Quantum gravity physics based on facts, giving checkable predictions

## Wednesday, January 18, 2006

Correcting the Hubble expansion parameter for spacetime: at present recession speeds are divided into observed distances, H = v/R. This ignores the variation with time! The distance R is increasing all the time, so is not time-independent. To get a proper Hubble ‘constant’ therefore you need to replace distance with time t = R/c. This gives recession constant as v/t which equals v/t = v/(R/c) = vc/R = cH. So the correct spacetime formulation of the cosmological recession is v/t = cH = 6 x 10^- 10 ms^-2. Outward acceleration! This means that the mass of the universe has a net outward force of F=ma = 7 x 10^43 N. (Assuming that F=ma is not bogus!) Newton’s 3rd law says there is an implosion inward of the same force, 7 x 10 ^43 N. (Assuming that Newton’s 3rd law is not bogus!) This predicts gravity as the shielding of this inward force of gauge boson radiation to within existing data! (Assuming that the inward force is carried by the gauge bosons which cause gravity.)

Causal approach to loop quantum gravity (spin foam vacuum): volume contains matter and spacetime fabric, which behaves as the perfect fluid analogy to general relativity. As particles move in the spacetime fabric, it has to flow out of the way somewhere. It goes into the void behind the moving particle. Hence, the spacetime fabric filling a similar volume goes in the opposite direction to moving matter, filling in the void behind. Two analogies: (1) 'holes' in semoconductor electronics go the other way to electrons, and (2) a 70 litre person walking south along a corridor is matched by 70 litres of air moving north. At the end, the person is at the other end to the end he was in when he started, and 70 litres of air has moved up to fill in the space he vacated. Thus, simple logic and facts give us a quantitative and predictive calculating tool: an equal volume of the fluid goes in the opposite direction with the same motion, which allows the inward vacuum spacetime fabric pressure from the big bang to be calculated. This allows gravity to be estimated the same way, with the same result as the other method. Actually, boson radiations spend part of their existence as matter-antimatter pairs. So the two calculations do not duplicate each other. If the fraction due to radiation (boson) pressure is f, that due to perfect fluid pressure is 1-f. The total remains the same: (f) + (1 - f)= 1.

Error causing dark energy problems, etc., in cosmology:

Existing cosmology: Hubble constant(H) = recession velocity (v) /observed apparent distance (R) = parameter measured in units of 1/time (reciprocal seconds, etc.).

Problem: spacetime says observed distance R is observed at time past t = R/c, where c is velocity of light. Therefore we are seeing back in time with increasing distance. Fact! So stars are not at the distances they were when observed, but have receded further in the time the light was travelling towards us from the stars. We cannot claim the recession is independent of time. Fact! In spacetime, we must write the recession as time-dependent:

Solution: the recession is: recession velocity (v) / time past (t) = v/t. Since t = R/c, and H is already defined as H = v/R, the correct recession is:

v/t = v/(R/c) = HR/(R/c) = Hc ~ 6 x 10^-10 m/s^2 (acceleration!).

'Objections' to the facts above:

1. Who cares? Solution: it's consequences include predicting gravity right, and many other things: http://feynman137.tripod.com/

2. The galaxies are not really accelerating, it's just an effect caused by spacetime (finite speed of light, gravity, etc.) as seen by the observer. If we could somehow see and feel gauge boson exchange gravity from the universe instantly without delay times, this problem would disappear. Solution: who cares? What you see is what you get. Sure, if you could see the universe without the delay times of light travelling from times in the past, it would look different. But you can't.

3.
From: "Igor Khavkine" <ikhavki@uwo.ca>
To: "Nigel Cook"
Sent: Sunday, January 15, 2006 4:53 AM
Subject: Re: Reformulated post

'As to the post in question. I have seen nothing to change my original opinion. Unfortunately, I do not have the time to point out its flaws in detail. Hence I could only reply with a rejection.' - Sincerely, Igor Khavkine, sci.physics.research co-moderator.

Solution: (see previous post discussion of this bumptious, insulting vague crackpot). You can't get more out of these people than self-promotion. Khavkine says he sees flaws, but does not have time to point them out in 'more detail'. Those he ignorantly claimed to point out last time (see previous post) were Newton's laws and spacetime, which apply here! Personal abuse is just nonsense, since neither Ivor Catt not Igor know me personally. Their prejudices are bad.

