gravity

Could CERN open a portal to… somewhere? (anywhere?)

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For general readers:

Is it possible that the particle physicists hard at work near Geneva, Switzerland, at the laboratory known as CERN that hosts the Large Hadron Collider, have opened a doorway or a tunnel, to, say, another dimension? Could they be accessing a far-off planet orbiting two stars in a distant galaxy populated by Jedi knights?  Perhaps they have opened the doors of Europe to a fiery domain full of demons, or worse still, to central Texas in summer?

Mortals and Portals

Well, now.  If we’re talking about a kind of tunnel that human beings and the like could move through, then there’s a big obstacle in the way.  That obstacle is the rigidity of space itself.

The notion of a “wormhole”, a sort of tunnel in space and time that might allow you to travel from one part of the universe to another without taking the most obvious route to get there, or perhaps to places for which there is no other route at all, isn’t itself entirely crazy. It’s allowed by the math of Einstein’s theory of space and time and gravity.  However, the concept comes with immensely daunting conceptual and practical challenges.  At the heart of all of them, there’s a basic and fundamental problem: bending and manipulating space isn’t easy.  

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Celebrating the Standard Model: The Forces of Nature

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A post for general readers:

This is the first of several posts celebrating the hugely successful Standard Model of particle physics, the concepts and equations that describe the basic bricks and mortar of the universe. In these posts, I’ll explain (without assuming readers have a science background) how we know some of its most striking features. We’ll look at simple facts that particle physicists have learned over the decades, and use them to infer basic features of the universe and to recognize deep questions that still trouble the experts.

The Elementary “Forces” of Physics: A Classification of Nature

Perhaps you’ve heard it said that “There are four fundamental forces in nature.” Whether you have or not, today I’ll show you how to verify this yourself. (Actually, there are five forces, though we’ll only see a hint of the fifth today.) The force everybody knows from daily life is gravity; ironically, this force has no measurable impact on particle physics, so it’s the only one we won’t be looking at in this post.

I’d better emphasize, though, that the word “force” is slippery. Normally, in everyday life, a force means something that will push or pull objects around. But when physicists say “force,” they often mean something much more general. Because of that they sometimes use the word “interaction” instead of “force”.

For example, static electricity that holds socks together when they come out of the dryer is an example of an honest electromagnetic force — the socks really are pulled together. So is the force that pulls a magnet to a refrigerator door. But when a light bulb glows, that doesn’t involve a force in the limited sense of a push or pull. Yet it still involves the “electromagnetic interaction”, i.e. the “electromagnetic force” in a generalized sense. That’s because, although it is far from obvious, the emission (or absorption) of light involves the same basic phenomena that govern the force between the socks.

[Physicists use “electromagnetic” rather than “electric” or “magnetic” separately because these two forces are so deeply intertwined that it is often impossible to distinguish them.]

So when physicists say there are “four forces” (or five), they are imposing a classification scheme on the world around us. They mean:

  • All fundamental physical processes in nature can be divided up into five classes.
  • Each class involves one of the following types of interactions:
    1. gravitational (holds the planet together and holds us to the ground),
    2. electromagnetic (creates light, controls chemistry and biology, and dominates daily life),
    3. weak-nuclear (essential in stars and in supernova explosions),
    4. strong-nuclear (forms protons, neutrons, and their agglomerations in atomic nuclei),
    5. Higgs-related (associated with the masses of all known elementary particles).

There are currently no verified exceptions to this classification scheme. And by examining basic facts about the various particles found in nature, we can see these classes (other than gravity) in operation.

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Black Holes, Mercury, and Einstein: The Role of Dimensional Analysis

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In last week’s posts we looked at basic astronomy and Einstein’s famous E=mc2 through the lens of the secret weapon of theoretical physicists, “dimensional analysis”, which imposes a simple consistency check on any known or proposed physics equation.  For instance, E=mc2 (with E being some kind of energy, m some kind of mass, and c the cosmic speed limit [also the speed of light]) passes this consistency condition.

But what about E=mc or E=mc4 or E=m2c3 ? These equations are obviously impossible! Energy has dimensions of mass * length2 / time2. If an equation sets energy equal to something, that something has to have the same dimensions as energy. That rules out m2c3, which has dimensions of mass2 * length3 / time3. In fact it rules out anything other than E = # mc2 (where # represents an ordinary number, which is not necessarily 1). All other relations fail to be consistent.

That’s why physicists were thinking about equations like E = # mc2 even before Einstein was born. 

The same kind of reasoning can teach us (as it did Einstein) about his theory of gravity, “general relativity”, and one of its children, black holes.  But again, Einstein’s era wasn’t first to ask the question.   It goes back to the late 18th century. And why not? It’s just a matter of dimensional analysis.

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Coordinate Independence, Kepler, and Planetary Orbits

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Could you, merely by changing coordinates, argue that the Sun gravitationally orbits the Earth?  And could Einstein’s theory of gravity, which works equally well in all coordinate systems, allow you to do that?  

Despite some claims to the contrary — that all Copernicus really did was choose better coordinates than the ancient Greek astronomers — the answer is: No Way. 

