The foundations of quantum theory rest
on its symmetries for example it should be impossible to distinguish our
universe from one that is a perfect mirror opposite in charge handedness and
the direction of time but one by one these symmetries were found to be broken
threatening to break all of physics along with them. In his famous lectures
on physics Richard Feynman talks about what it means to expect the universe to
be identical in the mirror for it to be parity symmetric he invites
us to imagine a clock in a mirror reflection. Numbers of backwards
components are all flipped left to right and it ticks counterclockwise and then
he asks us to imagine building that same mirror clock in reality everything is
constructed as though reflected - numbers get painted backwards every screw with
right-handed thread or right spiraling coil is replaced with a left-handed
version our intuition tells us that the mirror clock should tick in exactly the
same way except counterclockwise - our intuition would be wrong. The laws of
physics and so the laws of clocks are not symmetric to this sort of parity
transformation as we saw in our recent episode the experiment that first proved
this found that cobalt-60 nuclei decay by splitting an electron out in the
opposite direction to their nucleus speed axis but in a mirror reflected
universe the same decay should be in the opposite direction so with that spin
axis which is fundamentally different physical behavior. So, what does this have
to do with Feynman's clock? well, he proposes a clock whose ticks are
governed by the decay of cobalt-60. Imagine an array of cobalt-60 atoms in a
magnetic field, the cobalt nuclei have angular momenta that will align with a
magnetic field let's say upwards so the decay electrons
travel down. A detector is placed to intercept those
electrons and the clock ticks with every captured electron. In our reflected clock
we need to replace the cobalt atoms with their parity inverted counterparts but
now the decay electrons travel upwards with the nuclear spin and away from the
detector such a clock wouldn't tick at all taken to its literal extreme a
perfectly constructed mirror reflected clock behaves differently so what's the
big deal well the violation of parity symmetry
poses a threat to an even deeper symmetry cpt symmetry the combined
flipping of charge parity and time and this symmetry lies at the foundations of
quantum field theory physics must work the same if we flip all of these
properties if not physics as we know it goes out the window which does seem like
a big deal. To save physics, Richard Feynman proposes that we build a copy of
our clock out of antimatter. Uh... sure, Feynman - why not! electrons become positronsquarks become anti quarks and vice-versa sending protons and neutrons to their
anti versions in the nuclei of our now anti cobalt-60
and other anti-atoms sending matter to antimatter is the C part of cpt charge
conjugation all charges switch side electric charge but also quark color
charge weak hypercharge etc that's what a switch to antimatter means how does
this work in our Antion on a clock well antimatter atoms have negatively charged
nuclei which means their nuclear magnetic fields point in the opposite
direction to regular matter relative to their angular momentum the magnetic
field in our clock will align antimatter nuclei in the opposite direction to
matter nuclei so in our mirror reflected antimatter clock the direction of the
decay electrons are flipped once due to the mirror reflection and once due to
the switch to antimatter that leaves the electrons traveling in the original
direction down and the clock ticks as normal so even though the universe isn't
parity symmetric maybe it is under a charge parity a CP
transformation said right to left and send matter to antimatter at first
glance this CP symmetry appears to hold not just in an imaginary clocks but also
in the particles of the standard model the great parity violating process is
the weak interaction which only affects left chiral fermions right chiral fermions
don't feel the weak force at all but the opposite is true of antimatter right
chiral anti fermions fill the weak force while left chiral anti fermions don't so
a charged parity flip leaves you in the same situation regarding the weak
interaction if CP is what we call a good symmetry then you shouldn't be able to
do any experiment to tell whether you're in this universe or in a CP transformed
universe or physics should work the same theoretically but don't get too
comfortable we haven't looked at what the experimentalists have to say about
this you may recall from the parity episode that the first hint of parity
violation was the so-called tau theta problem we've turned out to result from
the fact that the positively charged Kaon meson decayed in ways that violated
parity conservation it turns out that these Kaon particles are great at
catching the universe doing weird stuff in 1964
James Cronin and Val Fitch looked at the outcomes of the decay of neutral Kaons
these things are extra weird and usual k on is a quantum mix of its own particle
and antiparticle there are two ways to do this mixing yielding two types of
mutual Kaon one time let's call it KS he is short-lived
and has what we call an even CP state which just means it doesn't change under
a combined charge parity transformation the other type KL is long-lived and has
an odd CV state it's wave function gets multiplied by -1 on a CP
transformation and that means well it's different to the KS state if CP
symmetry is conserved KS and KL should never transform into each other because
they have different CP symmetries Cronin and Fitch tested this by sending
a bunch of both types of neutral Kaon down a tube with a detector at the far
end. The KS particles should never have made the journey given their short
lifetimes and yet a small but significant number of decay products
from KS particles were found at the far end the only explanation is that KL
particles oscillated into KS's, violating charge parity conservation well that
sucks our mirror reflected antimatter clock doesn't work right after all nice
one Fineman and that's not the worst of it the violation of CP symmetry has much
more dire consequences than a broken imaginary clock although it does have a
lot to do with time this also suggests that time reversal symmetry is broken
and to understand this we do need to reverse time a bit and go back to the
1950s which coincidentally saw the breaking of another imaginary clock in
Hill Valley California the 1950s was also the decade of the foundations of
quantum field theory an SQFT emerged it became clear that there is a certain
symmetry that's not just intuitively expected but also theoretically required.
