Some electrons are Best Friends Forever
Susan J Feingold D.Sc.
Technion, Haifa Israel
For David H. who likes a scientific gambol now
1) A little Quantum Mechanics background music please!
Quantum Mechanics (hereafter referred to as QM) has often been called the most mysterious part of modern science. Even Nobel Laureates of the QM world admit that they do not really understand it in the way that physics was understood before QM was formulated in the first decades of the 20-th century. Gone was the determinism that used to be synonymous with the laws of physics. Probability is the field of mathematics used in QM.
It is true that probability is also used in such fields as Statistical Mechanics, the study of fluids and gases in which large numbers of molecules are involved. In Statistical Mechanics we assume that if you could follow each molecule of a gas, for example, it would behave deterministically. Whereas in QM, probability is basic to describing the behavior of the sub-atomic particles. (Please always keep in mind that sub-atomic particles like the electron are much, much smaller than molecules of a gas.)
The Uncertainty Principle
The best-known blow to determinism in QM comes from the uncertainty principle. In 1927, Heisenberg proposed that you can not determine the position and momentum (speed will do for this article) of a particle at the same time with any precision you wish. Instead he stated that the closer you know a particle’s position, the less you now about its speed and vice-versa. He viewed this as a fundamental property of QM and experiments have confirmed that this unusual idea is correct.
The Wave function
In QM, the complete evolution through space and time of a particle or system of particles is given by a “descriptor”. This descriptor is the solution of an equation proposed by Erwin Schrödinger 1926. Using this solution, an electron’s progress though space and time is described in terms of the evolution of a wave. You can imagine a particle-wave as similar to the one produced by throwing a pebble into a pond! You can see how the waves produced by the pebble move across the pond. The Schrodinger wave is our representation of the electron, as if we had a Schrodinger photograph of it. We conclude that every electron has its own Schrodinger wave representation. So instead of imagining electrons to be tiny little balls going through space and time, we can think of them as wavlets rippling their way through space and time.
2) GOD PLAYING DICE?
Most of us expect science to back up his/her gut feelings about how the world works. Einstein was no different from the rest of us in this matter.
He famously said – “God does not play dice”. What he meant was that, if it seems that God IS playing dice, (because sub-atomic particles are described in probabilistic terms) – this is only because QM is not “complete”.*
Einstein was sure that if QM were what he considered “complete”, then determinism would be restored to its rightful place in the laws of physics and the dice could be put away.
To prove his point, Einstein and two colleagues Podolsky and Rosen proposed an ingenious quantum mechanical ”thought” experiment, which led to a paradox referred to as the EPR paradox. The paradox was that in certain circumstances, information could be conveyed instantaneously, faster than the speed of light!
Impossible. Nothing can travel faster than the speed of light. That’s the result of Einstein’s theory of special relativity, which was not being called into question.
The EPR experiment involved pairs of particles that had interacted for some interval of time in some area of space. Through their interaction they became correlated.
This means that the quantum states of the two particles are re-defined by their interaction. Their states can no longer be decomposed into two separate wave functions.
When decomposition is not possible the particles are considered to be “entangled”. Their separate wave functions are replaced by a single wave function describing BOTH OF THEM.
After E, P and R posed their paradox, some physicists searched for a way to make QM “complete” in Einstein’s sense of the word. There was a search to find hidden variables – hidden because no one had ever encountered them – that would permit QM to become a deterministic science equivalent to Statistical Mechanics in its use of probability. But the results obtained were very complicated and did not solve the paradox to most people’s satisfaction.**
3) Bell’s Inequality
It wasn’t until 1964, that John Bell proposed a satisfactory reply to the 1935 idea. ***
Bell had the inspiration to define an equation that tested whether or not QM experimental results could ever follow Statistical Mechanics probabilities – those describing electrons as a great many little balls as you may remember. He defined a mathematical test one could apply to the probabilities describing QM experiments and compare them with SM probabilities.
The most important point of his reply was that he provided a mathematical equation showing that Quantum Mechanical probabilities and Statistical Mechanical probabilities are not only different, but that THIS DIFFERENCE CAN NEVER DISAPPEAR.
