Hyperspace engine (Heim's Quantum Theory)

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laurelelizabeth

A hyperspace (faster then c) engine is being worked on by the U.S. It would work by going into another dimension based of of Heim's Quantum Theory.
How realistic is this and could we go faster then c with enough energy like in the experiment. Obviously not relevant to us but in parallel? If you are using it linearly with c then it has a limit at c but how could the fabric of spacetime be changed to push slower particles through space faster? They say current rules of thought would have to change like now viewing the universe as one consistant linear stream.

http://news.scotsman.com/scitech.cfm?id=16902006 [Broken]

http://en.wikipedia.org/wiki/Heim_theory
I read the article and it seems like it's only hypothetical, and they have to prove the physics before working on it.

That would be awesome if they could do that!
 
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Now that Tajmar refernces the heim-theory explanation of Droscher/Hauser as one of the likely explanations of the artificial gravity effect, the theory is moving out of the realm of the hypothetical into that of the real.
 

Vanadium 50

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Heim's theory is inconsistent with data:

(1) He predicts five light neutrinos, not three.

(2) The masses of the neutrinos are inconsistent with measurements from neutrino oscillations.

(3) The masses of the proton, neutron and electron lie far (~100 standard deviations) outside Heim's predictions and quoted errors.

Now that I think of it, I can't recall a single prediction that Heim got right.
 
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Grossly unfair Vanadium: Heim theory doesn't claim to be complete as yet. Droscher, for instance, found recently that the neutral electron can be interpreted as secondary matter and might actually be what we term Dark Matter.

The neutrino masses were at least in the right ball park and predicted 20 years before most people accepted there were non-zero masses to them. Which other theory has done even that much? As for oscillations: this probably can be shown within Heim theory also, as it is an amalgam of GR & QM and so should have at least the standard model within it if enough research was done into its foundations.

As for proton and Neutron mass predictions wrong - Don"t make me laugh: String theory has nothing to say on these masses and the standard model, with more input parameters, can, via perturbative lattice QCD, now get to within a few percent ( > 2%) of the proton mass!!!!!! Hah! Pathetic compared to the Heim prediction, which gets to within 0.0007 % of the answer with analytical equations not needeing massive perturbative iterations.

No predictions right, eh? Also, there is the artificial gravity for which its discoverer, Tajmar, acknowledges Heim theory as one of 3 candidate predictions for the effect - the others being dubious extensions of the standard model.

Finally, the 3rd Heim gravity force matches dark energy pretty well... I rest my case.
 
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It strikes me that a good group of grad students with a sizeable budget could build a scaled down model of a drive unit. It doesn't have to lift any space craft into orbit or the next star system. But it could be used to pull a small cart, or possibly a small aircraft. I wonder how hard it would be to convince UNH that it would be a worthwhile endeavor?
 
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Hi Physicsforum, I'm new here ;)

As this is the most recent thread to Heim Theory, i decided to post in here:

I have a question regarding the sometimes assumed connection between Heim Theory and Loop Quantum Gravity: In Heim's theory, at the microscopic level, differential equations become difference equations. Is that also the case in LQG or any other QG approach? (I assume it's not in any String Theory; correct me if I'm wrong.)
 
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Hi Orbb - no, only Heim theory uses the differences method explicitly. LQG also avoids infinities due to the quantisation of space in that the finite size of a surface element in its spin networks or spacti-time foam means that quantum fluctuations do not go down to arbitarily small wavelengths. That stops the infinities that plague the stnadard model and string theory, which only avoid them by ugly artificial tricks such as renomalisation or worse.
 
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... compared to the Heim prediction, which gets to within 0.0007 % [of observed proton mass] ...
From what I've read, the surprisingly accurate Heim results you speak of were generated by a computer program which uses the empirical data as an input. In other words, you're using the value of X to solve for the value of X. It doesn't demonstrate anything about the Heim conjecture at all.

