
The Quantum Zeno Effect actually does stop the world - jonbaer
http://io9.com/the-quantum-zeno-effect-actually-does-stop-the-world-977909459
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zaptheimpaler
I have never understood why Zeno's paradoxes are considered so profound.

Consider what an instant of time is. Is it a non-zero chunk of time smaller
than any other finite chunk of time? In this case, we are defining an instant
as an infinitesimal chunk of time. If we posit that such a thing exists, then
why can't an infinitesimal distance (which the arrow travels in that time)
exist?

The other option is to define an instant of time as no time at all. Not the
smallest, simply zero. Saying that since you cannot move a non-zero distance
in zero time is valid. However, a chunk of time is not composed of an infinite
series of zero time chunks, just like 0.00000...1 is not equal to 0 + 0 + 0...
There is a gap between zero and infinitesimal that cannot be bridged by zeros
alone.

~~~
jamesrcole
> _Consider what an instant of time is. Is it a non-zero chunk of time smaller
> than any other finite chunk of time?_

Here's how I think of Zeno's paradox: it is saying that if time/space are
continuous then there are no such things as finite chunks of them, therefore
they must be discrete.

~~~
zaptheimpaler
Thats a nice way to look at it - Zeno's paradoxes are proofs by contradiction
that time/space are discontinuous!

~~~
monjaro
That's not true though. Zeno's paradoxes are all pretty easy to resolve using
first-year calculus. They certainly don't prove that time or space is
discontinuous.

~~~
jamesrcole
Calculus doesn't resolve the paradox. It's just a tool, and it doesn't involve
any literal division of anything into infinities. You're making a map vs.
territory mistake.

[edit] i can't reply to monjaro's comment, so I'll put my reply here: does
calculus prove that there are actually an infinite number of positions between
any two positions?

~~~
Jach
The map vs. territory issue at hand depends on whether you take Zeno's
paradoxes to be statements about physics or statements about logic. If it's
the latter, calculus resolves those with ease. If it's the former, well, then
you have to look at the physics. And the physics are described in our maps by
math which includes differential equations of complex numbers, and hence the
paradoxes are again resolved as best as we're capable unless some new
representation of physics comes along that makes the paradoxes manifest.

------
monjaro
This article is very low quality. The account of Zeno's paradox is wrong on
pretty much every count, which makes it hard to trust anything else the
article claims.

~~~
hemmer
The Ask A Mathematician page linked is quite a bit better.

[http://www.askamathematician.com/2012/03/q-is-the-quantum-
ze...](http://www.askamathematician.com/2012/03/q-is-the-quantum-zeno-effect-
a-real-thing/)

~~~
monjaro
You're right, that's a much better article.

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damian2000
More info here for those interested

[http://physics.stackexchange.com/questions/47252/simple-
expl...](http://physics.stackexchange.com/questions/47252/simple-explanation-
of-quantum-zeno-effect)

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molmalo
The picture in the article fits perfectly, not only because of Neo stopping
time, but because, more importantly, at least to me, this looks like if the
Universe has its own Garbage Collector. Which could mean that we are living a
simulated reality [1], something like the Matrix!

[1]
[http://en.wikipedia.org/wiki/Simulated_reality](http://en.wikipedia.org/wiki/Simulated_reality)

~~~
k__
I think so, too.

We have gaps in reality, the planck length, planck time etc.

Also, we have Gödel's incompleteness theorems, which tells us about the gaps
in theories we can't fill.

~~~
monjaro
You are assuming more about the Planck units than is currently known. Directly
from wikipedia:

"There is currently no directly proven physical significance of the Planck
length; it is, however, a topic of research."

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gus_massa
The problem with this explanation is that checking more often the state of the
quantum state makes it decay more "slowly" it doesn't stop it totally.

 _> ... Check on it after three seconds, and it probably will have decayed.
But, Misra and Sudarshan argue, check on it three times in one second
intervals, and it will most likely not have decayed. ..._

Let's invent numbers for an example, with 3->5\. It you check a system after 5
seconds the probability that it has not yet decayed "is" 1-0.05 . It you check
a system five times in the 5 seconds interval the probability that it has not
yet decayed "is" (1-0.002)^5=~1-0.01 . The measurements makes the decay
probability smaller, but it's not reduced to 0 as the article try to induce,
to make it similar to the Zeno paradox.

The important point is that at the quantum level every measurement changes the
system [1]. So the result of the experiment is affected by the measurements.
(At the classical level, some measurements are negligible, and it's safe to
ignore them.)

[1] of an operator that doesn't commute with the Hamiltonian of the system

------
ars
> In any given instant, the arrow has to appear motionless. If it wasn't
> motionless, there would be two instants, one in which the arrow was at one
> position and one in which the arrow was in another position.

I don't follow. Why can't the arrow be in both places at the same time? With
the probability of one vs the other dependent on the velocity and the size of
the time slice.

