[Bill S (OP)]

Sascha Vongehr says:

http://www.science20.com/alpha_meme/fundamental_nature_light-75861

In fact, we would experience about one second of travel time between earth and moon, if we moved with a velocity v that equals light velocity divided by the square root of two: v=c/√2. At 90% light velocity, i.e. at v=9c/10, our travel time will be only a third of a second! At 99.9% of the speed of light, the travel time we would experience has reduced to a thirtieth of a second, or 33.3 milliseconds.

The math looks fairly simple, but I think I must have become lost somewhere in trying to use it.

I'd be grateful is someone could de-fog me; idiot level, please.

[alancalverd]

Distance from earth to moon is about 384,000,000 meters. Speed of light is about 300,000,000 m/s, so at the speed of light it would take 384/300 = 1.28 seconds. This is confirmed by radar, laser and radio communication.

However thanks to relativistic time dilation the clock on the rocket would measure a time
t' = t/√(1-v²/c²) compared with a stationary clock so if v = c/√2 then v²/c² = ½ and t'= 1.28/1.41 ≈ 0.9 seconds.

[Bill S (OP)]

I knew, really, that Sascha's maths would be OK. The serarate bits made sense, but I ran into a mental block.  I think it's cleared now, thanks Alan.

[Bill S (OP)]

Still with Sascha's article; I run into some more problems later.  This is the first of them.

If we try to locate an electron inside an atom, once we succeed to localize the electron in a small, classically meaningful location, it does already, by the very fact alone of it being classically meaningful as an individual particle, not belong to the atom any more.

Why?

[Colin2B]

He's probably talking about free electrons which are not part of an atom, not subject to quantisation, and can exist as individual particles.

[Bill S (OP)]

That would seem to make sense, Colin, but he does say: "If we try to locate an electron inside an atom....."

[Colin2B]

Doesn't sound well worded to me, could be clearer.

[agyejy]

Basically for an electron to be considered to be bound to an atom the wavefunction of the electron must fall into a set of wavefunctions collectively known as bound states. These wavefunctions have certain properties such as quantization of energy and a high degree of delocalization within the immediate vicinity of the atom for example. The only way to localize an electron into a "classically meaningful location" is by changing the wavefunction of the electron so significantly that the wavefunction no longer has the properties of a bound state. Immediately after the "classically meaningful" localization measurement the electron leaves the atom because its wavefunction no longer corresponds to a bound state.

Another way to look at it is that due to the uncertainty principle the decrease in the uncertainty about the position of the electron increases the uncertainty in its momentum. When the uncertainty in the position of the electron is reduced to a "classically meaningful" level the uncertainty in its momentum must increase so much that electron is virtually certain to escape the atom. This is simply a consequence of the mathematics of the uncertainty principle.

It is important to keep in mind that these two explanations are correspond to different models of reality that currently make identical experimental predictions. Currently there is no compelling reason to choose one model over the other so you are free to use either explanation just be careful not to confuse the models with an objective reality. In fact we're not even 100% certain such an objective reality actually exists and even if it does exist there is no guarantee that we will ever be able to describe it exactly.

Overall the statement could have been worded more clearly however, nobody is perfect and sometimes less than perfect statements happen.

[Bill S (OP)]

Thanks folks, I think I'm getting there, one step at a time, but I'm struggling with this bit as well.

Our measurement of the electron being at x equals the ‘branch’ Bx coming out of its interference with all other branches Bx’ of the quantum universe, in each of which the electron is in another place x’.

[agyejy]

Thanks folks, I think I'm getting there, one step at a time, but I'm struggling with this bit as well.

Our measurement of the electron being at x equals the ‘branch’ Bx coming out of its interference with all other branches Bx’ of the quantum universe, in each of which the electron is in another place x’.

Here the author is referencing another potential model of reality that is also currently consistent with Quantum Mechanics. In this model of reality time isn't a string of single events stretching from past to future. Instead every time an event happens every possible outcome happens but a human can only ever observe one. Instead of imagining time as a line it instead becomes more tree like with every possible outcome of an event spawning a new line or 'branch'.

You could think of this model as saying that when a particle is acting like it is delocalized that is really just a bunch of possible universes (branches) interacting with each other and in each universe (branch) the particle is in only one place. As long as you don't try measure the location of the particle exactly all those universes (branches) are free to keep interacting but as soon as you make that measurement you essentially pick a universe (branch). In this model the only way for an electron to be bound to an atom is for the electron to be delocalized via this interaction of many universes (branches) interfering with each other. Once you pick a universe (branch) via an observation the interactions between universes (branches) cease and the electron can no longer be bound to the atom.