3.1 Instant Information Example – Bertlmann’s Socks
It is important to remember that the EPR paradox happens to pairs of particles that have interacted. In other words there are certain conditions have to be met in order to receive instantaneous information.
Bell gave a humorous example from every day life that explains how obtaining instant information is possible – given certain conditions. He gave the example of Bertmann, the absent minded and decidedly eccentric professor:
Bertlmann was an eccentric gentleman who wore pink socks and white socks. He never wore two socks of the same color. Whatever color he had on a given foot on a given day is unpredictable. However, if his left foot is in a pink sock, you know already that his right foot is NOT in a pink sock. Observation of the first sock and experience of Bertlmann’s habits give immediate information about the second sock. You could quite easily find out about correlated electron spins in the same way.
[forgive the French, but pink and not pink are in]
Today entanglement has been applied to fields many fields. Breaking extremely difficult codes is just one of them. The most exciting application of entanglement is in quantum computers. That deserves an article in itself. Many believe that they will be the computers of the future.
However, entanglement between a pair of particles is a very delicate thing and is easily destroyed. Currently, many scientists are working on making entanglement less fragile and, thus, easier to apply.
* A. Einstein, N. Rosen and B. Podolsky “Can Quantum-Mechanical Description of Physical Reality be Considered Complete” Phys. Rev. 47, 777 (1935)
**The hidden variable search was only definitely over when Prof. Alain Aspect did an ACTUAL experiment in 1976* which replicated the EPR thought experiment in a laboratory. No hidden variables were found.
Aspect, A. Phys Rev D 14, 1944 (1976)
*** Bell 1964
On the Einstein Podolsky Rosen Paradox
Physics Vol. 1, number 3, pp. 195-200, (1964)
John Bell: 1928 – 1990
He worked almost exclusively on theoretical particle physics but found time to pursue a major avocation, investigating the foundations of quantum theory. The result of this ‘hobby’ was his famous Inequality.
Six hours early
Susan J Feingold D.Sc
Technion – Haifa, Israel
If you are in high school you no doubt know the answer to this easy question:
A and B travel from C to D.
A and B start out from C at the same time, at the same speed. .
Which of them will get to D first?
That’s easy you say. Of course they’ll get there at the same time, anybody knows that. Well, what if I told you about an A and a B starting out from a C at the same time and at the same speed, and that one of them got to D six hours earlier than B. Before you ask me whether I failed algebra, I’ll tell you about a special A and B and a special C. D is simple. It’s down a mine shaft somewhere.
C is in outer space
I guess you’ve figured out by now that we are not talking about garden variety A’s, B’s or C’s. So I’ll have to tell you about the ones I have in mind, one at a time. I’ll start with C.
A supernova called SN1987A
The special place, C, where A and B start from is a supernova (SN) which exploded in 1987, called not surprisingly SN1987A. As you probably have heard, a supernova is a star which has exploded in a major way. 1A Supernovas are very interesting to astrophysicists because we know just how bright they are. That’s because they all blow up in the same way. For instance, if you took 100 sticks of dynamite and blew them up, and compared the explosion to another 100 sticks of dynamite someone else blew up, you’d expect the explosions to be the same. And that’s the way it is with 1A supernovas. If one of them looks dimmer than another, we conclude that it must be further away. If we know the distance to a close one, we can figure out how far away the dim ones are. Cool? Well, you have to do things like that in astronomy. You can’t exactly use a ruler. In fact it takes 160,000 years for light to get from SN1987A to the earth. That is so amazing because it means that what we saw in 1987 happened 160,000 years ago. If you want to time travel (unfortunately only backwards), just look up at the sky.
A and B – Particles with (just about) no mass
Mass is what gravity pulls on to give something weight. You, an iron ball, a feather, whatever. With the same mass you’d weigh more on Jupiter and less on Mercury.
When I went to high school atoms were very easy to understand. They were made of electrons, protons and neutrons. Since then life on the sub-atomic level has become more complicated. New particles have sprung up like mushrooms – well, a lot more have been discovered. These days, there is a branch of physics that just deals with particles. In fact particle physicists are even predicting particles which no one has ever seen.
Well we’re not going to go on The Great Particle Hunt. We’re going to concentrate on two particles, A and B, remember them? Which started out from supernova C and one of them got to D (earth), SIX HOURS EARLY!
