Well, I am back. I am trying hard to concentrate on my studies. I have a first exam at the end of August and then the second one at the end of September.But I fear I lack a good overview on what is going to be important.
And I hope to return to blogging more interesting stuff soon.
I am off for the Baltic Sea for some days. I hope the summer will stay for a little while.
Oh, there is a can of real
Spam standing beneath the printer here in our
Computer Pool at the
Institute. I have never before seen one of these. It looks the way that I am sure I would faint if somebody opened it. There is even a recipe for Spam and Broccoli Pasta on it. Poor Broccoli, I would rather die by herbicide than being cooked with Spam.
I had no clue that Spam was a registered Trademark.
Some days ago a friend of mine sent me this nice
link with a collection of ancient Swiss maps.
If somebody believes that quantum mechanics contradicts classical logic, he is probabely appealing to such phenomenons like entangled states of so called identical particles or the like.
Consider for example a two electron system let's say a He ground state. (We take Parahelium, which has a symmetric space wavefunction and a antisymmetric spin wave function), i.e.
S = |up1>|down2> - |down1>|up2>
Now the problem starts already with writing down the spin function in this way:
The numbers (1,2) label the two electrons, but precisely this labeling is
not allowed, or better it is
not possible.
It is not impossible because we do not know, the names of the electrons, but
if we were small enough to sneak into the He atom without beeing seen, we could
in principle determine it.
There just is no electron 1 and no electron 2.
Don't get misleaded by this, there are
certainly two individual electrons, the He does not consist of a core
surrounded by a single "particle" with charge -2e, since such a system would
have different properties.(that could be something like Cooper pairs or so)
So the expression above is only a bad "Eselsbruecke" to illustrate
the antisymmetry of the function.
What has this to do with logic?
People would probabely argue that the sentence:
(1) "Electron 1 has spin up." does
not have a definite truth value as long as the state is entangled, i.e. as
long as there hasn't been any measurement.
Well I would rather put it as follows: the sentence (1) has a definit
truth value,
since it corresponds to a measurement. Put it as follows:
(2) \exists a Electron with Spin up
Is perfectly true for the entangled state, it follows from the Pauli principle.
Now deducing (1) from (2) i.e. eliminating the quantifier in favour of a individual constant
is measuring the system and therefore destroying
entanglement.
You might say that's absurd since logic is a purely deductive theory
whereas measuring a spin is manipulating the physical world. I think it's not,
it's just quantum mechanics.
For an entangled state the term "Electron 1" is just empty. A logical
language describing a entangled quantum system cannot contain individual
constants. So the setence (1) is not a proper sentence of that language.
Certainly a language describing the non-entangled state contains the individual constants, and it is perfectly save to deduce (2) from (1).
within this language.
Maybe this is trivial.
I haven't read anything about what people really mean, when they say that quantum mechanics and classical logic are imcompatible, and much more sophisticated arguments to support the idea.
I am not firm at all in interpretations of quantum mechanics neither.
But somehow in this case you have to possibilities:
1. you leave the measurement aside then you have two isolated systems, the entangled one and the other and you need two different languates to describe them. That would correspond to a kind of "Kopenhagener Interpretation" which says that the measurement destroys the old system and creates a new one.
2. You let the measurement be an essential part of your system, then you need some mechanism in your logical language to describe it, that would be for example the introduction of individual constants. This point of view then corresponds to a von Neumann Interpretation.
Who would have
guessed? I always thought, flying is healthy for our climate, since there are no taxes on Kerosin. I was just considering to set up a cheap Airline from Bornholmer Strasse to Flugplatz Johannistal in Adlershof.
I mean it's ridiculous. Everybody knew for years that the number of airplanes cruising our skies and private cars on the streets all over this planet are a very big threat for good old pachamama.
I have never understood why traffic is such a neglected issue in politics. Especially for our Red-
Green-goverment. But instead of recognizing that a fast-well-organized-and-as-cheap-as-possible national and local railway system is essential for the environment and the economy one tries to privatize public transports. Of course that's much more fashionable.
I personally think that the state should garantee a good public transport system (national railways and local public transports, or let's say, they should support the most ecological transport, as long as it is reasonably fast. That means support underground, tramway, buses and cycling (!) on a local scale and trains on a national scale, at least for europeansized countries).
Anyway why shouldn't one pay for the ecological damage one causes? Since the effects of these damages are not any longer something that might maybe strike back in the far future. What about floods, storms, landslides because of melting glaciers?
Well, complaining about lousy public transport:
The
S-Bahn is fighting hard to charge you more and more for a even poorer Service. Since 2 weeks now many of the S8 are only running until Schöneweide, that's two stops ahead of Adlershof. I really don't understand that, in
Adlershof there are 6 Institutes of Humboldt University, plus many other firms, science Institutes and a quite huge media center, which means a lot of students and other hardworking people are travelling down here everyday. Whereas in Schweineöde there is a shopping mall without stores.
The only thing left in this Semester is a written exam, unfortunately I do not like the topic (solid state physics) too much, although it is important, and I have been quite lazy the last weeks. So there is still a lot to do. And I am fighting hard to motivate myself.
