Time to end all misconceptions for ever!

[Qfwfq]

As for the odd flip, I have been thinking about that already for a long time. You should be aware that

the phase angle for an electron complete a full circle at 4*PI and NOT 2*PI. This means an electron

turns around twice to turn around once. What is it doing the other half of the circle ? Could that be the

flipped side ??? Hmmm ?

Look up the homomorphism of SU(2, C) onto SO(3, R). The twice-round thing doesn't mean that thins aren't physically the same after once-around, which ends up giving you -1 times so the modulus squared is the same and hence the probability density.

 

BTW, I have done some projective geometry to me WebFeet isn't making much sense. So I am glad you

have found a way to comprehend what he is attempting to say. Maybe you could explain it to me...

Not much to me either. I only got an impression he means some things quite differently from how I had previously assumed.

 

Also, for expectation values in QM, I understand that one can use either eigenvector on either side of

the expectation value to write out the Schroedinger wave equation.

Sure you're not mixing time evolution with transition amplitudes? The Schrödinger equation is more like |psi(t)> = e^(i t H)|psi(0)> and the dual of this.

 

The expectation value <psi| H |psi> will at time t become <psi| e^(-i t H) H e^(i t H) |psi> which may be considered in either the Schrödinger or the Heisenberg visual. In the latter, it is H that's time evolving, rather than |psi>.

 

What if <x* and x> are related yet not within the same space.

The dual of a Hilbert space is the same space, in the sense of being isomorphic. The formalism becomes much more complicated for continuous spectra, because the eigeinstates are in a broader space, not a true Hilbert space and not self dual.

 

Can the operator be a Tensor and still

be Hermitian ?

This is so in Lorentz-covariant QM and, better, in RQFT.

 

The difficulty of quantizing the gravitational field is much more subtle than that, but it isn't a topic I know well. One thing I do know is the field would have spin 2.

[WebFeet]

Not much to me either. I only got an impression he means some things quite differently from how I had previously assumed.

Here's a simple worked example

 

The image shows 2 triangles with the same energy, one with half the amount of mass.

The refractive index of the region of space containing the red triangle is twice that of the region containing the blue one.

 

As for the measurement of time.

sine(Permittivity) / sine(Permeability) = Time.

 

For the blue triangle, the value of Time will be 1. For the red triangle the value will be 0.5. Halve the mass again and the value of Time will reduce further to 0.25

 

 

In this example, the red triangle is in motion. The value of the velocity angle is relative to c=1. In this case it is 163,000 miles or 61 degrees. The mass at this velocity will have double.

As for the Time, its value is 0.5. Same result as in the first example, but this time due to velocity.

[paultrr]

Personally, I've never heard or seen the triangle approach applied to PV before and I've had a few conversations with Hal himself. I think in general anything can be graphed out. However, graphing such given there are some unknowns even with the PV case does not actually translate to anything. One sort of debatable unknown is the vacuum value on all this the same exactly in all places and time. If it does vary as say a result of local vacuum energy differences then by how much does it vary. Its rather like the stress energy tensor from normal GR. There are variables there also. If however we started with say some sort of graph for the normal vacuum where we have a value of 1 versus say the value for air then perhaps one could use the form of graph he is refering to.

[paultrr]

Here's a simple worked example

 

The image shows 2 triangles with the same energy, one with half the amount of mass.

The refractive index of the region of space containing the red triangle is twice that of the region containing the blue one.

 

As for the measurement of time.

sine(Permittivity) / sine(Permeability) = Time.

 

For the blue triangle, the value of Time will be 1. For the red triangle the value will be 0.5. Halve the mass again and the value of Time will reduce further to 0.25

 

 

In this example, the red triangle is in motion. The value of the velocity angle is relative to c=1. In this case it is 163,000 miles or 61 degrees. The mass at this velocity will have double.

As for the Time, its value is 0.5. Same result as in the first example, but this time due to velocity.

 

Okay. In general you are simply graphing something out some of us just figure out in our head, so to speak. I at one point applied some simular logic in figuring out photon motion through an Alcubierre type field, via some fill in the blanks PV type modeling.

[maddog]

Look up the homomorphism of SU(2, C) onto SO(3, R). The twice-round thing doesn't mean that thins aren't physically the same after once-around, which ends up giving you -1 times so the modulus squared is the same and hence the probability density.

