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GR9677 #34
Problem
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Advanced Topics$\Rightarrow$}Particle Physics

Regularly, electrons are emitted in any direction. Thus, there is infinite symmetry. In the case of a magnetic field, electrons are more likely to be emitted in a direction opposite to the spin direction of the decaying atom. Place the atom in an x-y plane, with its spin-direction pointing along the z-axis. If the electron is mostly emitted in the -z axis, then reflection symmetry is violated since it's not (mostly) emitted in the +z axis, i.e., not mirrored across the x-y plane. Choice (D).
(This is due to Joe Bradley.)

Alternate Solutions
 dipanshugupta2017-03-29 10:02:01 Simpler answer. Beta Decay is a Weak Interaction. Weak Interactions are Parity Violating. Parity is a Reflection invariance as $P^\' (\\vec{x},t) \\Rightarrow P ( - \\vec{x},t)$. Hence, problem solved. Reply to this comment
dipanshugupta
2017-03-29 10:02:01
Simpler answer. Beta Decay is a Weak Interaction. Weak Interactions are Parity Violating. Parity is a Reflection invariance as $P^\' (\\vec{x},t) \\Rightarrow P ( - \\vec{x},t)$. Hence, problem solved.
Skribb
2009-09-26 05:21:20
This is the type of problem, and there are a number of problems, in which one would benefit from remembering which invariances deal with which conservation laws. From Griffiths intro to elementary particles, comes:

Symmetry..................................Conservation Law

Translation in time....................Energy
Translation in space..................Momentum
Rotation.....................................Angular Momentum
Gauge Transformation..............Charge

So a preferred spin would be a violation of the conservation of Angular Momentum and so the symmetry violation is the invariance to rotation.
 Skribb2009-09-26 05:24:04 Apologies, I mistakenly stated that there was a violation in rotation. What I meant to say was that in fact none of the 4 match the criteria so by process of elimination the answer must be D.
CaspianXI
2009-03-22 12:59:33
For those who haven't taken particle physics, this problem can be solved with eliminating a few choices and guessing.

Eliminate (B) because time invariance should NEVER be violated. (The few theoreis which claim to violate time invariance, are highly disputed, and the ETS hopefully won't be mean enough to make the right answer open for dispute)

Eliminate (A) because Gague invariance is based on quantum mechanics... usually, a quantum system violates a classical "rule of thumb"... a quantum system (hopefully) shouldn't violate part of quantum mechanics.

So, we're down to 3 choices and the odds are for us to guess now. Look at (D). We know that reflection invariance is a classical "rule of thumb" -- if you slide a block in front of your mirror, the physics will look correct both to the "real" block, as well as the block moving in the mirror. But what if you hold a wheel in front of a mirror such that the angular momentum vector points to the right. When you look at the wheel in the mirror, that wheel's angular momentum vector looks like it's pointing to the left.

We know the problem has something to do with spin... so, we know that reflection invariance has a problem with spinning things. Now, reflection invariance still works for classical spinning systems (even though the vector is flipped the physics still looks correct in the mirror), but you might be able to imagine what problems this vector flipping problem might cause when taken down to a quantum system.

So, guess (D). This isn't a proof... but just shows how you can make an educated guess without understanding the material. And yes, I reasoned through this before actually knowing the answer was (D) ;).
 WontonBurritoMeals2009-10-03 20:23:55 Actually, I think that CP violation is equivalent to T violation and there are some experiments that exhibit CP violation.
 wittensdog2009-10-30 16:32:10 Time invariance must be violated if QFT is to hold. It is a deep consequence of QFT that CPT is what must be invariant, and if CP is not conserved (which we know experimentally it is not), then T must be violated. Otherwise we basically would have to start modern physics all over again from scratch.
lowder.chris
2007-10-03 21:29:53
Whaaaaaa? Makes sense this does not. Can someone explain this solution?
 sawtooth2007-10-28 16:14:40 Look it up under parity violation in any textbook. This is the famous Madame Wu experiment.

LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces $\alpha^2_0$. type this... to get...$\int_0^\infty$$\int_0^\infty$$\partial$$\partial$$\Rightarrow$$\Rightarrow$$\ddot{x},\dot{x}$$\ddot{x},\dot{x}$$\sqrt{z}$$\sqrt{z}$$\langle my \rangle$$\langle my \rangle$$\left( abacadabra \right)_{me}$$\left( abacadabra \right)_{me}$$\vec{E}$$\vec{E}$$\frac{a}{b}\$ $\frac{a}{b}$