The Zeno effect

[stackpole]

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

[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.

[threaded]

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

[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]

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]

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.

[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?

[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

[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.