Source: http://www.geoffreylandis.com/Heim_theory.html

Also, there is the artificial gravity for which its discoverer, Tajmar, acknowledges Heim theory...
Tajmar's 2006 experimental results have not yet been reproduced, and seems not to be very widely accepted.

Source: http://en.wikipedia.org/wiki/Anti-gravity#Tajmar_et_al_.282006_.26_2007_.26_2008.29
 
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gabbagabbahey

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From what I've read, the surprisingly accurate Heim results you speak of were generated by a computer program which uses the empirical data as an input. In other words, you're using the value of X to solve for the value of X. It doesn't demonstrate anything about the Heim conjecture at all.

Source: http://www.geoffreylandis.com/Heim_theory.html
Perhaps you missed this line:

www.geoffreylandis.com/Heim_theory.html said:
in 2007, however, Reed changed his opinion. Working with Fortran code that Heim helped develop later that was not published, he says that he can derive particle masses without the use of that A matrix.
And Reed's quoted analysis that followed.
 

Vanadium 50

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I'm going to make the same complaint - previously called "unfair" - that Heim's theory does not agree with the data:

  1. He predicts five light neutrinos, not three.
  2. The masses of the neutrinos are inconsistent with measurements from neutrino oscillations.
  3. The masses of the proton, neutron and electron lie far (~100 standard deviations) outside Heim's predictions and quoted errors.

Now, it may well be that a future, Heim-like theory might agree with the data. But all we can discuss today is what exists today. And what we have today is a theory that is grossly discrepant with the data.
 
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yes, gabbagabbahey is right. I acted as intermediary between Anton Mueller, who did the first excellent coding of the Heim mass formula in fortran and John Reed. Eventually John was brave enough to admit his error - the A matrix (semi-empirical) was indeed used by Heim, but only in his 1982 mass formula version - in that case his interest was to see how well he could derive resonance states, given the ground states. So he just plugged in the data via the A matrix, never claiming it predicted the ground states. That part came later, in the 1989 formula, which dispenses with A and concentrates on the ground state derivation. John confirmed that Anton's 1989 code had no longer the infamous A.

When the gravity thing has been dealt with, D&H & co. will return to other aspects of the theory, including the mass formula. It will still take some work to retrieve some of the missing steps that Heim omitted in his delineation. He was working from memory and though he had all the steps in his head, didn't write them all down. Let's hope that gap is filled soon.
 

gabbagabbahey

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I'm going to make the same complaint - previously called "unfair" - that Heim's theory does not agree with the data:

  1. He predicts five light neutrinos, not three.
  2. The masses of the neutrinos are inconsistent with measurements from neutrino oscillations.
  3. The masses of the proton, neutron and electron lie far (~100 standard deviations) outside Heim's predictions and quoted errors.

Now, it may well be that a future, Heim-like theory might agree with the data. But all we can discuss today is what exists today. And what we have today is a theory that is grossly discrepant with the data.
The first two points I agree are legitimate problems with the theory and need to be resolved before I buy in to Heim theory. However, as HDeasy mentioned, it is a work in progress (hampered significantly by the death of its founder no doubt!) and these problems might be easily resolvable.

Your third claim, is completely contrary to the predicted and accepted values that I have seen and I would like to see your source for this info.
 
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I've glanced at the code. It's got constant's galore.
For example, in b0.07_HeimMassFormula/formula/AbstractParticle.java:
Code:
    // Since noone can seem to figure out W atm. this simply returns
    // values given in Selected Results
    protected double W() throws Exception {

