Hmmm ... there is so much misunderstanding in Gordon's post that it's difficult to know where to start.
Planck was looking at black body radiation. In order to get an equation that described the observed frequency spectrum, he made the assumption that energy could only be exchanged in amounts proportional to the frequency. This does not imply the existence of photons - something he opposed all his life. He certainly did not say that material objects are made of lumpy bits of energy. Mass/energy equivalence had to wait for Einstein't theory of relativity.
Time is not quantised. In all theories that work, it is continuous. If it were not continuous, you would not be able to differentiate with respect to it, and you would be unable to do any useful calculations.
The continuous spectrum is a bit odd. When you observe a continuous spectrum (e.g. black body radiation) for a given period of time, what you have observed is a finite (but very large!) number of photons, each with a specific energy. Planck's equation for black body radiation only tells us what proportion of the photons will be in a given energy range. It's a differential equation showing the derivative of the proportion with respect to the width of the range as the range tends to zero. When we plot a theoretical energy distribution as a continuous graph, we are plotting how that derivative varies as a function of energy. When we plot an observed spectrum as a line, we are merely joining up the closely-spaced dots. The spacing is determined by how much resolution our instrument has.
Now the Plank mass/length/time etc. These have absolutely no physical significance. They are units in just the same sense that the year, second, yard, metre, kilogram, ounce etc etc etc are units. Obviously, we can pick any units we want - the inch and the metre are completely arbitrary. The constants of nature will take different values in different units - e.g. the speed of light is 300,000,000 metres per second or 186,000 miles per second or 1 light-year per year or some silly number of furlongs per fortnight. What are these Planck units then? They are the units that result in the constants of nature that keep cluttering up our equations having the numerical value of 1.
The Planck mass certainly isn't the smallest mass there can be - obviously not, as it's the size of a grain of dust, and we know atoms are a lot less massive than that.
Phew, I'm going to abandon my promised attempt to post an explanation and leave it to you lot, you obviously know far more about this subject than me!
Please don't abandon your attempt umslopogaas! It's a good way to clarify one's thoughts by putting them down in writing for all the world to examine.
Obviously QM is best understood by those with background in physical sciences, who have lived with all the underlying concepts of the ways in which sense is made of experimental data. No one can actually see an electron or a boson, i.e. hold it in the hand and have a good look at it. We have to build pictures in the mind which conform with experimental data. As Gordon said, you don't need maths - but a strong imagination is required, and some "physical intuition". That was Einstein's great strength.
Last edited by Oddball; 12-07-12 at 15:20.
Strong imagination? I think what I meant by that is not necessarily a vivid imagination, but an ability to make a picture in the mind, and then turn the picture over, inside out, upside down, and then modify it until it fits all the "facts".
I shall respond in due course, but unfortunately my response has been prepared on my new computer, which uses later versions of all the software I employ. I cant find anything, move anything, and all the 'Edit' functions seem to have disappeared. But I'll get there, I have actually resorted to pencil and paper to make notes of things to do. If I seem to have gone quiet, its not because I have nothing to say.
Mutter, mutter, where the **** is the ****** command to *******-**** edit, oh ****!
Quantum superposition, which has been proven to exist in countless laboratory experiments, means that matter can exist in more than one state; ie, in theory it can exist at the same time at opposite ends of space and time (defying most of the laws that Einstein came up with about space and time, particularly that nothing can move faster than the speed of light). The really mind bending thing about quantum superposition - or perhaps the most obvious - is that it can only occur when not observed by us humans. To try and put it simply, our mathematics proves that quantum superposition takes place, but when we observe this phenomenon it can no longer take place. For me, the interesting thing about this is the link between that thing we call human 'consciousness' and the quantum world (and of course I'll hark back to my earlier point, that all brains, whether it's a fly's or a human's, work at a quantum level - there's no other way that I can see that a brain can compute so fast).
Originally Posted by Vile Consort
Without getting into another debate about transistors, modern computers wouldn't work without this weird thing called quantum superposition. It happens, but it only happens when us humans don't try to observe/measure/quantify it. No wonder Einstein called it 'spookey'.
I now understand why 'Higgs boson' should not be a possessive. Everytime I read it, though, it just begs an apostrophe.
umslopogaas, go for it. I for one will be very interested in your thoughts.
Originally Posted by umslopogaas
Particle stuff is still very much in the realm of theoretical physics; ie, no one really knows what the 'f' they are talking about.
ps. In my humble opinion, Schrodinger's Cat thought experiment just muddied the water even more for the general public's understanding of quantum theory. Schrodinger's execution of his fluffy cat was an attempt to show fellow theoretical physicists how ridiculous the concept of quantum superposition is. The fluffy cat was never intended to explain QM to the general public.
Last edited by Budapest; 12-07-12 at 22:29.
Reason: ps added
Existing in two places at once would violate the conservation of energy. And as we know, the equations of physics always conserve energy. Always, always, always. It's a consequence of their symmetry with respect to time - as the well-known theorem of Emmy Noether tells us. It would be a very brave man indeed (or a foolish one) who proposed a theory that violated the conservation of energy.
Originally Posted by Budapest
As I said, which interpretation of QM says this? Certainly the Copenhagen and many-worlds interpretations don't.
The wave function exists in a superposition of states. But not the particle. In the Copenhagen interpretation, it isn't possible to speak of the particle's position until you make an measurement of it (whatever that means), whereupon the wave function collapses so that only one state is left. This locates the particle at one and only one point in the universe at that time.
The objective collapse theories are similar but don't require the troublesome concept of measurement to cause wave function collapse.
In the many-worlds interpretation, there would be as many universes as there are superimposed states. In any given universe, the particle is on only one place.
I would be really interested to know which of the many mainstream interpretations has a particle in two places at once. It seems to me it is only the little-known Budapest interpretation.
The Neumann/Wigner interpretation is the only interpretation that requires consciousness in order to collapse the wave function. Hardly anyone thinks it is right. And even that doesn't have the particle in two places at once.
By the way, it is a well-known logical fallacy to say that one explanation must be correct because you can't think of another. By that logic, the Phlogiston theory was correct.