Counterintuitive Facts

[CraigS]

Been doing some reading this week, and have encountered some interesting facts. As a result, I thought it may be interesting to start a thread to capture some factual, counter-intuitive snippets. (The counter-intuitiveness, of course, depends on the viewer) .

Here’s a couple I’ve encountered this week (credits to others):

Gravity:
1. The force on a point mass decreases as (1/r^2), when the mass is located outside the sphere. If the sphere is hollow, the force on a point mass inside the sphere is zero, and is independent of r. If the sphere is solid, and of uniform density, the force on a point mass inside the sphere, decreases with decreasing radial distance between the point mass and the centre of the sphere (decreases linearly with r).

2. Imagine an infinitely long line of mass (ie: a cylinder). The acceleration, ‘g’, due to the gravity of the line mass, at a perpendicular distance r from the mass, decreases as (1/r). (The ends contribute zero gravity).

3. Imagine an infinite plane of mass. The acceleration, ‘g’, due to the gravity of the plane at a perpendicular distance r from the plane, is a constant ! Ie: the acceleration due to gravity for an infinite plane of mass, is completely independent of the distance, r, from the plane!

Time and Quantum Mechanics:
4. Time is not an observable quantity in quantum mechanics.
5. In quantum mechanics, the observer and the observed, can be one in the same.
6. If something isn't observed, then it can be said to be in all states simultaneously.

Interesting ... please feel free to contribute any other counterintuitive facts you may have encountered !
(I suggest contributers stick with ‘facts’ which can be demonstrated and are reproducible. )



Cheers

[renormalised (Carl)]

Here's one...when you're overtired you actually don't feel tired

[CraigS]

Originally Posted by renormalised

Here's one...when you're overtired you actually don't feel tired

Good one ...!!…
(I don't want to be the test subject, mind you).

I find it actually quite tricky to state a fact.
Stating a counterintuitive one makes it ... 'interesting' ..


Cheers

[sjastro]

One that you are familiar with Craig.

Excluding a vertical straight wire, what should the shape of a wire be such that a bead released from one end of the wire will slide to the opposite end under gravity in the shortest period of time.

Common sense says the wire should be straight but the answer is in fact a cycloid.
http://en.wikipedia.org/wiki/Cycloid

Regards

Steven

[renormalised (Carl)]

From a photon's point of view it sees the entire universe instantaneously, yet it takes light 8.3 minutes to get from the Sun to us. Yet both facts are true.

[ballaratdragons (Ken)]

You don't die, or explode, of liquify or anything else 'instantly' in the vaccuum of space like they do in movies.

Even without a spacesuit It is possible to live in the vacuum of space for up to 3 minutes.
So if you accidentally fell out of an airlock (I don't know how you can 'accidentally' fall out of an airlock ), you could be rescued if others are quick enough to get you.
Fact

[CraigS]

Interesting .. I'm enjoying this thread !

Just so we can justifiy this thread in the Science Forum, (and for the record), I found a reasonable definition of scientific 'fact':

Fact: A basic statement established by experiment or observation. All facts are true under specific conditions. Some facts may be false when re-tested with better instruments.

.. oh .. what the hell .. here's the rest of 'em … …

Law: A logical relationship between two or more things that is based on a variety of facts, and proven hypothesis. It is often a mathematical statement of how two or more quantities relate to each other. A law is a phenomenon that has been observed many times, and no contrary examples found, that it is accepted as a universal phenomenon.

Hypothesis: A tentative statement such as ‘if A happens then B must happen’, that can be tested by direct experiment or observation. A proven hypothesis can be expressed as a law or a theory. A disproven hypothesis can sometimes be re-tested and found correct, as measurements improve.

Theory: An explanation for an observed phenomenon. An explanation why certain laws and facts exist, that can be tested to determine its accuracy, make predictions and incorporate a statement to enable disproof of the stated theory.