I will. I have Abstract Algebra books by Herstein and Hergerford. I have studied in

the former (undergrad class), though I like using google to look up stuff.

Sure you're not mixing time evolution with transition amplitudes? The Schrödinger equation is more like |psi(t)> = e^(i t H)|psi(0)> and the dual of this.

I don't believe so. What I am considering the notion of the 10-Dimensional extension

of the Poincare group used in String Theory and allowing this manifold to be

bifurcated. One way conventially is roll up the extra dimensions. I am considering a

conjugate transformation similar to h-bar/2i (simplest case). I am seeing a symmetry

where we view the outside 3-dimensions. Topologically equivalent would be if the

the 3-spatial dimensions could be rolled up an the others are not. We would view the

world the same.

The expectation value <psi| H |psi> will at time t become <psi| e^(-i t H) H e^(i t H) |psi> which may be considered in either the Schrödinger or the Heisenberg visual. In the latter, it is H that's time evolving, rather than |psi>.

I didn't know the operator would be the evolving agent. That is interesting.

The dual of a Hilbert space is the same space, in the sense of being isomorphic. The formalism becomes much more complicated for continuous spectra, because the eigeinstates are in a broader space, not a true Hilbert space and not self dual.

I found this by looking up Hermitian Tensors. Verry Interesting! It turns out that this is

what Einstein was using in 1945 to create a Unified Field Theory (GR + EM). I found

a few papers on that I am going to study. In that I found that in any process with an

operator in the middle the either side elements must be of "like kind" (same dimension).

The difficulty of quantizing the gravitational field is much more subtle than that, but it isn't a topic I know well. One thing I do know is the field would have spin 2.

I remember that outcome verified from String Theory. A notion from a lot of current

day String Theories is this notion that the Gravitational Field might leak into the other

dimensions energy. Would be only a sink, or could there be a source ? ;)

 

Maddog

[maddog]

Okay. In general you are simply graphing something out some of us just figure out in our head, so to speak. I at one point applied some simular logic in figuring out photon motion through an Alcubierre type field, via some fill in the blanks PV type modeling.

I remember reading an article or two on an Alcubierre Field. I was wondering if you

knew of any papers that could effectively introduce the subject. ;)

 

Maddog

[paultrr]

I remember reading an article or two on an Alcubierre Field. I was wondering if you

knew of any papers that could effectively introduce the subject. ;)

 

Maddog

 

Most of the papers presuppose an certain level of understanding of GR and quantum field theory in general. To try and explain such a warp field can be done on a simple level. But remember this leaves aspects out.

 

The frontal portion of a warp field as proposed by Alcubierre was a gravity well, or a region where spacetime in contracted by a strong gravitational field. Such a field is not implying the usage of a blackhole. Just a very strong gravity field projected, as the case would be ahead of the craft.

 

The craft itself sits in a region where spacetime is normal or flat, unaccelerating on its own. Basically, think of a zero acceleration or at relative rest region in free fall.

 

The rear portion of a warp field requires exotic energy or at the very least an inflationary field working. The idea is sometimes stated that the craft rides between a region of contraction and expansion on a wave, so to speak. In this model spacetime itself is in motion with the craft being pushed and pulled along by such motion. In theory such a field could allow superluminal travel times. Guys like Natario have argued that the frontal portion of a warp field would encounter incoming photons with an infinite blue shift. However, his idea assumes C would remain the same or with a value of 1 across the whole field itself. Using the PV model, C's value would shift from point to point across that field making his assumption wrong. Using normal GR C would stay the same in the frontal and craft's region. While since the rear region has a lower stress energy C would be different there. Again, Natario's assumption would be in question.

 

There have also been raised many decent arguments against this idea out of what we term violations of quantum energy conditions. These arguments are sound in as far as the can be applied. However, if the exotic or negative energy is replaced with an inflation field then since nature itself by theory has had times when inflation was at work and since such requires a false vacuum state decaying to a stable one those arguments begin to loose ground somewhat then.

 

The major problem at the present is rather two-fold:

 

1.) We do not have the tech to create such a field.

 

2.) How does one fully control such a field once its going. The forward frontal region of a warp field is moving fast enough to require a FTL form of control unless one runs the field as a pulse. There is a small region of a warp field in which the field itself can supply a boost. That region can then be shut off. But part of the field is still going uncontroled. So one would have to propose and produce an honest control method for the field and also would need to be able to navigate once in warp, so to speak. The simplest solution is the pulsed field. Have it short duration with a built in decay time. Do one's look ahead scans for navigation in between pulses. Adjust speed, etc between pulses. How to fully do this is an unknown at present just the same as the tech would be.

