Globe Eld

Quantum probability: underlying classical variables

In our everyday World we’re used to Absolute deterministic predictions. Throw a ball in the air and it’ll fall along in the trajectory. Leave your umbrella parked on the street. And when you come back, it’s still there. Just one umbrella quantum physics is not like this because quantum mechanics doesn’t allow us to make absolute predictions about the future. It only predicts the likelihoods of different outcomes to happen and doesn’t say anything about which one will happen. Well, you might say that’s the same with the weather the weather man only tells you what the chance of rain is. He can’t tell you.

They’re not it will rain but maybe the weatherman just doesn’t have good enough knowledge of exactly where all the air and water molecules in the world are nor are good enough model of how they interact or fast enough computer to simulate all of their bajillion interactions may be in principle if he had enough data and a fast enough computer his weather model could tell you exactly where every raindrop would fall right this reasonable idea that if you just had a more data you could explain everything is the classical deterministic view of the universe and for a while many physicists. Including Einstein thought the same had to be true with quantum mechanics. Maybe we just didn’t have enough information to put into our Quantum models. Maybe there were classical variables that were hidden from us at our experiments inputs that explained everything perfectly with no need for quantum mechanics. And it’s I’ll give you a 50/50 odds on the cat being dead mentality except it turns out that we can actually test whether or not this sort of classical underlying explanation of quantum physics can exist even in principle. The details are a topic for another blog, but the experiments tell us

There is no classical everyday underlying description of quantum mechanics. And this means Einstein that the universe is quantum mechanical whether you like it with a 50% chance or not.

Time Symmetry:The increasing entropy

The basic laws of physics things like F=MA, Gravity is inversely proportional to the distance squared Schrodinger’s equation and so on don’t say anything about the direction of time sure. They relate what’s going on now to what happens next and to what happened previously, but there’s no distinction between forwards and backwards in time the past and future are on an equal footing as far as the microscopic laws of physics are concerned in the macroscopic world. However, there is one rule that does have

I’m going in One Direction only the second law of Thermodynamics that says that any isolated system will tend towards increasing entropy or disorder like how cold milk and hot coffee mix together into lukewarm coffee milk that will never unmix from each other once a system gets to it’s fully disordered state is equilibrium. There’s no more direction of increasing entropy to determine the arrow of time. So the fact that we experience the flow of time right now means that we’re not in equilibrium. There are basically two ways that could happen either the Verse just happens to be right. Now this particular low entropy configuration with two directions of time flowing out forward and backward from now with increasing entropy in both directions or at some point in the far distant past the universe started with even lower entropy and disorder has been increasing ever since spoiler alert. It’s option. Number two that low entropy configuration was the Big Bang 13.8 billion years ago. The universe was hot dense smooth and rapidly expanding.

Smooth dense plasma particles might not seem organized and low entropy. But when the density of matter is extremely high the gravitational force between particles is enormous smoothness in the face of such Tendencies is not equilibrium, but it’s actually a very delicately balanced low entropy state things wants to be gravitationally clumps together into concentrated configurations, like protostars Proto galaxies or even black holes. What would a high entropy equilibrium Universe look like it would be empty space and Deed that’s where we’re headed. The universe is expanding and diluting and eventually all the stars will burn out and black holes will evaporate and we’ll be left with nothing but emptiness in every direction at that point x Arrow will have disappeared and nothing like life or Consciousness will be possible the fact that our sky is decorated with billions of stars and galaxies and our biosphere is teeming with life is a reflection of our low entropy Beginnings. We don’t know why the universe started in such an orderly initial state, but we should be glad it did it gave

As the non-equilibrium starting point that’s necessary for the flow of time as we know it to exist everything that followed from the formation of stars and galaxies to the origin of life as in the story of increasing entropy. Time’s Arrow isn’t a deep feature of the most fundamental laws of physics. It owes its existence to the specific initial conditions of our universe. …

