stupid physics questions

[zip accident]

I was just thinking about things being spatially unique, as in, we can say that two things must be different if they are in different places. Then I thought, what would space have to be like for that to be untrue, and how do we know it isn't already like that?

I freely admit this question is stupid, which is what makes this thread marvelous.

So far as I know there is no absolute co-ordinate system, so the question seems worth asking.

[pogo]

To say two things are distinct we mostly appeal to common sense. You can see two things and we know they are different. You can use science in a few ways to confirm this. We know things can't travel faster than light, and can't travel in time, so if two objects are observed at distinct points at the same time they must be different objects as it's impossible to get from one of the spots to another in zero time.

Or you can do measurements. Measure the total mass of the two objects, and observe that it's greater than one object. If they're large enough measure the gravitational force they exert, or the gravitational attraction between them.

Perhaps related there's the Pauli exclusion principle which says two massive particles can't occupy the same space at the same time. This operates at the sub-atomic level, so doesn't say much about the world we can see, except it explains why many things have 'size' and so why the occupy space the way they do.

[Dio]

Not all massive things encounter the exclusion principle - superfluid helium atoms and Cooper pairs, for example, obey Bose-Einstein statistics. That still doesn't mean they can occupy exactly the same location in any way other than statistically though.

[zip accident]

To say two things are distinct we mostly appeal to common sense. You can see two things and we know they are different.

Yeah, but quantum mechanics breaks common sense.

You can use science in a few ways to confirm this. We know things can't travel faster than light, and can't travel in time, so if two objects are observed at distinct points at the same time they must be different objects as it's impossible to get from one of the spots to another in zero time.

What I mean is what theoretical proof do we have that any two points in space are distinct?

Or you can do measurements. Measure the total mass of the two objects, and observe that it's greater than one object. If they're large enough measure the gravitational force they exert, or the gravitational attraction between them.

Perhaps related there's the Pauli exclusion principle which says two massive particles can't occupy the same space at the same time. This operates at the sub-atomic level, so doesn't say much about the world we can see, except it explains why many things have 'size' and so why the occupy space the way they do.

Yeah, all of that's probably good. It's just a "what if?" that I don't remember coming across before.

[pogo]

What I mean is what theoretical proof do we have that any two points in space are distinct?

It's difficult to theoretically prove this, or anything about the universe. What we have is a model for the large scale universe, which is general relativity. This is almost universally accepted; it explains the universe very well and makes a number of predictions which have been confirmed very accurately.

General relativity says that locally, i.e. on the scale of us, the universe is flat. More precisely it has the structure of a four dimensional Minkowski space called spacetime, which is very well understood. And within that space distinct points are distinct. They are separated by time and/or space. If two points are not separated, so they have the same time and space coordinates, then they are the same point.

(More precisely in relativity you don't talk about points but events. An event is a point in time and space. Two events are different if their 3D positions are different or their time is different. in spacetime space and time are in a sense interchangeable so being separate in time and space are not different things but part of the same thing)

[zip accident]

Did these guys just exceed the speed of light?

http://arstechnica.com/science/2014/07/ ... te-speeds/

[pogo]

Can't read the original paper as it's behind a paywall but, er, no. It doesn't say that exactly. If you think it does there are two caveats. First these are quasi-particles not real particles; nothing is actually moving. Second this is a quantum effect, to do with quantum entanglement.

Quantum entanglement is a very odd thing which I don't fully understand. The idea is that you can entangle, i.e. associate so they share some property, two or more particles. You then measure the properties of one particle and find the same measurement on others. But this still works if they are separated, even by some distance, and if the measurements are done at the same time. There's no way of communicating between them, and doing so would violate the speed of light. But it's a real effect and has been measured.

There are other experiments which appear to violate the speed of light. E.g. if you had a round room, stood in the centre of it and shone a torch you could trace out a light beam. Do this fast enough (with a laser and a rotating prism/mirror perhaps) in a big enough room and the speed of the beam around the edge of the room can exceed the speed of light. But nothing is actually moving.

So I suspect it's something like this. Certainly if they'd found a way to go faster than light it would be being reported more widely than a dry report in Ars.

[zip accident]

Certainly if they'd found a way to go faster than light it would be being reported more widely than a dry report in Ars.

A very carefully dry report in Ars.

They implied it without stating it. They obviously expect rebuttals and attempted refutations. They have said it apparently breaks time. Which is quite a big deal

[pogo]

Certainly if they'd found a way to go faster than light it would be being reported more widely than a dry report in Ars.

A very carefully dry report in Ars.

They implied it without stating it. They obviously expect rebuttals and attempted refutations. They have said it apparently breaks time. Which is quite a big deal

No they haven't. They said "the speeds of the quasiparticles were such that they could no longer be described in terms of light-cones". But many things in quantum mechanics defy explanations in terms of classic relativistic physics. And even in relativistic physics there are 'things' that move faster than light, as I've already described. Many more are listed here:

https://en.wikipedia.org/wiki/Faster-than-light

[gumboot]

How long was the last day on the moon, before it went into tidal lock with Earth?

I figure it got slower and slower until it had so little remaining angular momentum that other forces overwhelmed its ability to complete the next full rotation. So there's a transition from going all the way around one more time to never passing the same point ever again. Perhaps the period of the last complete cycle can be inferred from the nature of those forces.

It's very hard to imagine that it's still turning freely at a rate that is still approaching zero asymptotically.

[Dio]

What's the exact definition of day in this sense? I mean, the sun rises and falls in its sky on a 29 day cycle.

[gravy]

And if you removed the rest of the universe it'd still rotate at the same rate?

[pogo]

It’s probably unknowable, and depends a lot how you measure it. But you can make a guess.

https://en.wikipedia.org/wiki/Tidal_locking

WP’s article says the Earth is slowly being tidally locked to the moon, with our days getting 15µs longer every year. That 15µs is 0.000015 / 86400 = 1.7361111e-10. Lets say 2 e-10. That’s the fraction it increases in a year.

Assuming day length increases linearly, on the last (calendar) year before being locked it will rotate only 2 e-10 of its total rotation, e.g. 360°, away from being tidally locked. In the two years before it will rotate about 4 * 2 e-10 (as it’s speeding up). In the three years before about 9 * 2 e-10. And so on. It will make one full revolution, one full “day”, when this equals one. So when n^2 * (2 e-10) equals one. Or about when n = √(1 / 2 e-10), or about 70,000. So about 70,000 years.

That’s for the Earth. It clearly happened much more quickly for the Moon, but how much quicker I don’t know. WP’s tidal locking article has formulae but you need to plug in lots of numbers, some you’d need to guess. It clearly happened more quickly than it’s happening to the Earth, so the last day would have been much shorter; hundreds or thousands of years maybe.

[Dio]

Presumably, the tidal locking implies that the 'heavy end' of the moon is the one pointing towards us, and the 'light end' pointing away? In that case, wouldn't the last phase of tidal locking have been characterised by oscillation?

[pogo]

It’s not that it has a heavy and light end. Tidal locking occurs even between stars, such as binary stars, that have no lumps / heavy bits. The ‘heavy end’ moves around the body as it rotates, much as high tide moves around the Earth as the Moon orbits us. It’s the torque exerted by that that slows and eventually locks the body tidally. So it won’t oscillate, if it overshoots it will keep going, keep slowing down.

(The moon doesn’t have water, so oceanic tides, but planetary bodies also experience tidal movement of their rocks as those distort due to gravity. This is measurable on the Earth and will be much greater on the Moon due to the Earth’s greater gravitational effect on it)