Dark Energy and (anti-)Gravity

Warning: Technical discussion ahead. This is not at the typical level of the book, and the graphics are far worse and the jokes nonexistent. It’s just something I’ve been meaning to jot down.

In the “User’s Guide,” our goal is to answer as many nagging questions about physics as completely and coherently as we possibly can, often with jokes thrown in for good measure. Our editors, Eric and Connie, asked a few questions which we couldn’t really tackle without taking a major digression (which we don’t object to) or without getting excessively technical (which we do object to). These questions never made it into the book. One, in particular, really had me stumped for quite while, and even after a chat with the estimable Rich Gott, I was still confused. The answer to the question was never in doubt. It was just a matter of why the answer was what it was. Without further ado:

“Can I make a ball of Dark Energy into an anti-gravity device?”

The short answer is, “No. Antigravity devices are impossible.” And, if that’s all you want to know, then you can stop reading now.

But the “why not?” is far more interesting. I won’t get into all of the details of Dark Energy here. For one thing, we talk about it a lot in the User’s Guide. For another, a simple Wikipedia search will quickly give you an overdose about the cosmological implications of Dark Energy. For now, all you need to know is that Newton was close, but not quite correct when it came to gravity.

Einstein’s general theory of relativity is much better, and in addition to all of the weird stuff about how time and space get warped, he noted that mass isn’t the only thing that causes gravity; pressure does as well. Normally we wouldn’t notice this because in galaxies, stars, or your living room, pressure (in the right units) is less than a billionth as important as the mass, and so it rounds out in the end. But basically, he said:

m_gravity=m_inertial(1+3w)

  • The m_inertial is the thing we normally think of as mass. It’s a measure of how hard an object is to move. It’s also the mass that goes into Einstein’s famous E=mc^2.
  • M_gravity, on the other hand, tells you how much a lump of stuff pulls on other bodies in the universe.
  • The “w” tells you about the pressure.
    • For ordinary atoms, or even Dark Matter, this w is close enough to 0 to ignore.
    • For radiation (light), which under normal circumstances only contributes a small amount of total energy (and hence mass), w=1/3.
    • For the mysterious “Dark Energy” which pervades the universe, w=-1.
      A negative pressure means that the Dark Energy actually has a tension instead.

So what happens if we have a lump of dark energy?

1+3(-1)=-2

In other words, the “gravitational mass” of Dark Energy is negative, and thus you’d expect it to push everything away from itself. This is why the concept of “Dark Energy” was invented in the first place. Distant supernovae were observed to be moving away from us at a rate suggesting the universe is accelerating.

But (and here’s where we get into the question) if this is true, why couldn’t we make a ball of the stuff, and push ourselves away? Okay, okay. There’s no practical way to collect Dark Energy. As near as we can tell, it pervades the entire universe equally, but I can’t manipulate wormholes at the present, either, and that doesn’t prevent me from talking about it. So here’s our (supposed) contraption:

Dark Energy Repulsion

Dark Energy Repulsion

See? This is what happens when I don’t have Jeff to do the artwork.

Anyway, this contraption seems like it might work. But there’s a problem! Our “stuff” (a moon, for example) creates a gravitational field of its own, meaning that it attracts the ball of dark energy:

We get a very awkward situation. The moon is attracting the Dark Energy, but the Dark Energy is repelling the moon. We seem to have inadvertently created perpetual motion! This is clearly wrong, but why?

It’s actually even worse than that. Einstein’s theory of special relativity says (essentially) that energy can’t be created or destroyed, but can can be converted to other forms. Imagine our ball originally contained ordinary stuff (half matter, half anti-matter). At that point, filled with “stuff”, it would have been gravitationally attractive:

Suppose we then turn the matter/anti-matter mix into Dark Energy. I know, we would have no idea how to do this, but we do know how to turn mass into radiation, and if you spend a few hours in a dark room, you’ll realize that that creates the same problems albeit on a different scale. After all, turning mass into radiation should double the overall gravitational strength.

But enough about radiation, we were talking about Dark Energy, and I want to know what happens if we take our matter/anti-matter and convert it to Dark Energy. All of a sudden, the ball goes from attractive to repulsive. This is absolutely counter to everything I’ve ever been taught about relativity. Provided it’s symmetric, there’s no way that we could be able to tell what’s going on inside the ball by measuring the gravity outside. How do we unravel these mysteries?

Answer: The answer is actually pretty prosaic, as it turns out. It’s all in how you make the ball. If the matter inside has ordinary (positive) pressure, then the ball membrane itself has to have a tension, gravitationally canceling the internal pressure out. On the other hand, if there’s dark energy in the sphere, then the membrane will have to exert a positive pressure itself to cancel out the dark energy’s tension. In either case, the numbers exactly work out so that the only thing you see outside the sphere is the gravity generated by: m_gravity=m_inertial.

Bonus Question: If that’s the case, then why does dark energy cause the universe to accelerate?

Bonus Answer: Because the universe doesn’t have any edges, and certainly not any rigid ones.

Whew. It feels good to get that off my chest.

-Dave

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3 Responses to Dark Energy and (anti-)Gravity

  1. David Hulsman says:

    My mind asploded of all the awesome and information 😛

  2. Jim says:

    There was a lot of awesome, I might asplode as well.

  3. Rohan Mcleod says:

    Rather than assume ‘anti-gravity drives are impossible and then try
    to explain ‘why’; it seems to me that a more useful approach is
    to firstly narrow the question to :
    What would be the mathematical consequences if an ‘anti-gravity drive’ with local conservation of mass, momentum and energy existed.?
    In the short essay at:
    https://docs.google.com/document/d/1MhV26WitsQooCyi5mw9l0cCCuO-DyTv2JrOhD48uxTA/edit
    This is the question which I have tried to ‘unwrap’;

    regards Rohan McLeod

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