A is a photon and B is a neutrino. Here’s what you need to know about them to understand to understand why there was a six hour difference in arrival time.
A neutrino was the first “I can’t see them but they’re there” particles. It was needed to conserve energy. Energy conservation is very important! Without it, the world would not be the world. Well not the world we are used to. Physicists get dewy-eyed when they think of how nice it is that energy is conserved. In addition, they get down right nervous if they think it might not be. So maybe it’s no big surprise that they feel obliged to do something about conserving energy, if at all possible. In 1930, Wolfgang Pauli, an Austrian physicist, predicted that there would have to be a neutrino to conserve energy in a reaction called beta decay. Whew, we saved energy conservation. But you have to go underground with lots of equipment to actually see a neutrino.
Why they are so hard to see
For starters, neutrinos have no mass to speak of*, and no charge like the electron and the proton. Neutrons have no charge either, but they feel ‘atomic strong’ forces. Neutrinos don’t feel that strong force. So they don’t interact with basic atomic particles. And that’s what everything is made of! They could go straight through you, and the entire earth for that matter. We detect neutrinos underground because we want to be sure that we are not seeing any other particle. All other particles would be stopped by the vast amount of material covering the underground detector.
* The neutrino does have a mass but it is extremely small – 100 million times smaller than the mass of the electron.
In the 19-th century light was shown to be made up of waves, which were reflected from mirrors and could be focused through lenses. The waves carried energy. The shorter the waves, the higher the energy. X-rays and radio waves and spot lights in a disco are all light rays. X-rays are shorter than the visible. Radio waves are longer.
Then in the early 20-th century an amazing property of light was discovered. Sometimes light acts like a wave, and sometimes it acts like a particle! The name given to the light particle is the photon. Charged particles interact by exchanging photons! So unlike neutrinos, photons are particles which interact with other particles.
Now we are getting to the important difference between photons and neutrinos. One of them interacts with other particles and the other doesn’t.
Photons and Neutrinos and Star Structure
Let’s assume that neutrinos and photons move at the same speed, the speed of light. If we don’t assume this we can stop right here!
When a star explodes into a supernova, it gives off photons and neutrinos. Now we are back to the old problem, A and B leave C at the same time and the same speed and reach D, but not at the same time. How can this be explained? Well it has to do with two factors, one of which I haven’t gone into yet.
1) The structure of the star.
You can consider the star as having two parts, outer and inner. The inner part is called the core which is very dense, where all the star’s energy is produced. The outer part or envelope consists of less dense gas. In a supernova explosion, the neutrinos come from the envelope, while the photons come from the core. Ah, you say, A and B both come from C, but their C is not EXACTLY the same place. Now we are getting somewhere. Not only is the core different from the envelope, it emits photons perhaps not at the same time as the envelope emits the neutrinos. So being emitted from the envelope versus being emitted by the core (which happens only when the envelope is blown away) makes for a difference in starting time, even though to get to us, they both have to travel 160,000 years!
2) Particle Interaction
We have to take into account that the photons in the core are being delayed in their progress outwards towards the earth, by their interactions with charged particles which are also to be found in the core. So instead of going straight out, their path may be similar that that of a drunk walking in a street filled with debris, knocking in to this and that while going forward. Even in space there are a few charged particles with which our photon will interact, zig zagging it’s path some more.
The little neutrino has no such problems. It just goes! It goes through space and doesn’t interact with the particles there any more than it interacts with the atoms in a rock or an ice cream soda.
Prof. Michael Longo of Michigan University* has done the calculation of the difference between the velocity of light versus the velocity of the SN1987A neutrino using all the big guns of general relativity. And he finds that the difference in velocities (divided by the speed of light) is less than 0.000000002 which is as close to zero as you can get. So my conclusion is that photons and neutrinos go at the same speed. Only the difference lies in the physics – that is, what actually happens in a supernova explosion, and what happens when the two particles do or don’t interact with the matter around them. This accounts for one of them being SIX HOURS EARLY.
*Longo, Michael J, in 1988 Physical Review Letters, volume 60 pages 173-175
The effects of General Relativity on Photons and Neutrinos
You may be surprised to know that gravity bends empty space. Einstein proposed this in his General Relativity Theory in 1916. General relativity is really hard to explain and has super hard mathematics. Even Einstein had to beef up his math to do it.
