An excellent point. Note that there are two other channels that will indicate the spin 0 property. Those signals are so small compared to the background that it will be a few years before that issue is resolved.
Here is the easy message: it is not a theory - a way to do many calculations, all confirmed by experimental tests. People who work on M-Theory hope it becomes a theory some day. Even us folks on the ultra-conservative fringe of physics (http://bit.ly/GEMblog) would not publish such silliness.
Be a real man, woman, or pre-op tranny and buy the "No Stinkin Higgs" t-shirt (http://bit.ly/GEMtshirt) that predicts, well, that they will not find the Higgs or some time-traveling singlet.
Wow! Thanks for the detailed technical reply. I read it twice and have bookmarked it. Grounded skepticism, nice.
Let's see if I can subtract away a bit of the jargon, to abstract the first two problems, so they sound similar. The horizon problem is that all parts of the Universe are traveling at the same speed, but they would always be too far apart from each other to reach an agreement on the speed. Let's call that the constant velocity problem instead. Everyone happens to be traveling at the same speed. Why they reach that particular speed is not known. Constant velocity problems happen in many physics problems.
The flatness problem is about the stability of the solution. Let's call it that then, the stability problem.
What the big bang needs is a stable, constant velocity solution that uses the force of gravity. So far, nothing accomplished, just a word game.
For the dark matter issue, I will focus on a smaller set of issues, just the rotation profile of thin disk galaxies. I don't read many papers in the technical literature, but did find one by Alar Toomre in the 1960s who figured out how to apply good old Newton's law to a disk galaxy. It is not trivial, and I really didn't understand how he applied elliptical integrals to solve the problem. Two things I do recall. First was that the solution was unstable. If a disk galaxy gets a slight nudge along the axis, it should curl up into a ball. It is not unusual to see one galaxy pass close to another (I think that is happening to the Milky Way), but the galaxies appear to be stable. Let's call this the stability problem.
Apply Newton's law to these galaxies, and you can get the velocities right as long as you stay near the core to the max velocity. It is out on the edge were problems live. Even where the stars don't shine, gas has been spotted going at the same darn speed. Everyone wants to go at the same constant velocity.
What the rotation profile of thin disk galaxies needs is a stable, constant velocity solution that uses the force of gravity. This is again a word game, it also does not cover the variety of cases seen for dark matter, but it is fun to construct a link based on reasonable abstraction of the problem descriptions (others may judge if I have been reasonable).
I do have a physics speculation for a stable, constant velocity solution that uses the force of gravity. Before I get there, I will define precisely what I mean by a physics speculation.
1. It must be a specific equation
2. It must be consistent with all partially successful earlier speculations
Apply this precise definition of a physics speculation to gravity. One could call Newton's law of gravity a speculation. It was the first, so didn't have any companions. It kept collecting more and more data to support it. About the only problem was a minor precession of the perihelion of Mercury. Jupiter all ready contributed 10x this amount.
Einstein spotted the problem with Newton's law soon after formulating special relativity: nothing travels faster than the speed of light, not even gravity. It took ten years to develop the field equations, then Schwarzschild found a solution, so that Einstein could then solve this small problem (he was giddy about this result for three days). The depth of the mathematical rewrite is stunning, but there is a way to pluck out Newton's law from Einstein's speculations. Those too have been confirmed for weak and strong fields.
As discussed above, Newton's law fails for the rotation profile of thin disk galaxies. Why not use Einstein's better law? It has been quantified how much that kind of shift would make for these low density, slow moving objects. This is the region where Newton does well in our planetary system, but fails for big stuff.
Is this a BIG failure? If you read technical literature or any popularization, they will trumpet the idea that this is beyond huge, super massive, because everyone describes it that way. Can you give me
As a cosmologist, how do you feel about rethought and reanalysis of 1. The particles that cause inflation, 2. Dark matter needed for various galaxies and clusters of galaxies, 3. Dark energy needed for the accelerating universe?
