Quantum Physics

Plutonium would be dandy! As I understood it, most kids traded bucky for cigarettes. But you had to be different...

I was willfully misled, I mistakenly traded buckie for American comics, and as a result was under the impression that sleeping with a rod of plutonium would embue me with super powers, it sort of worked, I became extremely crabbit.

Can you use it to heat your coffee in the morning?

What's coffee?

halfwise wrote:David has it right, particles are just ripples on the surface, which makes their ability to appear less mysterious; but of course ripples require energy.

The uncertainty principle allows fluctuations of energy within a short time; the larger the energy the shorter the time. So things really can appear out of nowhere so long as they vanish again shortly. To conserve charge and other quantum numbers they appears as matter-antimatter pairs, and typically annihilate each other soon after (but since they came from nothing they don't emit a flash of energy when they 'annihilate'). This popping of things in and out of existence is called the vacuum energy. It has been measured and is very real. Think of waves happening and then canceling themselves out.

I was going to make a pun about vacuums but it sucked.

talk about sucking...wheres Petty?

Probably with Yooper.

Mrs Figg wrote:talk about sucking...wheres Petty?

halfwise wrote:Probably with Yooper.

so.. sucking with Yooper?

Norc.....

NORC!!!

what?

I only suck buckie, through a straw, or out a hole in the barrel, or from the carpet when I spill it. Although there was that one time I spilled it on the cat.....

wot if you spilled it on a builders bum?

Is this a fantasy of yours, Figgy?

((Halfy can read my mind???)))) I reckon its that pesky Hobbit film give im ideas, he'll be beaming up next.

Quantum Interlude: the Infinity Improbability Drive

I was originally planning to add to the previous installment the most important refinement to Quantum Mechanics since it’s creation, done primarily by Richard Feynman in the 1940’s, but decided folks already had enough to absorb. It’s been a long while now, so I think it’s time to stretch people’s minds just a bit more.

Everything I present here can be found in the little book called “QED: the strange theory of light and matter” which was based on a series of 4 lectures Feyman gave to the general public. QED stands for Quantum Electro-Dynamics, and is known as the most successful theory in the history of physics. Quantum Chromo-Dynamics, the theory of quarks and the Standard Model, was based on it, so a basic understanding of QED will provide a glimpse of our deepest understanding of how the universe appears to operate (at least until something better comes along! I should point out that true scientific theories are rarely trashed, for they are firmly based on observations that worked very well within their domain. Even though quantum mechanics ‘superseded’ Newtonian mechanics, the basic F=MA will continue to be used until the end of time because it works beautifully in the domain of everyday life.)

Our story goes clear back to 1657 when the mathematician Pierre de Fermat (of the famous last theorem) had a realization about optics. We are all familiar with the idea that light moves in straight lines, but when it goes from one medium to another (such as air to water) it tends to change direction. Fermat realized that the path light takes from one point to another is the one that takes the shortest possible time. If the speed of light is constant, this would always be a straight line – but light travels slower in water (or glass) than in air. Let’s assume light is to travel from point A to point B in the figure below, taking one of several possible paths:



According to time honored instructional tradition, it’s helpful to think of point A as being the location of a lifeguard on the beach, and point B being the location of a swimmer apparently occupied in the diversion of drowning. Which route should the lifeguard take? Path 1 goes directly from point A to B by the least distance, but we must remember that our doughty lifeguard can sprint across the sand (moving through air in our example), but must swim through the water. If instead path 2 is taken, a slightly greater amount of time spent running would cause a reduction in the amount of time swimming, and it may be shorter in time if not in distance. If path 3 is taken, so much more time may be spent running that it can’t make up for the reduction of time swimming. Clearly the best path must depend on knowing the speeds in water and air, and finding the best overall solution. If the speeds in air and water were the same, the straight line solution of path 1 is the answer; if swimming through water is like swimming through molasses, you want to do everything possible to minimize the distance in water and path 3 would be best. Typically the best solution is in between.

But light is not a lifeguard, and this fact brings up two questions:
1. Why should light take the path that minimizes the time?
2. The lifeguard can survey the entire situation from beginning to end, and therefore choose the best overall path. But light is inanimate: without being aware of the situation in distant locations, how can it choose the correct path to minimize time?

Fortunately these two questions have the same answer, and it comes down to light being a wave (or a particle that conforms to the behavior of waves). Let’s see how.

Recall that light is brightest at a point when all beams of light that converge at that point arrive in phase: with the crests and troughs close to alignment. As light waves travel from one substance to another, the speed may change, the wavelength may change, but the frequency must stay the same because that tells you what the source of the light was doing. In the classical picture a vibrating electron would create waves in the electric field that spread out from the point of vibration, and any place or any time the waves go past, it carries the information about how fast that electron vibrated.

So if the frequency of oscillation of all waves emanating from point A stays the same throughout their journey, then if two waves travelling different paths take the same amount of time, the waves and crests will still line up when they come back together at point B. If we make a graph of the times taken by all possible paths between A and B, it will look something like this:



We see a constantlly varying set of paths going from A to B. Path 2 is the shortest time taken. Now here’s the interesting thing, and it’s a general property of minimization in mathematics: if you look at paths near path 2, the differences in the amount of time between paths is smaller than around paths 1 or 3. This is because the time curve (actually any curve) must flatten out near the minimum. So the bundle of paths near path 2 will be more in phase and less likely to cancel out than the bundle of paths near paths 1 or 3.