Simply, we can understand from it that space is not a smooth road. Space has ‘pot holes’ or distortions that are produced by the gravitation pull of stars and galaxies. So the neutrinos and the photons having the same speed also means that they go through the same pot holes on their way to earth.
A couple of good presentations on Neutrinos for high school students from PARTICLE 2005 at the University of Rochester
2) Neutrino detection
3) The Cambridge MINOS GROUP home page – a well known group doing Neutrino Physics
Most textbooks including modern physics will have a section on photons.
My first pop-science article published in November 2011
THE DOG DID_DID NOT EAT MY HOMEWORK
Wouldn’t it be great if there were two worlds, one in which the dog ate your homework, and one in which your best friend told you so much about the homework topic that you could do could do it yourself and still have time for your favorite video game. Astronomers and other scientists say maybe there are. Can you choose which one you like better? Read on to find out!
About Electronics and Electrons
Everybody knows that electronics are used in every fun thing that we have, from video games to smartphones. And electronics, put simply, is a way of making electrons do their thing for us. Agreeable little creatures aren’t they. Of course they’re really not creatures; they are parts of atoms and are so small no one can see them. Except scientists who have found a clever way of getting them to leave tracks in a “lets look at electrons” machine.
Now let me blow your mind. You could do an experiment in which electrons would go up or down in a magnetic field. But no one could say which way a particular one went! Maybe they’re uncertain till they actually get to where they’re going!Uncertain electrons
The up and down experiment might look something like this.
More than One Universe
Some scientists say that if a certain electron goes up in this universe, there is another universe in which the electron goes down! Like the ones in which the dog (or did not) eat your homework. There might also be two universes created when you get to a traffic light in your car – In one of those universes, the light is red and in the other one it is green. Universes upon universes. Like WOW.
But there is a problem. Each universe splits into other universes. And they keep dividing forever! So you can’t know what’s in store for you if you pick the universe you’d like for your homework. It may turn out to be a universe where you get stuck in traffic for eight hours on a highway. But hey, if the scientists could figure out how to get from one universe to another, you could get out of the traffic jam too.
Unfortunately, no one has figured out how to get from one universe to another. If you become a scientist maybe you could solve it some day. But it’s only fair to mention that, at the moment, scientists agree that it’s not really possible to get to any other universe. Well, maybe by going through a black hole. But that’s another story.
Then again, two hundred years ago no one knew about electrons and certainly not electronics. So who’s to say what the future will bring?
And so . . . .
There might be multiple universes, whether we can get to them or not!
Whoever said that science is dull.
HOW THE UNIVERSE LOST ITS WRINKLES
Susan J Feingold D. Sc.
Technion – Haifa, Israel
THINKING ABOUT THE UNIVERSE
One of the most important things to know about the universe is a fact that I am not going to explain:
I HEREBY STATE THAT THE UNIVERSE IS EXPANDING AND THAT I AM NOT GOING TO GO INTO THAT SUBJECT JUST NOW.
PLEASE DIRECT ANY QUESTIONS ABOUT THAT TO
You can think of the universe as a balloon with black dots on it. As you blow up the balloon, the dots get further away from each other.
The universe is like a balloon speckled with dots, BUT the space the inside the balloon is also speckled with dots. Like layers upon layers of little balloons each inside the next bigger one.
Let’s put ourselves at the center of all of the balloons. The dots on the outside balloon are getting pulled farther from us faster, than the dots near to the center.
THE RED SHIFT
The red shift is what happens to light that is moving away from you. If the dots on your balloon are galaxies (clumps of thousands of stars) they are each sending out light that is reaching the earth. And they are all moving away from the earth and the earth is moving away from them!
NOW – Imagine that the light that these galaxies are sending out are waves with crests, like a water wave made by a pebble thrown into a pond,
NOW imagine the waves being elastic bands, one end at the galaxy, the other at your telescope.. Now here I come with my Sharpie and I put a dot at each crest on the wave-elastic band.
AND, the crest-dots get further away from each other. It means that the light wave becomes longer. The longer a light wave becomes, the redder it gets. That’s how redness is defined.
