Ask a physicist anything. (8)

[Zippy the Wonderslug]

^ Sorry.

I'm such an idiot.

 

[Wiccan_Child]

Here's one.....

How on Earth is this thing even possible?

HUVr - The Future has arrived.

Given the prevalent meme of 'Scientists have X years left to make hoverboards', it fills me with glee that this video exists - with Christopher Lloyd, no less. It's like what they did when the Terminator movies' 'far and distant future' became the present day - and they created fabricated tie-in media.

Remake? Sequel? Back to the Future/Terminator crossover? I think so.

 

[Zippy the Wonderslug]

All I know is that I first, truly believed the video I posted.

Can someone here please pray for me.

 

[Elendur]

I'm thinking about creating a separate thread for this but, I'll ask here first anyway:

Are there any practical (i.e. possibly within physics) applications of integration over a finite distance on the real line, where the function in question has simple poles (which can be represented as f(x) = g(x) * 1/(x-x_j), where x_j is a pole within that interval, not lying on the endpoints) within that interval?

A simple example of a function, which I'm just using for demonstration purposes:
integration of f(x) = 1/x from -1 to 1
which has a simple pole in 0.
This specific result is quite obviously 0, if one is to use the trick of principal value and the fact that it's odd, but something like:
1/((x-1)*(x-2)*(x-3)*(x-4)) integrated over 0 to 10
would be harder to calculate, though exactly what I'm looking for.

Of course, there's no need to limit the functions to rational functions, they're just simple to represent without the possible removable poles.

I'm happy to delve deeper into what I'm talking about should this be too little to go on (I'm being a bit vague intentionally atm, I need to think about how much I'm willing to divulge).

 

[Justatruthseeker]

Here's one.....

How on Earth is this thing even possible?

HUVr - The Future has arrived.

That is so fake it's terrible.

 

[super animator]

How does one show that the earth goes around the sun using physicist and mathematics?

 

[lesliedellow]

How does one show that the earth goes around the sun using physicist and mathematics?

By showing that predictions made on the basis of that hypothesis correspond to what can be observed in fact. The relevant scientific theory is Newton's Theory of Gravitation.

 

[Wiccan_Child]

How does one show that the earth goes around the sun using physicist and mathematics?

By showing that predictions made on the basis of that hypothesis correspond to what can be observed in fact. The relevant scientific theory is Newton's Theory of Gravitation.

More directly, classical gravitation requires that the Earth go around the Sun.

It's a popular misconception that Einstein's theory of relativity implies that the choice between geocentrism and heliocentrism is simply one of inertial reference frames. This is untrue. First, the idea is based on the principle of relativity by Galileo, which predates Einstein. Second, the principle only states that velocity is essentially arbitrary - acceleration, which is the core phenomena at work in orbits, is not arbitrary.

If you set the Earth to be stationary and watched from an inertial frame on Earth, you'd see our planet accelerate away and orbit the barycentre of the solar system.

So heliocentrism is almost a de facto necessity.

 

[lesliedellow]

More directly, classical gravitation requires that the Earth go around the Sun.

No it doesn't. In principle gravitation could just as easily have the sun orbiting the Earth. The thing which settled the argument in favour of heliocentrism was that, with Newton's theory, it needed far less special pleading to explain the observable motion of the planets (relative to the Earth).

Prior to that, geocentrism still had supporters, including that of Newton's own university.

 

[Chesterton]

More directly, classical gravitation requires that the Earth go around the Sun.

No it doesn't.

I've heard astronomers say that the tip of my nose is as good as any other point to be the center of the universe. If all galaxies, all points in space, are receding from every other point, then geocentrism is as true as any other -centrism.

 

[Wiccan_Child]

I've heard astronomers say that the tip of my nose is as good as any other point to be the center of the universe. If all galaxies, all points in space, are receding from every other point, then geocentrism is as true as any other -centrism.

Well, the idea of an observation centre is valid, but it's unrelated to geocentrism (or rather, it's an issue geocentrists get muddled up). The observable universe is how much of the universe we can observe, limited as we are by the speed of light (anything so far away that its light hasn't reached us yet, is outside the observable universe). Every point is the 'centre' of the 'universe' in that sense, but this is more a mechanical conceit - if I stand on a hill, I am the centre of the circle of land that I can observe. If you stand on a hill, you are the centre of yours.

Wrt geocentrism, there are three core ideas:

• Big-G Geocentrism, where the Earth is fixed, unmoving, and non-rotating. The sun and stars orbit the Earth every day. Classically even the planets orbited the Earth, but nowadays I think the few strong geocentrists that are left accept that the planets orbit the sun.
• Little-g geocentrism, where the Earth rotates but is otherwise fixed. This has seen a minor resurgence because of relativity: because motion is relative and our choice of reference frame is arbitrary, they say, 'soft' geocentrism is as good a choice as heliocentrism.
• Heliocentrism, where the Earth and planets orbit the sun, and the sun orbits the galactic core, etc.

A non-rotating Earth is easy to disprove. The classic disproof is Foucault's pendulum, which was the final nail in the coffin of mainstream geocentrism. More recently, we are able to test a prediction of General Relativity: according to GR, rotating masses 'drag' spacetime around with them like a ballroom dancer twirling on a tablecloth (it gets caught in her heels and the whole thing drags and spins around with her). This Lense-Thirring effect would have a measurable effect on satellites, and we do indeed see it.

