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If there is a minimum physical length, that is a planck length, does that mean that nothing is technically continuous? Or, is it possible to imagine 'half a planck length'?
If there is a minimum physical length, that is a planck length, does that mean that nothing is technically continuous? Or, is it possible to imagine 'half a planck length'?
The quantum world is indeed discreet, and (as far as we know) half a planck length doesn't make any sense physically.
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The answers from benihana and cromulent are correct, but the following may possibly be a useful thought experiment. Imagine a balloon (our universe) with lots of ants crawling on it (photons moving at the speed of light). The ants can't walk any faster than 2mm/s. They can't take a message from any part of the balloon to any other faster than that. (And, let's suppose, there's nothing living on the balloon that moves…
Epanding into what??? This is what I cant wrap my head around... into what is the universe expanding? What if the universe is not a balloon - but a doghnut where the outer edges fold back into itself, the overall space it is in can be finite yet the surface is curved away. The light would travel along the curved surface of space-time and thus travel a greater distance than is linear.
That... is spectacular...
Earlier quoted context omitted.
The answers from benihana and cromulent are correct, but the following may possibly be a useful thought experiment. Imagine a balloon (our universe) with lots of ants crawling on it (photons moving at the speed of light). The ants can't walk any faster than 2mm/s. They can't take a message from any part of the balloon to any other faster than that. (And, let's suppose, there's nothing living on the balloon that moves…
Epanding into what??? This is what I cant wrap my head around... into what is the universe expanding? What if the universe is not a balloon - but a doghnut where the outer edges fold back into itself, the overall space it is in can be finite yet the surface is curved away. The light would travel along the curved surface of space-time and thus travel a greater distance than is linear.
So, you might be asking, whatever does it mean to say that space, or spacetime, is curved? It means, e.g., that if you measure the radius and circumference of a small circle very very very accurately, the relationship isn't C = 2 pi r. If the circumference is "too small" then space is positively curved there, like a balloon. If it's "too large" then space is negatively curved there, like a saddle. The curvature might actually be different depending on the orientation of the circle, but if space is the kind of thing we think it is then you basically only need six numbers to tell the whole story at each point of space. (In two dimensions -- the surface of that balloon -- there's only one possible orientation for the circle, so you only need one number to describe the curvature at each point.) Note that you can measure this thing without needing to go "outside" space: the radius and circumference are measured within the space. Distances along the surface of the balloon.
Yup, the universe could be curved and topologically nontrivial in all kinds of interesting ways: it doesn't have to be like the surface of a balloon. (There's some intriguing but inconclusive evidence suggesting that the large-scale geometry of the universe is a "Poincare dodecahedral space": take a dodecahedron, and apply some magic to its faces so that when you try to leave it by one face you come back in by the opposite face.) And yes, light travels along the shortest paths it can within the universe, and doesn't take out-of-the-universe short cuts even if there are any.
How not to feel sooooo small and insignificant after that !?
Some people get depressed when they find out how huge the universe is... What is the big deal about bigness? A cow is much bigger than you, but it is a ridiculous animal and you are a valuable person. You know it's a cow. It doesn't know anything. it just stands there eating grass (grass!) and mooing. And if it were bigger, that would only make it more ridiculous. - David Deutsch
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>Why can't Google maps do that? Because, fortunately, the world is not vector-based :)
> Because, fortunately, the world is not vector-based :) Why 'fortunately'?
Actually thinking about it, viewed in terms of quantum mechanics the universe from our scale looks more like a bitmap image than a vector image. (Note that I have no actual knowledge of quantum physics for the purposes of this meandering nonsense of a comment.)
How not to feel sooooo small and insignificant after that !?