Galaxies are getting farther away from the earth and from each other and the waves between them and us are getting longer BECAUSE THE UNIVERSE IS EXPANDING.
A couple of guys at Bell Telephone Labs, working with long wave lengths, found out something very spectacular about what was going on in the universe. They found the CMB or Cosmic Microwave Background. It is in the background of the entire sky. It is radiation which looks the same whether you see it from Australia or Alaska or Timbuktu. And it is radiation in the microwave region of the light spectrum.
This radiation is leftover from the Big Bang! In fact, this is the PROOF that there was a Big Bang! Before this discovery, the Big Bang was kind of a matter of opinion.
The CMB is made up of light waves which started on their journey at the beginning of the universe and only reached earth now!
THE SAMENESS PROBLEM
WHY IS THE UNIVERSE THE SAME IN EVERY DIRECTION?
It would be logical to think that the universe, at the beginning, was like a miniature of what we see today. As a doll house is a miniature of the house that we live in. Maybe at the start of the universe there were all little galaxies and tiny stars. And they just got bigger and bigger, since we know that the universe has expanded.
But the CMB is the same in every direction.
In fact, people started to ask – HOW COME?
The CMB is confoundingly uniform, EXCEPT for very little deviations here and there.
Its uniformity has been explained by a Theory called Inflation. It has not yet been proven, even though if it is correct, it explains a lot of mysterious things.
Scientists who believe in Inflation say that the universe was expanding MUCH, MUCH faster when the Bang occurred and that this expansion smoothed everything out!
It is further thought that during Inflation, gravity waves were produced which were tattooed onto the CMB!!!
Gravity waves would cause an imprint called B-mode polarization. This basically means that the direction of the radiation coming in is not totally random. Some rays are going in a preferred direction. And ‘B-mode’ is different from other kind of polarization.
B-mode polarization is very hard to detect! The deviations are small and few. And other radiation, even dust in the atmosphere might spoil the signal.
So the detector is deep underground where, hopefully, atmospheric contamination is minimal.
BICEP@ detector array under a microscope at the South Pole BICEP detector
Scientists working on the BICEPS2 experiment for two years. They thought they had succeeded in detecting the B-mode Polarization.
ONLY – since June, when these results about BICEPS2 were published, critics have complained that perhaps the results were not totally convincing.
Perhaps they were only seeing celestial static.
SO – back to the drawing board. In this case – back to doing an experiment more precise than BICEPS2.
Maybe next year we’ll know!
But the exciting fact is that we’re on the path to proving the Inflationary theory of the beginning of the universe which was first proposed in the 1980s,
A pretty long time ago.
So the study of the beginnings of the universe are taking a giant step forward, this is a great time to live in.
DOI: 10.1103/PhysRevLett.112.241101 PACS numbers: 98.70.Vc, 04.80.Nn, 95.85.Bh, 98.80.Es June 2014
Light waves similar to any other kind of wave, say like water waves.
Throw a pebble into a pond from a bridge. You will see that there are waves spreading out from where the pebble hits. The waves have crests and the wave-length is the distance from crest to crest.
waves in a pond
The length of lights waves goes from radio waves – from crest to crest about 1/10 of a meter (yard) all the way up to gamma rays, whose length, crest to crest is 1/100000000000 meters. Visible light is only a small part in the middle of the range.
Everything we know about the universe we find out through telescopes which look at light. It turns out that there are visible light telescopes, radio wave telescopes and telescopes which can ‘see’ X-rays coming from the sky and so on.
“color” of light connected to temperature of star(s)
Light of a given wave-length is emitted at a given temperature. The hotter the temperature, the shorter the light wave.
Now just having said that, we are going to show
that light with a long wave-length, meaning it’s emitted by something cool, may have started out as light of a very SHORT wave-length, emitted by something very hot.
We can look at the light coming into a telescope, measure it’s redness and know how far away the galaxy that we are looking at should be. BECAUSE:
We have some astronomical measuring sticks. Certain stars whose color varies with a period, like the phases of the moon, all have a similar temperature and color in near by galaxies, If we see these variable stars in a more distant galaxy, they will look redder. Using a formula, we can figure out how far away they are.
We can find out the distance of galaxies which are very far away by analyzing the light of super explosive stars in those galaxies.