Belief: A statement that is not scientifically provable in the same way as facts, laws, hypotheses or theories. Scientifically disproven beliefs can still be held to be true.

Keep 'em coming !! I'll probably update this thread when I uncover some more of my own, in the future !

Cheers (& thanks for the contributions !)

[Bassnut (Fred)]

Parallel lines meet at infinity?.

[mjc (Mark)]

0.9999 (recurring) is identical to 1 and not infinitesimally smaller than one.

Proof divide one by three
1/3 = 0.33333 (recurring)

Multiply both sides by three

1 = 0.99999 (recurring)

http://en.wikipedia.org/wiki/0.999...

Mark C.

[OICURMT]

Originally Posted by ballaratdragons

Even without a spacesuit It is possible to live in the vacuum of space for up to 3 minutes.

Could you supply a reference for this? I'm struggling to figure this out, as the partial pressure of H2O under a vacuum at body temperature would result in boiling...


I could surmise that the body itself must be under pressure due to "containment" by the epidermis... but don't know if that would be enough.

[CraigS]

Originally Posted by sjastro

One that you are familiar with Craig.

Excluding a vertical straight wire, what should the shape of a wire be such that a bead released from one end of the wire will slide to the opposite end under gravity in the shortest period of time.

Common sense says the wire should be straight but the answer is in fact a cycloid.
http://en.wikipedia.org/wiki/Cycloid

Regards

Steven

Ok .. so this one's got me stumped, also.
(I'm sure what Steven says is correct, but my brain needs more !! )

If a vertical wire is fastest of all, then why wouldn't a wire, slightly off the vertical, also be faster than a Brachistochrone Curve (cycloid) ?

If such a wire did result in a faster descent, then there must be an angle at which it wouldn't be a faster descent .. what is that angle if friction is excluded ?

(The second question may be irrelevant if the inference in the first question is proven invalid. I suspect the issue here is in the wording. There is something about the bead having to be 'constrained'. It would appear that there must also be constraints applying to the end-points, as well. (??). I'm not sure of the significance of these constraints, however .. ).

Cheers

[sjastro]

Originally Posted by CraigS

Ok .. so this one's got me stumped, also.
(I'm sure what Steven says is correct, but my brain needs more !! )

If a vertical wire is fastest of all, then why wouldn't a wire, slightly off the vertical, also be faster than a Brachistochrone Curve (cycloid) ?

Craig,

It depends if a cycloid can be formed in the first place.
The vertical wire not only takes of the shortest distance and time, but also a cycloid cannot reach the bottom point if the endpoints are vertically aligned.

If the wire is even slightly off vertical the cycloid path will take the shortest time if it is able to reach the lower point.

Regards

Steven

[mithrandir (Andrew)]

Originally Posted by sjastro

It depends if a cycloid can be formed in the first place.

I think you will find that the vertical wire is the limit case of the brachistochrone when the points become vertically aligned. I don't feel up to remembering enough of my Calculus of Variations course - more than 30 years ago - to prove it.

Andrew

[sjastro]

Originally Posted by mithrandir

I think you will find that the vertical wire is the limit case of the brachistochrone when the points become vertically aligned. I don't feel up to remembering enough of my Calculus of Variations course - more than 30 years ago - to prove it.

Andrew

What you will find is that the partial derivatives in Euler LaGrange equation vanish as there is no horizontal component. This reduces the equation to the trivial case 0=0. There is no stationary value.

From a physics perspective since the wire is frictionless, the wire does not provide a constraint when the endpoints are vertical. The bead falls purely under the effect of gravity which is in a straight line.

Regards

Steven

[mithrandir (Andrew)]

Originally Posted by sjastro

What you will find is that the partial derivatives in Euler LaGrange equation vanish as there is no horizontal component. This reduces the equation to the trivial case 0=0. There is no stationary value.

However, the function [image that won't paste] is particularly nice since x does not appear explicitly. Therefore, [another image] and we can immediately use the Beltrami identity ...
http://mathworld.wolfram.com/Brachis...neProblem.html

Are you suggesting there is no limit as delta x approaches zero, and the the vertical line is a discontinuity? Physics and discontinuities don't get on well together.

