago by pointing out now the trivial fact that an infinite series can have a finite sum... More subtle under the surface truth that Zeno's paradoxes is that even if one assumes the infinitely divisible space and time calculus does not really resolves the paradoxes but instead makes them even more paradoxial and leads to the conclusion that things cannot be localized arbitrarily sharply.

Sometimes I think theist's won't learn disciplines such as physics or math because, deep, deep, deep down they know their baseless superstitions will burn away if they are forced to turn on the lights of rational thought.

I always like to frame these "I'm an atheist and I'm the smartest person I know" moments because I hear them so frequently. I would hope that those who see these examples often enough will become much more aware of it. (It's also funny because some of the most accomplished physicists are theists such as Andrei Linde, Roger Penrose, Christopher Isham, etc..)

[wuntext]

You find real word solutions to real world problems inconvenient, so you retreat to the quantum world. OK, lets look at your quantum evidence.

The piece you linked to is quite clear about the result.

"This scheme implicitly assumes a continues monitoring of Achilles’ position and therefore he will fail even to start the race. Matters are not as simple however. Repeated measurement of a system effects its dynamics much more complex and delicate way than just slowing the evolution"

For Zeno's paradox to work at the quantum level it requires infinitely frequent measurements. But unfortunately for your argument, measurement affects the dynamics of any quantum system, as the authors of this article point out:

"The Zeno time for this unstable system is of the order of about &#956;s (one millionth of a second) and during this short time period the survival probability exhibits a t2 drop (the survival probability of the system drops by a factor of two after one millionth of a second!). For longer times we see a gradual transition from the t2 dependence to linear t dependence, which corresponds to the usual exponential decay law."

The longer the quantum measurements are made, the less stable the quantum state becomes, the system decay's exponentially, and it decoheres into a classical, non-quantum state - this is implicit in the Hamilton Operator on page 7 - that's why the infinitesimal calculus equations work.

They continue: "But in the context of Zeno paradoxes we are more interested in the limit of infinitely frequent measurements with complete inhibition of evolution. Although such limit leads to interesting mathematics, its physical realizability is dubious".

"Dubious": Mathematician speak for "If you think this has any basis in reality, your talking out of your rear end".

I always like to frame these "I'm an atheist and I'm the smartest person I know" moments because I hear them so frequently.

Of course, if you spent less time feeling hurt and victimized, you'd realize the sentence you are complaining about was a play on your smug little comment to Cathar1950 in post 49.
It seems your double standards don't stop at what you believe is an acceptable level of rigour for evidence for and against the existence of your invisible friend.
Apparently you are also to remain immune from being on the end of certain remarks whilst retaining the absolute right to dish them out yourself.

I would hope that those who see these examples often enough will become much more aware of it.

Oh Yes!

(It's also funny because some of the most accomplished physicists are theists such as Andrei Linde, Roger Penrose, Christopher Isham, etc..)

I do love that "etc..." It implies the list goes on and on. But if you want to play the "Appeal to Authority" game regarding the levels of belief or non-belief amongst scientists, you'll lose. Even in the USA, the most god fearin'western democracy -

"Our latest survey finds that, among the top natural scientists, disbelief is greater than ever — almost total".
Nature: Vol 394 1998

If anyone's interested, here's the stats..
.

Belief in personal God

Belief 7.0
Disbelief 72.2
Doubt or agnosticism 20.8

[harvey1]

For Zeno's paradox to work at the quantum level it requires infinitely frequent measurements. But unfortunately for your argument, measurement affects the dynamics of any quantum system, as the authors of this article point out:

You're conflating epistemology with ontology. Sure, epistemically speaking, the act of measurement affects the ability to know the thing-in-itself (to use a Kantian term). However, if we ask what is the facts about the thing-in-itself, that is, the way things actually are if we don't make a measurement, then the state of an unmeasured object does not change its own dynamics according to how you highlighted above.

