Comment Re:I am making the t-shirt (Score 1) 465
Wife said no to yellow w/black outline text on a white t-shirt. Going with fuchsia & black on the white shirts, white and yellow on the black shirts.
Doug
http://bit.ly/GEMtshirt
http://visualphysics.org/preprints qmn:1009.9466
You'll never see my work on the preprint server (wrong email address). You can buy it on a t-shirt, watch it on YouTube, or look at non-peer reviewed papers.
Doug
TheStandUpPhysicist
http://bit.ly/GEMtshirt the t-shirt
http://bit.ly/GEMpdf Close as I can do to a paper
http://bit.ly/GEMnb Transformed paper into a Mathematica notebook to check the math
http://bit.ly/GEMnbpdf The notebook as a pdf file
Lots of stuff on YouTube
In classical physics, for a collection of events in spacetime where changes in space are far less than changes in time (dR/dt < < c), events in spacetime are ordered by time, like a movie. In quantum physics, my own work with quaternions derivatives indicates that the reason things are "odd" is that for a different collection of events in spacetime, changes in space are greater than changes in time (dR/dt > > c). In the limit, changes in time go to zero before changes in space, so one loses the "movie-ness" of this set of events. One cannot say one event happened before another. There can be no causal link between any of the events in the quantum set. The events are too far apart to order in time. Instead, one can say there are a collection of possibilities and here are the odds of any particular thing happening. Doing 4D calculus correctly may explain the reason for the differences between classical and quantum physics.
If you want to reverse the time of a spacetime event, you use this member of the Lorentz group, diag{-1, 1, 1, 1}. Have that act on a 4-vector (t, x, y, z) and you get (-t, x, y, z). Now how are you going to get time back to were it started? Use exactly the same element. The Lorentz group is a global symmetry. It is to all levels of accuracy the same darn thing. Makes much math easier, but it is why physicists say the laws are identical if time goes backwards or forwards.
The important laws in physics are local. Both the standard model and general relativity depend on the values of t, x, y, z. Let's construct a local time reversal operator, call it B, such that B (t, x, y, z) = (-t, x, y, z). This can be done by presuming all three of these are quaternions, a 4D rank 1 tensor upgraded to also be able multiply and divide like real and complex numbers (full disclosure: I own quaternions.com). R can be calculated, it is (x^2 + y^2 + z^2 - t^2, 2 t x, 2 t y, 2 t z)/(t^2 + x^2 + y^2 + z^2). That will work every time, but if you want to reverse something, then reverse it again, the second B will not be identical to the first B. The first term is identical, but the 3-vector part flips signs, not magnitudes. When one makes time reversal local using quaternion operators, the arrow of time is not a problem because there is a mathematical difference between reversing the reverse of time.
Time will never have an arrow. Spacetime will, from the space part. If you take Minkowski's advice, that one should only think about spacetime, not time or space, then Carroll's question is poorly formed. It is good English, bad mathematical physics. Since Minkowski's observation was based on work with special relativity, people presume is observation applies only for relativistic systems. Sorry, Nature is more consistent than that: one needs to think about spacetime always, even if it contributes squat. Newton's 2nd law can be written F = m (d/dt. 0, 0, 0)^2 (0, x, y, z). What makes it classical are all the zeroes that appear in the spacetime operators.The handedness of times arrow comes from the space part whose contributions are stupidly small, but add up enough of them, and they are irreversible.
People have been telling stories - meaning making shit up - since the advent of language. If I was a storyteller, I would say that happened 120,000 years ago on a grassy plane when when one guy hunting warned his buddy about a lion on his left. A scientist would give a huge range of years, large tracks of land, and a long list of other qualifiers to describe when storytelling began.
The modern scientific method began about 400 years ago. A historian of science could give important events and dates. Nature doesn't want to give up her answers. It takes training to learn how to question.
There are many profitable storytelling businesses: movies, music, and the news. News organizations tell stories. Some try to make sure the story is accurate, an art called editing. Some try to get lots of attention. That can be done using pretty woman or hyping conflict.
In science, you can tell someone they are wrong. You can write out the reason they are wrong. And that wrong person can continue to claim they are correct. I have done that with someone who claims to have shown Einstein's special theory of relativity is wrong, all it takes is a little algebra. He is paying Google to advertise his message to the world. I looked into his math. If you only have a little algebra, you would not recognize a linear system of equations. I wrote him, making an effort to explain the idea that Nature sometimes uses 4 equations in place of 1 for spacetime, and it is wrong to think one of those four should say exactly the same thing as the others. He did not accept this idea, and ads to Google's sales to this day. Accepting a critique is rare.