Ivor Catt, a computer designer who has lifesaving inventions but prefers to promote his work by the 'discovery' that the Hubble recession is a hoax, claims - like Igor Khavkine - that my work is useless, and simply refuses to see the predictions it makes or comment scientifically, objectively. Instead, Ivor Catt makes personal comments, or political type sneers about spacetime. One favourite of Catt's is claiming that the sign of the Hubble expansion is 'wrong' because 'things are gaining distance but losing time'. This is political: it depends on whether you see distance or time as the more valuable. Spacetime says that any distance can be stated in terms of time t = R/c.

Big mouthed 'critics' can't do anything more than sneer. They have no facts, no scientific objection, just psychological crackpotism and personal belief in orthodox speculation, the personal pet theories of people like Dr Edward Witten and a few others. I've known this type of thing for a decade. Dr John Gribbin did not correct errors in new editions of his books when requested. Later he sent out an email to a long list of people suggesting that I might be sued for trying to get the life-costing errors in science corrected. See also my article here. As the quote at the beginning of my website says, the harder you try to better the world, the more objection from those who make money (selling books or whatever) about the old system they received their PhD in:

'The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore, all progress depends on the unreasonable man.' - George Bernard Shaw.

Nigel Says: January 14th, 2006 at 2:18 pm

Some kind of loop quantum gravity is going to be the right theory, since it is a spin foam vacuum. People at present are obsessed with the particles that string theory deals with, to the exclusion of the force mediating vacuum. Once prejudices are overcome, proper funding of LQG should produce results.

Lee Smolin Says: January 14th, 2006 at 4:41 pm

... Thanks also to Nigel for those supporting comments. Of course more support will lead to more results, but I would stress that I don’t care nearly as much that LQG gets more support as that young people are rewarded for taking the risk to develop new ideas and proposals. To go from a situation where a young person’s career was tied to string theory to one in which it was tied to LQG would not be good enough. Instead, what is needed overall is that support for young scientists is not tied to their loyalty to particular research programs set out by we older people decades ago, but rather is on the basis only of the quality of their own ideas and work as well as their intellectual independence. If young people were in a situation where they knew they were to be supported based on their ability to invent and develop new ideas, and were discounted for working on older ideas, then they would themselves choose the most promising ideas and directions. I suspect that science has slowed down these last three decades partly as a result of a reduced level of intellectual and creative independence avaialble to young people.

Thanks,
Lee

The fact that Dr Lee Smolin says this tells you that this is not a personal problem. There is a problem of authority being abused in science to support personal pet theories, like string theory and other untestable speculation.

UPDATE: Igor Khavkine above (and mentioned in previous post below) may or may not be the problem. A co-moderator with him on sci.physics.research is Urs Schreiber, a string theorist who emailed me once when he was a moderator at 'Physics Forums' a couple of years ago. My attempts to discuss the facts there were twarted by abuse from moderators under anonymous cover who claimed falsely that the divergence operator in mathematical physics is 'disproved' by a sum of line elements, then they cancelled my membership to prevent me responding! This is a similarly false approach as that taken by Igor Khavkine when he claims that spacetime and Newton's laws don't apply to the big bang, that he doesn't have the time to defend that false assertion, and that all further submissions on this topic will automatically be rejected. Dictators have plenty of fun being abusive to others. What a pity they can't pick on pseudoscience like string theory to ridicule. See Urs' defence of string theory here.

At 3:14 PM,  nige said...

Copy of comment to Motl's blog:

"But there will always exist people with a deeply totalitarian way of thinking who simply find the very existence of other opinions unacceptable and who will always be ready to go after those who bear different opinions, infiltrate their personal lives and anything else that can do the job - and they will actually do so as soon as they get the opportunity. Indeed, they don't find it sufficient to dismiss the arguments they don't like. They will try to connect these arguments with everything else that they may find helpful to damage those who bear the inconvenient ideas and insights." - Lubos Motl.

Those who suppress arguments that they "don't like", if those are actually correct arguments, do so largely for "fun". They have a pile of boring stressful work, and relieve the tension by suppressing other people. This is why you find racism most severe in some kinds of deprived areas that have otherwise high crime rates. The people take out some of it by racist behaviour. Those who are much wealthier and not living in overcrowded, underpaid poverty tend to commit less racist crime.

Dictatorial fascism is not so much a problem because different "opinions" are suppressed, but because FACTS are suppressed. For example, allowing people to voice opinions which are contrary to the facts and which lead to other people dying needlessly, is not a good democratic right of democracy.

