Astronomy Cast Ep. 249: Schrödinger’s Cat

18 Replies to “Astronomy Cast Ep. 249: Schrödinger’s Cat”

1. Schrodinger`s principal on Cat behavior is totally imaginary. This is not applicable in practical. Because, we do not know the internal functions of matter (m) of E = mc^2. I explained this facts in my book COMPLETE UNIFIED THEORY, page – 269, 1998. Complete unified theory is single theory and it is applicable to all fields from the particle to the universe. The calculated results are tallied experimental results. This book is unique and able to give answer known and unknown problems.
   You can get this book from :
   1. SB Berlin PK. Search Short List-[ Translate ], Andy Evans. Berlin [u.a] : Springer, 2000. Buch, Complete unified theory / Nirmalendu Das. 1. ed. Guwahati [u.a.] : Bani Prokash, 1998.
   2. National Library, Government of India , Ministry of Culture
   And other open libraries.
   Nirmalendu Das, Email: [email protected]

   1. No theory is personal. Scientific theory is for mankind. When it will proof by experiment, then the theory will be granted in all respect, but it need to know what is actually the science going on. We will not support the wrong ideas. In our traditional theories, some wrong ideas puzzling to progress in front. The Complete Unified Theory able to give answer of all truth. So, it need to focus to clarifying the thinking. .

2. Neat conversation. I’ll donate a Cat!!! Her name is Sadie and she’s not very friendly. 🙂

   1. Haven’t heard the podcast yet but, as a lateral thought experiment on the survival chances of the cat…

      Surely the box containing poor unsuspecting Whiskers has to be sealed – so that Schrodinger isn’t also at risk of being poisoned or irradiated and can’t cheat by peeking.

      Then, the longer Schrodinger takes to guess if Whiskers is still alive or the poison has had a chance to work, the more Whiskers is at risk of death anyway by means of asphyxia.

      On balance it’s not looking good for the Cat.

      PS I wuv Cats.

3. I have read that at the quantum level there is an energy associated with empty space. Can you expand or explain this.

   1. Hi Phil. I think you are referring to dark matter. I’d suggest researching the subject yourself, as I fear I don’t have a great enough understanding to correctly explain the phenomenon to you, but I hope this helps you regarding a place to start your search. Good luck!

   2. Vacuum energy is indeed a quantum effect related to Schroedinger’s predictions by way of Heisenberg’s uncertainty principle. (See lcrowell’s comment on that.) Every field, say of elementary particles, have a vacuum expectation energy value associated with them. According to quantum field theory that is the zero point energy.

      Many effects have been tied to or implied as consequences of absolute or relative vacuum energy. Spontaneous emission, Lamb shift, static and dynamical Casimir effects, Unruh effect, Hawking effect, and dark energy of standard cosmology.

4. Why hasn’t this showed up in iTunes, and why is your podcast Feedburner link to the right 5 years out of date? I’d like to listen to this on my iPod instead of sitting here looking at it.

   Also Pamela, you can’t “do science”! Science is a noun, not a verb. You can “perform a scientific [adjective] procedure” or “scientific [adjective] experiments [verb]”, but you can’t “do science”, and “science” is not “being done.” 🙂

   But this looks like a good show for the 10 minutes I saw.

   1. As we said in the previous post of the video version of Astronomy Cast, these videos from a Google + Hangout where Pamela and Fraser record Astronomy Cast are a new component of AC, but don’t fret, the audio version will be available soon. The ultimate plan is to record the audio in a Hangout, and make the video available right away, but within a week have the audio posted on the Astronomy Cast website as a podcast. The finished audio version takes longer because of the editing, and we’re still working out the logistics and timing. But that’s the goal.

      The feedburner link above is for Universe Today podcasts, which we haven’t done for awhile. Here’s the Astronomy Cast Feedburner link: http://feeds2.feedburner.com/astronomycast

   2. Of course you can do science.

      Maybe YOU can’t but lots of people can … even third graders. Ask any teacher.

      1. They teach grammar in third grade also, and would tell you that saying you “you do science” is like saying you “you do cheese.” You can study science, and you can eat cheese, but science is not an action.

         I know science and grammar too.

      2. In fact, cheese makers do cheese.

         If everyone uses it than it is grammatical, he said hopefully.

      3. Cheese makers do MAKE Cheese. 😉

         Instead of Googling, look it up in a dictionary. There is still no form where it’s OK to do science. And why would you want to sound dumb anyway?

         Next up will be; “Science – Why you no do?” 🙂

         I like Pamela, so a little good natured ribbing is OK. 😉
         Did anyone ever notice that Fraser sounds like Miles on Murphy Brown?