Quantum tunneling

Suppose you drop a ball down the side of the valley, Classical wisdom tells us that when the ball rolls up the hill on the other side. It can’t go any higher than the height from which you dropped it that’s conservation of energy. Even if there’s a nice big long slope to roll down on The Far Side of the Mountain the ball just can’t get there unless you give it enough energy to get over the barrier but in quantum mechanics things work a little differently you see the quantum world is probabilistic. So if you release a particle in a valley chances are the next time you see it. It’ll still be somewhere in that. But if there’s a nice big slope to roll down on The Far Side of the Mountain, well, that’s a place that particle would really like to be and it turns out there’s also a small chance that’s where you’ll find it. If this isn’t crazy enough, it’s even possible. You’ll find the particle in the middle of the mountain and in real life. This means that an electron sometimes hangs around inside the nucleus of an atom.

Quarks

When you’re a kid, you’re told that all the stuff around you is made of atoms and that atoms are made of protons and neutrons and electrons. And if you’re lucky you’re told what protons and neutrons are made of they’re made of three quarks eat, but if they’re both made of quarks, how are protons and neutrons different you’re not usually told this is a kid and you’re not usually told what quarks are and why they’re called quarks when they’re clearly spelled quarks. So protons are made out of three quarks. That’s the first lie. You’re told protons are not that At any given time the proton will have two up quarks with charge plus 2/3 and a down Quark with charge minus the third which of course all add up to positive one because that’s the charge of the proton. These three quarks are known as valence quarks and they’re definitely there but the proton could have an additional up Quark anti up Quark pair. An anti Quark is the antiparticle of a cork and it could have other types of quarks pairs of strange quarks and anti strange quarks charm quarks and antiquarks. In fact, the proton likely has tons of quark antiquark Pairs, but there’s more the quarks are held together by the strong force, which is carried by particles called gluons. So inside the proton there is zillions of gluons and quarks all zooming around close to the speed of light and colliding and annihilating and new ones are forming and it’s a crazy raging party such as the quantum World in a proton wouldn’t that violate some kind of conservation law of particles just appeared in the proton quarks can and do just appear and disappear but not out of nothing Einstein’s famous equation E equals MC squared means

Mass can turn into a lot of energy or a lot of energy can turn into mass. In fact, the quarks that comprise the proton only make up one percent of the total mass of that proton. That’s like saying I drop some quarters in a bag and suddenly it weighs 10 pounds. There is a lot of energy and all the motion of those crazy partying particles particles and there’s energy in the gluon field all of this energy contributes to the mass of the proton E equals MC squared. All we need to conserve is the total Mass energy of the proton and nothing is violated as Quark anti Quark pairs pop in and out of existence, but there are a few other constraints the total number of up quarks must be two more than the anti up quarks and there must be one more down Quark than anti down quarks so that the valence quarks come to a total of three and the Quark antiquark pairs of other types Must ALL cancel out like the top quark and the charm quark and the strange quark and the bottom cork when Quark pairs spontaneously appear in the proton other properties must be conserved as well like charge.

So for cork with charge positive 2/3 appears its partner must have charged negative 2/3 and the spin of the particles must be opposite and the colorlessness of the proton must be conserved. This is cool quarks all have color except it’s not like real color color and quarks is a type of charge like the electric charge except instead of the electromagnetic force. It corresponds to the strong force Works can be red green and blue like the three primary colors of light and when you mix those colors you get white light. So when I said that protons are colorless that Means that there are three valence quarks must be red blue and gray so clever the quarks can change color but the overall color has to stay white. It turns out that the anti Quark has the opposite color. So that would be like anti-red which cancels out red, but I think the most amazing thing about quarks is that we know all of this about them without ever directly detecting one. In fact, you can never detect this one because they’re never found alone. The more you separate the quarks the more energy you have to put in to pull the quarks apart and as you do so

You eventually put in enough energy to make up the mass of two new quarks that can then bind to the original to so next time you’re told there are three quarks in a proton. Hmm. There are three valence quarks and a sea of other quarks too many to count impossible to count. No really we can’t like take a snapshot

Brownian motion

One thing that’s astounding about Einstein’s Publications in 1905 is that they spanned a such a large range of physics after Illuminating the quantum nature of Light by explaining the photoelectric effect in March April saw Einstein turn to something apparently more mundane particles suspended in fluids in particular. If you look at tiny particles in water or dust Motes in the air, you’ll see that they did or about in a very odd and random way that is it appears odd and random unless you believe that the air or water itself is made up of even smaller particles called atoms or molecules.