In addition, I'd like to get back to the material causation issue since this is the subject of my reference to Cathar (btw, we really ought to be discussing these kind of topics in a separate thread...). This paragraph mentions this issue more explicitly referring to the Arrow paradox:

Stated differently, if a particle exists only at a sequence of discrete instants of time, what is the instantaneous physical properties of a moviing particle which distinguishes it from the not moving one? And if there is no such properties (well, the notion of instantaneous velocity requires the concept of limit and thus is inappropriate in discrete space-time) how the motion is possible? Modern physics changed our perspective of particles and motion and the Arrow seems not so disturbing today. For example, we can defy it by stating that the arrow cannot be at rest at definite position according to the uncertainty principle. Alternatively, we can evoke special relativity and say that there is a difference how the world looks for a moving arrow and for an arrow at rest: they have different places of simulataneity.

Notice though these answers do not rescue material causation. In the case of quantum vagueness, there is not one particular quantum vague event that materially causes another quantum vague moment. The vague moments would suffer just as much from Zeno's Arrow paradox since the vague events would not be materially connected as the same vague moment. This published paper mentions this issue explicitly:

As a natural consequence of this, if there is not a precise static instant in time underlying a dynamical physical process, there is no physical progression or flow of time, as without a continuous and chronological progression through definite invisible instants of time over an extended interval in time, there can be no progression.

Incidentally, Lynds paper received a great deal of publicity in the physics community, even Hawking himself was aware of it. It was never disputed.

(Btw, in the case of non-simultaneity, this would only mark an ontological distinction of simultaneity between an arrow in motion and an arrow at rest. It would not, however, solve the issue as to how material causation from one vague moment to the next is possible.)

Of course, if you spent less time feeling hurt and victimized, you'd realize the sentence you are complaining about was a play on your smug little comment to Cathar1950 in post 49.

Well, then, at least we both know how we see each others views. You apparently look upon theists as stupid, and I look upon a number of atheists as psychologically motivated. Incidentally, even Christopher Isham mentioned something along these lines (I suppose you'll say something negative about him too...):

"Perhaps the best argument in favor of the thesis that the Big Bang supports theism is the obvious unease with which it is greeted by some atheist physicists. At times this has led to scientific ideas, such as continuous creation or an oscillating universe, being advanced with a tenacity which so exceeds their intrinsic worth that one can only suspect the operation of psychological forces lying very much deeper than the usual academic desire of a theorist to support his/her theory" (Christopher Isham, "Creation of the Universe as a Quantum Process," in Physics, Philosophy and Theology: a Common quest for Understanding, ed. R. J. Russell, W. R. Stoeger, and G. V. Coyne [Vatican City: Vatican Observatory, 1988], p. 378).

I do love that "etc..." It implies the list goes on and on. But if you want to play the "Appeal to Authority" game regarding the levels of belief or non-belief amongst scientists, you'll lose. Even in the USA, the most god fearin'western democracy -

If you read my last post, I was not appealing to authority. I was responding to your claim that theists "won't learn disciplines such as physics or math." If that's true, then people like Isham and nobel laureate William Phillips are truly pulling off a miracle.

Our latest survey finds that, among the top natural scientists, disbelief is greater than ever — almost total".

The question asked was about a personal God. Buddhists, deists, and pantheists would have answered in the non-belief category. So, for example, Stephen Hawking is a pantheist and believes in God, but he doesn't believe in a personal God. (Hawking's view is similar to Einstein's regarding a cosmic God.)

[wuntext]

You're conflating epistemology with ontology. Sure, epistemically speaking, the act of measurement affects the ability to know the thing-in-itself (to use a Kantian term).

I'm not conflating anything. The phenomenon of observation/measurement effecting the observed/measured is a solid quantum mechanical fact - quantum indeterminacy.
You'll note that I didn't mention the word 'Uncertainty', and give you the opportunity to muddy the waters by pointing out "uncertainty" can be viewed as a epistemological concept.

However, if we ask what is the thing-in-itself, that is, the way things actually are if we don't make a measurement, then the state of the object does not change its dynamics.

What???? Explain the quantum eigenstate that allows this without also allowing the system to evolve. With equations please. I'm beginning to suspect your level of knowledge in this area.

Notice though these answers do not rescue material causation.

And I hope anyone reading this also notices that you have totally ignored the conclusion the authors came to:

"Modern physics changed our perspective of particles and motion and the Arrow seems not so disturbing today. For example we can defy it by stating that the arrow cannot be at rest at definite position according to the uncertainty principle. Alternatively, we can evoke special relativity and say that there is a difference how the world looks for a moving arrow and for an arrow at rest: they have different planes of simultaneity.