	if (index == AbstractFormula.E_MINUS) return 38.7;
	else if (index == AbstractFormula.E_ZERO) return 38.51;
	else if (index == AbstractFormula.MU) return 2830.26;
	else if (index == AbstractFormula.PI_CHARGE) return 3514.46;
	else if (index == AbstractFormula.PI_ZERO) return 3419.16;
	else if (index == AbstractFormula.ETA) return 9905.01;
	else if (index == AbstractFormula.K_CHARGE) return 8857.96;
	else if (index == AbstractFormula.K_ZERO) return 9332.36;
	else if (index == AbstractFormula.P) return 14792.56;
	else if (index == AbstractFormula.N) return 14828.61;
	else if (index == AbstractFormula.LAMBDA) return 16827.98;
	else if (index == AbstractFormula.SIGMA_PLUS) return 18124.03;
	else if (index == AbstractFormula.SIGMA_MINUS) return 18183.3;
	else if (index == AbstractFormula.SIGMA_ZERO) return 18179.6;
	else if (index == AbstractFormula.XI_CHARGE) return 18998.73;
	else if (index == AbstractFormula.XI_ZERO) return 18990.09;
	else if (index == AbstractFormula.OMEGA_CHARGE) return 23157.61;
	else if (index == AbstractFormula.DELTA_PLUSPLUS) return 18115.38;
	else if (index == AbstractFormula.DELTA_PLUS) return 18467.56;
	else if (index == AbstractFormula.DELTA_MINUS) return 18448.52;
	else if (index == AbstractFormula.DELTA_ZERO) return 18508.94; 
	
	throw new Exception("Unknown Particle");
    }
It wouldn't take more than David Blaine trickery to derive one set of constants from another set, if you chose the later set carefully.

I'd like to see a strait forward presentation of Heim's mass formula, but the best I've been able to get is this:
2m67bmd.png

(Taken from page 5 of http://www.heim-theory.com/downloads/F_Heims_Mass_Formula_1989.pdf [Broken])
This looks a lot more like numerology than physics.

But, what do I know, I'm only an unconvinced amateur.
 
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http://chsunier.ch/Books/Themata/beitraege/RESCH/D_Zur_Herleitung_Der_Heimschen_Massenformel.pdf [Broken] provides the derivation of the mass formula. However, this is a version that, according to heim-theory.com, still needs to be revised. Also so far, it is available in german only. But maybe it is of use to someone -the matter is yet too complex for me.
 
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I don't know what those constants are about. For the 1989 fortran code, apart from c, G, h, Pi , some values of the masses from other grpups are fed in from a table for comparison (e.g. the CODATA 1998 data): the output table then lists the program values alongside the CODATA values or also differences if that option is used.) E.g. searching for 4 in all the code gave:

