27 September 2005

A few anniversary musings.

On 27 September 1905, a paper was published in the journal "Annalen der Physik". The paper, titled, "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" ("Does the Inertia of a Body Depend Upon Its Energy Content?"), was only three pages long. It was the fourth published by the same author that year. None of the four papers was immediately embraced by the scientific community. In fact, most were initially considered to be fairly controversial. At the time, the author of the papers had neither a doctoral degree nor an academic position. He had a few prior papers to his credit, but was essentially an unknown in the field of physics.

Within a relatively short period of time, those four papers would be recognized as having revolutionized the field of physics. The author, who was a relatively obscure Swiss patent clerk in 1905, would become one of the icons of our time.

One of the interesting things about these papers is that all of them were theoretical. Not one presented experimental data. What they did do, however, was make predictions that could be experimentally tested. As the various hypotheses proposed in those papers past test after test, they became more and more accepted within the scientific community. One of the equations - the one published in the 27 September 1905 paper - is probably the best known equation in physics: E=mc2.

It is one hundred years to the day from the publication of that paper. At this time, science is faced with a group of people who claim that they have a brand new theory that explains how life started on the planet, and how individual species may have originated. Their theory has, thus far, not had much of an impact on the way that scientists actually conduct science. The proponents claim that their new hypothesis has sparked a controversy within science. The vast majority of the scientific community, including every major scientific organization in the United States, disagrees, saying that the "hypothesis" in question is too atrocious to make it even that far.

What separates them from Einstein? The proponents of the atrocious hypothesis would probably say that there isn't much that separates them from Einstein. More rational people disagree. Einstein worked within the established proceedures of the scientific community. They do not. Einstein's work made testable conditions. Theirs does not. Einstein's hypotheses were tested a number of times before becoming accepted. Theirs cannot be tested.

The biggest difference is this: Einstein did not appeal to the public and to school boards to have his work taught to public schoolchildren. Some of his work is taught to schoolchildren, but that came naturally, as his work gained respect and acceptance within the scientific community and made its way into textbooks.

Our modern Intelligent Design proponents have no hope of their work taking that course, and they know it. Their hypotheses make no testable positive predictions. This does not bother them much, however, because they do not appear to be investing much in the way of resources toward doing actual scientific research.

As a result, 100 years after Einstein's paper on mass-energy equivalence was published, there is a trial in Pennsylvania. The ID folks bypassed the normal scientific process, and forced their religiously-motivated fake science into a school, in flagrant disregard of the rights of those who do not want their children to be exposed to religious lies disguised as science.

Happy anniversary, Albert.

10 Comments:

Anonymous Anonymous said...

Happy Centennial Special Relativity!
But, truly though, anybody who thinks seriously about Special Relativity will have grave reservations about accepting it as being true. For example, let's say spaceships A and B are heading away from each other towards planets A and B respectively. Point C is midway between planets A and B. The passengers of both ships A and B are dropping pennies into a bucket at a rate of 1 per second according to their own clocks. Now, when they finally arrive at their respective planets, who will have more pennies in their bucket, A or B? Or will they have the same?
If you reply the same, then A will land while B is still travelling, since time is passing more slowly for B from A's frame of reference and B will land while A is still travelling, since time is passing more slowly for A from B's frame of reference. But if they each fire a rocket towards each other when they land, then the rockets will meet on both sides of C, which is of course impossible. This is your brain. This is your brain on relativity. Any questions?

6:33 AM  
Blogger Bob Davis said...

Well, I say that ID has posited at least one testable theory, the theory that the Cambrian Explosion happened all at once, rather than over millions of years. And my experiment, a modest experiment tests just this very theory. By September 31, 2006 we should know for sure whether or not ID is real or fake. If only the courts in Dover could wait another year, then they could make an informed decision. That is if I can get the rest of the 60 million volunteers I need by Saturday.

6:40 AM  
Anonymous Anonymous said...

My question for you, Anonymous1, is why do you think "your brain's on relativity" when you don't understand the effect of acceleration, which you have negelcted. You've just articulated a more elaborate version of the "twin (non)paradox".

7:15 AM  
Anonymous Anonymous said...

But, truly though, anybody who thinks seriously about Special Relativity will have grave reservations about accepting it as being true....