~~~
rosser
Remember, the arrow is one of Zeno's paradoxes. He's not describing reality;
he's trying to impose a conceptual-only understanding of reality on the thing,
itself, and ending up in a logically impossible situation.

His description of the arrow's motion, or the runner's traveling half the
distance to the finish line, and then half the remaining distance, and then
half the distance left after that, and so on, and thus never actually
finishing, are exactly that: _descriptive_ , not _prescriptive_.

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fauigerzigerk
That sounds nice. Unfortunately, knowing nearly nothing about any of this, I'm
having a hard time imagining what it means to "check on" an atom and how that
could influence its state.

Sometimes it seems to me that every day words become mere metaphors when
applied to physics.

~~~
KenoFischer
The problem with Quantum Physics (well, physics in general, but in classical
physics it's mostly ignored) is that in order to make a measurement, you need
to interact with the system thus changing it's state. You might for example
measure perturbations in an electric field, but by applying the electric field
you influenced the state of the system. This is also an important part of say
the uncertainty principle. One way to think about why you can't measure
position and momentum simultaneously to infinite accuracy is that perfect
measurement of one would require shooting it with photons of zero momentum,
while perfect measurement of the other would require shooting it with photons
of infinite momentum. The real fun comes in when you leave a system alone for
a while because then everything becomes probabilistic.

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ajuc
I don't know if I understand it correctly.

If space and time is discrete, and movement is deterministic - Zeno paradox is
a paradox - object moving at speed 1 minimal division of space (MDS) per 2
minimal divisions of time (MDT) isn't at any valid point of space after 1
minimal division of time which is paradoxical.

Calculus solved this, but it has assumption that space and time is continuous.

Now we have experiments that shows us it's not true, so probably the
assumption about determinism isn't true. So for example object moving 1 MDS
per 2 MDT "really" moves 1 MDT per 1 MDT with probability 0.5.

Am I getting this right?

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ars
> Every time you check on it, it will revert to its "original" measured state,
> and the clock will start over.

This makes me uneasy - I feel like there is a violation of thermodynamic laws
in there somewhere. Decay is not the only thing that is probabilistic,
tunneling is too, and if you can manipulate things so it's more like to go in
one direction vs the other, you can reverse entropy.

~~~
juhanima
Nothing wrong in reversing entropy, if you do it by adding energy into the
system. I guess shooting photons counts.

~~~
ars
Ah, like Maxwell's demon.

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chrischen
What I don't get is wouldn't you see the same effects in a classical
mechanical wave:
[http://en.wikipedia.org/wiki/File:Polarizacio.jpg](http://en.wikipedia.org/wiki/File:Polarizacio.jpg)
?

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jasimq
Saying that this effect "stops the world" doesn't seem right to me. It just
"appears" to have stopped only for the observer, who observes the world at
very very small intervals.

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asperous
A mathematician and an engineer agreed to take part in an experiment. They
were both placed in a room and at the other end was a beautiful naked woman on
a bed. The experimenter said every 30 seconds they would be allowed to travel
half the distance between themselves and the woman. The mathematician said
"this is pointless" and stormed off". The engineer agreed to go ahead with the
experiment anyway. The mathematician exclaimed on his way out "don't you see,
you'll never actually reach her?". To which the engineer replied, "so what?
Pretty soon I'll be close enough for all practical purposes!".

~~~
Jach
That's pretty funny, but the mathematician must be one who lived before the
invention of calculus, which resolves such paradoxes. (With either
infinitesimals or limits.)

~~~
phaemon
Not in this case. In Zeno's paradox, as the distance halves, so too does the
time. In this case, the time for each halving is constant at 30 seconds. This
means the mathematician is right and theoretically they'll never reach the
woman (except practically, as pointed out).

~~~
Jach
Good point, I guess I can see in this case the mathematician might realize
that while he can cross the full distance easily enough with infinite time, he
might not want to wait around for infinite time...

