Does the strong force distinguish between past and future ?-II

 

A popular introduction to the strong CP problem

Part II: From the spinning top to irreversibility in time

This blog post is a continuation of the previous one. In this post, I wanted to explain how we can experimentally know if the strong force breaks time-reversal symmetry.  Just as I was writing this post, some exciting results from the particle physics experiment at  Fermilab were announced.  There is a possibility that this measurement would turn out to be a major breakthrough in particle physics.  This was a fortunate coincidence because the same physical concepts underlie both the original subject of this post and the physics behind this exciting new measurement. Thus I will enlarge the scope of this post. While the first part of the post will be a continuation of the previous post, at the end I will touch upon this new development.

In this blog post I will try to explain how we can experimentally determine whether the strong force breaks time-reversal symmetry. Our story starts with the spinning top. As anyone who has seen a spinning top would know, a top doesn't just spin about its axis, the axis itself wobbles and rotates about the vertical direction as shown in the video below.

This wobbling of the axis is called precession and is caused by the gravity.  This is actually one of the more complicated things to understand even for college physics students. Although it is straightforward to understand precession mathematically, it is somewhat counterintuitive. For this reason Richard Feynman, in one of his famous lectures, devotes a lot of time trying to explain precession in a less mathematical way. What makes this wobbling  counterintuitive is that if the top was not spinning, gravity would apply a  rotational force that would make it fall. If the top is spinning, however, the same rotational force leads to this new unexpected rotation of the axis! 

Let us introduce some jargon that would become necessary later. The rotational force mentioned above is an example of what physicists call a torque. It is a very useful concept to understand rotation of bodies. For instance if we have a pendulum that moves to and fro due to gravity we can say that gravity applies a torque. Torques have a direction or sense, i.e. they can be either clockwise of anti-clockwise. Note that in these examples torque is a derived concept arising from the more fundamental idea of a force.

I will not even try to explain the phenomenon of precession more deeply. Let us just remember the following fact: 

no spin+torque=top falls down

whereas, 

spin+torque=precession! 

In fact the sense of the spin and the torque completely determine the sense of the precession. If the spin is anti-clockwise, the clockwise gravitational torque leads to an an anti-clockwise precession. If we reverse the direction of either the spinning or the torque it will change the direction of the precession. If we change the direction of both on the other hand the direction of the precession remains unchanged.

Let us now move on to the main subject of this post, the precession of sub-atomic particles like the electron and the neutron in electric/magnetic fields. The electric and magnetic fields will play the role gravity plays for the spinning top. So, what are electric and magnetic fields? It is the electric fields that cause electrons to move through wires giving rise to electric currents that power the modern world. Magnetic fields, on the other hand, originate from magnets but also from electric currents. In fact electric currents are actually the fundamental source of all magnetism; there are microscopic currents within the magnets themselves. Electric and magnetic fields are deeply connected to each other. They are now understood to be two aspects of the same electromagnetic interaction, one of the four fundamental interactions of nature. 

The connection of these sub-atomic particles with the spinning top arises because--in order to understand some of the important properties of these particles-- we must imagine they are constantly spinning like a top. Except that the spin of such particles differs in a fundamental way from that of the top. The spinning of the top is associated to the rotation of the particles that constitute it. On the other hand, an elementary particle like an electron is thought to have no constituents and thus its spin cannot be understood in the same way as in the case of the spinning top.  It is instead an intrinsic, fundamental property that does not have an analog that can satisfy our intuition. As we will see, however, many of the consequences of this intrinsic spin arise exactly as if these particles were spinning like a top.

Having discussed spin let us come to the other ingredient required for precession: torque. Just as spin can be fundamental for these microscopic particles, so can torque. Electric and magnetic interactions can result in a fundamental torque-like effect that acts on the spin of these particles. This causes a precession of the spin as shown in the figure below where the green arrow shows the direction of the electric/magnetic field and the black arrow shows the spinning particle. The electric/magnetic field plays the role gravity plays for the spinning top.

                        Precession of the spin of a sub-atomic particle

The green arrow above might give the wrong impression that the torque in the above case is clockwise. It is, in fact, more complicated to determine the direction of the torque in this case. To completely determine the direction of the torque we need to know the direction of the torque as well as the spin and one more ingredient, the so called electric/magnetic dipole moment (EDM/MDM). The EDM/MDM of a particle is an intrinsic property that tells us how large the interaction is between the spin and electric/magnetic field.   A larger EDM/MDM will give faster precession. It is the sign of the EDM/MDM that is crucial for determining the direction of the precession. For a positive EDM/MDM an electron with an anticlockwise spin with a upward electric/magnetic field generates a anticlockwise torque and vice-versa for a negative EDM/MDM. There is a key difference in the torque on the spinning top due to gravity and the torque on the spin of a particle in an electric/magnetic field.  In the latter case, as the interaction of the electromagnetic fields is directly to the spin of the particle, the direction of the torque is not independent of the direction of the spin, i.e. if the spin of the electron is reversed so is the direction of the torque.