      4. Hopefully you will google “do science” (google is a verb, you see), and see some of the 1,400,000 responses — among them “Do Science! – Science tricks, experiments and activities” (www.doscience.com/), “How do scientists really do science?” from 2004 (www.sci-ed-ga.org/pdfs/how-do-science-10-10-04.pdf), and “Born To Do Science” (borntodoscience.blogspot.com/).

         And don’t fail to see all the posters in Google Images. You will LUV the cute cat in “Stand back! Iz Goin To Do Science!” (http://cheezburger.com/conbarbie/lolz/View/3047049472)

      5. And “I CAN DO CHEESE ALL BY MY SELF – A Case of the Mondays # 51” (http://www.youtube.com/watch?v=fhXq1UvAaTs), “Tried to do cheese today” (www.smokingmeatforums.com/t/109448/tried-to-do-cheese-today) and “How To Do Cheese – a skinny girl’s guide” (http://laylarc.hubpages.com/hub/How-To-Do-Cheese-a-skinny-girls-guide). And skinny is from LONDON!

         Granted, laylarc says “I work as a reader on Psychic TV, and I’ve worked as a model and starred in a couple of movies. I write mainly about modelling, mythology and the supernatural, and I’m passionate about nutrition and health.”, but the English can’t be wrong about English, can they?

5. Is there a citizen’s science project, like zooniverse or other, that allows people to look for undiscoverd red and brown dwarf stars in the data of the WISE all sky IR surey?

   Stef De Decker, Belgium

6. The Schrodinger cat is a way of illustrating the question on where the cut-off in a measurement takes place. This was elucidated by Heisenberg in a letter to Bohr. Bohr advanced the idea that nature existed in a duality between a quantum domain and classical reality. Bohr stated that a quantum system must be measured by a classical system which absorbs a superposition in the so called collapse of a wave function. A quantum system exists as a Fourier summation of possible wave-states

   |?> = sum_n c_n|n>

   for |?> the state vector and |n> a basis state in some choice of bases. The collapse of the wave function is then a case where |?> — > |m> which occurs with a probability P_m = c*_mc_m. The c_n’s are amplitudes which have various frequencies and this summation is similar to the harmonics one might detect in listening to a musical note. Different superpositions lead to different probability distributions of outcomes, and we might compare this to how a violin sounds differently from a trumpet when they play the same note. The various Fourier modes then give probability distributions and the unity of the state vector is

   1 = = sum_{mn} c_mc_n

   where the basis vectors are perpendicular to each other = 1 only if m = n and so we get the probability rule 1 = sum_nc*_nc_n = sum_nP_n. The act of measurement has the effect of adjusting the probability distributions, so that if the mth state is detected the probability right after that detection is P_m = 1. Heisenberg noted something funny here, for where is the cut-off for a classical system that acts as an objective measurement system?

   I indicate below a more complete discussion of the measurement process, for those who are physics geeks who get into linear algebra and quantum states. Pamela used the term entanglement, and that is just exactly what happens. The superposition of states is replaced by an entanglement between the system measured and some quantum state associated with an apparatus needle. The question is then what measures the needle? So there must be an entanglement of the needle state with another state, say a heavier needle state. The heavier needle state means the uncertainty in the energy of the heavy needle state ?E < ?, but we know this can only exist in some idealization as a limit. Then in some hierarchy of needle states of increasing mass you can end up with entanglement of detector state which is huge, say a cat that can exist in a live and dead state. So then we need an observer of the cat. So Wigner’s friend is in a box which surrounds the box, say wearing an appropriate gas mask, can open the cat box to observe the cat and record the outcome: Dead or Alive. However, Wigner sitting outside his friend’s box can’t know whether his friend has written Alive or Dead, so he interprets his friend’s state, or the state of his notebook, as similar to the cat. This would be contrary to what his friend might at that moment have observed and be thinking. This is a case of logic where A or B may be a true statement, but correspondingly A is not true and B is not true.

   We then have a funny situation, where the observed state of a quantum system is ultimately subjective. By subjective I am using the word in the meaning of Bayesian statistics. Quantum mechanics is sort of the ultimate Bayesian system. The measurement cut-off occurs on the basis of the prior probability estimate used by an observer. A sequence of measurements, say in the above hierarchy, is similar to a Bayes’ rule regression where priors are refined. Where this regression cuts off is not determined by nature, but by the choice of experiment the observer makes.