Which just bounce off of each other according to very simple rules. This is called Brownian motion despite the fact that botanist Brown wasn’t the first to discover it and similarly Einstein wasn’t the first to describe it mathematically, but he did draw the conclusion that the mathematical description of Brownian motion is evidence for the existence of atoms even if you can’t see them directly and then he cleverly derived how big atoms should be based on how much the Brownian particles move that’s like measuring the size of a penguin just by looking at how icebergs jiggle talk about cold and calculating.

Gravitational Efficiency: The outrageous efficiency of Blackhole

E=MC², the most famous equation in the world describes the fact that anything with mass possesses a huge amount of energy in principle like a 5-kilogram cat has enough energy in its mass to power the entire country of Norway for a year. If only the energy could somehow be fully extracted from the cat, but it turns out that efficiently extracting energy from Mass is a very hard thing to do antimatter is the most efficient way of extracting energy from Mass since if you Light a cat with a cat made of antimatter a hundred per cent of the mass of the cat and anti-cat will be converted into energy powering Norway for two years, but the universe has almost no naturally occurring antimatter. So it’s not a practical choice for generating energy. Since you’d first have to use a lot of energy to make a large mass of antimatter since we can’t use antimatter. There are basically three options left to US Chemical Reactions nuclear reactions and gravitational reactions like matter falling into black holes to start chemical. Jeans are so bad at extracting energy from Mass that we don’t even think about what they’re doing as converting Mass to energy, even though it is as an illustration reacting a balloon of hydrogen and oxygen gases creates a nice big explosion, but the end products of the reaction only weigh half a nanogram less than the initial reactants which amount to a measly point zero zero zero zero zero zero zero zero one per cent efficiency of converting Mass into energy at that rate. You’d need to 10 billion cats to power know.

Wait for a year nuclear reactions are a lot more efficient, but still pretty mediocre on an absolute scale splitting uranium-235 into Krypton and barium converts only about point zero eight per cent of the uranium’s mass into energy and fusing hydrogen into helium, like in the sun converts about point seven per cent of the hydrogen’s mass into energy at that rate. You’d need a hundred and fifty cats to power Norway for a year. This is where black holes come in. They’re about as good as it gets in our universe for extracting energy. From Mass which may sound weird because as you’ve probably heard nothing can escape black holes once inside but the efficiency of black holes comes from what stuff does while Falling Towards them before passing the no turning back point of the Event Horizon anything that falls in a gravitational field speeds up gaining kinetic energy and if it then crashes into something, it can convert that kinetic energy into heat that heat can then radiate away as infrared radiation slightly decreasing the mass of the object.

Planets and stars this conversion of mass into energy is pretty pathetic an object falling to the surface of the Earth releases only about one-billionth of its mass as energy. That’s basically as bad as a chemical reaction and explains why we don’t think of falling to the ground as a way of converting Mass into energy. It’s a really bad way but black holes have something special going for them. They are stupendously small a black hole with the mass of the Earth would be about two centimetres across providing way farther for an object to fall and since gravity gets stronger and stronger the closer you are to an object objects falling into black holes get accelerated to ridiculous speeds specifically an object falling all the way to the event horizon of a black hole will have kinetic energy equivalent to roughly half of its E equals MC squared mass-energy. However, if the object continues to fall into the black hole, all of that energy will be stuck inside the black hole the way to actually convert mass into energy that goes out into the universe is to have the object slowly spiral into the black hole crashing into other stuff on