If someone says something like "in my opinion this or that race doesn't deserve to live", that sort of opinion doesn't deserve freedom of expression. Inciting hatred and violence doesn't deserve freedom of expression.

Intolerance of such fanatical hatred is necessary to combat it. I'm lucky in that I had a severe hearing impediment in my youth, so I know first hand that even kids can be extremely nasty to anyone with problems. What they do is to gang up and sneer and poke fun endlessly, which sounds minor but over a few years gets to you a bit.

The reason other people tend to behave like this is mainly for "fun". Bad behaviour is for those people a release from stresses. (That is the mechanism, not an excuse for them.)

If you stop their sadistic "fun", they then complain about you spoiling their fun. They never really see themselves as behaving badly, just having "fun".

I think sometime around 1982-3, President Ronald Reagan called the Soviet Union an "Evil Empire" for the first time. A lot of Americans deplored what he said, claiming that Russians were nice and communism was a fair, equal system, better than capitalism, and didn't deserve being called "Evil". I think it was the first time an American president really stood up to the Soviet Union on the PROPAGANDA FRONT. Reagan later increased the propaganda, with deployment of the neutron bomb in Europe to counter the 5-to-1 tank superiority of the Warsaw Pact, and he talked of a "star wars" shield to render Soviet missiles "impotent and obsolete". All this reduced the morale of Soviet leader Gorbachev, who increased the level of openness and this helped to allow the Soviet Union to collapse. There were other factors involved as well, such as the economic crisis in the Soviet Union caused by over-spending on arms (the Soviets outnumbered the fixed 1000 American Minuteman missiles etc by the mid 1970s, but kept on increasing arms production!).

So I think you just have to try to make the fascist dictators realise that they are behaving badly, but you also have to realise that their minds are so warped from their own prejudices that they see everyone else as stupid or corrupt!

All that you can realistically hope is that the fascist dictators will lose the respect of all their followers and will eventually be deposed. In a few cases fascist dictators have moderated in tone (General Franco of Spain was moderated after the fascists lost WWII, but he remained leader for decades, and a similar statement applies to Fidel Castro of Cuba after the Soviet Union collapsed).

Nigel

At 3:09 AM,  nige said...

I can assure you Regan had nothing to do with Soviet Union collapse. End of oil crisis did.

Regan bringing Soviet system to collapse is as much of a propaganda as Soviets telling the west that there are no prostititutes or drug addicts in USSR. Sometimes I am amazed how easily people are brainwashed. Ever watch Fox News?
Curious | 01.18.06 - 7:55 pm | #

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As originally stated, there were many factors involved, but the major failure of Soviet long term ambitions of propaganda domination led to Gorbachev taking a soft line which allowed changes.

In a hated dictatorship system, any slackening of "discipline" by state police means a revolution!
nigel | Homepage | 01.19.06 - 6:10 am | #

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By the way, in the UK I don't get your **** American TV like Fox news, so you have the advantage (of ill-informed, unsubstantiated opinion)...
nigel | Homepage | 01.19.06 - 6:12 am | #

At 7:50 AM,  nige said...

