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« "Strategy Of Defeat" | Main | Space Carnival »

Dr. Hawking's Excellent Adventure

Taylor Dinerman has a lengthy piece in the Journal that's a worthwhile read. There is one nit to pick, though (very few people get this right):

Being in microgravity (since there is always some gravitational effect, this is the correct term) for any length of time changes one's metabolism. The human heart, for example, becomes like a ball rather than the "heart"-shaped organ it is on Earth. Blood flows closer to the outer layers of the skin, giving astronauts a characteristic puffy face. It is estimated that a six-month stay on the International Space Station (ISS) causes an average 11% loss of bone density. NASA is working hard to find a way to keep its personnel healthy during long-duration space operations, either on the moon base planned for sometime in the 2020s or on a later trip to Mars.

No, "microgravity" is not the correct term. Microgravity means literally a millionth of a gee of acceleration. Using it in any other way is very confusing.

A quick tutorial.

First, there is no such thing as zero gravity, anywhere in the universe. Gravity, which is the force that one mass exerts on another, as a function of the product of the two masses and the inverse of the square of the distance between them, is ubiquitous, because the universe is filled with masses of various sizes and shapes. And in a so-called "Zero-G" flight, the gravity level is in fact almost exactly the same as it is on the ground, since the aircraft isn't flying all that high, relative to the distance from the center of the earth. Even in low earth orbit, gravity is still about 90% of what it is on the surface. We have to be very careful with the word gravity. In this context, we are using it as a unit measure of an acceleration, not the amount of pull that is exerted on us by the earth (or other objects).

What happens in both parabolic flight (which is technically a portion of an ellipse, rather than a parabola, but if one makes a flat-earth assumption for the gravity model, a parabola is close enough) and in orbit is that the craft is in weightlessness, or free fall, which are the proper terms.

When one is falling (and in a circular orbit, one is continually falling, with the rate of fall toward the earth the same as the rate of the horizon dropping in front of you, so you never get any closer), one doesn't sense gravity. Gravity is only sensed when one resists it, by standing on the ground, or sitting in a chair, or having air drag slow you down when you sky dive. Also, there is only a single point of your body that is in true free fall; most of it is experiencing various (tiny) levels of gravitational force. Because the trajectory is a line in space, only the portion of an object through which that line passes is in true weightlessness. But for practical (in this case, visceral entertainment) purposes, your whole body will seem to be floating. And the easiest way to describe it, if not the accurate one, is "zero gravity." Hence the company's name.

One other note, which is a pet peeve of mine. In Hawking's note to Taylor, he uses the phrase "risk-adverse" to describe NASA. The correct phrase is "risk averse." That is, one has an aversion to risk. Adverse has a different meaning entirely, but many people get this wrong.

Posted by Rand Simberg at April 26, 2007 06:42 AM
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When one is falling...one doesn't sense gravity.

Actually, Rand, to pick on your pick of a nit, I think your implication here isn't quite true. I think you're suggesting a privileged reference frame, that in which the Earth's gravity is "real" and the absence of that gravity only apparent. I think this is a Newtonian point of view, and that general relativity explicitly contradicts it.

That is, I think GR tells us that there is no difference at all between gravity and being in an accelerated reference frame. Hence it's not reasonable for a person in one frame (stationary with respect to the Earth) to suggest that a person in another frame (accelerated with respect to the Earth) is failing to experience a "real" force (the Earth's gravity). The person in "free fall" is entitled to view his gravity-free experience as "real" and see the person on the Earth as being in an accelerated reference frame.

Posted by Carl Pham at April 26, 2007 09:04 AM

The person in "free fall" is entitled to view his gravity-free experience as "real" and see the person on the Earth as being in an accelerated reference frame.

I'm not sure what "entitles" him to do so, or even what that means. Certainly, if he has a sufficiently sensitive accelerometer, he can detect that he's not in a gravity-free state. That's what gravity gradient is all about.

Similarly, the person on the ground can also tell that the acceleration isn't uniform, since it's a spherical field. That's why Einstein's elevator thought experiment was only that. You can in fact distinguish between a gravitational field and an acceleration.

