Schrödinger's Cat: Probability, Science & Medicine

Prologue
Atoms with unstable nuclei decay, emitting ionizing radiation, known as radioactivity. We cannot feel ionizing radiation. Small amounts can be detected with devices such as the fabled Geiger-Müller counter. Radioactive atoms are called radionuclides. Numerous radionuclides have been found. They are listed in the table of nuclides. With most types of radioactive decay, the nucleus transforms into another element with new physical and chemical properties. Since we cannot predict when precisely a radionuclide decays, we are left with probabilistic assessments. According to the law of radioactivity (1), the nuclei decay exponentially. The period of time in which half of the nuclei in a sample decay is constant and characteristic for the radionuclide. This period is known as half-life.

(1) N(t_exam) = N(t₀) x 2^-t_exam/τ,

where N(t_exam) is the number of radionuclides left at time of examination t_exam. N(t₀) is the number of radionuclides at time t₀ when we started our test. τ is the half-life.

After ten half-lives, the chance of finding a nucleus still undecayed has become fleetingly small. Only about one in a thousand nuclei is still left in its original form. We may consider the material decayed. However, when half-lives measure tens of thousands of years and the radiation is detrimental to our health, ten half-lives add up to a serious threat for generations to come. That is why the proponents of nuclear power show intense interest in Yucca Mountain.

Applying the law of radioactivity on just one atomic nucleus, our odds of finding this nucleus decayed after one half-live are 1/2 or 50%. That is, we are equally likely to find the nucleus decayed or in its original form. After seven half-lives, the odds to still detect the original nucleus are less than 1/100. We would call this find a rare event. After ten half-lives the odds diminish to roughly 1/1000. We would find the atom undecayed merely once in a thousand tests and perceive this observation as extremely extraordinary. Try it yourself:

half-lives:

odds: 1/

Schrödinger's Thought Experiment

The Austrian physicist and Nobel Prize-laureate Erwin Schrödinger always insisted that his was only a thought experiment. He never contemplated carrying it out in practice. Its design was the following:

Method: A Geiger-Müller counter is set up in front of a radionuclide. The radiation emitted when the radionuclide decays produces a voltage spike in the counter. The spike is used to trigger a hammer installed inside an opaque box, housing a cat. The hammer will smash a vial with poison gas, killing the cat.

Question: Is the cat already dead or still alive once one half-life has passed?

Answer: According to the law of radioactivity discussed above, the chances of finding the cat in either condition are equal. We will only know for sure, when we open the box and look.

Discussion: With this experiment, Schrödinger intended to explain the implications of the wave function, he derived to determine the energetic state of electrons in the shells around the atomic nucleus. In analogy to the solutions for his function, the cat could theoretically exist in both possible states alike. That is, the cat could be dead and alive simultaneously, until checking the box resolves the ambivalence.

Schrödinger's contention, though accurate, is difficult for us to comprehend. We like to live in certainty. Einstein believed that uncertainty was the result of our shortcoming in making the correct predictions. In response to the idea that uncertainty naturally exists, he supposedly exclaimed mildly dismayed: "God does not role dice!"

Our ambivalent feelings toward chance become crystal clear, when we are confronted with a diagnosis of cancer and options for treatment. To the question,"Doc, will I live?" the answer may be, "well, the prognosis in cases like yours is not outright brilliant. But, half of the people in your situation are still alive after two years." Analogous to Schrödinger's thought experiment, this means that in two-years time our odds are 1/2.

With bewilderment, we respond, "but, Doctor, I did not ask how many people on average will still be alive when. I wish to know, whether I shall be alive!" The honest physician will conclude, "I cannot answer this question. But experience tells us that your chances are much improved, if you want to live and remain hopeful."

This uncertain answer fully reveals the dilemma of the medical profession. The physician is asked to divine the faring of a patient based on statistical probabilities derived from groups of patients. As often with cancer, the precise causes of the disease may not be known. Only intensive fundamental research will provide us with a more effective grasp on such complex diseases. Only deepening our knowledge of the molecular signaling mechanisms that trigger tumorous tissue growth will permit us to predict accurately, how the cells will grow and what needs to be particularly done to stop them.

For example, researchers using proteomics may be able to uncover differences in the proteins synthesized in cancerous cells. With this knowledge, physicians may be able to decide which group of patients will benefit the most from a particular type of therapy, and further research will unravel the functions of the proteins.

As to Schrödinger's cat, the experiments at CERN's Hadron supercollider will drastically enhance our understanding of subnuclear particles and their interactions. The findings at CERN may perhaps permit us one day to predict the decay of an unstable nucleus, erasing the uncertainty in Schrödinger's thoughts. The experiments may as well prove this goal elusive or even impossible to attain. In any case, the results of the research at CERN will deeply influence how we reckon with the odds in our lives.

It is regrettable that the U.S. partake only on the sidelines in the pivotal experiments. In the late 1980's, the construction of an even larger collider than Hadron, known as the Superconducting Super Collider, was begun in Texas. After hundreds of millions of dollars spent on digging tunnels, the project was aborted. Another several hundred million dollars were spent to fill in the holes already dug.

Addenda

• An example for the use of proteomics to reliably predict therapy outcome in lung cancer is in press here: Stuart Salmon and others (2009) Classification by Mass Spectrometry Can Accurately and Reliably Predict Outcome in Patients with Non-small Cell Lung Cancer Treated With Erlotinib-Containing Regimen. Journal of Thoracic Oncology 4 (6) (04/20/09).
• Cells of some tumors have been found to contain salient genetic mutations. Notably, deletions at the BRAF gene and substitution at the KRAS gene have been found to promote neoplastic growth. Therapeutics are being developed that may compensate for the defects caused by the mutations, arresting tumor growth. Amy Harmon posted an extensive series of articles for the New York Times on the experimental drug PLX4032 used to stop melanoma in people with BRAF mutations. Her first article in this series with the title "A Roller Coaster Chase for a Cure" appeared Feb. 21, 2010. Today, Ron Winslow reports in his post for The Wall Street Journal with the title "Using Biomarkers to Tailor Cancer Treatment" on the preliminary success of similar strategies in targeting lung cancer. Notably, the drug Nexavar was beneficial to people with KRAS mutations. While the use of these drugs has only succeeded in arresting further tumor growth to date, they hold the promise of profoundly improving the odds (04/18/2010).
• Siddhartha Mukherjee, a hematologist/oncologist at Columbia University, wrote an informative book entitled "The Emperor of All Maladies: A Biography of Cancer" on recent advances in cancer medicine. The author was awarded a Pulitzer Prize for his exploration earlier this month. Note that he specializes in blood cell cancer and the particular experience influences his assessment of the role of stem cells in tumorigenesis and metastasis. Terry Gross interviewed him Nov. 11, 2010, on National Public Radio's Fresh Air in her show with the title "An Oncologist Writes 'A Biography Of Cancer'" (04/22/11).