If someone vaguely says the experimentally proved fact are false or wrong, they are asserting ignorance. The problem with Catt is that he does not know, nor want to learn, Maxwell's equations (the full equations, not just the bits used for mere transmission lines), or modern physics, but nevertheless asserts (without knowledge of them), that they have no content or are drivel. I can state correctly that string theory is not based on observables and does not predict anything potentially measurable, without reading all the maths speculations on the subject. This is not crackpot or "opinion" because it is based on unobserved extra dimensions and has no predictions that are testable. These are facts, and anyone can verify them. But it is false to do the same for modern physics (QFT, general relativity) because it us based on observables, even though the facts are usually embedded in maths. Wave-particle duality is observational fact to the extent that the maths for waves and particles can be applied usefully to the model different observations of the same thing (say, an electron or photon). Gravitation similarly is empirical, it is simply: (experimentally substantiated Newton's law, the low-energy, low-speed limit put into general relativity) + (light speed field spacetime) + (experimentally observed conservation of gravitational potential energy, expressed by the contraction term of Einstein's field equation). All this is both empirically defendable in construction, and also predicts other things that can be tested by measurement. Catt's confusion over what is right and what is wrong is due to a lack of physical understanding.

~~~~~~~~~~~~~~~~~~

At 12:33 PM,  nige said...

I've got to preserve copies of recent silly comments by string theorist Urs Schrieber on Woit's blog. He is such a poor loser and so incompetent it is FUN to see him struggle!

http://www.math.columbia.edu/~woit/wordpress/?p=329

Urs Says:

January 19th, 2006 at 2:51 pm
Peter,

the problem you mention is the problem of finding a phenomenologically viable background. The reason why we don’t check perturbative ST “locally” (simply by producing strings in the accelerator) is one of energy scales.

anonymous Says:

January 19th, 2006 at 3:19 pm
If perturbative ST predicted gravity, that would be a local prediction. It would tell you G and you would compare to measured value. It doesn’t predict gravity. Gravity is not a high energy phenomenon.

Urs Says:

January 19th, 2006 at 3:23 pm
Actually it does.

anonymous Says:

January 19th, 2006 at 3:25 pm
Witten said that, and Penrose exposed his error:

‘String theory has the remarkable property of predicting gravity’: false claim by Edward Witten in the April 1996 issue of Physics Today, repudiated by Roger Penrose on page 896 of his book The Road to Reality, 2004. String theory does not predict anything testable about gravity.

At 1:49 PM,  nige said...

Hilarious string theorist Urs Schrieber makes more custard pies and throws them in his own face:

http://www.math.columbia.edu/~woit/wordpress/?p=321 :

Urs Says:

January 19th, 2006 at 2:31 pm

"I think that when Gen Rel was published in 1915 there WERE already detectors able to see the effects."

Sure. But in 1815 there were not.

Today, entire high energy physics is suffering from the lack of good detectors. Theory is far ahead of experiment, unfortunately.

anonymous Says:

January 19th, 2006 at 4:44 pm

“Theory is far ahead of experiment, unfortunately.”

Indeed! I thought it was the other way round, with theory being unable to catch up with experiments. Perhaps I’ve missed a paper on arXiv.org that predicted the masses of quarks, coupling constants, and other Standard Model parameters. How careless of me.

At 2:47 PM,  Anonymous said...

Comment on Christine Dantas' blog:

http://christinedantas.blogspot.com/ :

Anonymous said...
Thanks. I'm interested in the statement on page 14 of hep-th/0601129:

‘… it is thus perhaps best to view spin foam models as models in their own right, and, in fact, as a novel way of defining a (regularised) path integral in quantum gravity. Even without a clear-cut link to the canonical spin network quantisation programme, it is conceivable that spin foam models can be constructed which possess a proper semi-classical limit in which the relation to classical gravitational physics becomes clear. For this reason, it has even been suggested that spin foam models may provide a possible ‘way out’ if the difficulties with the conventional Hamiltonian approach should really prove insurmountable.’

This is very positive. One problem seems to be that experts in QFT are not overly familiar with GR and cosmology. Peter Woit for example, is expert at QFT (he taught it for years and did his PhD in that area), probably has an undergraduate training GR and cosmology from the 1980s.

If quantum gravity is to be pictured by Feynman diagrams, with gauge bosons (the unobserved gravitons, or perhaps something else) being exchanged to give force, then the cosmic expansion would redshift gauge bosons coming from vast distances?

The issue is that gravity is such a long ranged force, cosmology must be built into it fundamentally, if gravity really is a gauge boson exchange process (quantum field theory). Do these comments make sense?

Thank you!

At 3:31 AM,  Anonymous said...

Peter Woit now has a post about the major new paper evaluating LQG (copied here in case he deletes it by "accident", as he has done with certain previous posts!):

http://www.math.columbia.edu/~woit/wordpress/?p=330

LQG for Skeptics
An interesting paper appeared on the arXiv yesterday, by Hermann Nicolai and Kasper Peeters, entitled Loop and spin foam quantum gravity: a brief guide for beginners. It includes some of the same material as an earlier paper Loop quantum gravity: an outside view that they wrote with Marija Zamaklar.

