Quantum Physics in a Mirror Universe

SPEAKER_1 (0:00)

College football is back, so Hilton called on me, the superstition concierge, to make your fan rituals a reality. Need a room to match your lucky number? We got you. Wanna make sure our team doesn't wash your lucky jersey? Ooh, that smells lucky.

Hilton's unmatched hospitality can keep up with any superstition. Even a marching band wake up call at 555 in 55 seconds. Hit it! When you need a team that will do whatever it takes on game day, it matters where you stay. Hilton, for the stay.

SPEAKER_2 (0:30)

Chronic migraine is 15 or more headache days a month, each lasting four hours or more.

SPEAKER_3 (0:34)

Botox, on a botulinum toxin A, prevents headaches in adults with chronic migraine before they start. It's not for those with 14 or fewer headache days a month. It prevents on average eight to nine headache days a month versus six to seven for placebo.

SPEAKER_4 (0:47)

Prescription Botox is injected by your doctor. Effects of Botox may spread hours to weeks after injection causing serious symptoms. Alert your doctor right away as difficulty swallowing, speaking, breathing, high problems or muscle weakness can be signs of a life threatening condition. Patients with these conditions before injection are at highest risk. Side effects may include allergic reactions, neck and injection site pain, fatigue and headache. Allergic reactions can include rash, welts, asthma symptoms and dizziness. Don't receive Botox if there's a skin infection. Tell your doctor your medical history, muscle or nerve conditions including ALS Lou Gehrig's disease, myasthenia gravis or Lambert-Eton syndrome and medications including botulinum toxins as these may increase the risk of serious side effects.

SPEAKER_2 (1:24)

Why wait? Ask your doctor, visit botoxchronicmigraine.com or call 1-800-44-BOTOXX to learn more.

Matt O'Dowd (1:33)

Thanks to brilliant.org for supporting PBS Digital Studios. When you look in a mirror, you might think you see a perfect reflection, but you're actually looking at a universe whose laws are fundamentally different.

When we think about symmetry, the first thing that comes to mind is mirror symmetry. Butterflies, raw shark tests and classically attractive faces all look the same when flipped left to right.

In physics, a symmetry is when the laws of physics are unchanged due to some transformation of coordinates. We've seen examples where this holds. The universe is symmetric to coordinate shifts in space, time, and even the rather abstract phase of the wave function in quantum mechanics.

So it might be surprising to learn that with all the weird ways in which the universe is symmetric, it's not entirely symmetric under the most intuitive one. The laws of physics work differently in the universe of the mirror. Let's talk about the physics of entering the mirror universe. The technical name for such a reflection is a parity transformation. And when something remains identical under such a transformation, we say that the thing is parity symmetric, p-symmetric. Parity is a weird type of symmetry. In the case of those other symmetries I mentioned, the shift in position, time, or phase can be by any amount small or large. These are continuous symmetries. But there's no such thing as a partial reflection. You either reflect or you don't. Parity is a discrete symmetry.

Other types of discrete symmetries include charge conjugation, flipping the sign of the electric charge, and time reversal, sending in the clock, ticking backwards. We'll come back to both of these. They are going to save us in the end. Parity transformations involve the flipping of spatial axes. If we define the mirror to be in the XY plane, reflections send Z to minus Z and vice versa. Objects are turned back to front and front to back. And it looks like your right hand becomes your left and vice versa as though you had actually flipped in the X direction, not the Z.

Well, actually, a true X axis reflection would look like this.

Left still goes to right, but forward-facing stays the same. This is exactly the same as a Z axis reflection plus a rotation. In fact, a reflection on any single axis can be reproduced by a reflection on a different axis plus a rotation. A reflection on two axes then puts things back to normal, while reflection on all three axes gives the same left-right switch as a reflection on one axis. But formally, a full parity inversion means flipping all three axes. Now, when you reflect the universe, obviously it is different. All position vectors point in the opposite direction. Same with velocity slash momentum. Throw a ball at the mirror away from yourself and its reflection looks like it's coming towards you. In the language of parity, we call properties that flip sign odd functions. Properties that don't change under reflections are called even. Things like the energy of the ball, its mass, the time on its clock and, as we'll see, angular momentum don't change in the mirror universe. Now, even though some signs do get flipped, the laws of physics should be unaltered in that mirror world. Newton's laws will still give the ball's trajectory. Those laws work the same, no matter the direction of motion. In fact, if we rotate the whole mirror ball's trajectory by 180 degrees, it's identical to the original trajectory.