You are trying to re-focus the discussion onto philosophical territory - it's not going to happen.

In the case of quantum vagueness, there is not one particular quantum vague event that materially causes another quantum vague moment. The vague moments would suffer just as much from Zeno's Arrow paradox since the vague events would not be materially connected as the same vague moment.
In addition, I'd like to get back to the material causation issue since this is the subject of my reference to Cathar

No, we'll stay on quantum mechanics if you please. After all, the subject we are discussing, the quantum implications for Zeno's paradox was brought up by you because you objected to the classical physics infinitesimal calculus resolution.
And if you're going to use quantum mechanics to rescue Zeno's paradox, will you please stick to quantum mechanical terms? 'Quantum vagueness' is mathematically meaningless B.S. coined by a philosophy professor. As Grumpy put it - "philosobabel".

This published paper mentions this issue explicitly:

And my suspicions about the level of your knowledge in this area are confirmed! Do you read the articles you use as 'evidence'? Or do you just Google "quantum" and "Zeno" and hope for the best? On the very first page we find this:


"This explanation is also shown to be the correct solution to the motion and infinity paradoxes, excluding the Stadium, originally conceived by the ancient Greek mathematician Zeno of Elea".

On page 5 we have this:

"Please note that the explanation provided here and previously throughout this paper is also the correct solution to the motion and infinity paradoxes the Dichotomy, Achilles and the Tortoise, the Arrow, and their other more modern variations, originally conceived by the Greek mathematician, Zeno of Elea."

Your 'evidence' is in fact a rebuttal of your postion! But it gets better! On the bottom of page 5 is a link to a PDF where Lynds specifically addresses and resolves Zeno's paradox.

Incidentally, Lynds paper received a great deal of publicity in the physics community, even Hawking himself was aware of it. It was never disputed.

So, as you hold Lynds in such high regard, you will now drop your attempt to justify your postion through quantum mechanics - right?

Well, then, at least we both know how we see each others views. You apparently look upon theists as stupid, and I look upon a number of atheists as psychologically motivated. Incidentally, even Christopher Isham mentioned something along these lines (I suppose you'll say something negative about him too...):

Hmmm...let's see. Me, Post 51 - "I think theist's won't learn disciplines...".

Won't, not can't. Now, can't would have given you a case, and you would have received an apology from me - because can't implies an inability to learn; i.e. stupid. Whereas won't implies an unwillingness to learn.
So, carry on feeling victimized because you think someone has implied you're stupid if you must, but please, don't try to justify it by quoting me.

If you read my last post, I was not appealing to authority. I was responding to your claim that theists "won't learn disciplines such as physics or math." If that's true, then people like Isham and nobel laureate William Phillips are truly pulling off a miracle.

Yes. I should have made the distinction between scientist's who are theist and non-scientist's who are theist's clearer - but as there are not so many of the former, I'll claim common usage in this matter.

The question asked was about a personal God. Buddhists, deists, and pantheists would have answered in the non-belief category.

If all the 93% of those who did not answer in the affirmative were in fact all Buddhists, deists, and pantheists, (which I doubt, and will continue to doubt until you provide some evidence) how does this improve the position of belief in a personal god's paltry 7%?

[harvey1]

I'm not conflating anything. The phenomenon of observation/measurement effecting the observed/measured is a solid quantum mechanical fact - quantum indeterminacy.

Okay, let's first be clear as to which Zeno's paradox you are referring to. I'm referring to the Arrow paradox:

If everything is either at rest or moving when it occupies a space equal to itself, while the object moved is always in the instant, a moving arrow is unmoved.

For this thought experiment, we do not have to consider the arrow as being observed or measured. Rather, we are considering the actual state of the arrow (i.e., state of affairs of the object). If you bring up the problem of measurement, then you are missing the point of the thought experiment since it does not require that we assume the arrow is observed or measured.

However, if we ask what is the thing-in-itself, that is, the way things actually are if we don't make a measurement, then the state of the object does not change its dynamics.