A rotating but non-moving Earth can also be disproven. While it's absolutely true that we can choose whatever inertial frame of reference we like, the fact is that the Earth is not an inertial frame of reference. It's inertia is not constant, it is being accelerated as it falls towards the sun.

If you state that the Earth has zero velocity when you start your stopwatch, that's fine. But as your stopwatch ticks on, you witness the Earth speed up - it moves. Specifically, it accelerates around the Earth-Sun barycentre (as does the Sun). So no matter what inertial reference frame you pick, the Earth always orbits the Sun (or more accurately, a point very close to the centre of the Sun).


(One could argue that, however inelegant, we could still pick a non-inertial frame and be done with it. The problem is this is demonstrably silly: it'd be like going on a merry-go-round and exclaiming that the entire universe is orbiting you, when quite obviously it's just you who's moving).


tl;dr: velocity is relative, acceleration is not. Whatever inertial frame you pick, the Earth orbits the Sun.

 

[Wiccan_Child]

No it doesn't. In principle gravitation could just as easily have the sun orbiting the Earth. The thing which settled the argument in favour of heliocentrism was that, with Newton's theory, it needed far less special pleading to explain the observable motion of the planets (relative to the Earth).

Prior to that, geocentrism still had supporters, including that of Newton's own university.

Not every consequence of a theory is known to its developers. I don't doubt that parsimony was one of the reasons people dropped geocentrism, but that doesn't mean it's the only one. Classical gravitation requires the Earth to accelerate around the barycentre of the Earth/Sun system. That Newton was unaware of this is irrelevant.

 

[TerranceL]

Wow this is thread 8 of this subject... how did I miss so many of the other ones? Last I knew it was on 4 then... BAM 8... I need to pay closer attention.

 

[Michael]

Wow this is thread 8 of this subject... how did I miss so many of the other ones? Last I knew it was on 4 then... BAM 8... I need to pay closer attention.

Ya, it's one of the most popular threads on this forum anyway. I like reading it too, but I usually just have to bite my tongue when it comes to some topics.

 

[Chesterton]

(One could argue that, however inelegant, we could still pick a non-inertial frame and be done with it. The problem is this is demonstrably silly: it'd be like going on a merry-go-round and exclaiming that the entire universe is orbiting you, when quite obviously it's just you who's moving).

Obvious to who?

 

[Michael]

Obvious to who?

I say you should stick to your guns. It turns out that if indeed you are the center of the universe, you can "explain away" the vast majority of the "mysteries of the universe".

 

[Michael]

A non-rotating Earth is easy to disprove. The classic disproof is Foucault's pendulum, which was the final nail in the coffin of mainstream geocentrism.

I used to *love* those things at the planetariums I visited as a kid.

 

[Elendur]

*Cough* Not to be more repetitive than I usually am, but if I could get some help with this problem I'd appreciate it (or let it die a horrible, horrible death) :
http://www.christianforums.com/t7648346-71/#post65156823

I'll link the notion of what I'm speaking:
Pole (complex analysis) - Wikipedia, the free encyclopedia

Again:
Integration over (a,b) in R, which is not an infinite interval, with simple poles on (a,b) and no singularities on {a,b}. Does that occur in physics as far as anyone here knows?

 

[Wiccan_Child]

*Cough* Not to be more repetitive than I usually am, but if I could get some help with this problem I'd appreciate it (or let it die a horrible, horrible death) :

Generally if I don't know the answer to something I tend to not reply - "I don't know" isn't a very interesting response . In any case, other people tend to reply... but I guess everyone's as stumped as me!

http://www.christianforums.com/t7648346-71/#post65156823

I'll link the notion of what I'm speaking:
Pole (complex analysis) - Wikipedia, the free encyclopedia

Again:
Integration over (a,b) in R, which is not an infinite interval, with simple poles on (a,b) and no singularities on {a,b}. Does that occur in physics as far as anyone here knows?

Not to my knowledge... but I feel there's an obvious answer that I'm not seeing. Black holes? Negative temperature/pressure? Maybe integrals across contours or manifolds in EM? Hmm...

 

[essentialsaltes]

I'm thinking about creating a separate thread for this but, I'll ask here first anyway:

Are there any practical (i.e. possibly within physics) applications of integration over a finite distance on the real line, where the function in question has simple poles (which can be represented as f(x) = g(x) * 1/(x-x_j), where x_j is a pole within that interval, not lying on the endpoints) within that interval?

Suppose there's an idealized point mass fixed in place (is this no longer practical?) somewhere along your interval.

You want to calculate the work done by gravity as another (test) mass moves from a to b through the point mass.

Work is the integral of F along the path.

Since gravity is an inverse square, F blows up when the test mass passes through the point mass.

You can use symmetry to eliminate the singularity and still get a sensible result. (Or even better, since gravity is a conservative force, the result is path independent, and you can write down the potential energy as a function and just take the difference in potential energy from points a and b.)

OK, now an inverse square is not a simple pole.

But if instead of a point mass, we have an infinite line of mass (is this impractical?), then the force goes as 1/r, and it's a simple pole.

If you add more infinite lines of mass, you can have multiple poles.