Starting with Julian Schwinger's "Spin statistics theorem" in 1951 it became
increasingly clear that quantum field theory demands symmetry under the
combined action of charge conjugation parity inversion and time reversal the
very axiomatic foundations of QFT state that an antimatter mirror reflected time
reversed version of our universe should have exactly the same laws of physics
this is the CPT theorem. Quantum field theory should be CPT-invariant and we
know that quantum field theory is right at least as far as it goes it's just
about the motor right theory we've ever come up with I'll get back to what this
new time reversal symmetry the T and CPT actually means but for now let's just
accept that the laws of physics must work the same under a simultaneous
flipping of charge parity and the direction of time that was certainly the
view of physicists in the late 1950s so then come the experiments that show
violation first of P, then of CP symmetry - big deal,
we still have T, CPT can be conserved. But here's the issue if CP symmetry is
violated and CPT symmetry holds then T symmetry must also be violated why
because that time reversal operation needs to bring us from a broken CP
reflected universe into a fixed CP T universe but that means a T
transformation from our working CPT universe sends us to a broken CP
universe. Burgo time reversal transformation changes the way the
universe behaves. Time symmetry is out the window,
theoretically. That sounds bad, isn't physics supposed to work the same
whether we go forwards or backwards in time? well as we talked about in this
episode don't we absolutely require time reversal symmetry in order to conserve
quantum information which itself is required for all of quantum mechanics to
make sense - well to get at this we're going to need to talk about what we mean
by reversing time the most obvious interpretation of time reversal is
literally reversing the arrow of time and causing the universe to travel
backwards in time. That is not what we mean by the T in CPT which I'll explain
in a minute but first let's think about this simple type of T transformation as
a literal rewind. Rewind the universe and you get back to where you started pretty
much by definition so presumably quantum information is conserved in this type of
time rehearsal. Mathematically, the particles in a rewinding universe actually look
like they underwent a charge parity inversion. Matter that was going forward
in time looks like parity flipped antimatter
going backwards in time. This interpretation of antimatter as time
reverse matter was first proposed by Ernst Stueckelberg in 1941 but is now largely
associated with Richard Feynman - it's essential to his path integral approach
to quantum mechanics and to Feynman diagrams maybe that's why he was so into
building antimatter clocks. So, yeah the universe is not symmetric under this
simple version of T reversal. It's the precise inverse of a
CP transformation, the two undo each other. Do a CP transformation and then a simple
T transformation and you get back to where you started. If CP is violated then
this simple time reversal is also violated and we see this violation in
the asymmetry between matter and antimatter
then there's the whole entropy business although it's connection to quantum
mechanics is still not well understood like I said this simple interpretation
of T as rewinding the universe is not what we usually mean by the T in CPT -
that T is more accurately thought of as flipping the direction of the evolution
of a physical system - an explosion becomes an implosion and particle decay
becomes particle creation. You're not rewinding time, you're not converting
matter to antimatter - you're just reversing all momentum and spin.
