general relativity

Is Einstein’s Theory of General Relativity Truly Elegant?

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  • Quote: . . . the Higgs field exhibits the most inelegant of the known laws governing fields and particles. There’s an amusing tendency for those who tout beauty to ignore this, as though it were an inconvenient family member, and to focus instead on Einstein’s elegant theory of gravity. Yet even that theory has its issues.
  • Endnote: Einstein’s theory of gravity is amazingly elegant as long as one ignores the puzzle of “dark energy,” which would have been easier to do had it been exactly zero, and as long as gravity is a very weak force, as its weakness leads to extremely simple equations. In string theory, Einstein’s equations become much more complex, and the elegant simplicity of the math shifts to the level of the strings themselves . . . perhaps.

I’ll expound below upon the second bullet point, hoping to draw attention to general questions concerning aesthetics in theoretical physics.

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What [Really] Causes our Twice-Daily Ocean Tides?

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More about tidal forces today (see also yesterday’s post) and the conceptual point underlying Earth’s ocean tides.

  • (Quote) Because gravity dwindles at greater distances, the Moon’s pull is stronger on the near side of the Earth and weaker on the far side than it is on the Earth’s center. This uneven pull stretches our planet’s oceans slightly, resulting in a small bulge of water, not much taller than a human, both on the Earth’s side facing the Moon and on the opposite side, too.
  • (Endnote) To explain why gravity leads to a water bulge on both sides of the Earth is too complex for a footnote, and I’d rather not repeat the most commonly heard explanations, which are misleading. One can see a hint of the cause as follows: if one drops a water balloon in constant gravity, it will fall as a sphere, whereas if it is pulled more strongly at the bottom than at the top, it will stretch into an oval as it falls.

Here I’ll explain this last observation more carefully.

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The Impossible Commentary: Is Gravity a Force? Is it an Illusion?

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[This is a tricky one… it’s easy to make confusing statements about Einstein’s theory of gravity (general relativity), and so I am especially hopeful of getting readers’ feedback on this subtle issue, to make sure what follows is 100% clear and correctly stated.]

  • (Quote) On Earth’s surface, we are roughly 4,000 miles from Earth’s center. But if you ascended another 22,000 miles, where you’d find the GOES weather satellites that monitor Earth’s weather patterns, you’d find your weight (but not your mass!) reduced to one-fortieth of what it is on Earth… And if you traveled out into deep space, far from any large object, you’d weigh virtually nothing. Yet all the while, your body’s mass—the difficulty I would face if I tried to speed you up or slow you down—would never change.
  • (Endnote) Confusingly, astronauts orbiting Earth inside nearby space stations appear to float as though weightless. From Newton’s perspective, they are not truly weightless; if they were, they’d coast, leaving the Earth’s vicinity and moving rapidly into deep space.
    Instead, they and their spaceship are pulled by gravity into a common orbit around the Earth. Since they travel on the same path as their container and as the camera which films them, they seem and feel weightless. (This subtle issue is turned on its head in Einstein’s view of gravity.)

Astronauts in a space station seem to float, as though they are weightless. Are they truly weightless? Or are they only apparently weightless?

The same issues arise for people in a freely falling elevator, accelerating downward with ever greater speed. They will feel weightless, too. But are they?

Newton would have said they are apparently weightless, subject to gravity but all falling together along with their vehicle. A naive (but instructive!) reading of Einstein might lead us to say that they are truly weightless… that the gravity that Newton claims is present is a pure illusion, a fictitious force. But a precise Einsteinian would say they are almost but not quite weightless — and the lack of perfect weightlessness is a clue, a smoking gun in fact, that they are indeed subject to gravity.

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About the News that Antimatter Doesn’t “Fall Up”

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The press is full of excitement today at the news that anti-matter — hydrogen anti-atoms, specifically, made from positrons and anti-protons instead of electrons and protons — falls down rather than rising up. This has been shown in the ALPHA experiment at CERN. But no theoretical physicist is surprised. Today I’ll explain one of many … Read more

Mass, Weight, and Fields

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Today a reader asked me “Out of the quantum fields which have mass, do any of them also have weight?” I thought other readers would be interested in my answer, so I’m putting it here. (Some of what is discussed below is covered in greater detail in my upcoming book.)

