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Essay Abstract

Beginning with an explanation of the historically accepted solutions to Zeno's paradoxes by calculus, the implications for physics, time, and space, of the conclusion that instants in time and instantaneous magnitudes do not actually exist and that calculus has its "limits" when applied to the physical universe are explained. This includes discussion of the solution to Zeno's paradoxes, why time, space, and space-time do not exist, and why time and space cannot be quantized. The article concludes with some general comments about the work.

Author Bio

Peter Lynds is a 33 year-old independent who lives in Wellington, New Zealand. His research interests largely revolve around the subject of time and physics and cosmology. Links to his papers are available at his website http://www.peterlynds.net.nz, while an FQXi discussion of a recent paper about time and cosmology may be found at http://www.fqxi.org/community/forum/topic/111

Download Essay PDF File

12 days later
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Very intriguing essay!

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As the pdf file doesn't seem to be enabling the link, I think it could be a good idea to include it and the following note (from the essay) here:

In order to meet the essay word limit, I was unable to include some material that I would have really preferred to. This included discussion of (1) the problem of time in quantum gravity, (2) the non-existence of instants, (3) the solution to William James' version of the dichotomy paradox, (4) others who have been on the right track with Zeno's paradoxes, (5) the non-existence of interval, and (6) why time and space cannot be quantized. The omitted material, along with references, may be found here

PS: Thanks Anon

23 days later
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Dear Peter,

Totally interesting essay.

In regard to non-existence of space, I remember a thought experiment that points to this direction. If our eyes had a mirror and we perceived the world as looking it in that mirror, (i.e. things that are now left would be at the right position and vice versa) then there would be no difference. Our brains would evolve in the way to work normally as it is now.

From this, one realizes that it is the relative order of the things that matters not the space itself. This sounds analogous to your solution of Zeno's paradoxes

Nice work, keep on

Best wishes,

Giannis

13 days later
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Dear Peter,

This essay was a great exposition of your work, which conveys an extremely important solution to Zeno's paradox. It crucially reminds us of the assumptions underlying the calculus. I can only hope that the time will come when people begin to see (and espouse) the importance of it and the breadth of the implications!

I also would like to add that in my own essay entry (see "The Here-and-Now") I referenced both your paper on time etc. and your paper on consciousness. I utilized these concepts to begin the construction of a new type of world-view: one that dispenses with the existence of the assumed "objective reality". Unfortunately the essay does not elaborate on all the information contained in the references (e.g., Paul Davies' paper on the implications of a cosmological information bound for the laws of physics) due to length constraints; however, the references are included for the interested reader.

Thank you again for your intrepid ideas!

I look forward to your response (and possible comments on my own work).

CKM

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Hello Mr Lynds,

a very fun paper. love the quotes. a very interesting argument. it reminds me a bit of Heisenberg's indeterminacy principle... can determine location or velocity, but not both at any given moment. 'cept you appear to have taken it further - can't determine either - no "moment".

i'll have to hang onto a copy, in case i should ever get a speeding ticket, present it in my defense - 'the citation states that this occurred at such and such a time. that would appear to be a physical impossibility to determine' ;-)

you might have fun reading some of the notes on the development of the cultural concept of time and the nature of perception in "some thoughts on time" elsewhere here.

it's an interesting experience reading the papers that have been presented. i'm reminded of the story of the group of blind men encountering an elephant, trying to describe it....

thank you :-)

matt k.

5 days later
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Thanks Giannis. Good to see you on this thread too.

Thanks Kyle. That's really nice of you. I'll have to read your paper, but I must admit that I don't have much time for arguments against the existence of objective reality. An assertion that a rock (or the universe) exists independently of a person may be subjective, but the rock is still there. All manner of philosophical objections can be made to this, but the bottom line is that, if someone gets fed up with a person talking about things such as brains in a vat, and throws a rock at him, it still hurts. Moreover, trying to assert (and decide between ourselves) what physically is and isn't, is what science is all about. Without this (in other words, a belief in objective reality), science is pointless.

Thanks Matthew. I hadn't thought of the speeding ticket defence. I should give it a go one day.

In relation to the uncertainty principle, it is often assumed that if it weren't for quantum uncertainty, all physical magnitudes would be exactly determined. However, the non-existence of instantaneous magnitudes means that, even if there were no such thing as quantum uncertainty, physical values would not be precisely determined anyway.

Best wishes

Peter

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Peter,

Thank you for you response!

I probably should have been more explicit in my account of "objective reality". I regard this as more of a 'material objective reality'.

"An assertion that a rock (or the universe) exists independently of a person may be subjective, but the rock is still there."

I agree that the 'universe' exists independently of us, however, What is the universe? Does it need to be a material universe? Could it be a information-based universe? Could it be a 'universe of possibilities'? Could physics *really* be a part of statistics? (Please see the attached high-lighted article.)

"All manner of philosophical objections can be made to this, but the bottom line is that, if someone gets fed up with a person talking about things such as brains in a vat, and throws a rock at him, it still hurts."

I like this one, good point. But, in my essay, this example would be only possible in the here-and-now.