Essentially you're taking all particles in the universe and pointing them back
in the direction they came from. If the T in CPT is conserved then after
reversing all particle motion those particles should perfectly retrace
their steps and perfectly reverse all reactions in their histories. As this
motion reverse universe evolves forward in time it should end up back in its
starting configuration. On the other hand broken T symmetry says that if you do
this reversal the future won't perfectly mirror the past. One prediction of this T
symmetry is that all processes should take the same amount of time going
forwards as backwards for example a quantum transition between
one particle type and another should take the same time in either direction
and that gives us a test: in 2012 physicists from the BaBar collaboration
at the Stanford Linear Accelerator Center tested the speed with which B
maisons transition between two types in a T symmetric universe the speeds should
be the same in either direction they were not the same
reversing the direction of the interaction changed something fundamental
about the physics indicating a violation of T symmetry. But remember, killing T
symmetry is a good thing because it may save CPT symmetry. The last 70
years have been a true roller coaster ride for the symmetries of nature as
experiments found broken symmetries one, by one the first parity then charge
parity the hallow'd CPT symmetry looked in danger unless we gave up on the
symmetry of time itself but now with time reversal symmetry also looking like
it's broken the CPT theorem looks safe Feynman's mirror reflected antimatter
clock will work just fine but as well as ticking backwards every atom every
subatomic particle needs to tick backwards also so we've discovered our
perfect mirror universe it's a reflection of all three: charge,
space, time. Hey everyone, I'm back from the event horizon,
aka. Australia, which as you know is the CPT inverted version of Canada. The last
episode before the break was, "Why string theory is Wrong". Today, I want to address
the comments to that episode or catch up on last week's comments next time - in
fact, I really want to address a few points made by FieldStrength on the PBS
Space Time subreddit: they covered all the most important points, now first I
want to clarify that despite the title, "Why String Theory is Wrong", the point of the
video was not to argue that string theory is wrong instead it was a playful
follow-up to why string theory is right I'll reiterate my real opinion on the
matter after addressing fill strengths specific than very reasonable criticisms.
In the video we note that string theory pretty much requires supersymmetry in
order to be right and that supersymmetry hasn't yet been detected at the expected
energy scale that's the energy scale expected if supersymmetry is to also
provide a neat resolution to the standard models hierarchy problem but
string theory doesn't require supersymmetry to be at that
scale at all for the purpose of string theory supersymmetric particles could be
far beyond the energies detected by the Large Hadron Collider - so FieldStrength
argues that our current non detection of supersymmetric particles is no
falsification of string theory and, of course, that's correct but I didn't say
otherwise - apologies if it seemed implied. However, I do argue that this non
detection is a bit of a hiccup supersymmetry is highly compelling if it
provides an answer to the hierarchy problem and gives us super string theory
it will be odd if supersymmetry existed as part of super string theory but did
nothing to help with the hierarchy problem because it was at far too high
an energy scale. But then as I did mention in the video the current Large
Hadron Collider results do not yet completely rule out all energy scales
useful for the hierarchy problem only at the energy scales that solved the
problem most neatly. FieldStrength's other point is that the large undefined
parameter space of string theory - the so called 'String landscape' is no more of a
problem for string theory than it is for the standard model - I totally agree. In
fact it's less of a problem for string theory because in the standard model
many parameters are hopelessly unconstrained by the theory itself while
in string theory it's arguable that only one parameter is hopelessly
unconstrained. My point is not that string theory is more wrong in the
standard model it's just that it's not yet "right" -
in this sense. To quote me it was never really right and to quote Peter Weitz
quoting Pauli, "it's not even wrong". The point being that while not wrong there's
not yet a way to properly test his rightness or wrongness. FieldStrength's
final point is that the untestability of string theory is connected to the
extreme energy scale of quantum gravity and that problem is not unique to string
theory. Now we do talk about that in our first episode on general quantum gravity
so apologies for not repeating it here. So yeah string theory is apparently not
yet testable, but I disagree with those who say that
this type of untestability means that the field is not science. String theory
may be currently untestable due to the energy scales involved but the universe
has no obligation to make itself currently testable to any particular
particle collider building technology level. It's under no obligation to make
every next layer of reality accessible to the next generation of physicists. We
blasted through several reality layers from atoms to quantum fields in the past
hundred years or so but maybe the next layer will take another thousand years
or more. Randy Copeland brilliantly notes that
physicists are a bit like 'House' M.D. trying to find a diagnosis that fits the
symptoms with the symptoms being all of reality itself.
Nice observation also makes me feel better when I put my title down when I
buy airline tickets in the hope of getting an upgrade. I'm still dreading
the day when the crew come to me because there's some medical emergency on board
and I have to tell them what type of doctor I am.