 

Basically, nothing in this prohibits such a field from being used at sub-light velocities if we could actually produce such a field to begin with. As long as one remained sub-light there is no control problem or even any incoming infinite blue shifted photons to worry about. What Alcubierre had attempted to show is that there are solutions out of GR that do allow in principle for superluminal travel. His basic model was never designed as a workable field to begin with. However, some of the proposed modifications since that time are possibly more workable if we ever discovered the tech to produce such a field.

 

BPP studied the idea a bit of the warp field. BPP was canceled as a program long before anything firm ever came out of that study. Marc Mills own ending report on BPP left the subject as open. Some of the original researchers on this have kept in contact and still work on the model. I correspond a bit from time to time with some of them and belong to one research group which still looks into this and other ideas as far as propulsion goes. Some of our own members where also authors on a couple of the Lanl preprint articles on the Alcubierre field. Our general thrust has been to answer the objections as best we can and then to try and figure out ideas on how one might create or experiment with such a field in the first place. That leaves one with the big million dollar question mark and is about where the research stands at present. The one exception to this is a bit of ongoing experiment with the Woodward effect.

 

I might add that ideas of using wormholes for travel run in the same line as this type of research. Its all theory based at present. If anyone is interested a bit of the history of ESAA, as we where originally called can be found on Yahoo in the groups section and also at the reformed group we have at present called Stardrive. No this is not Jack's offshoot Stardrive group at all. Most of us there have problems with Jack's Bohm based UFO/ESP junk science to begin with. We split at about the time of Natario's article and abandoned the old ESAA groups for the most part.

 

One of our original founding members went off after a hyperspace idea involving concepts out of brane and M-Theory. Most of us tended to the more conservative GR and PV approaches over that avenue. We just could not agree and decided to form our own group. Fernando got a couple of major publications done. But nothing concise ever arose out of that and in fact, the idea he proposed was somewhat shot down itself on physical grounds. I myself did a Cern article in rebutal of one of his ideas. Basically, that article is in the now closed open Cern document forum. The link to such still is there and works. But the general search done on Cern will not show it. My own posting on the website section here has the link to that and some other articles. However, his idea was PV based. The still open links there show some of my own look at his PV based model and one can figure out using relativity of the dual frame comparison form why his model does not work to get around C in the first place.

 

Basically, if one takes two frames where C has a different value and tried to jump to one and then back to our own all one does is travel into the future there faster which implies that once back here one has traveled quicker there into our far future here. At the best case one can only match C time travels with such a method. Another words you're still stuck with someone leaving earth here and arriving far into the future. The whole idea behind field propulsion was to travel superluminally to shorten travel times to begin with. That's travel times for ship's crew and those left behind on earth. His idea fails at doing that. However, if his idea was ever shown to work it might solve the forward warp field control problem via that path.

 

Hope that perhaps helps a bit. Like I said that is a simplestic explination of how an Alcubierre field was supposed to work.

[WebFeet]

Personally, I've never heard or seen the triangle approach applied to PV before and I've had a few conversations with Hal himself.

That's hardly surprising as this has nothing to do with Hal. Until your mention of PV in another thread, I'd not actually come across it, but his work does provided a useful comparison to GR.

I think in general anything can be graphed out.

Of course you can.

However, graphing such given there are some unknowns even with the PV case does not actually translate to anything.

Firstly, the triangle isn't based on PV.

Secondly, you've been shown a single tool that can be used to provide the same results as GR and SR. Not only that, but the same relationships (you'd have to change the labelling) can provide Boyle's Law, Ohm's Law and many others.

And that translates to nothing ?

 

One sort of debatable unknown is the vacuum value on all this the same exactly in all places and time. If it does vary as say a result of local vacuum energy differences then by how much does it vary.

The first example showed you two masses with the same energy. You just have to compare the values of permeability and permittivity.

[paultrr]

That's hardly surprising as this has nothing to do with Hal. Until your mention of PV in another thread, I'd not actually come across it, but his work does provided a useful comparison to GR.

 

Of course you can.

 

Firstly, the triangle isn't based on PV.

Secondly, you've been shown a single tool that can be used to provide the same results as GR and SR. Not only that, but the same relationships (you'd have to change the labelling) can provide Boyle's Law, Ohm's Law and many others.

