Instants, inertia and quantum motion by Shan Gao

Hello Shan Gao,

that you have focused on motion in order to address the question of time is a novel but very fitting approach. it is indeed the perception of relative motion which gives us a sense of time.

i'm not an expert in physics, but, when i read:

3. Understanding RDM in terms of instants, for example, how a particle "knows" which position it will be at next instant in the sense of probability.

my first thought was "Feynman". he's fairly much the master on probability and motion.

a quick search of the web turned up:

Feynman's path integrals and Bohm's particle paths

and Feynman's path integral formalism have something to do with particle .... provided a probability distribution on the space of all paths, ...

www.iop.org/EJ/article/0143-0807/26/3/L01/ejp5_3_l01.pdf - Similar pages

by R Tumulka - 2005 - Related articles - All 6 versions

downloading the pdf, i found:

"This theory would have the same ontology as Bohmian mechanics, but a different, in fact stochastic, law of motion."

he also has time as discrete. Tumulka appears to be looking at very similar things as you are. what he has to say in the paper may be helpful to you. his writing appears to be about as clear as your own.

you might also find 'time counts', another entry here, of interest, though maybe not as specifically relevant.

matt kolasinski

It is true that time is 'commonly' assumed as composed of instants - and that from 'instants' follows an idea of discontinuous time.

'Commonly', that is to say in technological langage first of all.

But compared to matter, langage is always discontinuous, either it is Chinese or Italian or mathematical or musical langage! It is the function of langage to enable a conventionnal common approach of things, Nature, phenomenons, social relationships. The discontinuity is the RanSom of langage.

Your approach is not new because you can still find this debate on Time in Motion in Antique Physics, in the Greek one but probably in the Egyptian too, until modern Metaphysicians or mathematicians such as Marx or Heidegger, Einstein, Russell, Berkeley...

I do not agree that the 'Wave equation' of de Broglie and Schrödinger is continuous space-time. The discontinuous motion of Einstein can be broken in 'arrows' but the Wave Mechanics can be broken in 'arcs' too.

matt,

Thank you very much for your interest in my idea! A more popular introduction of the idea of random discontinuous motion can be found in my book God Does Play Dice with the Universe (2008). I have read the article by R Tumulka. Many thanks for this very helpful information. I also read your interesting essay concerning the relation between perception and time, and I have learned much. I especially like the quote "When the bird and the book disagree, always believe the bird." Thank you!

Shan

Rouge,

Thank you for your comments. I have also pointed out in my essay that two ancient thinkers Epicurus and Al-Nazzam had ever proposed similar ideas. You can read the more detailed version of the essay on my website http://www.quantummotion.org/, where I present a further discussion of their ideas.

Besides, I don't understand "The discontinuous motion of Einstein" refered by you. Could you explain more clearly? Thank you!

Shan

hello again Shan Gao,

a way big grin here. :-)

yes, i like your perspective on motion very well.

glad the paper i'd refferenced was useful - i hadn't read the whole thing myself but it appeared to be quite similar thinking.

glad you enjoyed my paper also.

delighted to meet you.

matt.

The 'measurement' of Time drives to discontinuous Time. It is an 'idea' of Time that you can brake in as many 'pieces' of Time that you want, according to the seasons or not.

And that is what Einstein is doing: he is starting from two measurements of speed (including Time): the measurement of the speed of a train from a fixed point, and the measurement of the speed of the same hypothetic train from a moving point. One train, one Speed, one Time but two measurement.

This may seem like a simple question, but:

if time is discrete, not continuous, then the "units" of which it is composed are either temporally extended, or not. If they are temporally extended, then are they not divisible? (If they are divisible, they are not discrete unite). If they are not temporally extended, then adding them up will not make a temporally extended whole.

So, it seems to me that temporal extension must be continuous, rather than discrete, just as dimensive extension is. I understand that conceiving of these as discrete may be useful in mathematical models, but in reality, I think they must be continuous.

Your essay wonderfully highlights the duality of the continuous and the discrete in the context of motion. The duality depends upon our choice of basis, just like the existence of particles versus waves. You might agree that particles lose their energy- their mass- to waves, and the discrete particle behavior is only realized again at another particle... the observer.

Thanks for your insights!

anonymously wrote above:

"...If they are not temporally extended, then adding them up will not make a temporally extended whole..."

I think this is a common misconception about discrete theories of Time/Becoming (like this one and mine). It is perfectly consistent to postulate that Time/Becoming is discrete and composed of instants, while claiming that these instants or moments of Becoming are not themselves temporally extended. This postulate works because we never postulated that Time has the structure of a continuum from the beginning, and so it's not necessary for the collection of all instants to fill a continuum. To make connection with time duration in discrete theories of Time/Becoming, we simply need to define a unit of Time in terms of a definite number of instants of occurrence of a certain recurring process (such as the modern practice of defining the second as 9192631770 cycles of the process corresponding to the radiation from the transition between the two hyperfine levels of the ground state of the Caesium 133 atom). This way we can define duration between instants without having to postulate the reality of a physical continuum of Time/Becoming.

Shan,

Just wondering how your RDM theory is different from the spontaneous collapse model of Ghirardi-Rimini-Weber. Could you please comment on that? Thanks.

Chi Ming:

Thank you for your interest in my essay. GRW theory is a mathematical model about the dynamical collapse of the wave function. The RDM theory aims to provide more content than it based on a new physical analysis of motion. The theory explains the wave function in quantum mechanics as a mathematical complex that describes the motion, and further shows that the equation of motion is a revised Schrödinger equation, which can naturally result in the dynamical collapse of the wave function. Besides, the concrete dynamical collapse equations in these two theories are also very different.

You can read my paper in International Journal of Theoretical Physics (http://www.springerlink.com/content/p84722072t6805rl/) or my book Quantum Motion (http://www.quantummotion.org/books/qmb.pdf) for more information. Thank you!