How badly does the Sun’s path, nearly circular in Earth-centered (geocentric) coordinates, violate the Earth’s version of Kepler’s law?  (Kepler’s third law is the relation T=R3/2 between the period T of a gravitational orbit and the distance R, which is half the long axis of the ellipse that the orbit forms.)   Since the Moon takes about a month to orbit the Earth, and the Sun is about 400 = 202 times further from Earth than the Moon, the period of the Sun would be 4003/2 = 8000 times longer than the Moon’s, i.e. about 600 years, not 1 year. 

But is this statement coordinate-independent? Can it serve to prove, even in Einstein’s theory, that the Earth orbits the Sun and the Sun does not orbit the Earth? Yes, it is, and yes, it does. That’s what I claimed last time, and will argue more carefully today.

Of course the question of “Does X orbit Y?” is already complicated in Newtonian gravity.  There are many situations in which the question could be ambiguous (as when X and Y have almost equal mass), or when they form part of a cluster of large mass made from many objects of small mass (as with stars within a galaxy.)  But this kind of ambiguity is not what’s in question here.  Professor Muller of the University of California Berkeley claimed that what is uncomplicated in Newtonian gravity is ambiguous in Einsteinian gravity.  And we’ll see now that this is false.

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Earth Goes Around the Sun? What’s Your Best Evidence?

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It’s commonly taught in school that the Earth orbits the Sun. So what? The unique strength of science is that it’s more than mere received wisdom from the past, taught to us by our elders.  If some “fact” in science is really true, we can check it ourselves. Recently I’ve shown you how to verify, in … Read more

From Kepler’s Law to Newton’s Gravity, Yourself — Part 2

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Sometimes, when you’re doing physics, you have to make a wild guess, do a little calculating, and see how things turn out.

In a recent post, you were able to see how Kepler’s law for the planets’ motions (R3=T2 , where R the distance from a planet to the Sun in Earth-Sun distances, and T is the planet’s orbital time in Earth-years), leads to the conclusion that each planet is subject to an acceleration a toward the Sun, by an amount that follows an inverse square law

  • a = (2π)2 / R2

where acceleration is measured in Earth-Sun distances and in Earth-Years.

That is, a planet at the Earth’s distance from the Sun accelerates (2π)2 Earth-distances per Earth-year per Earth-year, which in more familiar units works out (as we saw earlier) to about 6 millimeters per second per second. That’s slow in human terms; a car with that acceleration would take more than an hour to go from stationary to highway speeds.

What about the Moon’s acceleration as it orbits the Earth?  Could it be given by exactly the same formula?  No, because Kepler’s law doesn’t work for the Moon and Earth.  We can see this with just a rough estimate. The time it takes the Moon to orbit the Earth is about a month, so T is roughly 1/12 Earth-years. If Kepler’s law were right, then R=T2/3 would be 1/5 of the Earth-Sun distance. But we convinced ourselves, using the relation between a first-quarter Moon and a half Moon, that the Moon-Earth distance is less than 1/10 othe Earth-Sun distance.  So Kepler’s formula doesn’t work for the Moon around the Earth.

A Guess

But perhaps objects that are orbiting the Earth satisfy a similar law,

  • R3=T2 for Earth-orbiting objects

except that now T should be measured not in years but in Moon-orbits (27.3 days, the period of the Moon’s orbit around the Earth) and R should be measured not in Earth-Sun distances but in Moon-Earth distances?  That was Newton’s guess, in fact.

Newton had a problem though: the only object he knew that orbits the Earth was the Moon.  How could he check if this law was true? We have an advantage, living in an age of artificial satellites, which we can use to check this Kepler-like law for Earth-orbiting objects, just the way Kepler checked it for the Sun-orbiting planets.  But, still there was something else Newton knew that Kepler didn’t. Galileo had determined that all objects for which air resistance is unimportant will accelerate downward at 32 feet (9.8 meters) per second per second (which is to say that, as each second ticks by, an object’s speed will increase by 32 feet [9.8 meters] per second.) So Newton suspected that if he converted the Kepler-like law for the Moon to an acceleration, as we did for the planets last time, he could relate the acceleration of the Moon as it orbits the Earth to the acceleration of ordinary falling objects in daily life.

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From Kepler’s Law to Newton’s Gravity, Yourself — Part 1

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Now that you’ve discovered Kepler’s third law — that T, the orbital time of a planet in Earth years, and R, the radius of the planet’s orbit relative to the Earth-Sun distance, are related by

  • R3=T2

the question naturally arises: where does this wondrous regularity comes from?

We have been assuming that planets travel on near-circular orbits, and we’ll continue with that assumption to see what we can learn from it. So let’s look in more detail at what happens when any object, not just a planet, travels in a circle at a constant speed.

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BICEP2’s Cosmic Polarization: Published, Reduced in Strength

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I’m busy dealing with the challenges of being in a quantum superposition, but you’ve probably heard: BICEP2’s paper is now published, with some of its implicit and explicit claims watered down after external and internal review. The bottom line is as I discussed a few weeks ago when I described the criticism of the interpretation … Read more

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