Nicolai and Peters (as well as Zamaklar) are string theorists, and given the extremely heated controversy of the last few years between the LQG and string theory community over who has the most promising approach to quantum gravity, one wonders how even-handed their discussion is likely to be. They identify various technical problems with the different approaches to finding a non-perturbative theory of quantum gravity that are often referred to as “LQG”. I’m not an all an expert in this subject, so I have no idea whether they have got these right, and whether the problems they identify are as serious as they seem to claim. Their main point, which they make repeatedly, is that

.. the need to fix infinitely many couplings in the perturbative approach, and the appearance of infinitely many ambiguities in non-perturbative approaches are really just different sides of the same coin. In other words, non-perturbative approaches, even if they do not `see’ any UV divergences, cannot be relieved of the duty to explain in detail how the above divergences `disappear’, be it through cancellations or some other mechanism.

What they are claiming seems to be that LQG still has not dealt with the problems raised by the non-renormalizability of quantum GR. They don’t explicitly make the claim that string theory has dealt with these problems, but the structure of their argument is such as to imply that this is the case, or that at least string theory is a more promising way of doing so. Their one explicit reference to string theory doesn’t really inspire confidence in me that they are being even-handed:

The abundance of `consistent’ Hamiltonians and spin foam models … is sometimes compared to the vacuum degeneracy problem of string theory, but the latter concerns different solutions of the same theory, as there is no dispute as to what (perturbative) string theory is. However, the concomitant lack of predictivity is obviously a problem for both approaches.

While they are being very hard on LQG for difficulties coming from not being able to show that certain specific constructions have certain specific properties, they are happy to state as incontrovertible fact something about string theory which is not exactly mathematically rigorous (the formulation of string theory requires picking a background, causing problems with the idea that all backgrounds come from the “same” theory, and let’s not even get into the problems at more than two loops).

The article is listed as a contribution to “An assessment of current paradigms in theoretical physics”, and I’m curious what that is. Does it contain an equally tough-minded evaluation of the problems of string theory?

It should be emphasized again that I’m no expert on this. I’m curious to hear from experts what they think of this article. Well-informed comments about this are welcome, anti-string or anti-LQG rants will be deleted.

This entry was posted on Friday, January 20th, 2006 at 12:39 am and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

3 Responses to “LQG for Skeptics”
Robert Says:

January 20th, 2006 at 5:03 am
Just to repeat it in plain English: When Peter says that string theory is not predictive he refers to the fact that there is likely a very large number of possible low energy effective theories (say in terms of particles and couplings). This is in contrast to LQG which according to the experts can be coupled to _any_ particle content (and possibly even anomalous) with any set of couplings. But this is not the problem that Nicolai and Peters address.

anonymous Says:

January 20th, 2006 at 5:32 am
String theory has always been an attempt to model untestable phenomena such as SUSY, particle phenomena at energies that would require particle accelerators larger than this planet, etc.

String theory focusses on “predicting” unobservables like spin-2 gravitons, then claims to have “predicted gravity”. It can’t predict any fact, so that is a fraudulent claim. It makes outsiders and even many physicists in other areas, falsely believe that string theory predicts gravity. It just doesn’t.

Spin foam vacuum is an attempt to model REALITY, i.e., known QFT Feynman path integrals, properties of the quantum vacuum. Modelling things that are known is a good way to develop theories that predict things which are not yet known.

Hence Newton, Maxwell, Einstein, build their equations around observables, and the results began to predict other things!

String theory deserves a prize for trying to buck the trend, by trying to model unobservable particles, universes, dimensions, etc. Unfortunately, it doesn’t work.

anonymous Says:

January 20th, 2006 at 5:46 am
Page 14 of hep-th/0601129: ‘… it is thus perhaps best to view spin foam models as models in their own right, and, in fact, as a novel way of defining a (regularised) path integral in quantum gravity. Even without a clear-cut link to the canonical spin network quantisation programme, it is conceivable that spin foam models can be constructed which possess a proper semi-classical limit in which the relation to classical gravitational physics becomes clear. For this reason, it has even been suggested that spin foam models may provide a possible ‘way out’ if the difficulties with the conventional Hamiltonian approach should really prove insurmountable.’

At 1:20 PM,  nige said...

New comment to Dr Motl's blog:

http://motls.blogspot.com/2006/01/review-of-loop-quantum-gravity.html

Dear Lubos,

'... it is thus perhaps best to view spin foam models ... as a novel way of defining a (regularised) path integral in quantum gravity. Even without a clear-cut link to the canonical spin network quantisation programme, it is conceivable that spin foam models can be constructed which possess a proper semi-classical limit in which the relation to classical gravitational physics becomes clear. For this reason, it has even been suggested that spin foam models may provide a possible ‘way out’ if the difficulties with the conventional Hamiltonian approach should really prove insurmountable.' - Page 14 of http://arxiv.org/abs/hep-th/0601129

