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The relevant theory here is Bell's Theorem (or Bell's Inequality.) The principle of entanglement has been shown experimentally using some clever approaches based on probability.

If you measure a specific property of two entangled particles, you are correct in saying that there is no way we could know if the result of the measurement was predetermined. However, experiments were set up in which a large number of pairs of particles were measured. Each measurement recorded one of several possible properties, chosen at random. Sometimes the same property would be measured for both particles, and sometimes different properties would be measured for each particle.

It can be shown mathematically that if the particle properties were predetermined, we would see certain probabilities emerge. In other words, for each pair of measurements, the same result would be found N% of the time. However, if the particle properties are determined at the time of measurement, the math changes, and we expect instead for the results to correlate P% of the time. This latter result is what was observed.

That is just a quick overview of the concept. I suggest reading Brian Greene's "The Fabric of the Cosmos", which provides a great explanation involving Mulder and Scully. (Really!)

I also found a nice, clear explanation of the probabilities involved here.

Here's another. Look at the pdfs entitled "The Cosmological Consequences of the Product Rule" and "Einstein's Vision" for a compelling model without dark matter.

You're thinking of The World. See http://www.theworld.com/about/internet.shtml.

U.S.S. Cavalier!

I still have it printed out somewhere. Nebula of the Living Dead (name?) was really good too! :P

You can still find Cavalier (packed in an ancient .Z file) here: http://www.theworld.com/obi/Star.Trek.Stories/

Another favorite of mine was the one where Picard and Crusher's daughter (ok, that one was a bit of a stretch) commanded a later Enterprise. And Moriarty became the computer! (It was written before they resolved the Moriarty storyline on the show. :))

Your impression sounds correct to me. The vacuum field equations I use are linear, and NOT a linear approximation of GR. Instead of binding gravity to the second rand field strength tensor T^uv, the coupling is between a 4-potential and the 4-momentum density. The difference between these two is not big. The only difference is that gravity fields are not sources. This is consistent with EM, were EM fields are not sources. Consistency is good.

The trick here is to be like EM when necessary, and different where necessary. There are no photon-photon interactions (unless things get odd), and likewise, there are no graviton-graviton interactions. That does not prove they theory is renormalizable. I don't have the skills to prove or disprove that point. I am hopeful, because it is basically the manifestly Lorentz invariant quantization of a 4D wave, but with 2 spin fields, a spin 1 for EM, a spin 2 for gravity. In text books, two of the modes of emission for the manifestly Lorentz invariant quantization of a 4D wave have to be made virtual. I put those virtual modes to work.

I am not a professional, so cannot post to Arxiv. I consider this paper a draft since it has not been read and reviewed by anyone with real qualification. http://www.theworld.com/~sweetser/quaternions/ps/e m2gem.pdf

doug

Hello:

The standard model has the symmetries U(1)xSU(2)xSU(3). The one in the middle, SU(2), is a unit quaternion, where a quaternion is like a real or complex number, but has four parts. I have developed the software to visualize quaternions at http://quaternions.sf.net/ using one number for time, three for space. SU(2) can be represented by the quaternion function exp(q-q*). Feed a thousand random quaternions into exp(q-q*), and get POVRay to make a nice animation. Do the same for q/|q| exp(q-q*), and you have a visual representation of the electroweak symmetry. Smash two of these together, and you get the symmetry of the standard model.

Visually, there is a clear message: if you want to smoothly represent all possible events in spacetime as quaternions, the group description must be U(1)xSU(2)xSU(3). You won't read that in a journal because it has to be done with animations.

http://www.theworld.com/~sweetser/quaternions/quan tum/standard_model/standard_model.html

doug

I am working to be analytical about animations using quaternions. The brain SUCKS at remembering visual stuff. Instead, the brain is great at shop & compare. That is why artists use easels by the way - it's not just to hold up the canvas, but because visual memory is so bad, but comparison is so good, so the artist's work can quickly be compared to "the real thing".

an example animation - http://www.theworld.com/~sweetser/quaternions/qema tion/Dynamic_graphs/1276.html
the project - http://quaternions.sourceforge.net/

Hello Mark:

> That is a situation [hair standing up due to a wee bit of static electricity] where forces cancel out.

There are two ways to look at what gravity and EM do: as fields or as forces. If one takes the Lagrangian, and does the variation with respect to the potential, one gets the field equations. If one takes the same Lagrangian, and does the variation with respect to the velocity, one gets the force equations. I still remember exactly where I read that in Landau and Lifshitz! So sure, one can view the issue as forces canceling (which really only makes technical sense for my GEM or gravitomagnetism, not GR). One can describe the exact same thing using a field equation approach. The Maxwell equations are logically consistent, so the story generated by looking at forces must be the same as the one for fields.

> It is demonstrably different from this.

Even if I concede this point, it does not address my reply that we know darn well how to characterize a vacuum, whose algebra is the same as Jq - Jm = 0, Jq != 0.

> And when you square that term you don't get the E&M action.

