Q: How can electrons “jump” between places without covering the intervening distance?

Posted on August 12, 2010 by The Physicist

Physicist: Frequently in quantum mechanics you’ll find that particles are restricted to only a certain set of states or locations, and yet somehow they can move from one to the next. It’s like moving between islands without crossing any water.
“Classically” (19th century, pre-relativity, pre-quantum) this is impossible. If you see a particle in one place and then see it again, but in a new place, then of course it must have traversed the distance from one to the other.
But here’s the essential difference between quantum mechanics (correct) and classical physics (wrong): particles aren’t solid objects that have a genuine position, instead they’re waves that are “smeared out”.

A standing wave (like a guitar string, or an electron orbital) usually has “nodes” where the wave is always zero.

The string remains stationary in the middle, but the wave has no problem getting past that point. This image stolen, unrepentantly, from http://people.rit.edu/andpph/text-string-vibrations.html.

But of course there’s a big difference between the wave being zero at a node, and the wave being unable to get to the other side of that node. It’s the difference between the string in the above picture, and what you would have if you nailed that string to a piece of wood at the node and left the bottom half dangling.

For you calculus buffs out there, the difference is hidden away in the derivatives.

If you have a particle (wave) like this and you measure where it is many times you’ll find that it’s on the top about half the time, on the bottom about half the time, and never ever in the middle (ever).

The shape of the standing waves formed inside a microwave oven. The peaks and troughs move up and down, but the lines in between are stationary and zero. This is why microwaves have rotating plates, to keep food from sitting in the nodes (and staying cold) or from staying in the peak areas (and burning).

One of my personal fave examples of “large scale” quantum weirdness is microwave ovens.  A microwave oven creates a standing wave of photons with a “plus-shaped” (+) node, which leaves the center of the chamber especially cold.  The chance of finding a photon anywhere on the plus-shaped-node is zero.  So there are four different cells that it should be impossible for the microwave photons to move between, but they don’t seem to mind at all.  It’s not like particles exist or something.

So thinking of things like electrons as particles leads to incorrect conclusions.  Thinking of them as waves is really  the way to go.

Posted in -- By the Physicist, Physics, Quantum Theory | 20 Comments

Q: Why do we only see one rainbow at a time?

Posted on August 11, 2010 by The Physicist

Physicist: A rainbow is an angle-dependent illusion.  They don’t actually exist anywhere, they just appear to.  Since they can only exist at a particular angle (with respect to you and the Sun), you can never see them anywhere else in the sky.

All rainbows form a circle 84° across and exactly opposite from the Sun, no matter where you are.

The next time you see a rainbow, draw an imaginary line from the sun through you.  You’ll notice that this line goes exactly through the middle of the rainbow.  This comes about because of how rainbows are created.  No matter where you are, the red line is 138 degrees from the sun and the purple line is 140 degrees from the Sun.

For very small drops of water the surface tension overwhelms all other forces, and the drop is pulled into a nearly perfect sphere (which has nice optical properties).  When light encounters the surface of water (or anything at all really) it splits into its component colors.  As the light travels into the drop the various colors mostly end up getting scrambled so much that almost anywhere you look you’ll see a more or less even combination of them (white light).  However, light that enters the drop, reflects off the back, and leaves again at about 42° from the direction it came from produces colors that stay separated.

The path taken by light through a water drop with one reflection (upper left) and with two reflections (upper right). At 42° the light is not recombined into white light, and thus forms a rainbow. The recombined white light makes the sky under rainbows brighter than the sky above.

This happens again at around 52°, but this time the effect is caused by two reflections inside the water drop.  As a result of there being two reflection (instead of one), the colors in secondary rainbows are reversed compared to the primary rainbow at 42°.

Pretty rainbow, bright sky underneath, and reverse-color-order secondary rainbow above.

Entirely unimportant fun fact: the only way to see a complete, full circle, rainbow is to be flying (or falling).  Otherwise whatever you’re standing on will cast a shadow that will cut off the bottom of the circle.

Posted in -- By the Physicist, Physics | 27 Comments

Q: Why does putting spin on a ball change how it moves through the air?

Posted on August 8, 2010 by The Physicist

Physicist: This question is especially perplexing after a first year physics course, where every question starts with “ignoring air resistance…”. There are a couple of different way to approach the answer, but I like this one best.

Way back in the day a dude named D’Alembert came up with the unsurprisingly named “D’Alembert’s paradox” which essentially says that in air and water an object traveling at subsonic speeds experiences neither drag nor lift. That’s obviously not the case which is why this is “D’Alembert’s paradox” and not “D’Alembert’s well known fact”.
The resolution is to take into account vorticity and the rotation of air flow around the object in question.
Rotation of air allows the air to flow faster over the top or the bottom of the ball. But a funny thing happens when air moves quickly; the transverse air pressure (pressure to the sides) drops. This effect is called the Bernoulli effect or, in certain cases, the Venturi effect.

