In one of Jeff Shallit's recent posts on the Panda's Thumb, he mentioned that Tom Bethel, aside from

being a creationist, was also a relativity denier. In general, relativity denial is a veritable mine

of bad math. So I went looking - and found Bethel's anti-relativity site. As I expected, we've got extremely silly bad math. In fact,

it's the worst kind of bad math - it's a lack of math masquerading as being math. It's also, sadly, full

of pathetic errors.

For instance, there's this:

The argument that gravity must travel faster than light goes like this. If its speed limit is that of light, there must be an appreciable delay in its action. By the time the Sun's "pull" reaches us, the Earth will have "moved on" for another 8.3 minutes (the time of light travel). But by then the Sun's pull on the Earth will not be in the same straight line as the Earth's pull on the Sun. The effect of these misaligned forces "would be to double the Earth's distance from the Sun in 1200 years." Obviously, this is not happening. The stability of planetary orbits tells us that gravity must propagate much faster than light. Accepting this reasoning, Isaac Newton assumed that the force of gravity must be instantaneous.

Astronomical data support this conclusion. We know, for example, that the Earth accelerates toward a point 20 arc-seconds in front of the visible Sun -- that is, toward the true, instantaneous direction of the Sun. Its light comes to us from one direction, its "pull" from a slightly different direction. This implies different propagation speeds for light and gravity.

The problem here is that this isn't math - it's presenting things *as if* they were mathematical results, but without actually showing the math. In effect, it's trying to pretend

that there's math backing them up, when what they're really doing is bullshitting.

The math doesn't support them *at all*. To see why, you just need to remember for

a moment what gravity is, in terms of relativity. Gravity is a warp in the shape of space. Space

is literally bent around objects with mass. Gravitational fields change the shape of space. Objects

are affected by the shape of space that they pass through.

That's not what the argument above says. To anthropomorphize a bit, it says that the sun

is constantly looking around itself in space, and sending little packets of gravity to the things that it sees. So at a given time t_{0}, it looks at the earth, which is in position p_{0}. At that time, the gravitational force that should be exerted on the earth is pointed toward the center of mass of the sun. (See the diagram to the side.) At t_{0}, the sun creates a packet of gravity,

with a force vector pointing at the center of the sun. The sun sends this packet of gravity to the earth - when it arrives, it will accelerate the earth in the direction that it's pointing. But it takes 8 minutes to get there. So when it gets to earth at time t_{1}=t_{0}+8 minutes,

the earth has moved to a new position - position p_{1}. In this new position, the packet of gravity isn't pointing at the center of the sun anymore - because the earth has moved, the packet

of gravitational force is pointing a little bit ahead of the center of the sun. That's what they're arguing - that there should be a directional error in the gravitational force because of the time

delay.

That's not how gravity works. The sun doesn't look at where the earth is, pick a packet of gravity for that position, and send it to wherever the earth will be 8 minutes later. According to relativity, the

earth is accelerated by a gravitational force created by the shape of space that it's passing through. There's no magically aimed packets of gravity. The sun doesn't emit specific bits of gravity for the earth - it creates a field permeating the space around it; the earth is affected by the field that it passes through. The earth is accelerated at any moment by the gravity field *that it's passing through* at that moment. It doesn't matter at what rate that field propagated through space - what matters is what field the earth is passing through. The rate of propagation of gravity only matters when something *changes* - then the change takes time to propagate. But that's not what they're talking about.

But there's another error - an even more obvious one - in the nonsense argument above.

According to Bethel, The sun sends a packet of gravity containing direction to the earth at time t_{0}. It arrives at time t_{1}. But the earth isn't where it was when the sun sent

the packet of gravity. If the sun sent it to the position where the earth was at t_{0}, then the packet of gravity will *miss the earth*. So the sun needs to send a packet of gravity matching

the earths position at t_{0} - but it needs to aim it at t_{1}. In other words, the sun

needs to correct for the kind of direction error that they're arguing should exist, in order to make

that direction error exist.

That's the kind of error that you make when you're not actually doing the math.

One other error that I can't resist pointing out, which comes later in the article, when he's

talking about GPS.

Both theories, Einsteinian and local field, would yield the same results. So far. Now let's turn back to the Global Positioning System. At high altitude, where the GPS clocks orbit the Earth, it is known that the clocks run roughly 46,000 nanoseconds (one-billionth of a second) a day faster than at ground level, because the gravitational field is thinner 20,000 kilometers above the Earth. The orbiting clocks also pass through that field at a rate of three kilometers per second -- their orbital speed. For that reason, they tick 7,000 nanoseconds a day slower than stationary clocks.