What???? Explain the quantum eigenstate that allows this without also allowing the system to evolve.

What do you mean "without also allowing the system to evolve"? That's false. Nothing prevents the system to evolve.

No, we'll stay on quantum mechanics if you please. After all, the subject we are discussing, the quantum implications for Zeno's paradox was brought up by you because you objected to the classical physics infinitesimal calculus resolution.

And, both papers showed that this "solution" is not correct. At this point I've cited two peer-reviewed papers that have shown that Zeno's paradoxes have not unequivocally been solved. Do you have any recently published papers to say that it has?

And if you're going to use quantum mechanics to rescue Zeno's paradox, will you please stick to quantum mechanical terms? 'Quantum vagueness' is mathematically meaningless B.S. coined by a philosophy professor. As Grumpy put it - "philosobabel".

I can't address this issue since this term is already in use in academic circles.

And I hope anyone reading this also notices that you have totally ignored the conclusion the authors came to:

Modern physics changed our perspective of particles and motion and the Arrow seems not so disturbing today. For example we can defy it by stating that the arrow cannot be at rest at definite position according to the uncertainty principle. Alternatively, we can evoke special relativity and say that there is a difference how the world looks for a moving arrow and for an arrow at rest: they have different planes of simultaneity.

Did you not read my response to that issue? Please re-read my last post again.

No, we'll stay on quantum mechanics if you please.

My response mentioned quantum vagueness. So, I don't think I'm changing the subject.

After all, the subject we are discussing, the quantum implications for Zeno's paradox was brought up by you because you objected to the classical physics infinitesimal calculus resolution.

Are you still defending the so-called calculus resolution after two papers shot that down? I need you to provide a peer-reviewed paper in an academic journal to show that these authors are just wrong in their criticism about the calculus solution. Otherwise, why should anyone believe you?

On the very first page we find this:

"This explanation is also shown to be the correct solution to the motion and infinity paradoxes, excluding the Stadium, originally conceived by the ancient Greek mathematician Zeno of Elea".

On page 5 we have this:

"Please note that the explanation provided here and previously throughout this paper is also the correct solution to the motion and infinity paradoxes the Dichotomy, Achilles and the Tortoise, the Arrow, and their other more modern variations, originally conceived by the Greek mathematician, Zeno of Elea."

Your 'evidence' is in fact a rebuttal of your postion!

How so? Lynds rejects that there's a "now" or even that time flows in a progression. He's is an anti-realist of time (see his Wired interview in June, 2005). The whole point of his paper is that there is no exact value for position, velocity, time, and momentum. Obviously, if there is no identity of time for an event, then causation is not possible since event E1 does not exist to cause event E2.

This published paper mentions this issue explicitly:

Your 'evidence' is in fact a rebuttal of your postion! But it gets better! On the bottom of page 5 is a link to a PDF where Lynds specifically addresses and resolves Zeno's paradox.

He claims to solve Zeno's paradox, but in fact it's not a solution. If a moment in time always represents a duration, then how many durations are there? If there's no distinction of one duration from another, then there's only one duration--meaning that the Whole Shebang is uncaused. This is exactly what Zeno tried to show. The paradox succeeds in making it's point in that case.

So, as you hold Lynds in such high regard, you will now drop your attempt to justify your postion through quantum mechanics - right?

I don't hold him in high regard. I hold those physicists who looked at his argument and agreed that Zeno's paradox is unsolved in high regard (e.g., Julian Barbour, Paul Davies). If you can show that this interpretation is flawed, then you ought to write an article and submit it to a reputable journal of physics or philosophy to argue against the position taken of these two papers. Perhaps you'll get published. While the world waits, I would suggest that the reader accept the conclusions of both papers: Zeno's paradoxes are unsolved using calculus.

Won't, not can't. Now, can't would have given you a case, and you would have received an apology from me - because can't implies an inability to learn; i.e. stupid. Whereas won't implies an unwillingness to learn.
So, carry on feeling victimized because you think someone has implied you're stupid if you must, but please, don't try to justify it by quoting me.

This sounds really unprofessional.

If all the 93% of those who did not answer in the affirmative were in fact all Buddhists, deists, and pantheists, (which I doubt, and will continue to doubt until you provide some evidence) how does this improve the position of belief in a personal god's paltry 7%?

