The Zeno effect

[OwlHoot]

Lets try a simpler example to show my point: When a ball is thrown into the air, the current mathematical model says that at some moment between going up in the air and coming back down the ball is stationary.

I say that is bollox.

Simple really.

But that's all it is threaded - a model, in other words an idealization. Why does not being exact make it "bollox"?

Oh and it has nothing to do with Zeno's "paradox", which is no more than stating a conclusion without the qualifying condition necessary to make it correct - As Bogeyman mentioned or implied (I think - can't go back and check now), because successive distance _and_ time intervals are being halved, and both sum to a finite limit, the proper conclusion is that Achilles can't overtake the tortoise within a certain time. It's only the omission of that condition that creates the so-called paradox.

[OwlHoot]

Hey, don't get me wrong, I teach that stuff to my students so they can pass exams.

You can't be serious.

It's just that I don't believe in it, cause it's all mathematical bollox made to fit the observations. None of it has made any truely new predictions, just confirmed stuff already observed, and often times it has been twisted some more to fit the observations.

You mean like Adams and Leverrier using Newtonian mechanics to predict the existence and position of the planet Neptune before it had been observed? Good point.

An awful lot of these people who believe in quantum theory are just as bad as these fundamentalist xtians, and potentially do even more damage to scientific progress.

If there's one criticism of typical quantum theorists I reckon it's that they've made a virtue of necessity by not even trying to find reasons and principles underlying quantum behaviour, to the extent that they're quick to scoff at people like string theorists who are (although admittedly hordes of kooks are also!)

[OwlHoot]

OK, whilst we are on the subject of whacky physics, would someone please explain this to me (or support my argument)

Someone recently tried to convince me that 'time' is relative to your altitude. He was suggesting that if you had 2 clocks sat next to each other that had been perfectly in sync for lets say a year, it would be reasonable to assume that they would continue to be perfectly sync'ed (assuming batteries or whatever never ran out).
I'm in agreement so far
He then went on to say that if you sent one of them up to a higher altitude for a period of time (lets say a mile for another year), when it came back down after that year it would read a different time to the other one (albeit a minor difference). (cant remember whether he said it would be faster or slower)

What a load of bollox

It's not. According to General Relativity the stronger the gravitational field the slower time passes compared to a clock higher up (assuming the gravity is radial, which for practical purposes it always is).

And it's not just clocks. The same effect applies to anything, including light - Experiments (e.g. by Pound and Rebka ) show that light emitted at the bottom of a tower has a slightly lower frequency by the time it reaches the top.

As you say, the effect is usually tiny. But in extreme circs it is dramatic - If you lower a clock towards the horizon of a black hole it will appear to stop when it reaches the horizon, although some brave soul who volunteered to stay with the clock would see it working quite normally as they and the clock crossed the horizon to their doom! And they would see clocks and everything else in the outside universe running faster and faster until it all converged to a bright blue spot and disappeared (up the frequency scale) as they approached the singularity.

Less dramatically, the same effect explains the advancing perihelion of Mercury (any planet in fact, but most noticeable with Mercury as it is closest to the Sun). Having an elliptic orbit, when it gets closest to the sun, so that time for it slows down, it dawdles slightly longer close to the Sun than it would further out and therefore gets further round its orbit.

(That's not the way the actual effect is calculated but the same principle applies - and whereas Mercury's anomalous motion used to baffle astronomers like Newcomb pre-relativity, its position now been measured by radar to within 6 inches of where relativity predicts it should be!)

[stackpole]

I've been worrying about bogey and the train. Or more to the point, I suspect threaded is correct.

If bogey is stationary as he passes between +5kph and -200kph, then the train must be stationary too, because the stationary bogey is splatted on the front of it. But the train is never stationary.

Can one of you qualified physicists explain? I must admit that sounds like contrived bollox, just as threaded suggests.

[bogeyman]

I've been worrying about bogey and the train. Or more to the point, I suspect threaded is correct.

If bogey is stationary as he passes between +5kph and -200kph, then the train must be stationary too, because the stationary bogey is splatted on the front of it. But the train is never stationary.

Can one of you qualified physicists explain? I must admit that sounds like contrived bollox, just as threaded suggests.

So you're suggesting that a body can go from +5 to -200 kph (relative to a trackside observer) without ever being stationary? Wow! How does that work then?

Because poor old Bogey is 'stationary' for an instant it doesn't mean the train has to also be 'stationary'. I don't understand why some of you find this so difficult to comprehend.

Draw a graph of speed vs time with speed on the axis Y and time on the X axis. Now plot Bogey's velocity. Doesn't your plot line cross the X axis at zero?

From his posts on the subject, Owlhoot sounds like the nearest to a 'qualified physicist' - perhaps you'd better ask him.

[bogeyman]

Numbskulls, all accelerations have gravitation, it's called the equivalence principle. So going up (and down) the hill has one effect on the clock, and staying up the hill has the opposite. Go up and straight down the hill will cause the clock to lose time, going up and staying there for a time long enough will cancel this out and eventually the clock will appear to go faster.

Suppose we reset the both clocks to zero at the same instant once they are in place (thereby cancelling the effects of acceleration in a gravitational field).

Will the clock at the top of the hill keep perfect time with the clock at the bottom of the hill? Or will the one at the top of the hill still run faster?

[Jabberwocky]

Time is continuous, and time measurement can be discrete, but they are different things.

Hold on a minute there sh*t for brains. What makes you think time is continuous ? We model it as continuous, but that doesn't mean it is. What is time ? It is always measured discretely, so why shouldn't it be discrete ?

[threaded]

Suppose we reset the both clocks to zero at the same instant once they are in place (thereby cancelling the effects of acceleration in a gravitational field).

Will the clock at the top of the hill keep perfect time with the clock at the bottom of the hill? Or will the one at the top of the hill still run faster?

Well, this is a fun one, and brings us back to the initial point of this thread. Does not the clock at the top of the hill have a "memory" of being accelerated even though it was switched off? (You can go even further, and sillier, the components of a clock manufactured at the top of the hill were accelerated there.)

[threaded]

So you're suggesting that a body can go from +5 to -200 kph (relative to a trackside observer) without ever being stationary? Wow! How does that work then?

The model says to draw a smooth curve. I say the function is discontinous, and yes the body can go straight from +5 to -200 kph. Saying the acceleration is therefore infinite is just an artifact of the model, because you are driving the model in a circumstance it does not work in.

You get the same effect in astonomy with singularities/black holes, these are just places in the model where you are trying to divide by zero. Silly really.

[stackpole]

So you're suggesting that a body can go from +5 to -200 kph (relative to a trackside observer) without ever being stationary? Wow! How does that work then?

Well, threaded's argument seems to be that, if bogey is stationary, then so is the train.

1. Bogey is only stationary for zero seconds (the point where your graphs cross)

2. Ergo we measure the train for the same period of zero seconds

3. If you measure the velocity of anything for zero seconds, it has not moved, therefore during that time it is stationary (the basis of the stationary bogey argument)

4. Ergo the train is stationary too

This is just as counter-intuitive as your point about your body reversing direction. Perhaps you could demonstrate that bogey is stationary for longer than zero seconds.