I posed a similar question to my physics professor in college. He said that there is no such thing as simultaneity in the relativistic world. Though, that seemed like a thin answer.

There are experiments that have been done - not with prople, but with satellites and subatomic particles. Satellites, though they travel well below the speed of light, experience the effects of relativistic time dilation. Ultimately what this means is that satellites must account for relativistic effects. Case in point - GPS satellites - they allow people on earth to determine their position based on small timing differences between the satellite signals - they include relativistic effects into their timers so that GPS actually works.

Also, if you accelerate atomic particles with a short half-life to near-light speeds, you can dramatically extend their half-life. Knowing their speed, calculations show that the extended half-life of these particles correspond to relativistic time dialation.

Some links:
GPS satellites and relativity
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

See "Time Dilation for Particles"
http://www2.slac.stanford.edu/vvc/theory/relativity.html

2:59 PM  
Anonymous Anonymous said...

Anonymous1 asked about the so-called twin paradox, which - incidentially - is nothing of the sorts. The incarnation presented here says:

Two spaceships set out towards two different planets with the same speed v, as measured by an observer on the planet they leave. Each ship measures the time it takes to reach its own target planet using its own clocks.

In which order do they pass their planets?

What do their clocks read when they pass their planets?

When they pass their respective planets, they chuck a rock with a speed u relative to their own ship in the direction of the other target planet. Where do the rocks meet?

The answer to the first question is that it depends on the observer.

Spaceship A will say that it passes its planet before spaceship B arrives at its target, because B moves at less than 2v relative to A (and the Lorentz contraction of the distances between the planets caused by A's movement are symmetrical).

From the PoV of an observer on the origins planet, the situation is symmetrical, and the two spaceships arrive simultanously.

From the PoV of B, the situation is exactly as described for A, only with A and B swapped.

Notice that while this result is the effect Anonymous1 claimed we would see, his explanation is wrong. It is caused by the non-linear velocity transformation, not - as Anonymous1 claimed - by the time dialation effect.

The answer to the second question is that their clocks read the same when they pass their target planets in every inertial frame of referance. I won't prove this here, but I'll give the two most relevant examples: In the A frame, A passes its planet before B, but the time dialation effect means that B's clocks are behind A's (by exactly the factor neccessary for the clocks to show the same when the two ships pass their target planets), and vice versa for the B frame. In the O frame (O being the planet of origin), the clocks must read the same (symmetry argument).

The answer to the third question is that the rocks pass each other exactly midway between planets A and B in both frame A, frame B and frame O (but I'm not sure if this holds for every other frame as well).

This is trivially true for frame O (symmetry again), and is true for A and B because the rocks are launched with the same speed relative to their own ships. This means that in the A frame, B's rock is moving faster relative to B than A's rock is moving relative to A. This extra speed exactly balances out the fact that B's rock was chucked later than A's. As always when dealing with symmetrical systems, one can move from frame A to frame B by replacing all As with Bs and inverting the sign of all velocities (which differ from speeds in that velocity has a direction).

I have tacitly assumed that the spaceships coincide at the time of launch, and that the planet of origin is placed precisely midway between the target planets on the line connecting them. If these assumptions are discarded, one arrives at essentially the same conclusions, but the math gets rather more tangled.

Now the canny reader will have noticed that a lot of effects cancel out in the above description (e.g. length contraction, velocity transformations of stones/rockets etc). This is no coincidence. In fact it drops beautifully out of the equations, and this symmetry is one of the great appeals of Special Relativity.

For an accessible and more complete treatment of Special Relativity I can recommend:

D. J. Griffiths
Introduction to Electrodynamics, 3rd Edition
Prentice Hall, 1999
p. 477-522

It has clear and concice language, lots of examples and explanations and not excessive amounts of math.

5:15 AM  
Anonymous SR is not true said...

This means that in the A frame, B's rock is moving faster relative to B than A's rock is moving relative to A. This extra speed exactly balances out the fact that B's rock was chucked later than A's. As always when dealing with symmetrical systems, one can move from frame A to frame B by replacing all As with Bs and inverting the sign of all velocities (which differ from speeds in that velocity has a direction).

Obviously impossible...The rocket from ship A is approaching me faster than the rocket from ship B and the rocket from ship B is approaching me faster than the rocket from ship A? Impossible!

5:39 AM  
Anonymous Absolute Time said...