From a physics perspective since the wire is frictionless, the wire does not provide a constraint when the endpoints are vertical. The bead falls purely under the effect of gravity which is in a straight line.

Doesn't that assume a non-rotating frame of reference? A falling object in a rotating frame follows a parabola. (Ignoring any effects of air resistance.)

[sjastro]

Originally Posted by mithrandir

However, the function [image that won't paste] is particularly nice since x does not appear explicitly. Therefore, [another image] and we can immediately use the Beltrami identity ...
http://mathworld.wolfram.com/Brachis...neProblem.html

The Beltrami identity doesn't apply.
If you look at equation (4) if the endpoints are vertical, dx=0 hence ds=dy.
The integrand in equation (6) becomes dy/(2gy)^.5

The functional (http://en.wikipedia.org/wiki/Functio...tics)#Integral ) in this case is of the format f(y, x, x')dy not
f(x, y, y')dx as in the mathworld link where there is both a vertical and horizontal component of the endpoints.

In the f(y,x, x')dy format the partial derivatives of the Euler Lagrange equation are with respect to x and x' (for f(x,y,y')dx are these are with respect to y and y').

Since x and x' do not appear explicitly in the integrand, all the partial derivatives in the Euler LaGrange equation are zero.
Hence we have the trivial case of 0=0.

Are you suggesting there is no limit as delta x approaches zero, and the the vertical line is a discontinuity? Physics and discontinuities don't get on well together.

I'm not sugesting anything of the kind.

The Euler Lagrange equations applies to functionals not functions. A functional that satisfies the EL equation has a stationary or extremal value. Vertical endpoints are simply a particular case. Here the functional does not have a stationary solution.

Doesn't that assume a non-rotating frame of reference? A falling object in a rotating frame follows a parabola. (Ignoring any effects of air resistance.)

The Brachistrome problem assumes there are no fictitious forces.

Regards

Steven

[OneOfOne (Trevor)]

Originally Posted by sjastro

One that you are familiar with Craig.

Excluding a vertical straight wire, what should the shape of a wire be such that a bead released from one end of the wire will slide to the opposite end under gravity in the shortest period of time.

Common sense says the wire should be straight but the answer is in fact a cycloid.
http://en.wikipedia.org/wiki/Cycloid

Regards

Steven

I recall seeing something like this on "Why is it so?". They had a series of clear tubes finishing at a lower point to one side, each with a ball inside, one straight, one cycloid, one parabolic. All three balls were dropped simultaneously, with the one in the cycloid finishing first. Do we have a dilemma? Loved that show!

[CraigS]

Changing the topic slightly … I love Mark's (mjc's) contribution !!

Such simplicity … tremendous stuff !

Hard to top that one … a real beauty !


Cheers

[renormalised (Carl)]

Here's a counterintuitive fact.....Anthony Peratt = plasma cosmology/EU advocate (nut) = respected scientist

[CraigS]

Originally Posted by renormalised

Here's a counterintuitive fact.....Anthony Peratt = plasma cosmology/EU advocate (nut) = respected scientist

Actually, I'm going to have to (sort of) challenge part of that one … from the Los Alamos National Laboratory 'Plasma Universe' website …

The Plasma Universe and Plasma Cosmology have no ties to the anti-science blogsites of the holoscience 'electric universe'.

Now, whilst the Los Alamos Laboratory site doesn't fully represent Peratt's views, this IS where most of his papers are found, and he IS quoted on their homepage, and he WAS a 'Member, Los Alamos National Laboratory Associate Directorate for Experiments and Simulations, 1999–2003".

… close ... but I don't know that we can assume he's an EU advocate (nut).

Perhaps a co-conspirator of a slightly different ilk ???

… perhaps a 'plasma cosmology (nut)' ???


Cheers