The asymmetric tensor gets contracted, and the result is

L_GEM = - rhom/gamma
-(rhoq -rhom) phi + (Jqx - Jmx) Ax + (Jqy - Jmy) Ay + (Jqz - Jmz) Az
- 1/2 (d^2 phi/dt^2 + d^2 phi/dx^2 + d^2 phi/dy^2 + d^2 phi/dz^2
+ d^2 A_x/dt^2 - d^2 A_x/dx^2 - d^2 A_x/dy^2 - d^2 A_x/dz^2
+ d^2 A_y/dt^2 - d^2 A_y/dx^2 - d^2 A_y/dy^2 - d^2 A_y/dz^2
+ d^2 A_z/dt^2 - d^2 A_z/dx^2 - d^2 A_z/dy^2 - d^2 A_z/dz^2)

Take the derivative of L_GEM with respect to A^mu, and the resulting field equations should have a familiar look to it as far as EM is concerned. This Lagrangian will not look familiar with expectations based on linearized GR or GR itself. The proposal works differently, using only one connection, not the divergence of two connections as happens in the Riemann curvature tensor.

There is nothing wrong with being skeptical. I am of my own work. Starting from the above Lagrange density, I have derived the field equations, solutions to those equations, and put it all in Mathematica (it is not pretty, such is the nuts and bolts nature of the software, but it is available here:
http://www.theworld.com/~sweetser/quaternions/ps/L agrangian_to_tests.nb.pdf and http://www.theworld.com/~sweetser/quaternions/note books/Lagrangian_to_tests.nb).

Any well-trained person will remain skeptical until with good old paper and pencil they calculate for themselves the divergence of the Christoffel of the exponential metric. I would bet you did not do that, so your stance is reasonable.

At the end of the day, I only care about technical issues, they last.
doug

Hello Mark:

> That is a situation [hair standing up due to a wee bit of static electricity] where forces cancel out.

There are two ways to look at what gravity and EM do: as fields or as forces. If one takes the Lagrangian, and does the variation with respect to the potential, one gets the field equations. If one takes the same Lagrangian, and does the variation with respect to the velocity, one gets the force equations. I still remember exactly where I read that in Landau and Lifshitz! So sure, one can view the issue as forces canceling (which really only makes technical sense for my GEM or gravitomagnetism, not GR). One can describe the exact same thing using a field equation approach. The Maxwell equations are logically consistent, so the story generated by looking at forces must be the same as the one for fields.

> It is demonstrably different from this.

Even if I concede this point, it does not address my reply that we know darn well how to characterize a vacuum, whose algebra is the same as Jq - Jm = 0, Jq != 0.

> And when you square that term you don't get the E&M action.

The asymmetric tensor gets contracted, and the result is

L_GEM = - rhom/gamma
-(rhoq -rhom) phi + (Jqx - Jmx) Ax + (Jqy - Jmy) Ay + (Jqz - Jmz) Az
- 1/2 (d^2 phi/dt^2 + d^2 phi/dx^2 + d^2 phi/dy^2 + d^2 phi/dz^2
+ d^2 A_x/dt^2 - d^2 A_x/dx^2 - d^2 A_x/dy^2 - d^2 A_x/dz^2
+ d^2 A_y/dt^2 - d^2 A_y/dx^2 - d^2 A_y/dy^2 - d^2 A_y/dz^2
+ d^2 A_z/dt^2 - d^2 A_z/dx^2 - d^2 A_z/dy^2 - d^2 A_z/dz^2)

Take the derivative of L_GEM with respect to A^mu, and the resulting field equations should have a familiar look to it as far as EM is concerned. This Lagrangian will not look familiar with expectations based on linearized GR or GR itself. The proposal works differently, using only one connection, not the divergence of two connections as happens in the Riemann curvature tensor.

There is nothing wrong with being skeptical. I am of my own work. Starting from the above Lagrange density, I have derived the field equations, solutions to those equations, and put it all in Mathematica (it is not pretty, such is the nuts and bolts nature of the software, but it is available here:
http://www.theworld.com/~sweetser/quaternions/ps/L agrangian_to_tests.nb.pdf and http://www.theworld.com/~sweetser/quaternions/note books/Lagrangian_to_tests.nb).

Any well-trained person will remain skeptical until with good old paper and pencil they calculate for themselves the divergence of the Christoffel of the exponential metric. I would bet you did not do that, so your stance is reasonable.

At the end of the day, I only care about technical issues, they last.
doug

The World, http://www.TheWorld.com , the oldest commercial internet dial-up service on the planet* (go ahead, start the usual grousing), offers a $9.89 account and is a local call from the contiguous 48 states in the US (1500+ numbers.)

BUT SOMEHOW PC WORLD'S CRACK REPORTING COULDN'T FIND US!

The $9.89 acct is limited, but for example it gives you squirrelmail which isn't metered, so if you only really need a little dial-up and a good maildrop with web mail it works, and other services (web page etc) can be added a la carte.

Disclaimer: I'm not just the President of The World, I'm also a user.

* Since November 1989, see RFC2235 for example.

was started in 1989 - Software Tool & Die - now known as the world right here in my neighborhood - Brookline MA in the Peirce Building - a center of American Commerce in the 1800s. It was not started in 1990 as said on the map - Someone apologize to Barry!

I wrote some code that uses this package to test the quality of the Java Math.sin method, if you would like a starting example.

Note that The World (also known as Software Tool and Die) was also started in 1989, but it was (and is) a full-service public dialup ISP. Also of interest in this thread is that they own the "circled at-sign" trademark.