Only about 260 scientists responded and those were broken up by responses from biologists and physical scientists. I acknowledge that most of these scientists are probably agnostic if not atheist, but until I have results that show pantheists and deists represented in the survey, I would be skeptical of making too much hay about this result. We simply don't know how many percentage of top scientists are agnostic or atheist.

[wuntext]

If everything is either at rest or moving when it occupies a space equal to itself, while the object moved is always in the instant, a moving arrow is unmoved.
For this thought experiment, we do not have to consider the arrow as being observed or measured. Rather, we are considering the actual state of the arrow (i.e., state of affairs of the object). If you bring up the problem of measurement, then you are missing the point of the thought experiment since it does not require that we assume the arrow is observed or measured.

Such an experiment is based on post priori speculation and Zeno’ erroneous notion of individual points of time.

What do you mean "without also allowing the system to evolve"? That's false. Nothing prevents the system to evolve.

"Nothing prevents the system to evolve." If so, where are your equations for the initial quantum eigenstate that allows for this astonishing statement.
I asked specifically for your equations in my previous post. I’ll ask again - Where are they?
Post them, use the link below, because if you can formulate a mathematical equation that allows quantum system evolution from your initial conditions without automatically decohering, you have won yourself a Nobel Prize.

And, both papers showed that this "solution" is not correct. At this point I've cited two peer-reviewed papers that have shown that Zeno's paradoxes have not unequivocally been solved. Do you have any recently published papers to say that it has?

Your first source's unequivocal claim regarding the Arrow paradox:

"we can defy it by stating that the arrow cannot be at rest at definite position according to the uncertainty principle. Alternatively, we can evoke special relativity and say that there is a difference how the world looks for a moving arrow and for an arrow at rest: they have different planes of simultaneity."

Your first source dismisses the Arrow paradox both through quantum mechanics and special relativity. There is not one equation in this source that supports the Arrow paradox, and I specifically pointed out the Hamilton Operator in your 'evidence' that disallows Zeno's initial premise - and you ignored it.

Your second source is even more unequivocal:

"This explanation is also shown to be the correct solution to the motion and infinity paradoxes"

I'm getting tired of your dismissal of conclusions written in plain English - does anyone else reading this thread have a problem understanding the simple statements above?

From this moment onwards we will discuss quantum and non-quantum mathematical issues with mathematical equations only. You can download the relevant math symbols here: www.maths.tcd.ie/~dwilkins/LaTeXPrimer/MathSymb.html post them as gif images in conjunction with your variables.

I can't address this issue since this term is already in use in academic circles.

Which academic circles? Pure evasion.

My response mentioned quantum vagueness. So, I don't think I'm changing the subject.

So, if it mentions quantum, it will do? Relevant or not? Don't you check?

Are you still defending the so-called calculus resolution after two papers shot that down? I need you to provide a peer-reviewed paper in an academic journal to show that these authors are just wrong in their criticism about the calculus solution. Otherwise, why should anyone believe you?

The infinitesimal calculus resolution was a real word geometric solution to the arrow paradox, it is a resolution based on the way the world really works, through a non-denumerably infinite number of unit sets of points, rather than Zeno's flawed concept of individual points of time. And as you said yourself in post 46 - "The way the world actually is makes things true."
This is a mathematical issue, the mathematical symbols are available from the link above, my post is still there, now you can "shoot it down" by showing others reading this thread and myself why - and where - it is wrong as a classical resolution, i.e. "The way the world actually is..."
I really don't need to provide evidence for either the classical or non-classical resolutions to Zeno, the classical resolution is there waiting for your critique, and you're doing a great job yourself in providing the non-classical ammunition against your own position.

He claims to solve Zeno's paradox, but in fact it's not a solution

Equations please. I'm really looking forward to this. The link above is there to to back up your statement.

I would suggest that the reader accept the conclusions of both papers: Zeno's paradoxes are unsolved using calculus.

Waiting for you on this one above, use the link

This sounds really unprofessional.

????