If you combine the flow of air rotating around a ball, with the flow of air past a ball, then the result is a faster flow past one side and a slower flow past the other side. In this example there is less pressure on the top than the bottom.

So how can you induce air to rotate around a ball in the air? Base balls, golf balls, and especially tennis balls are designed to have rough surfaces that grab the air a little bit. So if the ball spins as it moves it’ll drag the air around it a little, which leads to air rotating around the ball, which makes the air on one side move faster than the air on the other, which leads to a lower pressure on one side compared to the other, which creates a net force, which pushes the ball around.
So if you want the ball to curve downward you make it spin as though it were rolling away from you. If you want it to curve up (well… Stay in the air longer, no Human can make a ball actually curve upward in flight) you’d want the ball to spin as though it were rolling toward you.  And of course, you can also make the ball veer left or right using the corresponding spin.

Posted in -- By the Physicist, Physics | 19 Comments

Quantum mech, choices, and time travel too!

Posted on August 6, 2010 by The Physicist

Physicist: Recently I sent a series of emails back and forth with a reader that seem interesting enough to post. Conversations (near a chalkboard especially) are the best way to learn just about anything.

 

Q:
I wake up at 6am.
I brush my teeth get dressed and go downstairs.
I eat my breakfast at 7am and I’m just about to leave out the door.
when i notice there is an apple and an orange in a fruitbowl on a table next to me
at exactly 7:02am. I CHOOSE to take the apple.

I then make a choice whether I should choose to take my car or save gas and take the bus.
I CHOOSE to take the bus.

SUDDENLY. when i walk into the office, a strange event occurs and time starts moving backwards.
It goes back and back and back until finally it’s 6am in the morning and i wake up,
brush my teeth get dressed and go downstairs to eat my breakfast.

Here’s my tough quantum mechanics question for you,
at exactly 7:02am will I still choose to take the apple?

And if this process were repeated over and over and over again for about a million times. will the choice I make ALWAYS BE the apple?

 

A:
I’m working on a (to long) post about Bell’s theorem. The thought experiment you propose, about going back in time, is one of the better ways to understand it.

To actually answer your question: if choosing the apple is based on some quantum mechanical process in your brain (and there’s a good chance that at least some part of it is), then every time that choice is made the result is random. Time travel or not.
Part of the weirdness comes from the fact that every possible thing that can happen does. So (even when you time travel) some versions of you take the apple and some versions don’t.

 

Q:
Ok, remember how I took the bus in the thought experiment?

My question is, does quantum mechanics also apply in a reversal of time?

For instance, lets say that time started to slowly reverse.
Will I always get onto the bus backwards and head home.

OR.

will my car magically appear (even though i didn’t take it)
and will I backwards drive home in that?

So the concluding question is,
do quantum principles apply in a reversal of time as it does when time moves forwards?

 

A:
You’ll often hear “everything that can happen does” so if a particle can take two different paths it will actually take both.
If I understand your question correctly, the answer is yes. It turns out that “everything that could have happened did”. The “branching” goes both forward and backward in time. This is demonstrated by things like the “Franson experiment” that demonstrates the interference of a single photon with an earlier version of itself.
Driving a car, for example, will leave telltale signs that later make it impossible for you to have actually taken a bus. Chair fibers, leaving tire tracks, you’ll remember it, etc.
But if, in every way, you could have done either one, then you did both (no magically appearing cars).
This is actually the backbone of the Feynman path integral technique.

 

Q:
So are you telling me that just next to us, could exist a place where the Nazis won the second world war?
A place where there exists a flying spaghetti monster? (to quote richard dawkins)

Or even a place out there in a dimension somewhere where there exists an all knowing omnipresent, omnipotent, all encompassing being who “watches over us” etc..

 

A:
Sure. BUT, it’s impossible to interact with things that are even a little bit different. For example, a stream of identical photons (lasers) will all interact with each other strongly. You can see evidence of this in effects like speckling. Non-coherent (regular) light is made up of all kinds of different photons, and the best way to figure out how they’ll behave is to assume that they’ll ignore each other. This is sort of a metaphor, and sort of a concrete example.
So while, yes, there are almost certainly universes where the Nazis won, it doesn’t matter. It’ll never have any impact on our universe whatsoever.
A good rule of thumb is: if there is any conceivable way, whatsoever, for anything to tell the difference between universes, then they can’t interact (from the perspective of that thing that can tell the difference).