The reason for the technical problems like an infinite number of potential solutions is simply a lack of connection to reality. This is the same problem which stops string theory from succeeding after 20 years of intense funding, which LQG has not had!

I don't think the aim of science is just to link GR and QFT by some kind of mathematical fiddle of the Feynman path integral, but the broader picture of understanding why gravity is so much weaker, and being able to predict it.

The conventional aim of producing a theory that "predicts gravity" by merely being consistent with unobserved hypothetical spin 2 graviton conjectures is no good.

Maxwell fiddled his theory to fit the facts, but at least his equations allow me to calculate electromagnetic phenomena.

With both string theory and LQG you have a mathematically far more complex and incomplete version of something like Maxwell's aether electromagnetism, but the equations are useless for practical things. You can't calculate Standard Model parameters with them, or anything.

So you are left with the physical picture - 10/11 dimensional strings and 10^500 vacuua. This is why I think LQG spin foam vacuum is more realistic - it is tied to reality.

It's a pity you people are so constrained to only seeing abstract mathematical approaches and technical details of speculative conjectures. Top physicists should be resolving the reasons why Maxwell's equations wrongly predict continuous and not discrete electromagnetic waves for atomic phenomena. Once this is sorted, then you will a correct model for one observable unified force (electromagnetism) which will be a foundation for getting a grasp of quantum gravity. At present, anomalies between real observed physics phenomena and the mathematical models are swept under the carpet. And some people have the cheek to speculate on SUSY and other unobservables.

Nigel

At 1:22 PM,  nige said...

From a discussion on Wikipedia:

Kevin: before the TEM step arrives at any part of the cable, there is zero voltage. As it arrives, the voltage increases and with it the current. Once it has peaked, it remains steady. The only period of interest is while the voltage is rising. Ivor ignores this, and also introduces other errors like the claim that displacement current flowing where the voltage is steady. Your sine wave radio signal versus square wave logic step argument is vacuous, since radio emission occurs so long as di/dt is not zero in any part of the aerial. Fourier analysis is useful to me for the purpose of translating a plot of current or field strength versus time into a frequency spectrum. According to Fourier analysis, you can represent a square wave as a series of sine waves! But that's not my main argument.

Consider the 2 conductor transmission lines as 2 parallel radio aerials. If you feed one with a signal (of any type) and leave the other passive, the first transmits energy to the passive one which receives energy only as a result of di/dt in the first one. This is indistinguishable from Maxwell's "displacement current" equation. Maxwell says vacuum "displacement current" i = e.dE/dt = e.dv/(x.dt) where e is permittivity and x is the width over which the step rises (definition: x = ct, where t is the rise-time). We see that if x = 0, then i = infinity. This disproves the idea of a truly abrupt step. Moreover, the current rises over the rise-time from 0 to its peak, and since radio emission occurs in proportion to di/dt, it becomes more intense as the step rise-time is made smaller.
Now here is the proof. Taking the 2 parellel aerials or transmission line conductors. Feed one with any signal, and feed the other with the inversion of that signal. While the signal strength rises, electrons accelerate and radio emission occurs in a perpendicular direction.

I've done this experiment and proved it experimentally. During the rise-time, each conductor transmits a radio signal that is the exact opposite of that emitted from the other conductor. At a long distance (several times the distance of the gap between the two conductors) there is no observable radio transmission at all, because each radio emission cancels out that of the other: perfect interference. (The same concept is often used as white noise to suppress sounds, but that is less effective.)
The point is that the entire radio energy emitted by each conductor during the step is transmitted to, and received by, the other conductor. This is the process by which the TEM wave is allowed to propagate. Catt, ironically, gives the conventional textbook slab of drivel on this point! See [23] (that web version misses out the formulae, but they are widely known) where Catt calculates the inductance of a single wire and finds: "The self inductance of a long straight conductor is infinite. This is a recurrence of Kirchhoff's First Law, that electric current cannot be sent from A to B. It can only be sent from A to B and back to A." I think it is unhelpful for Catt, having defined E and B in fixed ratio for a TEM wave (E=cB), then goes along with the unfruitful textbook treatment of inductance which considers inductance as a B field effect! The magnetic field loops around each conductor instead of going from one conductor to the other line "displacement current" or in fact radio energy. This is probably where the conventional theory went wrong! It is clear that the entire energy needed to propagate the TEM wave is transmitted as radio from one conductor to the other during the step. No loss occurs because the step in each is inverted with respect to the other in a TEM wave. I'm going to do the calculations to demonstrate how this solves the Catt anomaly. 172.209.113.91 20:52, 20 January 2006 (UTC)