So this is a local method to find the shortest path: if you are a ray of light, and rays of light traveling close to your path stay in phase with you, you will survive to the target. If rays of light traveling close to you begin to go out of phase, you will cancel out and will not make it to the target.

There’s something mind boggling built into the last statement: light doesn’t take just one path from one point to another, it must sample all possible paths, and we only observe those that don’t cancel out. This may sound like baloney, but there’s a kind of logical proof to it based on thinking about the double slit experiment and waves. Remember that when a wave goes through a slit, it spreads out. This means that you can make light do all sorts of crazy things just by placing slits in different arrangements.

Let’s start by reminding ourselves of the difference between a single slit and a double slit. With a single slit we just see the wave spreading out. With a double slit the two waves spread out, then interfere with each other to make the characteristic interference pattern. In the diagram below, the intensities of the waves (the difference between trough and crest) is shown on the right. If the intensities of two slits just added we’d get a hump, but since they interfere, we get fringes.



So by opening the second slit, some parts get darker than they would be if only one slit was open, while of course other parts get brighter. It’s not simple addition because of the wave nature.

Now let’s split the source light as before, but this time put in a series of slits and blockades. One beam will go straight through as before, but the other beam we’ll lead on a merry chase taking advantage of the fact that when going through a slit the light spreads. To clarify the picture I leave out the wave drawings.



So we see the green beam of light doing what we expect it to do: follows a straight line from the source to the top slit, and when the light spreads out on passing through the slit we choose the path that ends up at point P. But the red beam is led on a merry chase through several slits, changing direction each time. We begin to get the idea that light perhaps doesn’t have to travel in a straight line, for we can continue to add slits until we get a continuously curving path. If we go crazy with the number of slits (and drop them from the diagram for clarity), we may get the following:



The blue lines show our old idea of how light travels; the orange line shows what we now see light is capable of. It was Richard Feynman’s insight in the late 1940’s that instead of thinking of all the slits in the previous figure as causing normally straight light to spread out and change direction, that instead light was always doing this; in fact doing every possible thing it could at all times; the slits only had the effect of limiting what was possible so that we saw one particular path.

If this is true, why do we normally see the blue rays of light and not the endless variations of orange ones? If we go back to our lifeguard, he has an infinite variety of possibilities, but only the paths closest to the least amount of time work best. Other paths may happen but cancel themselves out in general. But if you put up roadblocks to prevent the lifeguard from running the straightest path, only then will you see him running more circuitous paths.

But does light actually take these other paths? Well it turns out that if you take very careful measurements of something like the double slit experiment, it turns out that if you make the straight path assumption for light, it’s almost exactly right, but not quite. Feynman found that by adding in contributions of all the other possible paths, paths which almost completely are cancelled out by other strange paths, you get an answer which agrees better with very finely done experiments. Light really does take all possible paths, no matter how crazy!

It is of course impossible to calculate all the crazy possibilities, but physics is saved by the fact that the further away a light path is from going in a straight line, the more likely it is to be cancelled out by paths that are also not in a straight line. So what you do it first add paths that are slightly out of a straight line, and your accuracy improves at the cost of some extra calculation. Then if you need more accuracy, you add in contributions from paths are slightly more out of a straight line, etc.

His genius was in finding ways to do these calculations and keep track of them. Other physicists, Julian Schwinger and Itiro Tomonaga came up with similar results by tweaking standard approaches to quantum mechanics, but it was Richard Feynman who provided the ‘sum over all histories’ approach that was a whole different conceptual model for how the universe worked. For this he is considered the true father of what is now known as Quantum Electrodynamics, or QED. It remains the most precise theory in physics, but comes with considerable imaginative cost.

For his theory requires that anything that can happen, must happen, if the calculations are to be believed. So far the only way we have been able to improve precision is to add yet wilder and wilder paths to our calculations, so his vision carries weight.

And so we come to the infinite improbability drive: a spaceship that travels by doing everything possible at once, then selecting one of the possibilities. It’s not just a figment of Douglas Adam’s imagination, it’s a great complement to his intellect that he did indeed grasp the essence of the theory well enough to have fun with it.

Excellent explanation Hlfy that actualy makes sme sor tof sense to me! Given my buckie brain a testiment to your grasp of your subject and ability to convey it.

"And so we come to the infinite improbability drive: a spaceship that travels by doing everything possible at once, then selecting one of the possibilities."

All very well but what happens when whole planets start turning into banana fruitcakes?

Feynman never actually got beyond photons going in loops and changing into electrons and back into photons again. I think he'd have to do raisins before reaching fruitcakes. Unfortunately he died before he even reached the sesame seed level. Others are carrying on his work but I suspect that ever since the advent of nouvelle cuisine a sense of despair has permeated the enterprise.

molecular gastronomy has raised some hopes, though.

Apparently the scope for scientific scrutiny in cooking is pretty deep.

Bistromathmatics.

Dave must know something about it.