Is Quantum Theory As Fundamental As It Seems? by Michael James Goodband

Michael,

Please re-read my last post first paragraph, for this is the issue. You are trapped in the orthodoxy of tensor calculus and (with emphasis again) *ITS* attendant *ALGEBRA*. Yes, algebra, the algebra of n'th-rank glorified matrices and their assumed form invariance under transformations, in which the concept of differentiation is made good through the addition of Christoffel symbols in the covariant derivative. This algebra *is not* the more robust O algebra, and you should not assume its calculus to be universal. I am not arguing that it is incorrect, for it is not for its intended usage. I am arguing it does not apply to O, and is replaced by my ensemble derivative. You can't divorce the algebra from the analysis, or worse assume there is no algebra. Additionally you are trying to create the D'Alembertian as its own stand-alone form, which I have stated is not appropriate. You must take all the other stuff along with it juxtaposed as O algebra demands. Hope this helps, at least to explain my position.

Would you please address my statement that the radii of S^n are assumed positive definite quadratic forms, and how a split signature is reconciled with this?

Rick

Rick,

"...the algebra of n'th-rank glorified matrices and their assumed form invariance under transformations, in which the concept of differentiation is made good through the addition of Christoffel symbols in the covariant derivative."

That's the most appropriate putdown of (what I find to be extremely ugly) tensor calculus I've ever seen, and it makes me feel even more strongly that geometric algebra really is the better approach. I have been very unhappy with the connections, or Christoffel symbols, (Susskind calls them "Christ awful" symbols) but your description makes even more transparent what an ugly mess tensor calculus is. When one first learns this stuff, it's presented as if it were "the ONLY way", and after a while most of us simply use it, if and when necessary, and do not question it, even after we find out that tensor calculus really isn't enough for general relativity and QM but that we need 'spinor's as well. Thanks for making it crystal clear just what is achieved by these things, that is, rescuing the covariant derivative. Although at some level I already knew this, I could never have summarized it so succintly.

This thread continues to offer a wealth of insight and Rick's comments some of the most insightful.

Edwin Eugene Klingman

Tom,

I'm not saying time is an illusion, I'm saying it is an effect.

If those balls were water molecules in a pot, we wouldn't assume some underlaying thermal scale determines how fast they are moving, because there is a thermodynamic effect. Just as with time, there is no real dimension along which these events exist. Those balls exist physically. They are present. If they were the basis of your clock, like a cesium atom and they moved around faster, you would say time has speeded up. Just like the atomic clocks on GPS satellites move faster than ones on the ground. It is not the present moving along a dimension, as with Newton's "absolute flow," from prior to succeeding events, but the physical movement creating change.

It is no more a mystery why the same clock in conditions that affect the dynamic of its process would move at different rates, than a pot of water would be different temperatures under different conditions.

I like that comment Ed.

I can't claim to have mastered tensor calculus, but I share your disdain for the fact that workarounds are used to overcome their inherent limitations. Without spinors and the Christoffel symbols; tensors are too lame for the job they are assigned, and it makes you wonder "why am I learning something that doesn't quite work right, anyhow?" Perhaps it's better to ponder "what kind of Math would actually handle this more naturally?"

I guess that's why it's good we have Rick around.

I was going to comment, Joy;

Perhaps it is a good thing that S15 yields only three Hopf fibrations, if those cases link to C, H, and O uniquely - through S1, S3, and S7. But you seem to have gotten that message loud and clear. When you commented "This does not look good," I thought you must know what you are talking about, but then I imagined it could be a blessing instead of a curse. I'm still trying to wrap my head around some of the possibilities implied, but this line of reasoning seems very promising indeed.

Have Fun,

Jonathan

Yes it was me.

My login must have expired. But I claim the words above.

Jonathan

Michael,

"By the way, your comment about the conscious mind being a look-out on a ship is similar to my view of the conscious mind being the captain of the ship. The view seen by the look-out is generally filtered before it is passed onto the captain, hence we suffer from optical illusions because what we see is not the same as what we perceive."

Our slightly different views on this are likely due to different life experiences. Personally I've spent my life working with horses, in a extended family situation. Not being the managerial type, I've mostly worked with the horses themselves. In terms of the people, I'm not the captian of this particular, rather organic enterprise and in terms of the horses, it is most effective to zen out. To take a light hold and not worry too much.

The result, in both directions, is that my consciousness has to take a back seat and just plug in, as a bit of circuit breaker, or "lookout." You would be surprised how much information is absorbed when you are not focused on points of concentration.

