Reply to: The Zeno effect

[expat]

Hmmm. I hear a sound of big ideas zooming effortlessly over my head. Anyone know a (relatively non-mathematical) book where I can explore some of these ideas?

Not offhand (it's not that I'm ignoring your question).

Einstein's own "Relativity, A Popular Exposition" is rather old but is actually quite good.

[Fungus]

My argument is that this is what the model says.

I say there is'nt a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined. There is no such thing as an objectively progressive time. The 'present moment' are derivative notions without actual physical foundation in nature.

Objects do not, and also can not, move in space-time, they exist in space-time.

You indirectly make an important point, namely that we are talking about a model.

In quantum mechanics you cannot precisely specify a dimension, be it spatial or temporal. This is of course summarised in the well known Heisenberg's uncertainty principle, and it does not just apply to space and time.

But as I understand it, in relativity - special and general - position is well defined.

"The 'present moment' are derivative notions without actual physical foundation in nature."

Mmmm. Sounds a bit too Buddhist for my tastes. Would you be one of the contemplative round belly mob?

There was a poster call Threaded.
Whose posts we all dreaded.
His equations were long.
His sanity gone.
But on impact with the train he was deaded.

I thank you. (With apologies to MF.)

Fungus

[sasguru]

But I see that the other guys seem to have given up, which is probably also a sign of understanding.

Hmmm. I hear a sound of big ideas zooming effortlessly over my head. Anyone know a (relatively non-mathematical) book where I can explore some of these ideas?

[expat]

The argument is becoming circular now: giving time it's own dimension and then saying this can be differentiated / integrated creates the Zeno paradox.

I'm sorry, but it is treating it as though it can't be that is at the root of the paradox.

And the fact that one can treat anything measureable as a dimension in mathematics, is not the point of relativistic space-time. Newtonian physics in effect already treats time as a dimension (via the Cartesian transformation between algebra and geometry). What relativistic, or more precisely Minkowskian, space-time does is treat it as a dimension on the same footing as the spatial dimensions, thus greatly simplifying the mathematics (a sure sign that you've hit on understanding).

But I see that the other guys seem to have given up, which is probably also a sign of understanding.

[threaded]

The argument is becoming circular now: giving time it's own dimension and then saying this can be differentiated / integrated creates the Zeno paradox.

[expat]

No, I'm saying that time doesn't change. Clocks change. Giving time it's own dimension is silly.

Time doesn't change any more than distance changes. That's exactly why it does make sense to consider it as a dimension rather than as something that passes.

[threaded]

No, I'm saying that time doesn't change. Clocks change. Giving time it's own dimension is silly.

[expat]

Objects do not, and also can not, move in space-time, they exist in space-time.

Well quite: that's what space-time means. An object existing in space-time is the reformulation of the idea of an object moving in space relative to time.

It is meaningless to talk of whether there is an instant in space-time when something is or is not so: time is part of space-time.

But the equivalent of saying that there is an instant in time when a certain position is occupied and the velocity is zero, is to say that there is a certain point in the space-time object where the derivative of position w.r.t. time is 0. This if course requires that the space-time curve be continuous, otherwise the derivative is not defined.

Basically you're just saying that its path is like > and not ). Nothing non-Newtonian about that.

[stackpole]

In other words, to measure motion, you need non-zero time.

[threaded]

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.

My argument is that this is what the model says.

I say there is'nt a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined. There is no such thing as an objectively progressive time. The 'present moment' are derivative notions without actual physical foundation in nature.

Objects do not, and also can not, move in space-time, they exist in space-time.

[threaded]

A single point on the bonnet of the crash test car will rapidly decelerate, come to a standstill, and accelerate in the reverse direction.

So, what happens if this single point is right at the very front?

[Churchill]

Indeed.

Look at crash test videos where they crash a car into a stationary concrete wall.

Does the car stop at the instant it's bumper contacts the wall? No, of course not. The wall absorbs the energy of the moving car as it rapidly decelerates (crumpling up as it does so).

Now, supposing the same section of concrete wall was on a big forklift truck and trundling towards the crash test car at, say, 5kph- similar to "Bogey and the Train" problem.

A single point on the bonnet of the crash test car will rapidly decelerate, come to a standstill, and accelerate in the reverse direction.

Why? Because the crash test car has mass and velocity. The wall has mass and velocity (maybe zero velocity, but it doesn't matter).

Due to it's far greater mass (and thereby inertia), the wall will win the argument - even though it may shift slightly as it absorbs the kinetic energy from the moving car.

The car will decelerate from its original speed to 0, quite rapidly - but not instantaneously!

Might I refer the learned congregation to ESL? The European Simulation Language based on the Cosby Hay Discontinuities algorithm?

BTW, did I tell you that I ported the original Fortran based Simulation Engine when I was SNOBBUTAYOOT?

Churchill in "Blatant Threaded" mode!

[bogeyman]

The problem only arises if you consider the train and threaded as solid non compressible objects. In practice they both consist of layers of atoms. As the train hits threaded, so atoms compress, the elecstrostatic repulsive forces between them increase, and gradually Threaded is accelerated.

Indeed.

Look at crash test videos where they crash a car into a stationary concrete wall.

Does the car stop at the instant it's bumper contacts the wall? No, of course not. The wall absorbs the energy of the moving car as it rapidly decelerates (crumpling up as it does so).

Now, supposing the same section of concrete wall was on a big forklift truck and trundling towards the crash test car at, say, 5kph- similar to "Bogey and the Train" problem.

A single point on the bonnet of the crash test car will rapidly decelerate, come to a standstill, and accelerate in the reverse direction.

Why? Because the crash test car has mass and velocity. The wall has mass and velocity (maybe zero velocity, but it doesn't matter).

Due to it's far greater mass (and thereby inertia), the wall will win the argument - even though it may shift slightly as it absorbs the kinetic energy from the moving car.

The car will decelerate from its original speed to 0, quite rapidly - but not instantaneously!

[Fungus]

Very good fungarse, but what if I fire one atom at 200mph at a stationery atom - does the stationery atom suffer infinite acceleration.

Who rattled your cage you complete Tosser.

The forces are electrostatic. The mechanics are quantum not classical.

[Jabberwocky]

Very good fungarse, but what if I fire one atom at 200mph at a stationery atom - does the stationery atom suffer infinite acceleration.