There will always be many places for storytellers to complain about the process and results of the scientific method. These conflict can get personal, they can get ugly. Storytellers can profit from that situation.
Doug Sweetser
Telling stories of new visual math at visualphysics.org
I don't know about your unified field theory, but mine predicts there is no Higgs particle. The standard model works so long as no particle has mass. That is silly. To get around the problem, there is the Higgs mechanism. The standard model + the Higgs mechanism says not a thing about gravity. Oops.
Why I do is rewrite the Maxwell action using quaternions. The scalar is exactly the same as the tensor approach, B^2 - E^2. Because I am using quaternions which can form products (unlike tensors), I can represent SU(2) - also know as the unit quaternions with quaternions (duh). It is a simple exercise to write the gauge invariant action with all the symmetries of the standard model (U(1), SU(2), and SU(3)).
To get to gravity, switch out the rules of multiplication. These types of numbers are known as hypercomplex numbers, and are even less popular that quaternions. Crank through Euler-Langrange, and out pops the field equations which in the static case is Newton's law.
What is particularly fun is that one can combine the gauge-invariant Maxwell action with the gauge-invariant relativistic gravity action in a way where both of the field strength tensors are gauge-dependent, but those cancel each other out, leaving the action gauge-invariant. It is all up on YouTube, http://www.youtube.com/watch?v=BrVW4QG8ei4 for a talk I gave last weekend at an APS meeting.
Doug
U(1) is Abelian, usually taught to people who accept what they are given as a normalized complex number. Note that q/|q| exp(q - q*) = exp(q - q*) q/|q| because the normalized quaternion commutes with its exponential. Hello electroweak symmetry.
Take two of these, multiply them together, and you get another element of the group because that is group theory. Toss in a conjugate operator, that changes the multiplication table, but the norm stays the same. Eight numbers go in, something with a norm of 1 comes out. Sounds like a way to represent SU(3). You are so right, it ain't associative, a huge pain, but that is how the strong force behaves.
The road to gravity will not be paved with quaternions. It requires the hypercomplex numbers. Drop that into a Maxwell-like action, and out pops a version of Newton's law that has a time dependent term, and thus no need for general relativity. It is gauge invariant in only one special case: for a massless particle. Otherwise it will politely break gauge symmetry without messing up the U(1), SU(2), and SU(3) symmetries that appear when using quaternions in the action. No Higgs mechanism needed.
For the record, I refused to take my meds while certified.
Doug
visualphysics.org
hoping to animate any expression in mathematical physics
When gravity is unified with the other 3 forces, there will be no need for the Mexican hat trick because gravitational mass will break the symmetry politely. Of course I know how to do this by first writing the Maxwell equations using quaternions, then doing a rewrite using hypercomplex numbers to nab gravity because Nature uses two sets of division algebra, thus outfoxing the string theory clowns by being clever in 4D.
Doug
visualphysics.org
Thanks for spending about an hour at the site
I hope that the rhetoric was limited to the "slams" page. One motivator in physics is putting another serious camp down. The one pathologically rude person I know promotes work on strings. As long as the harsh critiques are about areas of study and not people, I will let them remain on the slams page. When looking at other sections of the site, I hope to make sure it stays technical. Some of that tone may get into the forums, but that might be unavoidable. I will be more aware of that now.
Professors are absurdly busy. The only ones I do email from time to time are folks I have chatted with in person (1-2/year, rarely get replies, don't expect them either). I get the fringe emails too, and always look into the work. My first screen is to see if it has any math. Half do not have any. The second screen is to see if they talk about actions, Hamiltonians, or Lagrangians. None has passed the second test.
There was a web site a while ago that had collected a list of fringe sites, including the fellow who claims TIME IS MASS, always in capital letters. My site was in a special section of odd-and-not-quite-fringe (I forget how he phrased it, or the URL for that matter).
One dream I have is going through Needham's book and animating everything he writes about. That would be quite the mountain time, and I can only do this work after the 9-5 job and family effort are done and some lunch time. Those are my time constraints.
After an hour on VisualPhysics, and some time on quaternions.com, you get a sense of what I am working on. That is too much to reasonably ask from technical people. I don't know how to solve the social riddle - "I'm the one fringe guy that is not utterly-useless fringe" - so I don't worry too much about it. All I can do is make more content. My current focus is on simple harmonic oscillators. Once again the result was not what I expected, but so it goes.
Again, thanks for your time and effort.
Doug, sweetser@alum.mit.edu
Doug
VisualPhysics.org
The solution of this problem is trivial and is left as an exercise for the reader.