There are problems with the classic big bang model, with velocities seen in galaxies, and the acceleration of the galaxies. My money is that all of these are hard math problems, not a new type of matter. I even have a specific equation I would like to apply to these problems in particular, but I am not good enough at relativistic rocket science to give it a go.
I am with you on the no Higgs/no supersymmetry.
Doug
Gravity is literally a universal love force: no matter what you are made of, everything else in the Universe wants to get closer to you (whether you have showed or not). We all want to rush to the center of the Earth - a fall that would take a little over 20 minutes - but are stuck in an atomic-level traffic jam. How can we make universal attraction a law? My proposal is that the rule for multiplying 4 numbers together does not have a single minus sign. Without a minus sign, repelling does not happen. That is the accounting secret. The all-positive product is the box-times symbols on the t-shirt, or hypercomplex numbers/Klein 4-group on wikipedia. Physicists use something known as tensor calculus, and that blocks a direct road to this kind of multiplication.
A fine question. x is the "implied" multiplication. In C programming, you have to write A * B. In physics books, you write A B. So any implied multiplication uses quaternions, any box-times is hypercomplex.
The video is geared towards people who can do 1st year college calculus, or high school level if you are headed off to MIT.
The idea: Maxwell's field theory is the best one we have, the basis of the standard model by swapping out the gauge groups. I figured out how to write the Lagrange density (every way energy can be exchanged inside a box) using quaternions. That is not so hard. Do you know how to factor (B^2 - E^2)? If so, then (Del A - (Del A)*)(A Del - (A Del)*) is the same thing, quaternion style. The quaternions cannot do gravity which involves totally symmetric changes in a metric. Therefore I used an even less popular algebra known by names such as the hypercomplex numbers or the Klein 4-group. Put that into the Lagrangian, which flips exactly half the signs. That makes my proposal for gravity.
Combine the EM quaternion rewrite with the hypercomplex gravity Lagrangian, but without that -(Del A)* thing which was subtracting away the gauge term. The gauge term is there in both the gravity and EM portion, but they wipe out each other, so gravity and EM apply to massive particles, but overall the Lagrangian is gauge invariant. The Higgs mechanism works via a clever solution. My unified standard model works via a clever Lagragian.
By the end of 2012, I will know if my t-shirt is wrong because the Higgs and/or supersymmetric particles are found, or my t-shirt is barking near the right tree.
Doug
Supporting material about the t-shirt
http://bit.ly/GEMIAPday1video
http://bit.ly/GEMIAPday1pdf
Got my own theory where gravity and the symmetries of the standard model (U(1), SU(2), and SU(3)) live together in the Lagrange density. To make the Lagrangian gauge invariant, the difference between the part for gravity (which is not gauge invariant and thus applies to particles with mass) and the one for the other three (which is also no gauge invariant and thus dito) creates a Lagrangian that overall in gauge invariant. No Higgs particle needed, nor 5 Higgs particles.
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.
Neither. The Higgs mechanism is not needed if gravity is correctly unified with the other 3 forces, as the t-shirt I am wearing now asserts. Full disclosure: of course I did all the math, you can check it yourself in this mathematica notebook.
No, I am bringing up an accounting issue. There is no time without space, no space without time, so while it is good English to talk about time, it is bad mathematical physics. One is restricted to only talk about spacetime. We all experience changes in spacetime - we all get older in almost the same place in space.
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.
It is Storytelling versus the Scientific Method, both done by people.
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.
One needs U(1) symmetry, SU(2), SU(3), and a way to do oh-so-symmetric gravity. SU(2) is known as the unit quaternions, or one way to write a representation is exp(q - q*). That uses 3/4 degrees of freedom in a quaternion.
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
The Higgs will not be necessary when gravitational theory is correctly unified with the other 3 forces of Nature. Think about it. The standard model is about 3 of the 4 known forces of Nature: EM, the weak, and the strong force. Problem is all that is done for particles with Zero mass. The Higgs mechanism fixes this obvious problem without breaking the symmetries of the other 3 (U(1), SU(2), and SU(3)) using a cute Mexican hat trick.