Posted by Rand Simberg at April 26, 2007 09:10 AM

"and in orbit is that the craft is in weightlessness, or free fall"

While we're being ultra-pedantic, nothing is ever actually in free fall, but rather the minute accelerations caused by constant collisions with diffuse matter, escape of matter from vehicles, and the effects of radiation will result in a net deviation from gravitational acceleration.

Posted by Brian Swiderski at April 26, 2007 10:46 AM

I disagree, Rand. In the first place, for the guy in free fall, his accelerometer will register zero, by definition. That's what being in free fall means. Maybe you're referring to tidal effects? How would he distinguish those from the centrifugal effects due to a uniform rotation?

For the guy on the ground, I think you are again assuming there exists some privileged or "absolute" set of acceleration-free frames. You're saying the guy can change reference frames -- move parallel to the surface of the Earth, to check the symmetry of the "gravity field" -- and be sure that he has merely changed inertial frames, and not changed to a frame that has a different acceleration than his old frame. That's saying he can identify a privileged set of inertial frames that are in some state of "absolute" zero acceleration. But GR denies the existence of such a thing, and I believe says there's no experiment the guy can do to determine whether he's changed from one inertial frame to another within a gravity field, or whether he's changed from one accelerated frame to another.

That's why Einstein's elevator thought experiment was only that. You can in fact distinguish between a gravitational field and an acceleration.

I don't think so. I'm not a GR guru, but I believe GR says that acceleration and gravity are mathematically indistinguishable. That's what the principal of relativity implies: only relative changes in acceleration are meaningful. You can't assign an unambiguous meaning to the experience of acceleration, and say this acceleration is "pure gravity" and some other experience is "pure acceleration" and still another is some mixture of the two. Any point of view between pure gravity and pure acceleration is equally valid. (By equally valid, I mean experiment offers no way to choose between them, even if habit and personal preference do.)

Hence, someone experiencing no gravity is perfectly entitled to argue there is no gravity, and people nearby who think there is are merely accelerating relative to his frame.

Perhaps there are those better skilled in GR who can correct me on this, if I'm wrong. I thought there were some HEP people around here somewhere...you can always tell by the smell of reheated vile coffee...

Posted by Carl Pham at April 26, 2007 11:47 AM

Maybe you're referring to tidal effects?

I am.

How would he distinguish those from the centrifugal effects due to a uniform rotation?

By the asymmetry of the acceleration field.

I'm not a GR guru, but I believe GR says that acceleration and gravity are mathematically indistinguishable.

In theory, perhaps, but not practice, at least as I understand it. My recollection of the description of the elevator experiment was that acceleration was indistinguishable from a uniform gravitational field. But in the real universe, such a thing doesn't exist. It's approximated on an earthly elevator, but it remains spherical. But I could be wrong.

Posted by Rand Simberg at April 26, 2007 12:08 PM

By the asymmetry of the acceleration field.

Huh? What asymmetry? Since when are tidal effects asymmetric? You saying the tide goes higher on the side of the Earth nearer the Moon than on the other side?

In theory, perhaps, but not practice,

I don't think fundamental theory works that way. We might as well say the Coulumb force is inversely proportional to distance in theory, but not in practise. I think you can only make that kind of statement about theory that is approximate, has built-in limitations, and which people can try to push beyond its proper limitations. You can say the Navier-Stokes equations describe a fluid in theory, but not in practise, because they are approximate, and there exist realms of experiment that violate those approximations. There are no approximations in GR. (Excepting its classical nature, that is, but no one knows what kind of approximations, if any, that implies.)

My recollection of the description of the elevator experiment was that acceleration was indistinguishable from a uniform gravitational field

Linear acceleration is not distinguishable from a uniform gravity field with a plane of Cartesian symmetry. Other types of more complicated acceleration would not be distinguishable from fields with more complicated symmetry.

I think the symmetry issue is a red herring. How can the equivalence of gravity and acceleration depend on such a changeable and meaningless thing as the exact symmetry of the field? It sounds like you're saying Einstein told us that it's possible to set up certain systems that mimic gravity, so sometimes you can't tell the difference. I don't think so. That would be a pretty ordinary thought, not Nobel prize-winning genius.