Before we start, we need to rephrase the question, because fields do not have mass.

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Why Current Wormhole Research is So Important

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Once we clear away the hype (see the previous posts 1, 2, 3, 4), and realize that no one is doing anything as potentially dangerous as making real wormholes (ones you could actually fall into) in a lab, or studying how to send dogs across the galaxy, we are left with a question. Why bother … Read more

Send Your Dog Through a Wormhole?

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A wormhole! What an amazing concept — a secret tunnel that connects two different regions of space! Could real ones exist? Could we — or our dogs — travel through them, and visit other galaxies billions of light years away, and come back to tell everyone all about it?

I bring up dogs because of a comment, quoted in the Guardian and elsewhere, by my friend and colleague, experimentalist Maria Spiropulu. Spiropulu is a senior author on the wormhole-related paper that has gotten so much attention in the past week, and she was explaining what it was all about.

  • “People come to me and they ask me, ‘Can you put your dog in the wormhole?’ So, no,” Spiropulu told reporters during a video briefing. “… That’s a huge leap.”

For this, I can’t resist teasing Spiropulu a little. She’s done many years of important work at the Large Hadron Collider and previously at the Tevatron, before taking on quantum computing and the simulation of wormholes. But, oh my! The idea that this kind of research could ever lead to a wormhole that a dog could traverse… that’s more than a huge leap of imagination. It’s a huge leap straight out of reality!

I’ve been trying to train our dog, Phoebe, to fetch a ball through a wormhole. She seems eager but nervous.

What’s the problem?

Decades ago there was a famous comedian by the name of Henny Youngman. He told the following joke — which, being no comedian myself, I will paraphrase.

  • I know a guy who wanted to set a mousetrap but had no cheese in his fridge. So he cut a picture of a piece of cheese from a magazine, and used that instead. Just before bed, he heard the trap snap shut, so he went to look. In the trap was a picture of a mouse.

Well, with that in mind, consider this:

  • Imaginary cheese can’t catch a real mouse, and an imaginary wormhole can’t transport a real dog!

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How Do You Make a Baby Cartoon Wormhole In a Lab?

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This post is a continuation of the previous one, which you should read first…

Now, what exactly are these wormholes that certain physicists claim to be trying to make or, at least, simulate? In this post I’ll explain what the scientists did to bring the problem within reach of our still-crude quantum computers. [I am indebted to Juan Maldacena, Daniel Jafferis and Brian Swingle for conversations that improved my understanding.]

An important point from last post: a field theory with quarks and gluons, such as we find in the real world or such as we might find in all sorts of imaginary worlds, is related by the Maldacena conjecture to strings (including quantum gravity) moving around in more dimensions than the three we’re used to. One of these dimensions, the “radial dimension”, is particularly important. As in the previous post, it will play a central role here.

Einstein-Rosen Bridge (ER) vs. Einstein-Podolsky-Rosen Entanglement (EPR)

It’s too bad that Einstein didn’t live long enough to learn that two of his famous but apparently unrelated papers actually describe the same thing, at least in the context of Maldacena’s conjecture. As Maldacena and Lenny Susskind explored in this paper, the Maldacena conjecture suggests that ER is the same as EPR, at least in some situations.

We begin with two identical black holes in the context of a string theory on the same curved space that appears in the Maldacena conjecture. These two black holes can be joined at the hip — well, at the horizon, really — in such a way as to form a bridge. It is not really a bridge in spacetime in the way you might imagine a wormhole to be, in the sense that you can’t cross the bridge; even if you move at the speed of light, the bridge will collapse before you get to the other side. Such is the simplest Einstein-Rosen bridge — a non-traversable wormhole.

What, according to the Maldacena conjecture, is this bridge from the point of view of an equivalent field theory setting? The answer is almost fixed by the symmetries of the problem. Take two identical field theories that would each, separately, be identical to one of the two black holes in the corresponding string theory. These two theories do not affect each other in any way; their particles move around in separate universes, never interacting. Despite this, we can link them together, forming a metaphorical bridge, in the most quantum sense you can imagine — we entangle them as much as we can. What does this mean?

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