 

Q:
Couldn’t that then solve the entire God dilemma? I mean if in only one of these infinite dimensions there existed an all encompassing all knowing all powerful entity, wouldn’t this entity then transcend all dimensions? (since he is all encompassing)

 

A:
If you want to consider God, then it’s best not to do it in any kind of physics based context. That being said:
Remember that if two universes are even slightly dissimilar, they won’t interact at all. By “slightly dissimilar” I mean something like a single electron being conspicuously out of place.
So any existing Gods that follow the most basic laws of logic and quantum mechanics will be stuck in their native worlds.
If you’re not worried about Gods that follow physical laws, then, again, physics is literally the worst possible forum.
Also, you have to be careful with this kind of reasoning. You can make up just about anything and claim that it should exist in every version of the universe.
The rule “anything that can happen does” carries a bit more heft that it seems to at first. If something can’t happen, then it doesn’t happen in any version of the universe.
For example, spaghetti can neither fly nor think, so the FSM (pasta be upon him) can’t exist in any universe, no matter how much anyone dresses like a pirate.

Posted in -- By the Physicist, Philosophical, Physics, Quantum Theory | 6 Comments

Q: Why is the speed of light finite?

Posted on August 3, 2010 by The Physicist

Physicist: That is such a hard question.  Holy crap.

If you kept the laws of the universe the way they are, but ramped up the speed of light to infinity you’d end up with a surprising array of effects.  Newton would have been right about a lot more (nicely done, old dude), there would be no magnets of any kind, the amount of energy tied up in matter would also be infinite (E=MC2) so you’d have to be extra careful not to bring it near anti-matter, but not too careful because anti-particles probably wouldn’t exist (probably).  Also, all the weirdness of relativity would be out the window.

But, why is the speed of light finite?  I don’t know.  I think this is one of those culdesacs of science.  It is what it is.

The question, as it was originally asked, was about what keeps light from going any faster.  The answer to that question is that there is no faster.  If you shove a stone of mass X and it goes flying off at speed V, then if you shove a stone of mass X/2 it’ll fly off at speed 2V.  So, you might suspect that if you shove a stone of zero mass that it would go flying off at an infinite speed.

Well, that’s pretty much what photons (which have zero mass) do.  If you think of infinite speed as how fast you’d be going if you accelerated forever, then the speed of light is exactly that.  If you got into a rocket that could accelerate forever (using some kind magic fuel, such as the Schwartz), and you let it run for an eternity or two, then you’d be moving at the speed of light.

So it’s not that there’s anything slowing light down, so much as the laws of the universe are such that it doesn’t really make sense to talk about something moving faster.  More here:

Q: What’s it like when you travel at the speed of light?

Q: Why is the speed of light the fastest speed?  What makes light so special?

Also, if you’d like to find more “culdesacs of science” get yourself a toddler during their “Why?” phase, and try explaining something to them.

Posted in -- By the Physicist, Philosophical, Physics, Relativity | 25 Comments

Q: Why is the speed of light the fastest speed? Why is light so special?

Posted on August 3, 2010 by The Physicist

Physicist: The best way to think about it is; there is a speed (C) that is the fastest speed and, by the way, light goes that fast. There’s nothing special about light, it’s just a useful way of describing C (“the speed of light”). Photons are just another podunk massless particle, whipping around the universe as fast as fast can be.
Historically, the derivation of the strange properties of C (relativity) relies on a pretty straight forward piece of Einsteinian logic, based in part on an understanding of light.

1) All the laws of physics work the same, whether you’re moving or not. There is no experiment that can tell you whether or not you’re moving.

2) Light is an electromagnetic wave, and the velocity of these waves can be derived from Maxwell’s laws.

3) Maxwell’s laws, like all physical laws, are independent of how fast you’re moving. So the speed of light must also be independent of how fast you’re moving.

4) So, there exists a speed (the speed that light travels at) that is the same to everyone, no matter how fast they themselves are moving. Holy crap! There’s your special relativity!

So when you see equations like E=MC^2 (“energy equals mass times the speed of light squared”), you may ask yourself “what in the hell does light have to do with how much energy is stored in the mass of an object?” Well, the answer is it doesn’t. C is just a speed, and E=MC^2 and all the other equations with C would stay the same even if light didn’t exist at all.

So why is C the fastest speed? A good way to think of it is to first ask; how do you know when you’re moving faster than something else? If you’re driving down the highway and you’re moving faster than the car in front of you, then eventually you’ll pass that car. However, C is the same to everyone, no matter what. So, say a photon goes past you, and you try to catch up. But no matter how much you speed up, the photon will always be moving away at the speed of light. You can never catch up (or even come close to starting to catch up). So, regardless of perspective, the photon is always moving faster than you.
Some of this may seem seem contradictory, but surprisingly, it’s all self consistent. Very surprisingly.

Posted in -- By the Physicist, Physics, Relativity | 54 Comments