Case in point - GPS satellites - they allow people on earth to determine their position based on small timing differences between the satellite signals - they include relativistic effects into their timers so that GPS actually works.

The relativistic equations are not programmed into the clocks. The clocks are simply set to run at a different speed prior to launch. Do the clocks run at a different speed because of SR or is it because of less gravity?

5:47 AM  
Anonymous Anonymous said...

\sigh

All of this has been gone over a quazillion times. It is mathematically impossible to create the kind of paradox you envision using the equations of special relativity.

All the equations are symmetrical (in fact it is one of the fundamental conditions invoked when deriving the actual equations), hence for all symmetrical problems, you get a symmetrical solution.

And the transformation equations are all identity operators when all four space-time coordinates coincide, so (obviously) all problems which involve objects being at the same position at the same time will be at the same position at the same time under all Lorentz transformations.

"Obviously impossible...The rocket from ship A is approaching me faster than the rocket from ship B and the rocket from ship B is approaching me faster than the rocket from ship A? Impossible!"

Yes and no. An observer midway between the two target planets is in frame O. He would see the two rocks approaching him with equal speed from opposite directions. An observer in frame A, however, would see the rock launched from ship B approaching the planet in the centre faster than the rock from ship A. Meanwhile the observer in ship B would see the "A" rock approach faster than the "B" rock. The rocks would still hit the planet at the same time, though.

You cannot trivially transform velocities from one frame to another.

FYI this is the velocity transformation equation for velocities parallel to the relative velocity between the frames you want to transform between:

u' = (u - v)/(1+v^2/c^2)

Where v is the relative velocity of the frames, u is the velocity of the particle in one of the frames, and u' is the velocity of the particle in the other frame.

The signs of u, u' and v depend, of course, on the direction of your transformation and your choice of positive x-direction.

Try it out on a few numerical problems and be consistent when you apply it. You'll see that the paradox vanishes. (Note, though, that you can only use that equation to transform between inertial frames whose relative velocity is parallel or antiparallel to the velocity of the particle in either frame.)

"The relativistic equations are not programmed into the clocks. The clocks are simply set to run at a different speed prior to launch. Do the clocks run at a different speed because of SR or is it because of less gravity?"

AFAIK, the clocks are made using the same isotopes, which means that in the same inertial frame they would run at the same speed. The effects of moving them into orbit (assuming that you calibrate correctly to compensate for the outrageous number of things that could screw them up during launch) fall within the realm of General Relativity, since orbit is a non-inertial frame of reference. General Rel is a whole 'nother can of worms, and one that I'm not going to open here, save to say that it rests on just as solid empirical grounds as SR and Quantum Mechanics.

7:52 AM  
Anonymous SR is garbage said...

He would see the two rocks approaching him with equal speed from opposite directions. An observer in frame A, however, would see the rock launched from ship B approaching the planet in the centre faster than the rock from ship A. Meanwhile the observer in ship B would see the "A" rock approach faster than the "B" rock.

So...regarding the velocities of A and B...
1. A > B
2. A = B
3. A < B
All three statements are true? When you start believing in things which are physically impossible you have real problems.

11:04 AM  
Anonymous Anonymous said...

\sigh

Not, obviously, in the same frame.

From A's PoV, vA < vB
From the PoV on someone stationary with respect to O, vB = vA
From B's Pov, vB < vA

Where vA is the speed of the rock chucked by A and vB is the speed of the rock chucked by B

But since the B frame is moving with respect to the A and O frames (which are also moving with respect to each other), this discrepancy is a rather trivial result of the relativistic velocity transformations.

A few links on Special Relativity:

http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html

http://www.mathpages.com/home/kmath307/kmath307.htm

http://www.ux1.eiu.edu/~cfadd/1160/Ch27SpRl/Vel.html

These should pretty much cover the ground required to understand the solution to your non-paradox. The math could have been more elegantly done, but it will have to suffice. If you want to see a more elegant deriviation I refer you to Griffith.

And one final thing: I am getting mighty pissed with your flamebaiting. I have so far gone considerably out of my way to avoid responding to your more or less (though considerably less than more) subtle insinuations of mental deficiency on my part, but that doesn't mean that I haven't noticed them. They were unamusing to begin with and have been going rapidly downhill from there.

1:53 PM  

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