And that translates to nothing ?

 

 

The first example showed you two masses with the same energy. You just have to compare the values of permeability and permittivity.

 

Hal was one of the original developers of PV itself, though the idea predates him also. Taking Ohms Law one could also say it boils down to simple algebra which has always had the ability to be graphed out in one form or another. Back in Junior High I found algebra rather hard because of the cold way it is sometimes taught. But later after studying electronics for a bit I noticed that it is actually used commonly everyday of our lives. We just forget that having say $2.00 and wanting to know how many apples(X) we can buy is actually algebra.

[WebFeet]

Taking Ohms Law one could also say it boils down to simple algebra which has always had the ability to be graphed out in one form or another. Back in Junior High I found algebra rather hard because of the cold way it is sometimes taught. But later after studying electronics for a bit I noticed that it is actually used commonly everyday of our lives. We just forget that having say $2.00 and wanting to know how many apples(X) we can buy is actually algebra.

I must admit having a similar first impression when being taught algebra - What use is it?, but as you say we use it everyday.

 

What I've tried to show here is that when it comes to energy there is a common set of relationships which holds true in all circumstances.

 

Taking Ohms Law as an example. Yes you could say that it boils down to basic algebra. You could also say that Boyle's Law boils (no punn intended) down to basic algebra. You can say that about a great many things in physics.

 

When you can boil them all down to the same algebra, is that just coincidence and that everything can be graphed in one way or another ?

[Qfwfq]

Actually Maddog, I wrote <psi| H |psi> and <psi| e^(-i t H) H e^(i t H) |psi> somewhat absen-mindedly. Sorry. H commutes with its own exponentiation and this is why it is a conserved quantity, the time evolution is identity. Write instead:

 

<psi| A |psi> and <psi| e^(-i t H) A e^(i t H) |psi>

 

If A doesn't commute with H the second doesn't reduce to the first, so A isn't a conserved quantity.

 

I didn't know the operator would be the evolving agent. That is interesting.

It can be seen one way or the other. Evolving state or evolving operator. ;)

[WebFeet]

In general you are simply graphing something out some of us just figure out in our head, so to speak.

Here's a link to some software that allows you to play with the relationships.

 

Triangle software

[Kirk Gregory Czuhai]

ATTENTION!!!

the speed of light in a vacuum IS A DEFINED QUANTITY!!!

it was not always that way but it has been for some time.

it is NOT measured.

love and peace,

and,

peace and love,

and,

love and peace

(kirk) kirk gregory czuhai * ;)

p.s. i will give you a little time to google the specific value of c on the internet that is

its DEFINED value and i will post it later with a link. i am just too lazy to look it up for

you now and no i do not have it memorized other than its of course slightly less than

3.0*10^8meters per second or 186,000 miles per second. ;)

[Qfwfq]

Yes, c is a defined quantity and not a measured quantity, but the defined value is no more or less than 1.

 

The values such as 3*10^8 m/s or 186000 miles/s are measured values and not defined ones. What is the meaning of such measurements?

[Little Bang]

I'm curious Maddog, how do you write about something that varies over time without using time?

[maddog]

I'm curious Maddog, how do you write about something that varies over time without using time?

That is actually a good question. If I were to take "time" as a concept out of the discussion and think

only in terms of Calculus then this becomes easier.

 

Given a function f(x) and it was defined in terms of x, how could we describe the derivative f ' (x) in the

form that was independent of x ? Two ways both similar; define x in terms of something else

 

x = g(w)

 

Then we would have f(x) = f(g(w)) thus it's derivative could use the Chain Rule to produce

 

f '(x) = f '(g(w))g'(w)dw Since this did not depend on x, this would be the answer.

 

I could have used t (time) for x and viola` you a changing value dependent upon time not in terms of

time. Without a more specific example, I am not able to give a better describption. Maybe you can

inform me what you are specifically driving at.

 

maddog

[Dark Mind]

p.s. i will give you a little time to google the specific value of c on the internet that is

its DEFINED value and i will post it later with a link. i am just too lazy to look it up for

you now and no i do not have it memorized other than its of course slightly less than

3.0*10^8meters per second or 186,000 miles per second. :xx:

 

For some reason I have the exact speed of light memorized, it is 299,792,458 m/s. I have had it memorized for slightly under a year now. My love of physics is boundless :).