Only about 260 scientists responded and those were broken up by responses from biologists and physical scientists. I acknowledge that most of these scientists are probably agnostic if not atheist, but until I have results that show pantheists and deists represented in the survey, I would be skeptical of making too much hay about this result. We simply don't know how many percentage of top scientists are agnostic or atheist.

So, your personal disbelief aside, you have no evidence whatsoever to rescue the paltry 7%? Nothing at all?

[harvey1]

If you bring up the problem of measurement, then you are missing the point of the thought experiment since it does not require that we assume the arrow is observed or measured.

Such an experiment is based on post priori speculation and Zeno’ erroneous notion of individual points of time.

I didn't see your response to the paradox. Can you respond to my comments?

"Nothing prevents the system to evolve." If so, where are your equations for the initial quantum eigenstate that allows for this astonishing statement.

Can you explain a little more as to what you are talking about? You know of course Schrodinger's equation, so why are you asking me for an equation on how a non-relativistic quantum state evolves? My argument applies to all states, so I'm not sure why you are looking for a specific initial eigenstate.

Post them, use the link below, because if you can formulate a mathematical equation that allows quantum system evolution from your initial conditions without automatically decohering, you have won yourself a Nobel Prize.

I'm not saying that a quantum system evolves without decohering. I never said that. I'm saying that there's a fact of matter to an evolving quantum state even if there is no measurement.

Your first source dismisses the Arrow paradox both through quantum mechanics and special relativity. There is not one equation in this source that supports the Arrow paradox, and I specifically pointed out the Hamilton Operator in your 'evidence' that disallows Zeno's initial premise - and you ignored it.

Where did you point out that Zeno's initial premise is disallowed by the Hamilton operator? Please state what you think the premise is in your own words, and then state what you think is the contradiction with the Hamilton operator. Also, please respond to my response to this issue. I didn't see your response to my comments about that paragraph.

Your second source is even more unequivocal:

"This explanation is also shown to be the correct solution to the motion and infinity paradoxes"

I'm getting tired of your dismissal of conclusions written in plain English - does anyone else reading this thread have a problem understanding the simple statements above?

No one I know accepted Lynds' conclusions on space-time. (If they did, then a number of articles have it all wrong since they explicity state that few accepted his anti-realist conclusions.) Rather, the editor and referees of Foundations of Physics Letters accepted to publish Lynds assertion that Zeno's paradoxes are unsolved. There has to be a very valid reason for publishing a paper, and if an issue is unequivocally solved: they wouldn't have published the paper. Similarly, the Acta Phys. Polon journal's editor and referees must have accepted Z.K. Silagadze's assertion that each of Zeno's paradoxes are unsolved by calculus (otherwise again they wouldn't have published a paper about a solved issue of physics):

One can superficially think that the resolutions of the paradoxes was provided by calculus centuries ago by pointing out now the trivial fact that an infinite series can have a finite sum... More subtle under the surface truth that Zeno's paradoxes is that even if one assumes the infinitely divisible space and time calculus does not really resolves the paradoxes but instead makes them even more paradoxial and leads to the conclusion that things cannot be localized arbitrarily sharply.

If these editors and referees believed as you do, I can't see them publishing these papers.

In any case, as I mentioned before, Lynds achieves his solution of the Arrow paradox by denying a central claim of material causation: that there is an instant in time that causes an instant effect. I'm still waiting to see your response to this issue.

From this moment onwards we will discuss quantum and non-quantum mathematical issues with mathematical equaions only.

I wish I could help you out, but most of philosophy is not reducible to mathematics. It can be phrased in terms of predicate logic, but that would take a great deal of time (and the help of a logician). If you want to discuss physics and not philosophy, then I recommend that you visit the physics forum that you originally recommended. On the other hand, if you want to address philosophical issues (e.g., Zeno's paradoxes), then we can discuss here--but in the English language.

Which academic circles? Pure evasion.

