Xeno's paradox...just for fun
 

Lots of heavy 'stuff' discussed in more than a few threads lately. I thought it might be interesting and fun to raise a question somewhat germane, but as well, lacking the teeth to bite anyone.

There are, as I'm learning, more than a few scientists here. jlm made me think of this while reading one of his responses regarding an infinite number of cores in an IC.

According to Xeno's first paradox, if you stood in the path of a medieval archer's arrow, it would never reach you. This is possible because space can be divided into ever smaller segments of the previous.

Now lets take this paradox and apply it to one of the pistons traveling up and down in the Mini's block. Does the piston stop upon reaching TDC or BDC, or does it 'instantaneously' accelerate?

What say you?

It has to stop since it reverses direction. If you plot its position vs time, there will be two points where the slope of the curve is zero: TDC and BDC.

Mark

FYI - I'm trying to get this thread moved to engine mods. Dunno how I did this.

Thread Moved
 

Thanks for dropping me a not over the contact us link on the left column. You could also have dropped me a PM. :smile:

As for the paradox, the piston doesn't stop since it is in continuous motion. :wink:

You can definately have zero velocity and any quantity of instantaneous acceleration. If you consider the piston's motion to be linear, this would be the case. If you think the external forces acting on the piston at TDC cause it to rotate maybe ever so slightly about the pin (piston rock), then you have some velocity in an unexpected direction :thumbsup:

--
Devil's Advocate

Well since at the atomic level all things are moving, to get something to ever come to a complete stop you have to get it to 0 rankine/kelvin or -459.67 fahrenheit

Physics is fun!

not only does the piston's velocity pass through zero at TDC, but also the time the piston spends from say 10 degrees before and after TDC can vary from engine type to type. The crankpin has a linear velocity parallel to the bore that is a sine wave function, but due to the connecting rod link, the piston veocity equation is dependent on rod length/stroke ratio. There is considerable yap about the ideal ratio, 1.75:1 being the current optimum. As far as I can tell, the factors are the amount of sidewall thrust wear and more time in the high compression zone to improve burn and develop more force on the piston. to held visualize the effect of r/s ratio, imagine an extremely long rod; the piston velocity would approach the pure sine wave with minimal side force; compare that to a very short rod.

jlm,

It's been a long time since calculus. Can you explain at perhaps a more bone-head level?:confused: I think I understand, just not sure. I'm extremely visual if that helps. Thanks.

The atomic level response was creative!:thumbsup:

for the piston to be moving, it has to have non-zero velocity. If you consider the upward velocity to be in the positive direction, the opposite direction is negative. the velocity has to pass through zero to go from pos to neg.

Got it.

Imagine these thoughts applied to current F1 piston speeds; up to 350 rpm/sec. Wow! It's a wonder these things don't stretch out to a half litre bigger by races end.

i love paradoxes, probably why i'm such a big BTTF fan. heres one to think about....

40 year old john smith goes back in time to see his 10 year old self.

40 year old john smith has a meat cleaver in his right hand....

40 year old john smith cuts off the right hand of the 10 year old john smith...

what happens next?

40 year old john smith cut his own right hand off, so in the 30 year up to the time he cuts his own hand off, he didnt have a right hand to cut his own right hand off with.

like i said, i love paradoxes.....

If you like paradox, read up on "EPR". As far as I know, this one is still bothering physicists. It's real, it's apparently measureable, and it makes no sense.

The 'E' in EPR is for Einstein. Despite the fact that he won a Noble prize for pioneering work in quantum mechanics (photo electric effect), he never accepted quantum theory, and EPR was his one of his arguements against it.

Despite the fact that EPR doesn't make sense, in the words of one of my quantum mechanic professors, "nature is under no obligation to make sense to YOU."

The Wikipedia has a nice writeup on the EPR paradox.

Mark

the thing to remember about theoretical physics is that it doesn't try to give a literal interpretation of nature; rather it creates analogies and constructs that we can make use of, like electrons, holes, quarks, pi-ons, etc.


the conflict I always liked was the particle/wave explanation of electromagnetic radiation (light); both views had their pros and limitations:
"wave theory" explanied how light could get through solid objects (like glass), particle boys had trouble with this.
"particle theory" explained how light could propagate through space (the void) where there was presumably nothing there to "wave" which stumped the wave boys.

I don't think that's exactly the right interpretation of wave particle duality. Everything displays wave / particle dualtiy, it's just that most things have such small wavelengths that they are not observeable by us. DeBroglie realized the truly deep nature of wave particle duality, and the phenoma is named after him, 'matter waves' are characterised by the "deBroglie" wavelength.

Wave particle duality is one of the very fundamental concepts that lead to QM. Einstein was able to explain photoelectric effect by treating light as a particle which carried momentum. Treating light purely as a wave cannot explain the photoelectric effect so light has to be a particle.

However light clearly displays the properties of refraction (which particles cannot), so it also has to be a wave.

Solids can travel inside of other solids, a common example of this is diffusion of like a dopant into a semiconductor. Granted, that is not very "fast" travel, but it's still solids moving inside of solids.

This also explains why an object placed between a viewer and the sun, for example, appears to posses a life-like outline...because light travels in waves. This concerns the part of my background responsible for persuasive and architectural illustration.

Intersting jlm, that computer software folks developing packages for computer renderers could not mimic a 'realistic' quality of light until they studied how light waves and photons actually behave. It was a, excuse the pun, quantum leap. I kill me!

Two great reads: Opticks and Colour - Art and Science

The chicken







or the egg?

the history of modern physics is a great read, full of wacky, but useful logicical constructs.

for example, if you picture a loose electron migrating across a semiconductor from atomic site to atomic site, it is intuitive enough to calculate a speed of propagation.

the wacky part is that you can think of the holes, or the sites that the electron is migrating from, also propagating, but in the opposite direction. and as I recall, the speed is different.

I readily defer to satay for more. (I almost said diffute...:lol: )

edit: "to" changed to "from"

Sort of like the road was already paved once??? Very whacky!

To the best of my understanding, that's exactly right. The best analogy I've ever heard for helping to understand holes in a semiconductor is to think of them as "bubbles". Like if you grab a bottle of shampoo and flip it over, and watch the bubble go up. Is the bubble moving up, or is it really the shampoo flowing down?

I'm also a great fan of modern physics, much more a fan than a practicitioner. I have taken a lot of grad level physics classes, but only really have enough knowledge to appreciate the genius that these guys had who developed the theory. I don't understand any of the high energy junk or advanced quantum stuff, I just barely have a tenative grasp on what most physicists consider to be "simple" condensed matter physics. To me that's hard enough :grin:

The answer: The rooster:wink: (any hen can tell you)


Paul