What Einstein sad, I believe, is that you can never tell the difference for sure between gravity and acceleration, not even in principle, not even with theoretically perfect instruments, that in fact there is no difference, that by choosing a particular frame of reference you can arbitrarily shift what you observe from pure gravity to pure acceleration and back again.

This is the counterpart to his observation in special relativity that you cannot distinguish, even in principle, between the distance in space between two events and the distance in time. By shifting frames you can change spatial separation into temporal separation and back again. And none of the viewpoints is more "correct" than any other.

Again, I speak under correction if there are those more skilled in GR than I who can do so.

Posted by Carl Pham at April 26, 2007 01:07 PM

Seems to me it's a minor terminology quibble. I've never heard "microgravity" to literally mean gravity a millionth that of Earth's, but instead to acknowledge that in free fall in real spacecraft with significant extent, other factors (gravitational fields of nearby objects, tidal interactions, rotations, etc.) mean that it isn't precisely zero gravity. But nothing ever can be in the real world, so the distinction is kind of moot. I think both the quibble and the quibble's quibble are in the realm of semantics.

As for the equivalence principle of general relativity, it applies only locally -- i.e., in the vicinity of a point. Non-uniform gravitational fields obviously can be detected by extended objects (e.g., tidal forces come into play). But that isn't surprising. If you're in a closed room and you're trying to determine whether the weight you feel is due to the gravitational field of a planet or a rocket that's uniformly accelerating, there's an easier way to find out: Look out the window.

Posted by Erik Max Francis at April 26, 2007 03:29 PM

Seems to me it's a minor terminology quibble. I've never heard "microgravity" to literally mean gravity a millionth that of Earth's

Then you've never read requirements for NASA space stations, and their science experiments...

Posted by Rand Simberg at April 26, 2007 03:46 PM

Interestingly, all the nit-picking involves a flight by a man who might answer the questions better than any of us...

As I mentioned elsewhere, if it's true that Newtion was inspired by observing the fall of an apple, who knows what insights the experience might give Hawking?

Posted by Frank glover at April 26, 2007 04:01 PM

Since when are tidal effects asymmetric? You saying the tide goes higher on the side of the Earth nearer the Moon than on the other side?

Ummmmm...yes.

Think about it.

If that doesn't help, do some math...

Posted by Rand Simberg at April 26, 2007 06:28 PM

If I may have your indulgence to bring up another misunderstanding of gravity, I refer to the famous photo of Bob Beamon during his astounding world record long jump at the Mexico City Olympics. The photo shows Beamon at the apex of his jump, with his legs extended forward anticipating his landing. As I recall, the Sports Illustrated reporter, in pointing out the extraordinary aspects of the jump, said something to the effect of Beamon's incredible abdominal strength, being able to hold his legs horizontal. As more than one commentator remarked, when you're free in the air, it takes no strength to hold your limbs in any attitude you wish.

Posted by Bruce Lagasse at April 26, 2007 08:15 PM

A "tidal force" is simply the difference between gravitational force exerted on the front (or rear) of a body and on its center of mass. If the distance between centers of mass of a planet and a moon is A, and the planet's radius is B, then the tidal force moon exerts on the planet's near face is proportional to:

1/(A-B)^2 - 1/A^2

Which after transformations converts to:

(B^2 + 2AB) / [A^2 * (A-B)^2]

And the tidal force moon exerts on the far face is proportional to:

1/A^2 - 1/(A+B)^2

Which transforms to:

(B^2 + 2AB) / [A^2 * (A+B)^2]

The nominator is the same in both formulae, but the denominator is larger in the second. Hence the second value is smaller. So yes, the tide does go higher on the side of the Earth nearer the Moon than on the other side.

Posted by Ilya at April 27, 2007 12:12 PM

I think you mean "numerator," rather than "nominator". Also, I don't think that you can ignore the rotation of the system, because it does create a centripetal acceleration that affects tide height, in addition to gravity. You really have to work off the common center of mass of the two bodies.

Posted by Rand Simberg at April 27, 2007 12:51 PM

You are right about the spelling of "numerator" :) As for rotation of the system, I will have to think about that one. It is not as easy as straight distance-force calculation.

Posted by Ilya at April 27, 2007 01:34 PM


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