Well, what about Copenhagen Interpretation then?
Well, what about Copenhagen Interpretation then?
Otto Stern and Walter Gerlach performed a groundbreaking experiment in 1922 illustrating a so called two-state-problem. They used a collimated beam of silver atoms (in y-direction) and let it go through an inhomogeneous magnetic field so that the atoms did not only experience torque but also a force.
For our purposes it is sufficient to look only at the z-component (x is going to be neglected in the further discussion. Still we should keep in mind that simplification is not quite correct because we need to fullfill Gauss’s law for magnetism). Assuming a constant magnetic momentum we can conclude:
Thus Atoms with magnetic momentum larger than zero experience a downward force and vice versa.
Thinking in terms of classical physics one could assume that this experiment gives us a distribution of the distracted atoms looking like a gaussian curve. Why? Because the orientation of the atoms is random, thus the angular momentum (following from the electrons in the atom’s hull) and the magnetic momentum is random. The conclusion would be a somewhat continous gaussian looking distribution (in z-direction!)
This is the moment when “strange” quantum mechanic stuff comes into the picture. Our assumption was wrong. What Stern and Gerlach measured was the following distribution:
What does this mean? There is a quantization of the magnetic moment’s z-component (thus also of angular momentum)! It can be described mathematically as follows:
This kind of quantized “angular momentum” the electrons got is the spin we wanted to understand. In this two-state-problem the spin’s value is either +(½) hbar or -(½) hbar. Any analogies using rotations from everyday life are wrong! Spin is way more abstract. There is simply nothing in our everyday lifes corresponding to it – we can only accept that fact.
Actually this experiment does not really help to understand the nature of spin but at least we can understand why we need the concept of spin and that it really exists.
What we undergrad students (at least I did for a long time) take for granted is that Bell’s inequality proofs there is for sure no deterministic theory of quantum mechanics. Is it really that “easy”? Maybe it’s pretty naive to accept the Copenhagen Interpretation without further thinking. Tim Maudlin who studied philosophy and physics at Yale University explains why we should consider less conventional “interpretations” of quantum physics.
You can find his corresponding paper here.
“[T]he temperature in the core of our sun is usually cited at 15 million degrees Celsius or so. […] What I don’t get is this: some mid-sized thermonuclear test detonations done by the old Soviet Union and the USA have been recorded at (if only very briefly) 200 or even 300 million degrees Celsius. How can our pithy 3 stage hydrogen bomb blasts be so much hotter than the dense hell of the Sun’s monster fusion oven?”
The Sun, the greatest source of energy in our Solar System, converts a total of 700 million tons of mass into pure energy every second through the process of nuclear fusion. And yet, even in the hottest, densest, innermost part of the Sun, the temperature “only” reaches up to 15 million degrees. Somehow, on Earth, we’ve developed nuclear bombs that, despite having much, much smaller yields than anything occurring in the Sun, can exceed any temperature the Sun achieves. How is this possible?
Brian Greene is going to do this new video series from tomorrow onwards – I think it’s worth it to check it out 🙂
Btw do you know why Brian Greene is an extraordinary cool physicist? Because he’s vegan 😉
“In physics, we have to be willing to challenge our assumptions, and to probe all possibilities, no matter how unlikely they seem. But our default should be that the laws of physics that have stood up to every experimental test, that compose a self-consistent theoretical framework, and that accurately describe our reality, are indeed correct until proven otherwise. In this case, it means that the laws of physics are the same everywhere and for all observers until proven otherwise.
Sometimes, particles behave differently than antiparticles, and that’s okay. Sometimes, physical systems behave differently than their mirror-image reflections, and that’s also okay. And sometimes, physical systems behave differently depending on whether the clock runs forwards or backwards. But particles moving forwards in time must behave the same as antiparticles reflected in a mirror moving backwards in time; that’s a consequence of the CPT theorem. That’s the one symmetry, as long as the physical laws that we know of are correct, that must never be broken.”
Are the laws of physics the same, here and now, as they are at all other times and places in the Universe? If they are, then that means a certain symmetry exists. It appears, to up to 18 orders of magnitude in some experimental cases, that specific symmetry is good and respected by our Universe. If a theory demands its violation, that theory is presently unsupported by all of the evidence. The reason?
“My question is, in the equation E = mc², where does the energy in the "m” come from?“
It’s still hard, more than 100 years after Einstein demonstrated its truth, to wrap our heads around the idea that energy and mass are equivalent. There are many forms of energy that can all be converted into one another, and mass is just another one of them. You can create particles with mass if you have enough available energy, and if you set up the right conditions to destroy mass, such as in a nuclear reaction or an antimatter annihilation, you can turn mass back into pure energy.
But what about the question of where that energy responsible for creating the “m” of rest mass comes from? It might be a tempting answer to assume that it’s the Higgs, since we all heard last decade about how the Higgs gives mass to the Universe. But for the matter we know of, predominantly made of protons, neutrons, and electrons, the Higgs is responsible only for about 1% of the mass in the Universe.
How does one get this idea [for the proof]? The answer is: I don’t know! It is like asking: How did Michelangelo do this?
Happy Pi Day to the math fellows out there!