To offset these two effects, the GPS engineers reset the clock rates, slowing them down before launch by 39,000 nanoseconds a day. They then proceed to tick in orbit at the same rate as ground clocks, and the system "works." Ground observers can indeed pin-point their position to a high degree of precision. In (Einstein) theory, however, it was expected that because the orbiting clocks all move rapidly and with varying speeds relative to any ground observer (who may be anywhere on the Earth's surface), and since in Einstein's theory the relevant speed is always speed relative to the observer, it was expected that continuously varying relativistic corrections would have to be made to clock rates. This in turn would have introduced an unworkable complexity into the GPS. But these corrections were not made. Yet "the system manages to work, even though they use no relativistic corrections after launch," Van Flandern said. "They have basically blown off Einstein."

The GPS satellites *do* have to make a correction in their clock speeds to adjust for the differing rate of time in a different gravitational field. That, in itself, is an astonishing thing:

we can predict, with incredible accuracy, just how much you need to modify the clock rate of a satellite

for the difference in the relative speed of time between the surface of the earth and the orbit of

the satellite. Bethel waves past that - an incredible feat, a spectacular example of how precise

relativity is when you do the math correctly - as if it's a trivial and unimportant thing. And

he moves on to his supposed point - that GPS doesn't need to do any other relativistic corrections

depending on the location of a GPS receiver on earth. Except that he's wrong - and he's wrong

because he doesn't do the math.

You see, modern GPS receivers *do* do relativistic corrections.

But back when the article was written, GPS was using something called SA, which was a deliberate degredation of the signal. This was done so that non-military users couldn't take advantage of the full precision of the GPS. The relativistic errors caused by receivers being in different locations on

the earth was dwarfed by the amount of imprecision introduced by SA. So in the early receivers, there

was no point in doing the relativistic correction - not because there was no effect, but because the signal quality was degraded too much for the correction to be doable.

Once again, if Bethel sat down and did the math (which he describes as no more complicated than

high school algebra), actually plugged the numbers into the equations to see how much error

could be introduced by the predicted effects of relativity, and compared it to the known precision

of SA GPS, he would have known how stupid this argument was. But he didn't.

As usual - the worst math is no math.

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Bethell denies *everything* even remotely scientific. Chris Mooney took him to task on global warming; a chapter of his was my first post on AIDS denial. I guess I should have known he'd add math in there too.

I hate to say this, but I don't think you addressed a key point in his argument:

It is not that the sun "sees" the Earth and sends out a "packet of gravity". No, it is sitting there emitting gravitons in all directions exactly the same as it is emitting photons in all directions. Wherever the Earth is, it intercepts those photons and gravitons and detects a vector pointing at the source. If gravitons and photons both travel at the same speed, should the gravitational vector perfectly align with the photons? If his statement about the difference in the vectors is true, isn't he then correct about the difference in their speeds of propagation?

addendum: The reason the rate of propagation matters is that something is indeed changing, the sun is moving and so it does matter where the sun was when it emitted its gravitational field.

I do love the image though, of the sun sitting there, shooting gravity packets at the earth, but forgetting to aim for where the earth

will be, and missing every time. There's something very Elmer Fudd about that imagery.Actually, SteveM, if you bothered to do the math, you'd see that your analogy argues against the error. Photons (or if you want to look at it classically, EM waves) travel, obviously, at the speed of light. But Coulomb forces show no such delay; a charged particle feels a force in the direction from its current location (unless it's accelerating), not its location long enough in the past for a photon to travel to it. John Baez has a good explanation of this at his USENET Physics FAQ: http://www.math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

Oh, and Bethel's a hoot; I seem to remember him having a new perpetual motion machine every few years. Van Flandern's a laugh riot, too. Years ago I saw him take the most hilariously one-sided pummeling on the USENET skeptic group, and the man just kept coming back for more.

When you meet a multidenialist, a good start to get to know them is often talkreason.org. Several posts references Chris Hillman's review of Bethell and Van Flandern.*

Van Flanderns problem is that he uses a naive force carrier picture. Separating "disturbances" (waves) from "field changes" makes him propose separate velocities and "light" faster than light.

* Chris Hillman had a good science and pseudoscience resource posted on John Baez science site, originating from the Usenet era. I was sad to see that he withdraw the effort June 2007. He also mentions creative differences:

:-) :-( Fortunately, the Wayback machine keeps the site's memory with us.

When you meet a multidenialist, a good start to get to know them is often

Talk Reason. Several posts references Chris Hillman's review of Bethell and Van Flandern.*Van Flanderns problem is that he uses a naive force carrier picture. Separating "disturbances" (waves) from "field changes" makes him propose separate velocities and "light" faster than light.