Way heating up radiating that energy away. Thereby losing mass and speed slowing down more spiralling to a yet lower orbit. And so on all the way down to the innermost possible orbits, and this is exactly what accretion disks around black holes do so how good are they at converting Mass to energy well for a non-rotating black hole the innermost possible circular orbit is actually three times farther out than the Event Horizon. And in order to spiral into that point and object has to convert around six per cent of its mass into energy radiated away to the outside University. Worse after that point, if it loses any more energy, it will plunge down into the black hole and no more energy can be extracted. But at this six per cent Mass to energy conversion rate, you’d only need to throw 17 cats into a black hole to power Norway for a year compared to the point zero zero zero zero zero zero zero zero one per cent efficiency of chemical reactions and the point 1 to point seven per cent efficiency of nuclear reactions 6% for a non-rotating black hole may seem pretty good but rotating black holes are Bend space-time they literally dragged the things orbiting them along with them in the direction of their rotation, which means the innermost possible orbit can be much closer to the black hole the details depend on how fast the black hole is rotating, but for a very quickly rotating black hole the innermost possible orbit coincides with the Event Horizon instead of being three times farther away. And the Event Horizon itself is half as big as for a non-rotating black hole combined together. This means that matter falling into rotating black holes can convert as much as forty-two per cent of its mass into energy or equivalently you’d only need two and a half in spiralling cats to power Norway for a year. So if you really want to take advantage of equals mc squared and convert the mass of an object into energy don’t bother with chemical reactions or nuclear fission or nuclear fusion. Just throw it into a black hole.

Muons:Life example of the theory of relativity

Every second thousand of cosmic rays mostly hydrogen and helium nuclei strike every square meter of the Earth’s upper atmosphere. We don’t really know where they come from. But we do know that when cosmic rays crash into air molecules in the atmosphere. They create a shower of other fundamental particles pions crayons positrons, electrons neutrons neutrinos gamma and x-rays and muons. We know this because we have particle detectors in Labs down on the surface that detects the directions and energies of the particles in these. Showers, and use them to study the original cosmic rays, but there’s something fascinating about the fact that we detect a lot of the muons from cosmic rays down on the surface of the Earth because muons if you make them in a laboratory only have a 1 .5 microsecond half-life before they spontaneously Decay into an electron or positron and some neutrinos and yeah, the Greek symbol mu is used for both muon and four microseconds, which can certainly be a little confusing. But the lifetime of muons is really close to a microsecond. So it’s also kind of beautiful. We appropriate anyway, the point is that if you have a bunch of muons, you’ll only be left with about 50% after one point five microseconds and 25% after three microseconds and after 10 microseconds. There will only be point one per cent of the muons left muons. Don’t live very long just to point to microseconds on average to put that time into perspective light travels fast enough that in one second. It can go around the earth seven times but in two-point two microseconds light will only travel 660 meters or less than half a mile. So even

Muons travelling at essentially the speed of light wouldn’t make it more than a kilometre or two before the vast majority of them decayed Which is far less than the 10 or 20 or 30 kilometres that muons do regularly travel from the upper atmosphere to the ground. So how do muons travel dozens of kilometres through the atmosphere without spontaneously decaying when in fact they should only be able to travel less than one-kilometre time dilation. Yes, because the muons are travelling close to the speed of light their time literally passes more slowly. Slowly at a speed of 99.5 percent, the speed of light to point 2 microseconds for them would be about twenty-two microseconds for us enough time for the average muon to travel at least six kilometres before decaying instead of half a kilometre and even higher energy muons going even faster would even more easily reach our detectors on the Earth’s surface before they decayed at 99.995% The speed of light the average mu 1 would live for 220 microseconds and travel at least sixty six kilometres before decaying so from our perspective.