   This has interesting connections to black holes and the relationship between quantum mechanics and general relativity. In particular it concerns aspects of semi-classical gravity with

   R_{ab} – 1/2Rg_{ab} =

   for this really obtains in the case where the expectation is evaluated on some choice of a frame. The is a quantum expectation for the matter-field operators which act as a source of gravitation. This expectation is expressed according to some basis choice used in a measurement. This basis choice is set on a particular reference frame in spacetime, where on that frame a measurement is performed, giving the right hand side , whereas on the left we have a covariant expression of curvature. So something is rather amiss with this, for the left hand side is frame independent, where the right hand side is represented in some basis and frame set by an observer. The right hand side is the appropriate in some pseudo-tensor form, and to make this consistent we have to include all possible measurements on all possible frames. So there is then some summation over all decoherent histories with pseudo-tensor outcomes. The most important dichotomy which happens is with respect to the quantum physics an observer outside a black hole measures verses an observer interior to a black hole. The two observers detect quantum fields or strings in complementary basis states. Even though these two outcomes will be completely different, there is nothing in nature herself which tells us which is correct.

   I have to write something concerning the question posed by the British man in San Francisco about the Wheeler Delayed Choice Experiment (WDCE) on cosmic distances. The idea is that large elliptic galaxies act as beam splitters. Photons with the same wavelength reaching a detector can exhibit the Hanbury Brown-Twiss effect, whereby they fall into the same state. So if we observe a photon coming from a source it can have a superposition of having traveled along one side of the beam splitter or the other. If we use radio telescopes with a narrow frequency band pass so the momentum uncertainty is ?p ~ 0 then by the Heisenberg uncertainty principle ?p?x = ? (minimal uncertainty) the spread in x is very large ?x >> 0. In this way the difference in distance between the two “arms” of the galactic beam splitter can be made smaller than the uncertainty. In this set up it is then possible to perform certain experiments which can select which path the photon traveled in a WDCE. This is even if the photon traversed billions of light years from a galaxy billions of light years away.

   As I indicated above, I give an account of the measurement process for the two slit experiment. Suppose you have a two state system of some sort you are looking at. In the case of a double slit there are two possible superposed states |+> and |-> for quanta occurring at the + slit and the – slit. These states then have some expansion according to their appearance on the screen, so we have

   |+> = sum_n a_n|n>, |-> = sum_n b_n|n>.

   It the slits are opened then the state which occurs on the screen is the summation of these two, so then

   |?> = 1/sqrt{2}(|+> + |->) = sum_n(a_n + b_n)|n>,

   where I have absorbed the normalization into the amplitudes. So we then compute

   = 1 = sum_{mn}

   = sum_n(|a_n|^2 + |b_n|^2 + a_nb^*_n + a_n^*b_n)|n>.

   If the amplitudes are a_n = e^{inkx} b_n = e^{ink’x} then

   a_nb^*_n + a_n^*b_n = 2cos(n(k – k’)x)

   which is the interference pattern we expect.

   Now let us suppose we couple this to some auxiliary system. Suppose there is a little detector at one of the slits, so that it goes into the “up state” |u> if the quanta passes through the upper + slit. So we have the up and down slit states as

   |+,u> = sum_n a_n|n,u>, |-,d> = sum_n b_n|n,d>,

   and now the total state is the sum of these

   |?> => 1/sqrt{2}(|+,u> + |-,d>) = sum_n(a_n|u> + b_n|d>)|n>,

   where now we have two orthogonal conditions due to the fact we have entangled the double slit states with some other state. The result of the entanglement means we now have that the cross terms a_nb^*_n + a_n^*b_n are multipled by and which are orthogonal and zero. The entanglement condition has destroyed the interference pattern, where one strange aspect of quantum mechanics, the superposition of two states is taken up by in an entanglement with another pair of states.

   This is the so called collapse of the wave function, and is the source of all this trouble with quantum mechanics. Now for the first situation the density matrix of the two slit experiment is a matrix with probabilities which can equal 1/4 in all the entries for the particle reaching the screen center. By contrast the density matrix reduced to the slit states have entries 1/2 when the system is entangled with this auxiliary spin state. The Schrodinger cat argument involves a hierarchy of measurement “needle states” which measure this auxiliary spin state, and a measurer of that needle state and so forth up to a large scale system — say the brain of a physicist.

   LC

   1. In principle a hierarchy of states, but in practice it seems the environment decohere states fast enough if I understand it correctly. So you can have entangled states survive for a long time, and you can reversibly go into and out of decoherence, but in practice observations are correlated (Wigner and Wigner’s friend).

      The upshot is that decoherence can be studied now.

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