* Chris Hillman had a good science and pseudoscience resource posted on John Baez science site, originating from the Usenet era. I was sad to see that he withdraw the effort June 2007. He also mentions creative differences:

:-) :-( Fortunately, the Wayback machine keeps the site's memory with us.

When you meet a multidenialist, a good start to get to know them is often

Talk Reason. Several posts references Chris Hillman's review of Bethell and Van Flandern.*Van Flandern's problem is that he uses a naive force carrier picture. Separating "disturbances" (waves) from "field changes" makes him propose separate velocities and "light" faster than light.

[Cont.:]

* Chris Hillman had a good science and pseudoscience resource posted on John Baez science site, originating from the Usenet era. I was sad to see that he withdraw the effort June 2007. He also mentions creative differences:

:-) :-( Fortunately, the Wayback machine keeps the site's memory with us.

The post describes the problem efficiently, but the difference between other fields (so called gauge fields) and gravitation isn't really clear. Baez focus efficiently on this - while general relativity is a field theory, it doesn't give gravity as a "force" but a warping of spacetime.

In reality we have at least 4 different theories to juggle.

1. Newtons field theory of gravity. Gravity is described by a potential and forces from accelerated masses are immediate.

This is analogous to other classical non-relativistic field theories, like Maxwell's EM theory.

2. General relativity. Gravity is described by curved spacetime, and field changes from accelerated masses travels with light speed.

This is analogous to other covariant formulated field theories, like the EM four-vector formulation. (Panofsky-Phillips, "Classical electricity and magnetism".)

3. A low-energy effective quantum field theory of gravity. Gravity is described by quantizing a Lagrangian, and field changes from accelerated masses travels with gravitons at light speed.

This is analogous to other low-energy effective quantum field theories, like Fermi theory (see link). It is only valid for weak fields, as a semi-classical approximation.

4. Quantum gravity. A non-perturbative quantum theory. Gravity is described by quantizing ???, and field changes from accelerated masses travels with gravitons at light speed.

This is analogous to other quantum field theories, like QED. The current best bet for ??? is M theory. (Non-perturbative string theory.) Perturbative string theory gives gravitons as closed strings.

Usually you do fine with #1. But here we have to mix in a little bit of #2 as well. Gravitons are optional. :-P

The best bit of his explanation has got to be that if it were true, light would also 'miss' the earth due to the delay (or perhaps appear to be coming from a different part of the sky; I haven't done the math ;).

Haha, seeing the headline I thought you had som IDist denying that scientific knowledge is possible. Wrong kind of relativist.

No, I didn't "bother" to do the math, the point I was trying to focus on was Bethel's assertion that the gravitational pull of the sun is not in the same direction as the light we receive from it. Is this really true? How can this be if both light and gravity travels at the speed of light? In fact, after reading the link to the Usenet Physics FAQ, it would seem that the vectors should align regardless of the speeds of propagation, so how could this misalignment occur at all?

The objections to the talk of the sun sending out packets of light/force are silly and misguided. There's no 'aiming'. It's just a convenient way to talk about the solar emissions that will end up hitting the Earth.

And like Steve M, I would also like an explanation for this supposed disjunction between what the Earth orbits and what we see - if the claim is true, which I doubt, it would mean that gravity really *doesn't* propagate at the speed of light. The statements about fields of force being centered on the actual locations of particles, if taken literally, means that fields could be used to send messages faster than light.

I'm pretty sure that, in your rush to attack nonsense, you've only propagated more nonsense yourself. Making fun of fools is fun, but is it worth it if you make a fool of yourself in the process?

Hey TorbjÃ¶rn, looks like the Wayback machine worked -- there are three of you in this timeline all posting the same thing.

Bethel's "gravitational aberration" argument about gravity being directed towards the Sun's instantaneous position is the same as Tom van Flandern's. The error is clearly explained in this paper by Steve Carlip.

As it turns out,

exactly the same effectoccurs in Maxwellian electromagnetism, but we don't see Bethel claiming that light travels faster than light!The attraction is not really towards the Sun's instantaneous position. It depends only on the Sun's retarded position, as expected, but in a functional form that is a linear extrapolation of the retarded position which, to first order, looks like the Sun's instantaneous position.