The fact that so many cosmic ray muons reach our detectors on the earth’s surface is direct evidence for special relativity and time dilation. But what about from the muon’s perspective where they do only live on average two points two microseconds. Well for them the answer to the apparent Paradox is also relativistic length contraction from the muon’s perspective. It’s the earth and the atmosphere which are moving at 99.995% The speed of light towards the muon and the lengths of moving objects are literally Contracted by a factor dependent on their speed in this case 50 kilometres of our atmosphere is to the muon literally only half a kilometre which is thin enough for even a muon with a lifetime of 2 points 2 microseconds to Traverse. Well, actually from this perspective the atmosphere and ground move past the muon but at a speed of 300 meters per microsecond and a distance of only 500 meters the ground has no problem reaching the muon before the muon decays this in my mind are one of the most awesome experimental verifications of special relativity the unequivocal time.

Action or length contraction depending on your perspective for objects moving close to the speed of light. They literally couldn’t get here if it weren’t for time dilation

The Universe: constant Conflict

The universe. How big is it? Does it have a center? Does it have an edge? Is it getting bigger? And if so, why well, we know that there are two different meanings for Universe first. The observable universe is everything that we’ve been able to see or observe thus far and second the universe or the whole universe means everything that exists or has existed or will exist more specifically the observable universe is the region of space is visible to us from Earth. And since the universe is only about 13. Eight billion years old and light takes time to travel through space then regardless of what direction we look we see light that’s been traveling at most 13.8 billion years. So it’s logical to think that the observable universe must then be 2 times thirteen point seven seven equals twenty seven point five billion light years across but it’s not that’s because over time space has been expanding. So the distant objects that gave off that light 13.8 billion years ago have since moved even farther away from us today. Those Distant objects are a bit more than 86 billion light years away multiply times 2 and you get 93 billion light years the diameter of the observable universe to give you a sense of scale the size of the Earth within the observable universe is roughly equivalent to the size of a virus within the solar system. Although that doesn’t help much because we can’t really appreciate the incomprehensible smallness of a virus nor the bewildering bigness of our solar system either. So let’s just say that the observable universe is stupendously big but the whole universe as far as we can tell is a lot bigger.

Space is most likely infinite or at least it doesn’t have an edge though. The difference between those is another story unto itself. Now, what about the center of the universe? Well, the observable universe has a center us. We are at the center of the observable universe because the observable universe is just the region of space visible from Earth and kind of like how the view from a very tall tower is a circle centered on the tower. The piece of space we can see from here is naturally centered here. In fact, if you want to be more precise each one of Of us is the center of our own observable universe, but that doesn’t mean we’re at the center of the whole universe just like the tower isn’t the center of the world. It’s the center of the Peace of the world that it can see up to the Horizon. But just because you can’t see Beyond the Horizon doesn’t mean there’s nothing there and so it is with the observable universe looking up at the sky. We see light. That’s at most 13.8 billion years old and coming from stuff. That’s Now 46 billion light years away. Anything farther is Beyond the Horizon but each second we see new

Older light coming from slightly farther away three light-seconds farther to be precise. And so our view of the cosmos is literally getting bigger all the time. All we have to do is wait and watch as the universe ages and light from more distant places as the time to get to us. So here we are sitting at the center of our observable piece of the whole universe. How big is the universe? Well, the observable universe is currently 93 billion light years across the whole universe is probably infinite does the universe have an edge. Age the observable universe does its 46 billion light years away in any direction and the whole universe has a temporal Edge or what we call a beginning but almost certainly not a spatial one does the universe have a center again the observable universe does you the universe as a whole almost certainly not and is the universe getting bigger? Yes space is expanding which makes both the observable universe and the whole universe bigger plus overtime. We see older and older light coming from farther and farther away so are

The universe gets bigger that way too and that in a nutshell is our view from the tower you are the center of the universe and so am I and so is everyone else and so is no one.