Here's a bibliography just to give you a background as to how well-trodded this subject is within the philosophy of physics (and even more generally in philosophy). (Btw, most philosophers of physics have physics degrees usually with at least an M.S. in physics, and often Ph.D.'s in physics, so I don't think it makes sense to criticize them for not knowing physics. Many philosophers of physics were also once physicists, but realized they had a love for philosophy. )

The infinitesimal calculus resolution was a real word geometric solution to the arrow paradox, it is a resolution based on the way the world really works, through a non-denumerably infinite number of unit sets of points, rather than Zeno's flawed concept of individual points of time. And as you said yourself in post 46 - "The way the world actually is makes things true." This is a mathematical issue, the mathematical symbols are available from the link above, my post is still there, now you can "shoot it down" by showing others reading this thread and myself why - and where - it is wrong as a classical resolution, i.e. "The way the world actually is..." I really don't need to provide evidence for either the classical or non-classical resolutions to Zeno, the classical resolution is there waiting for your critique, and you're doing a great job yourself in providing the non-classical ammunition against your own position.

I asked for a published paper to dispute these resolutions. Can we assume by your silence here that this is because you couldn't find such a published paper? Why don't we then assume the editors and referees are all competent and say that Zeno's paradoxes are not considered as unequivocally solved using calculus?

He claims to solve Zeno's paradox, but in fact it's not a solution

Equations please. I'm really looking forward to this. The link above is there to to back up your statement.

Huh? I realize that you feel comfortable by writing out math, but that's not how philosophy is mostly done. It is based on laying out one's premises and showing how one's argument logically follows.

I would suggest that the reader accept the conclusions of both papers: Zeno's paradoxes are unsolved using calculus.

Waiting for you on this one above, use the link

I suggest that we stick with the premises of published work as being sound. If they aren't at all sound, they don't get published.

So, your personal disbelief aside, you have no evidence whatsoever to rescue the paltry 7%? Nothing at all?

What do you mean by "rescue"? I never introduced the fallacy of misleading authority in the first place. You said "theist's won't learn disciplines such as physics or math" and I gave the names of prominent physicists who know one or two things about physics and math. I was surprised by you bringing up the whole issue of authority, and I just responded by stating that this was never my intention to use Linde, Penrose, Isham, etc., in a numbers game. I also pointed out that this survey didn't actually specify that these scientists were non-theists--rather it could only identify them as non-monotheists (i.e., a rejection of a personal God). I think you went off on a tangent of trying to push the whole misleading authority fallacy as somehow significant to our discussion (for unknown reasons). Personally, I'm a lot more concerned by what leading philosophers say about God than I am what leading physicists say (although it's interesting either way).

In any case, wuntext, you sound like you are getting overly frustrated. If this discussion is not a pleasant one of exchanging ideas about science and religion, then perhaps we should stop? You seem like you have a great deal of knowledge and I'm more than happy to learn from you. However, I'm a little addled by your insistence to write philosophical dilemmas into mathematical equations. Nobody does that. Perhaps you really want a physics discussion, and if so then since I'm not a physicist I won't be of much fun.

[wuntext]

Let’s see if another method will get some equations out of you. I will respond to your point’s one at a time, please reply with your equations backing up your position, then we will move on.

Can you explain a little more as to what you are talking about? You know of course Schrodinger's equation, so why are you asking me for an equation on how a non-relativistic quantum state evolves? My argument applies to all states, so I'm not sure why you are looking for a specific initial eigenstate.

Because Zeno’s paradox relies on a specific eigenstate. An eigenstate of discrete points that, in effect, can be ‘frozen’ at any one particular point, this directly contradicted by quantum indeterminacy. Zeno’s paradox is an unstable quantum system that cannot evolve past [&#956;1s], (Fig. 1, Page 7, your link, Post 52) it begins to decay from [t>&#956;1s], because every discrete point in Zeno’s system, has to have exact position DE Dt ³ h / 4 p, and exact momentum Dx Dp ³ h / 4 p within that point (where h is the Planck Constant).

In quantum mechanics such a system cannot hold both the [Dp] and [Dt] properties simultaneously, it is unstable, and will decohere into a classical non-quantum state, as I highlighted using you own evidence in Post 53:

“…during this short time period the survival probability exhibits a t^2 drop. For longer times we see a gradual transition from the t^2 dependence to linear t dependence, which corresponds to the usual exponential decay law.”

So, for Zeno’s arrow to remain coherent, you must reject quantum indeterminacy. And if you reject quantum indeterminacy you have to replace it with something else.

Mathematical equations please.