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.
Thanks for spending about an hour at the site:-) No one has played analytically with animations since infancy, so these images are odd. I find I have to spend 10 minutes with people explaining the 4D wire cube, that the vertices are traveling in time.
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
"Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
What physicists do now is put spacetime into a 4-vector, to be added or multiplied by a scalar. They do not multiply one event in spacetime by another, or take the sine of an event in spacetime. My money says no one here knows what the sine of spacetime events looks like. When you take Minkowski seriously and start doing math beyond addition to spacetime, everything changes.
Slashdot Mirror
An excellent point. Note that there are two other channels that will indicate the spin 0 property. Those signals are so small compared to the background that it will be a few years before that issue is resolved.
Be a real man, woman, or pre-op tranny and buy the "No Stinkin Higgs" t-shirt (http://bit.ly/GEMtshirt) that predicts, well, that they will not find the Higgs or some time-traveling singlet.
Doug
http://visualphysics.org
Wow! Thanks for the detailed technical reply. I read it twice and have bookmarked it. Grounded skepticism, nice.
Let's see if I can subtract away a bit of the jargon, to abstract the first two problems, so they sound similar. The horizon problem is that all parts of the Universe are traveling at the same speed, but they would always be too far apart from each other to reach an agreement on the speed. Let's call that the constant velocity problem instead. Everyone happens to be traveling at the same speed. Why they reach that particular speed is not known. Constant velocity problems happen in many physics problems.
The flatness problem is about the stability of the solution. Let's call it that then, the stability problem.
What the big bang needs is a stable, constant velocity solution that uses the force of gravity. So far, nothing accomplished, just a word game.
For the dark matter issue, I will focus on a smaller set of issues, just the rotation profile of thin disk galaxies. I don't read many papers in the technical literature, but did find one by Alar Toomre in the 1960s who figured out how to apply good old Newton's law to a disk galaxy. It is not trivial, and I really didn't understand how he applied elliptical integrals to solve the problem. Two things I do recall. First was that the solution was unstable. If a disk galaxy gets a slight nudge along the axis, it should curl up into a ball. It is not unusual to see one galaxy pass close to another (I think that is happening to the Milky Way), but the galaxies appear to be stable. Let's call this the stability problem.
Apply Newton's law to these galaxies, and you can get the velocities right as long as you stay near the core to the max velocity. It is out on the edge were problems live. Even where the stars don't shine, gas has been spotted going at the same darn speed. Everyone wants to go at the same constant velocity.
What the rotation profile of thin disk galaxies needs is a stable, constant velocity solution that uses the force of gravity. This is again a word game, it also does not cover the variety of cases seen for dark matter, but it is fun to construct a link based on reasonable abstraction of the problem descriptions (others may judge if I have been reasonable).
I do have a physics speculation for a stable, constant velocity solution that uses the force of gravity. Before I get there, I will define precisely what I mean by a physics speculation.
1. It must be a specific equation
2. It must be consistent with all partially successful earlier speculations
Apply this precise definition of a physics speculation to gravity. One could call Newton's law of gravity a speculation. It was the first, so didn't have any companions. It kept collecting more and more data to support it. About the only problem was a minor precession of the perihelion of Mercury. Jupiter all ready contributed 10x this amount.
Einstein spotted the problem with Newton's law soon after formulating special relativity: nothing travels faster than the speed of light, not even gravity. It took ten years to develop the field equations, then Schwarzschild found a solution, so that Einstein could then solve this small problem (he was giddy about this result for three days). The depth of the mathematical rewrite is stunning, but there is a way to pluck out Newton's law from Einstein's speculations. Those too have been confirmed for weak and strong fields.