What happens if we flip the electron/neutron spin ?  Quite remarkably the direction of precession does not change. This is because, the direction of the spin and torque go hand in hand, so that flipping one automatically flips the other. This is unlike the case of the spinning top where we can flip the spin while keeping the torque direction unchanged. For the top therefore such a flipping reverses the precession direction. The direction of  precession of the spin of sub-atomic particles, however, remains unchanged when the spin is flipped because the torque also flips its direction simultaneously [1]. Thus both ingredients in our mantra spin+torque=precession flip directions together resulting in the precession direction not changing!

Consider first the case when an electric field is applied. For this case this is an example of a fundamental process which has an intrinsic directionality. For a given sign of the EDM and a given direction for the electric field the precession direction of a particle is fixed irrespective of the direction of the spin, i.e. it is either always clockwise or always anticlockwise.  As you may have guessed it is this fixed directionality that violates T-symmetry. This is because if time ran backwards, it will change both the direction of the spin and precession (a clockwise rotation would become anti-clockwise if time ran backwards). But this is not allowed as the precession direction must remain unchanged even if the spin flips. The precession of the spin of these particles in an electric field is thus inherently irreversible in time. This brings us to the main point of this post. It turns out that if the strong force violates time reversal this shows up as the presence of an EDM for the neutron. This is not unexpected because the the neutron is made of constituents called quarks that are held together by the strong force.

Precession of these particles under the effect of a magnetic field, however, does not violate time reversal symmetry. Almost everything is identical here except that it is now the magnetic dipole moment interaction that is important. How is it then that with  a magnetic field, such a precession is still reversible ? The crucial difference is that magnetic fields, unlike electric fields, flip their direction under time reversal. This is because, whereas electric fields can be generated by static charges that remain unchanged if we reverse time, magnetic fields are generated by currents, or moving charges. Time reversal, reverses the motion of these charges and also the direction of the magnetic field. This implies that both the magnetic field direction and the spin direction flip under time reversal. As a result, the torque direction, which is a function of these two remains unchanged. So in our 'formula' spin+torque=precession  only one of the ingredients, the spin, flips under time reversal which in turn means that the precession does change direction if time is reversed making this a perfectly reversible process. The precession of atomic nuclei in a magnetic field is, in fact, the phenomenon that underlies Magnetic Resonance Imaging (MRI) Scans.  

                     MRI Scans utilise the precession of the atomic nucleus

These EDMs and MDMs have been measured for many particles with astoundingly high precision. We will briefly discuss three such landmark measurements that directly tell us something deep about the laws of nature.  Our current understanding of the laws of nature as they apply to these sub-atomic particles--and thus all of the universe, which is after all constituted from these particles-- is called the Standard Model. EDM and MDM measurements are capable of testing the Standard Model extremely precisely as well as potentially disproving it. So here are the three measurements: 

(1) The neutron EDM and reversibility of the strong force

As I already mentioned, if the strong force violates time reversal it will show up as the presence of an EDM for the neutron. Experimental results are consistent with the neutron EDM being zero, i.e. the neutron has not been found to wobble at all due to the presence of an electric filed.  In other words there is no evidence that the strong force is irreversible.  Of course it is still possible that a very tiny neutron EDM still exits, but it is too small to be detected even by these extremely precise experiments [2]. The present results, however, tell us that if a neutron EDM exists, it must be at least 10 billion times smaller than what we would naively expect the strong interactions to induce.

(2) The electron MDM and the most precise test of the laws of nature

The precession rate for an electron in a magnetic field, i.e. its MDM, has been measured extremely precisely. The latest experimental value is

2.002319304361

where the Standard Model prediction is:

 2.002319304364.

This matches precisely except the last digit in the 12th decimal place. I have actually rounded up the last digit here as it is affected by theory and experimental errors. The mismatch in the last digit is within the combined expected error of the theory and experiment numbers [3]. The prediction and measurement of the electron EDM counts as one of the most spectacular tests of the present theory of electromagnetism called quantum electrodynamics. The value for the magnetic moment is engraved in the tomb of Julian Schwinger, one of the founders of this theory.

(3) The muon MDM and the first evidence of physics beyond the Standard Model ?

Results announced on April 7 by Fermilab indicate that the muon wobbles in a magnetic field faster than  the Standard Model prediction, by 1 part in 10 billion.  Both the experimental result and the Standard Model prediction need further scrutiny. But if indeed these hold up it would mean we have the first evidence that the Standard Model breaks down. This would make this measurement amongst the most important particle physics developments in decades.  Here is an official Fermilab video that explains their result in a popular way:

I know this post has become perhaps too long and I do not expect you to remember all the details. But there is one take-home message that I would like to convey. The humble wobbling  of the spinning top has an analog for tiny particles like electrons and neutrons. Measuring the tiniest variations in the rate of wobbling of these particles compared to standard predictions can unlock deep secrets about the universe.

Footnotes:

[1] The torque is given by the cross-product d.(S X E)  or m.(S X B). Here S is the spin vector; E and B are the electric and magnetic fields respectively; d and m are the EDM and MDM respectively.

[2] Actually the weak interactions do induce a very small neutron EDM, that experiments are not sensitive to yet.  

[3] For the experts, I have used the Rb numbers from this reference (Eq.3.4). There is actually a hint of a (2 sigma) tension even for the electron MDM. The tension is even larger if Cs numbers are used for determination of alpha_em.