Steve, it's because you're talking about two different sorts of phenomena: electromagnetic

waves, which propagate outward at the speed of light, and a gravitational "field". You're not dealing with an electromagnetic field and a gravitational field. We observe the same abberation for the Sun's magnetic field as we do for the gravitational field (to a first approximation), and gravitational waves should show the same delay as light. Now, you can eitherbother to do the freaking math, though you seem to think that would be a bad thing, you can read through Carlip exhaustively running through the math for you in the link Ambitwistor helpfully provided, or you can actually read the non-mathy FAQ I linked instead of skimming it (emphasis added for the reading comprehension impaired):Now, I can understand not doing the math -- it's friggin hard, especially the GTR. But if you're

notgoing to do the math, I suggest you not ignorantly talk up cranks like Bethell, and not sneer at the thought of actually working though it. At the very least you could stop to think through the reasoning (did you even bother to think for one second about your analogy and what EM abberation tells you about it?). For some reason I'm reminded of the possibly apocryphal Mark Twain quote, "better to keep your mouth closed and be thought a fool than to open it and remove all doubt."Ambitwistor, as TorbjÃ¶rn reminded me, van Flandern actually

doesclaim that light travels faster than light, and I wouldn't be surprised if Bethell echoed this.Physics is so awesome and wonderful. I wish it didn't make my head hurt quite so much.

I think the crux of the matter is the presumed mis-alignment of the acceleration of the Earth. It certainly would be a problem if it were true as described. After a little calculating, it would seem to me that the rotation of the Earth around the Sun would not produce any misalignment no matter if the speed of light and gravity were the same or different, because the vector of each as they arrived at Earth would always be at the center of the Earth-Sun system, namely at the actual position of the Sun.

ok, for us non-mathematicians, one simple question in regards to the "speed" of gravity. If the sun would suddenly convert large amounts of its mass into energy in form of a supernova event (and yes, this is an overly simplified example), would we find out due to some change in gravity before the flash reaches us 8 min later?

In computing relativistic effects relative to the solar system, one must consider the fact that not only do gravitational interactions travel at the speed of light but that gravitational charges (i.e. masses) are velocity dependent. In the case of electromagnetism, where the electric charges are independent of speed, the Leonart/Wickart retarded potentials take account of the finite speed of electromagnetic interactions. On the other hand, the calculations made in general relativity ignore the finite speed of gravitational "forces" by assuming that the bodies of interest (e.g. the planet mercury) move in a static gravitational field (or more correctly a static curved space), thus ignoring the effect of recoil which is not calculable. For instance, in computing the relativistic effect on the orbit of Mercury, recoil is ignored, and the Sun is treated as if it were a fixed object generating a static gravitational field (or static space curvature). The contribution of general relativity to precession of Mercurys' orbit is then entirely due to the variable mass of Mercury due to its variable speed.

qubit, I find that sometimes the best way to learn something is to actually open my mouth and reveal my ignorance so that I can be corrected. I do not for a second give any credence to Bethel's theories, but was genuinely confused by the "misalignment" of the gravitational and EM fields. Excuse me for asking.

Religious beliefs should have nothing to do with how science is conducted, as long as one manages to keep God out of the equations.

What is the difference between polynomial and complex time?

Sorry about my "multipostialism" on multidenialism, the spam filter didn't like my links. And so I threw in a partitioned copy to see the @$%! thing.

Imaginary.

SteveM,

I hope you don't stop asking questions just because someone has treated you so rudely. I thought you raised a good question and I too was interested in the answer.

I think qubit is a very smart individual and has made some nice contributions in the past. Maybe he is just treating you rudely because he respects you and he has a habit of taking people he respect to task. Then again maybe he is just being rude.

Mu2:

In general relativity, such a change to the Sun would affect us gravitationally at the same time that the light reaches us: 8+ minutes after it happens. This is discussed in the FAQ to which qubit linked (which was written by Steve Carlip and others, not John Baez).

Whats next, a GMBM debunking of time cube :?)

SteveM --

I owe you an apology. I've become a little cynical with time about comment sections; too many times in the past I've tried to explain someone posing as an honest inquisitor who turned out to be arguing in bad faith. Maybe it's made me somewhat misanthropic behind the facelessness of teh intertubes. Part of the reason I don't pop up to comment many places anymore. But you're right, there was no reason for me to jump down your throat like that.

Um, I don't see any expert addressing this as I expected when I made my jest.

I'm not really sure what you mean by "polynomial" time, but you can use a transformation to and back from complex time when you solve some physical problems.

note that he does the same thing rhetorically with relativity that ID'ists do all the time with evolution: he calls it 'einsteinian' theory (like the ID'ists use 'darwinism'). if they can pin it on a single individual, it seems less authoritative, and then any errors that individual might have made (due to incomplete data at the time, for instance) can be held against the theory.

very clever, but we see through it.

Is this the same Tom Bethel who wrote the Politically Incorrect Guide to Science? It does seem like Regnery picks the absolute nuttiest people possible to write those books...

I wrote about Bethell's nonsense for Salon back in 2000. And more recently an update for Cosmos.

k ramo?//????/