stupid physics questions

[pogo]

I think the scientist in that discussion wins, as his arguments make good scientific sense. That we don't have experiments that can test string theory does not make it an invalid theory. People theorised that Black Holes exist long before they were detected in space. Much of modern science is like that. We no longer rely on doing experiment after experiment until we chance on an interesting result. We work it out theoretically, and then look for ways to apply it or test it.

[zip accident]

I think the scientist in that discussion wins, as his arguments make good scientific sense.

I thought on first reading that they are both being touted as scientists, just one of them anti-string theory. On second reading, maybe not.

That we don't have experiments that can test string theory does not make it an invalid theory.

That we currently don't, sure. If, however, it were proven that it is impossible to test string theory experimentally, that would be entirely different.

[Darkflame]

If you can't and haven't tested something, its a hypothesis surely?

[gilesgoat]

Suppose you have a 5mm diameter led that generates a beam of light with 15 degrees divergence.

Suppose you want to make it do the tinyest possible ( or let's even say a specified diameter ) light dot at a certain ( pretty short , 1 cm or so ) distance D.

What do you need ?

Do you need a lens at all cost or could it be done with just a tiny hole in something ?

[pogo]

A simple convex lens would work. It would have to be very small for what you're trying to do but placed between the LED and dot it should work. Not sure where you'd find something so small: disassemble an iPhone camera?

You'd run into two problems that I can think. First the LED itself isn't a point source; the source is a chip usually, a mm or so across. So that's the smallest dot you will get it with the simplest set up. There are ways around this but they need more lenses and/or more space.

Second different colours refract differently, so you might see coloured fringes at the edges. Normally this would not matter but if you try and make it as small as possible then the size of these fringes will be a limiting factor. Unless it's a monochromatic LED. Again this can be fixed with multiple lenses but that would be hard to do in the space you have.

[gilesgoat]

A simple convex lens would work. It would have to be very small for what you're trying to do but placed between the LED and dot it should work. Not sure where you'd find something so small: disassemble an iPhone camera?

You'd run into two problems that I can think. First the LED itself isn't a point source; the source is a chip usually, a mm or so across. So that's the smallest dot you will get it with the simplest set up. There are ways around this but they need more lenses and/or more space.

Second different colours refract differently, so you might see coloured fringes at the edges. Normally this would not matter but if you try and make it as small as possible then the size of these fringes will be a limiting factor. Unless it's a monochromatic LED. Again this can be fixed with multiple lenses but that would be hard to do in the space you have.

Let's say the led is nearly monochrome so Aberration is not a problem.

Let's say the lens I find has a focal distance of 30mm, does it means, in theory, the led should be positioned 30 mm away from the lens and the dot will appear 30mm the other side or what ?

[zip accident]

The problems will include spherical aberation, the refractive index of the air-lens interface (or the LED-lens interface), and the short distance between the LED and the target.

I forget how the focal length of a lens is defined, I suspect it's not obvious.

Well according to Wikipedia, it sort of is the obvious, but also not:

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

The problem with a 1cm focal length from a 0.5cm diameter lens is that the lens will be considerably thick, which means spherical aberation will be strongly present.

If all you care about is a small spot of light, and the brightness isn't important, a pinhole or something like it may be a simpler approach.

[pogo]

The focal length is the distance of the focus for a source at infinity. To focus a point source at another point you need to place both twice as far away, so 60mm on either side. More generally the distances satisfy

1/a + 1/b = 1/f

where a and b are the distances and f the focal length. It's easy to show that a + b is minimised when a = b. Having a and b different though lets you make the image differently sized than the source, so may be useful if you want it as small as possible, and have some space to play with.

[gilesgoat]

"Bathtub meditation".

I was thinking .. "what makes the water come to the first floor ?" .. well pressure of course ..

But HOW MUCH pressure and how far can it go ?

If the house would have 10 floors instead of 1, would there be enough pressure so the 10th floor will get water or
something should be needed to increase it ?