As discussed above, Newton's law fails for the rotation profile of thin disk galaxies. Why not use Einstein's better law? It has been quantified how much that kind of shift would make for these low density, slow moving objects. This is the region where Newton does well in our planetary system, but fails for big stuff.
Is this a BIG failure? If you read technical literature or any popularization, they will trumpet the idea that this is beyond huge, super massive, because everyone describes it that way. Can you give me
There are problems with the classic big bang model, with velocities seen in galaxies, and the acceleration of the galaxies. My money is that all of these are hard math problems, not a new type of matter. I even have a specific equation I would like to apply to these problems in particular, but I am not good enough at relativistic rocket science to give it a go.
I am with you on the no Higgs/no supersymmetry.
Doug
A legit concern, but J. R. R. Albert Tolkien was Jewish, more by tradition than some sort of ultra-conservative flavor, and not born a Roman Catholic.
Nope. I can remember the custom bit.ly strings, but not YouTube strings. There may be better ways, but for now it is the way I know how to do it.
Gravity is literally a universal love force: no matter what you are made of, everything else in the Universe wants to get closer to you (whether you have showed or not). We all want to rush to the center of the Earth - a fall that would take a little over 20 minutes - but are stuck in an atomic-level traffic jam. How can we make universal attraction a law? My proposal is that the rule for multiplying 4 numbers together does not have a single minus sign. Without a minus sign, repelling does not happen. That is the accounting secret. The all-positive product is the box-times symbols on the t-shirt, or hypercomplex numbers/Klein 4-group on wikipedia. Physicists use something known as tensor calculus, and that blocks a direct road to this kind of multiplication.
The video is geared towards people who can do 1st year college calculus, or high school level if you are headed off to MIT.
The idea: Maxwell's field theory is the best one we have, the basis of the standard model by swapping out the gauge groups. I figured out how to write the Lagrange density (every way energy can be exchanged inside a box) using quaternions. That is not so hard. Do you know how to factor (B^2 - E^2)? If so, then (Del A - (Del A)*)(A Del - (A Del)*) is the same thing, quaternion style. The quaternions cannot do gravity which involves totally symmetric changes in a metric. Therefore I used an even less popular algebra known by names such as the hypercomplex numbers or the Klein 4-group. Put that into the Lagrangian, which flips exactly half the signs. That makes my proposal for gravity.
Combine the EM quaternion rewrite with the hypercomplex gravity Lagrangian, but without that -(Del A)* thing which was subtracting away the gauge term. The gauge term is there in both the gravity and EM portion, but they wipe out each other, so gravity and EM apply to massive particles, but overall the Lagrangian is gauge invariant. The Higgs mechanism works via a clever solution. My unified standard model works via a clever Lagragian.
By the end of 2012, I will know if my t-shirt is wrong because the Higgs and/or supersymmetric particles are found, or my t-shirt is barking near the right tree.
Doug
Supporting material about the t-shirt
http://bit.ly/GEMIAPday1video
http://bit.ly/GEMIAPday1pdf
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
Neither. The Higgs mechanism is not needed if gravity is correctly unified with the other 3 forces, as the t-shirt I am wearing now asserts. Full disclosure: of course I did all the math, you can check it yourself in this mathematica notebook.
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.
Hello: Time for me to fight the LHC propaganda machine with my own efforts. The unified standard model doesn't need the Higgs mechanism. http://www.zazzle.com/the_stand_up_physicist_said_tshirt-235942932145293980
Just like car racing, I want to watch.
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 :-) No one has played analytically with animations since infancy, so these images are odd. I find I have to spend 10 minutes with people explaining the 4D wire cube, that the vertices are traveling in time.
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
"Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
What physicists do now is put spacetime into a 4-vector, to be added or multiplied by a scalar. They do not multiply one event in spacetime by another, or take the sine of an event in spacetime. My money says no one here knows what the sine of spacetime events looks like. When you take Minkowski seriously and start doing math beyond addition to spacetime, everything changes.
Doug