Galaxies:The Birth, the manoeuvre

Most things in the universe happened to slowly for us to see them happening stars, like the sun take tens of millions of years to form and hundreds of millions of years to orbit there galaxies and colliding galaxies take billions of years to merge and yet we have a pretty decent understanding of how all these things happen because there are so many of them in the observable universe that we can look out and see different versions of similar events happening in different places and because light takes time to get here we see places at different distances at different times throughout the history of the universe. And from all that we can piece together an understanding of how stars are born and how they died how galaxies develop an interact and so on it’s kind of like if you only had 10 minutes to study how humans grow you couldn’t see any one person grow very much in that time. But by looking at humans of different ages all around the world, you can get a pretty good picture of what a human life looks like. However, the very first galaxies to ever form were so small and dim that we don’t have nearly as good an idea of how baby galaxies are born as we do about how they behave and interact later in life. Life our current understanding is that in the early Universe before any stars had formed everything was just spread out gas and a lot of Dark Matter dark matter is matter that doesn’t interact with things other than by gravity so we count dark because we can’t see it gravity would have caused slightly denser areas of dark matter to attract into clumps pulling in bits of gas until they were dense enough on their own to gravitationally collapse and start thermonuclear Fusion a star many stars clusters of stars and their Associated Dark Matter attracted together and merge

And then those clustered clusters clustered together eventually forming the most distant and longest ago galaxies. We see today, but we don’t know exactly how soon after the big bang the clumps of dark matter and gas formed or when during the process of clumping and clustering the first Stars ignite it or if there was a minimum Dark Matter Clump sighs necessary to attract enough gas to form stars or if the very 1st star clusters came together to form galaxies at all. They might have been so small and fragile. They were blown apart when their own Stars went supernova and the first galaxies He’s may have actually formed from a second round of clumping of gas and dark matter as well as dust from the explosions. To be honest. We don’t even have a good enough definition of what a galaxy is to know when to stop calling something a cluster of stars. And when to start calling it the Galaxy what we do know is that today? We have bajillions of galaxies in our universe. None of which existed 13.8 billion years ago. So somewhere in between, they must have all been baby’s big gassy babies surrounded by clumps of dark matter

Perspective: A truth game of shifted view frame

When Galileo pointed his telescope at Jupiter in 1610, he was the first person to see the giant orbs attached to it by Springs. In his actual drawings compared night after night show these bright spots moving back and forth past Jupiter exactly the same as if they were balls hanging off of Springs. I mean, yeah Galileo was looking at the moons of Jupiter, but if you plot their motion back and forth and back and forth over time, it forms a sine wave and that motion is mathematically identical to the motion of something bouncing up and down on Spring with a linear restoring Force also sine waves over time from a side-on perspective that projects two Dimensions down to one things in circular orbits. Look exactly like they’re springing back and forth on giant coils of wire. Now. I’m not saying that we should think of the moons of Jupiter is being held on by giant invisible Springs, but it’s a valid mathematical model when viewing them from a distance. It’ll make the same predictions about the Motions of the moons as the orbiting in circles due to Invisible gravity model and one can be mathematically transformed into Into the other the moons of Jupiter aren’t alone in having multiple, mathematical descriptions projectiles and storms on Earth experience a force called the Coriolis effects that causes them to turn but viewed from an external perspective at the projectiles and storms are what goes in a straight line while the Earth turns beneath them both models. If you use them carefully make correct predictions about reality and Quantum phenomena can be modeled in at least three different ways that all give the same predictions as a particle being Guided by a spread out pilot wave or

As a spread out probability wave that collapses to a single point or as a particle exploring all possible paths. It could take and interfering with itself along the way all three of these mathematical models suggest different ways of thinking about what’s actually going on in Quantum systems and the fact that all three of them give the same experimental predictions suggest that perhaps none of them is the right way to picture what’s happening mathematical models. Give us nice easy to digest pictures of how the universe works moon’s orbit around planets atoms bind together into molecules electrons. Ron’s are clouds of probability and so on but we need to be careful how much weight we give to the models in our heads or on our blackboards or computer screens do Jupiter’s moons move. Like they’re pulled back and forth by the invisible force of Springs or held in orbit by the invisible force of gravity or are they following helical paths, which are actually straight lines in curved space-time the way we describe the world influences the way we think the world is even when there are other equally correct ways of describing the world that painted entirely

Pictures from our own that’s not to say we should accept wrong ideas, but we should be aware that sometimes a different correct picture one. We haven’t considered is the one we need to see.