Then again "how many floors are you guaranteed you'll reach water without any extra aid ?" and then ? What do you do ?

Add pumps to lift a "water reservoir" after each X floors ? Increase pressure in the water ? Special tubing needed ?

How the heck they do that ?

[pogo]

Generally you use water tanks. Most homes have one to feed the hot water supply at a constant pressure. In communal and/or tall buildings you can have one for the whole building, on the roof where it's not in the way.

Gravity will only raise water as high as where the tank/reservoir it's feeding is. So I would think pumps are needed even when you don't have tall buildings just to get it into homes, especially where there's not enough elevated land nearby. The water company probably only guarantees it will go up a few stories, after which you'll need a pump in the building. Otherwise there would be lots of extra pressure for no purpose for most customers, in some cases so much it might be damaging.

[zip accident]

"Bathtub meditation".

I was thinking .. "what makes the water come to the first floor ?" .. well pressure of course ..

But HOW MUCH pressure and how far can it go ?

If the house would have 10 floors instead of 1, would there be enough pressure so the 10th floor will get water or
something should be needed to increase it ?

Then again "how many floors are you guaranteed you'll reach water without any extra aid ?" and then ? What do you do ?

Add pumps to lift a "water reservoir" after each X floors ? Increase pressure in the water ? Special tubing needed ?

How the heck they do that ?

Yes it's pressure. The pressure at the bottom has to rise as the height increases. What you can't do, is pull it up from the top. Air pressure is about 15 psi, which gets water about 30 feet up (36 feet? (Wikipedia says 34 feet)), but only pushes mercury about 30 inches because mercury is much heavier per unit length. After that, you get a vacuum (or actually pure vapour of the liquid at pretty low pressure) at the top.

http://en.wikipedia.org/wiki/Suction

[Orava]

And for really tall buildings you have to do it in stages.

Extreme plumbing: Pumping water up the Shard

[gilesgoat]

This comes from a Mafalda comic strip, I call it "Miguelito's theorem", the strip in question
Is a bit surreal/metaphysics with some poetry in it.

But let's go back to the "theorem" we could say it states :

"There are more stars of what we need them for." - Miguelito

The comic part of the strip continues with Mafalda asking "and what do we need them for ?" leaving Miguelito stunned with no answer staring all night at the sky again.

However I was thinking "there could be something in this" , I was thinkng "could we say that if we need a number of something , we probably mean that we need a countable number of something ?"

In that case I think we could say that Miguelito's theorem states that the set of stars is a non countable set, thefore as we have only naturals, rationals and irrational numbers the cardinality of the stars set must be the same of irrationals.

Now the question is : can really exists a set of something that does exist in the real physical world that has the same cardinality of the irrational numbers ? I.e. cannot be counted no matter what ?

Or not ? Or everything in the real world must have cardinality of naturals ?

[pogo]

Current thinking is the universe, so everything in it, is finite, and so not countably or uncountably infinite. It's also unimaginably vast and old, and if you try and write down how big it is in metres, kilograms or seconds you end up with a number with so many zeroes that it's incomprehensible. But it is a number, not infinity.

On the other hand the standard model of physics says there's a limit on how small things can be. This time you're dealing with unimaginably small things, but because there's a limit you can't get an infinite number by subdividing forever. You have to stop and so only ever generate a finite number of pieces.

The biggest calculable number? The number of atoms in the universe perhaps, about 10^80. As they are mostly hydrogen it's also about the number of protons or electrons. There may be more of other things (neutrinos, photons, whatever makes up dark matter or dark energy) but we have little idea how many of them there are.

[Dvorak]

Or not ? Or everything in the real world must have cardinality of naturals ?

It was in one of the first physics lectures at uni (not that I had many of them), when my prof talked about the fundamental forces.
He came to Gravity and said:

"After all we know, the range of Gravity is..."
He hesitated.

"...unlimited", I completed in my mind.

"...quite large", he finished his sentence.

I'll never forget that.