I have some thoughts about time, which I will share once my words are together.

But briefly; I think the meaning of the term 'arrow of time' changes as the universe evolves. The initial arrow of time may have more to do with the metric signature, but there are also the procedural and entropic aspects of time's passage to consider, the contrast of duration with interval - and so on.

More later,

Jonathan

"If those balls were water molecules in a pot, we wouldn't assume some underlaying thermal scale determines how fast they are moving ..."

Yes we would, John. Statistical mechanics averages the fast moving and slow moving molecules. It's a matter of semantics whether the statistics "determines" the motion, because we know that the energy content of the molecules does the actual determining -- we just wouldn't know what that energy content is, until we use the statistics (and the Hamiltonian) to describe the molecular motion. At the quantum mechanical level, we are concerned with the energy content of even smaller particles.

If you actually tried to answer my question -- "instantaneously?" -- the point should dawn on you. The answer will not come as easily as saying "time is an effect," however.

Tom

Hi Michael,

I have been considering the wrong fibration. The one to be considered is this one

S1 ---> S15 ---> S14.

This separates out time, S1, from the outset, and locally gives

S15 = S1 x S14.

Now S14 can be further decomposed (at least locally) as

S14 = S7 x S3 x S4,

giving total spacetime as

S15 = S1 x S7 x S3 x S4.

Note that S3 is shared between your S10 ---> S3 x S7 and my S7

Last couple of line of my previous message got cut off; trying again:

Hi Michael,

I have been looking at the wrong fibrations. The one to be considered is this one

S1 ---> S15 ---> S14.

This separates out time, S1, from the outset, and locally gives

S15 = S1 x S14.

Now S14 can be further decomposed (at least locally) as

S14 = S7 x S3 x S4,

giving total spacetime as

S15 = S1 x S7 x S3 x S4.

Note that S3 is shared between your S10 ---> S3 x S7 and my S7 ---> S3 x S4.

I don't see why this cannot work, with closed universe and cyclic time.

Best,

Joy

Tom,

"because we know that the energy content of the molecules does the actual determining"

The scales emerge from the effects, ie. freezing to boiling points of water at sea level for celsius, etc. With time, the intervals/durations emerge from the actions, rotation of the planet, cycles of a cesium atom, etc.

Tom,

"If you actually tried to answer my question -- "instantaneously?" -- the point should dawn on you."

The duration is a measure of the action. If I take a picture and another when the ball has moved a foot, the duration is an effect of its movement. If your clock was the series of pictures, your time would depend on how fast the ball was moving, rather than some underlaying dimension determining how fast the ball moved. This is why the observation of whether it is the present moving past to future, or the events going future to past is important. The first is an effect, like the sun moving across the sky. The second is a process of change that is creating and dissolving these configuration points. Just as temperature is a statistical measure of the energy, time is a cyclical measure of the process.

John, I've run out of things to say. If you don't see that your ideas not only contradict known physics but logically contradict themselves, I can't add anything more that would likely change your mind.

Tom

Tom,

As you said some years ago, spacetime is a "physically real model." I realize you are never going to change your views on that, but bumping heads with you has certainly required me to look at the issue from many angles I wouldn't have otherwise thought of.

Hi Michael,

It is extraordinary how different people see different things in the same picture. Your reading of my attachment is fantastic. Where I am seeing geometry and topology of Hopf fibrations, you are seeing a lot of physics. That is great!

I have a problem with your last two sentences, however:

"A critical thing to explain here is still why is time different? If time were associated with R in some way, and the S3 and S7 spaces with the imaginary parts of H and O we could perhaps get a natural looking space-time split."

I have a different take on time---not necessarily relevant for our concerns here---where I distinguish between "tense-less time" and "becoming" in a physically viable theory. But that is a different story. We have a much simpler problem of time at hand. We would like to understand, as you put it, how time differs from space, given our current preoccupation with the S15-space.

The suggestion in your last sentence, however, is not the way I would like to go about the problem. Identifying the real part of either H or O with time would be the last thing I would want to do. I prefer to have the space-time split without having to break up either H or O. Isn't it more natural to break up S15 from the outset into S1 and S14 by means of Hopf fibration (as I suggested in my previous message)? This would break up S15 into S1 ~ R and S14 ~ CP7, giving the separation of S15-space into a real time R and an imaginary space CP7. I am not entirely sure whether this is kosher from the point of view of Hopf fibration, but this way of going about the problem would be far more acceptable to me than breaking up either H or O.

Best,

Joy