"Moreover, trying to assert (and decide between ourselves) what physically is and isn't, is what science is all about. Without this (in other words, a belief in objective reality), science is pointless."

Might we be trying to decide what physically is and isn't *possible*. Do we need to extend our theories as an ontology? Could there be a more parsimonious theory of 'what is'?

I look forward to seeing your response!

CKMAttachment #1: Theories_of_almost_everything.pdf

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I also wanted to add: that I feel although this "belief in an [material] objective reality" without which "science is pointless" is indeed common among many in our society. Yet it may be so common, in our belief structures, that it is almost taken for granted. (Think about the first time you consciously realized that you can die.) I think it should be every scientists job to make sure that they articulate this state of epistemology--that, in fact, all of reality is perception--which is a profound fact we have discovered. Just as the church goer believes in a 'God' we, scientists, believe in an 'objective reality'. Without this faith--life would be meaningless--as death would be but an idea, and not a conscious-realization.

So it is, in a funny way, that death makes us human.

"Reason dreams of an empire of knowledge, a mansion of the mind. Yet sometimes we end up living in a hovel by its side. Reason has shown us our capacity for power, both to create and to destroy. Yet how we use that power rests on our deeper capacities which lie beyond the reach of reason, beyond our traditions and culture, stretching far back into the depths of the evolutionary process that created our species, a process that ultimately asserts the power of life over death. And, ironically, even death, as part of the process of life, asserts that power. That is how we have come into being and now find ourselves committed to the unrelenting moral struggle of ordinary human existence." - Heinz R. Pagels

CKM

9 days later
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Dear Peter and commentator Kyle,

This is my first posting on the essay. Whenever, one breaks a new background, only he understands it fully. The rest need time to comprehend in silence! Science started as philosophy but soon got tempered with more and more precise measurements. However, all measurements are subject to limitations of instruments used and basically no measuremental accuracy has reached the limits set by the Uncertainty relations. Thus there is full scope for precepts and concepts based on critical observations and analysis both external and internal. The latter is confined to our most important laboratory, the human brain. If i am allowed to add, the human brain as also the cosmos is covered by the non-physical entity called 'consciousness'. We are thus subjected to the interaction with the cosmos. The 'wider' is one's conception the better one interacts with the cosmic consciousness and higher the chance to reach closer to the truth or 'relative truth' being sought in science.

Space & time are concepts that may get replaced with suitable others in a new explanation for gravity. However, gravity will remain a fact. There is a problem in modern physics as one attempts to unify the four known physical interactions,viz., strong and weak nuclear, electromagnetic and gravity. The last one continues to defy this conceptualization. Perhaps it was the first to emerge as soon as the Universe was created. What the nature desired for the Universe to evolve in the early stages of the 'volatile' Universe is somehow unobservable in the cosmological experiments conducted thus far. i have made some speculations in this regard in my essay posted in the competition and have also provided two other manuscripts in my own first two posts that led me to the main essay i posted. i will greatly appreciate comments of all authors/ interested public on the aspects discussed therein. NN

8 days later
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I like your essay and use of classical philosophy, but I think Heisenberg disagrees with you:

Your essay is a classical Newtonian argument, but taking ever smaller intervals of time and space makes the fundamentally a quantum mechanics argument. Heisenberg disagrees because Zeno's Paradox assumes you know both the position and velocity of the arrow with certainty. A counter paradox is for an arrow with a velocity near the speed of light. The relativistic Lorentz contraction would make the arrow appear shorter. Would the arrow look like a quantum object to an observer? Is it possible for a Lorentz contraction to be smaller than the Planck length?

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Dear Brian,

Zeno's paradoxes assume exact position, but not necessarily exact velocity. For the paradoxes to result, all that is required is that the respective body be in motion. I don't really understand your comment, as, in addition to the above, the main point of the essay is that instantaneous magnitudes do not actually exist. Trying to deny the applicability of Zeno's paradoxes is something different. Moreover, quantum uncertainty is unrelated to a moving body not having a determined or instantaneous position. Even without qm, instantaneous position would not exist.

Best wishes

Peter

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Dear Peter,

your response to my post of Oct 31 still awaited! hopefully you don't find my comments ae irrelevant so as not to deserve your enlightened comments. Nature of my essay on this website follows such perspectives about the mysteries of the Universe!

NN

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Peter,

I have found my faith in a sort of cosmic religion, based on a hypothesis:

Sometimes I feel like we are funny looking black holes existing on a whole different scale, and that somewhere and somehow our brains are connected to that "deeper level," so just as each black hole has its singularity we have our "I's" whose even horizon--coupling with electromagnetic force--exists in our eyes: because the connection of light goes at the speed of light, so objectivity there is no time between "you" and "me," our intersubjective beings, with subjective memories that lay beyond "your" even horizon, forever missing from "it" by that funny information paradox that just won't quit... as we live in this combination of interconnection and introspection delivered by light for our perception.

The objective reality is gravity.

The only certainty is death.

CKM

9 days later
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Let me give a more straight forward example of quantum mechanics being violated. The arrow has momentum which must be conserved. The bow and arrow must be considered. The bow and string are composed of atoms and when Zeno draws the string potential energy is stored in the bow. When he releases the string the potential energy is converted to kinetic energy and the arrow takes flight.

Planck solved the ultraviolet catastrophe with the revelation that energy is absorbed and emitted in discrete, whole, amounts. If the kinetic energy is:

E = 1/2 mV^2

then how can there be discrete energy but not discrete velocity? In fact, accelaration, velocity, position, force, momentum and energy are all related; how could some be continuous and others discrete?

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Dear Brian,

I think your point/question this time is a good one. Time and space cannot be quantized (see my comment and/or Carlo Rovelli's response on his essay thread). If time and space cannot be quantized, velocity and acceleration cannot be either. I don't think that the idea of velocity or acceleration being quantized even actually makes sense as a concept. This, however, does not stop magnitudes such as momentum, mass and energy from being quantized. I don't really understand what the equation for kinetic energy is supposed to illustrate, as if mass is quantized, so will the energy, but velocity needn't be.

Also, because magnitudes such as mass and energy are quantized, does not mean that motion is. It just means that a moving body is made up of discrete parts. If the body in question is one of those discrete parts, it moves along just as continuously as anything else. That is, although Planck time and length represent operational roadblocks for rulers and clocks, and the constitutes of clocks and rulers are also quantized, intervals of time and space are not. They do not exist.

Best wishes

Peter

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Dear Peter,

The quantization limits for energy are beyond the capability of our present day instruments to measure directly. Indirect measurements indicate the truth about the same and that is fine. What i wish to say is that we are so much worried about getting close to the truth. But what we achieve is just a broad limit. This limit can be lowered but will it help us better in real science to progress. For example, The large Ion Beam Collider at Geneva is already a money guzzler and more of the higher energy accelerators will not be able to carry us to the end , as the end has its way of receding from us further!! What we need to do is to think out alternate strategy for the growth of science through Expanding its present Paradigms, e.g., we may think of modifying our 'Methodology of Science'

by including extensive research on the levels of 'consciousness'. i have hinted at the state of meditation in my essay, as a state that is beyond the three awareness states of wakeful, dream and deep sleep. It is the state of human mind ( we call ingeneous levels)that has resulted in bright ideas of science developed thus far. Now we need to much higher levels of consciousness for our mind to come with something called path-breaking development!

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Peter, this will be my final comment for your essay. I believe you are wrong but don't fret, everyone else who has submitted an essay is probably wrong too. I may give you a restricted vote because your essay is easy to understand and forced me to think deep about the fundamental nature of the universe.

Carlo's response to your comment agrees with me:

[The "atoms of space" and the "atoms of time" of LQG are only figures of language, to indicate that certain physical

observables aspects of the gravitational field have a discrete spectrum.]

An example of an observable is energy and he believes such observables are discrete as I do. Carlo is discussing LQG in his post; I am discussing Planck's century old observation that energy is discrete. My first comment on the uncertainty principle still holds, but it requires esoteric physics. I felt there should be a counter example that matched the elegance of Zeno's paradox.

E = 1/2mV^2 is the kinetic energy equation it is one half of the mass multiplied by the velocity squared. The mass is not changing because the relativistic effects for a classical arrow in flight are negligible. However, just in case you want to push the relativistic energy/mass issue please read this:

http://www.physorg.com/news146415074.html

As Zeno releases the bow string the kinetic energy of the arrow increases as the potential energy in the bow decreases. The increase and decrease in energy is discrete on a fundamental level. The mass in the kinetic energy equation is a constant as is the 1/2 coefficient. The only variable in the equation is the velocity. If the kinetic energy of the arrow is increasing by discrete amounts then the velocity MUST increase by whole amounts too.

I dislike using psychology in physics, but I think it is needed in this case. We have two different frames or mental pictures of how to think about the universe. Last week I came across a TED lecture that shows the different frames we are using.

http://www.ted.com/index.php/talks/lee_smolin_on_science_and_democracy.html

Your frame is four minutes into the video.

Thank you for the essay,

B^2

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Thanks Narendra.

Thanks Brian. In relation to your comment about Carlo's, all right-minded physicists believe that observables such as energy are quantized. My point was obviously that time and space cannot be. In respect to your argument about kinetic energy and velocity, however, I unthinkingly made a mistake. Two actually. I was thinking of constant velocity rather than an acceleration, and secondly, I said/agreed that energy is quantized. Of course, in many cases it is, but translational kinetic energy - the relevant one here - isn't. As such, again, it doesn't follow that velocity is.

I'm a little bit baffled by your comment about the video. I can only assume that you're missing the point about quantum mechanics being unrelated to there being no so such as thing as instantaneous magnitudes in Nature.

Best wishes

Peter

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Peter,

Your essay is well-written and innovative. I enjoyed your examination of the classical notions of time, as expressed by Heraclitus and Zeno, and found it interesting how you have developed an alternative formulation of time as a way of resolving age-old paradoxes as well as modern issues.