grep 4 *.f
Hprog.f:C (Powerstation 4.0 under NT4.0 SP6 using an AMD K7 processor)
Hprog.f:C character*20 t1,t2,t3,t4,t5,t6,t7,t8
Hprog.f: integer*4 NN1,NN2 ! limits for NN
Hprog.f: integer*4 iL
Hprog.f: real*4 fma,GG4,SS4,FF4,FI4,sum14,sum24! result
Hprog.f: iprint = 0 ! no output of parts in eq.4
Hprog.f: Rg = 376.730313461 D0 ! CODATA'98 # const
Hprog.f: beta = 1.D0/1.00001411D0 ! #const
Hprog.f: call fmass(fma,GG4,SS4,FF4,FI4,WN0,sum14,sum24 )
Hprog.f:301 format(1x, a, 1pE14.7 , 11I4 )
Hprog.f: write(6,*) ' sum1=',sum14,' sum2=',sum24
Hprog.f: write(6,*)' G =',GG4, ' S=',SS4,' F=',FF4
Hprog.f: write(6,*)' FIFI =',FI4
Ibin.f: integer*4 Function Ibin(n,k)
Ibin.f: integer*4 N,K, ibi, ilo, ih ,iden ,ibinom ,i
Ibin.f:3 write(6,*) ' n over k is restricted to n <= 17 using integer*4'
WN0fu.f: integer*4 IBIN
WN0fu.f: integer*4 B,H,ieq, Lex
WN0fu.f: real*8 z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13
WN0fu.f: real*8 teil1,teil2,teil3,teil4
WN0fu.f: + -dfloat((3*q-1)*(k-1)) + 0.5d0*dfloat((PP-QQ)*(4+(B+1)*(1-q))
WN0fu.f: z4 = dfloat(PP)*( 0.5d0*dfloat(B)+2.d0 + dfloat(q) )*dfloat(2-k)
WN0fu.f: z5=-dfloat(QQ)*(0.5d0*dfloat(B)+dfloat(1-4*(1+4*q)))*dfloat(2-k)
WN0fu.f: teil2 = z4 + z5
WN0fu.f: teil4 = ! # KLAMMER ergaenzt
WN0fu.f: + -0.25d0* dfloat(q)*dfloat((1-q)*(B-4))-0.25d0*dfloat(B-2)
WN0fu.f: a2 = teil1 -(1-r)*( teil2 + teil3 +teil4 )
WN0fu.f: z2 = (PP-QQ)*(4+(B+1)*(1-q))/2.
WN0fu.f: z4 = PP*(B/2.+2+q)*(2-k)
WN0fu.f: z5 = -QQ*(B/2.+1-4*(1+4*q))*(2-k)
WN0fu.f: z6 = (B-2)*(1+3*(PP-QQ)/2.)/4.
WN0fu.f: z9 = -(B+2)*(1-q)/4.
WN0fu.f: z11 = -q*(1-q)*(B-4)/4.
WN0fu.f: z12 = -(B-2)/4.
WN0fu.f: teil2 = z4+z5
WN0fu.f: teil4= -ibin(PP,3)*( (2*(1+ieq)+z10 -q)+z11+z12+z13 )
WN0fu.f: a2 = teil1 -(1-r)*( teil2 + teil3 +teil4 )
WN0fu.f: write(6,*) ' z3 =', z3 , ' z4 =', z4
WN0fu.f:C write(6,*) ' teil3=',teil3, ' teil4=',teil4
WN0fu.f: goto 400
WN0fu.f:c zw =(wet/dfloat(k))*(4.d0*(2.d0-wet)
WN0fu.f:c & *dfloat(4*B+PP+QQ))
WN0fu.f:cc zw =((wet/dfloat(k))*(4.d0*(2.d0-wet)
WN0fu.f:cc & *dfloat(4*B+PP+QQ))
WN0fu.f:c z4= ( dfloat((PP-QQ)*(H+2))+dfloat(PP )*( dfloat(5*B*(1+q)*QQ) +
WN0fu.f:c + ( z3 + z1 + z4 + z5 )
WN0fu.f:c write(6,*) ' z4 = ' ,z4
WN0fu.f:400 continue ! neuer code fuer y
WN0fu.f: zw = ( wet/k)*( 4*(2-wet)-pi*ebn*(1-eta)*wet)*(k+ebn*wet*(k-1))
WN0fu.f: + + 5*(1-q)*(4*B+PP+QQ)/(2*k+(-1)**k)
WN0fu.f: + -q*(1+ieq)*( k*(PP*PP+1)*(B+2)+(PP*PP+PP+1)/4.)
WN0fu.f: z4 = ( (PP-QQ)*(H+2)
WN0fu.f: zw1= z2+ibin(PP,2)*(1-ibin(QQ,3))* ( z3+z1 )+z4+z5!)
WN0fu.f: y = r*zw + (1-r)*zw1 ! KLAMMER versetzt 4.5.03
WN0fu.f:c write(6,*) ' z4 = ' ,z4
WN0fu.f: a3 = dfloat(4*B)*y/(1.d0+y)-1.d0/dfloat(4+B)
WN0fu.f: eque = a3/dfloat(4*B) ! alt1
compini.f:C integer*4 igam ,ialfpm ,iparm ,itab
compini.f: pi = 3.14159265358979 D0
compini.f: hq = 1.054571596 D-34 ! CODATA'98 (+-82)
compini.f: c = 2.99792458 D8
compini.f: ! # const: from table page 54 :
compini.f: qn(2) =24
compini.f: qp(2) =34
compini.f: HH(2)=104
compini.f: oc = 4.D0/3.D0 ! # const
compini.f:C Rg = 376.730313461 D0 ! CODATA'98 # const c.f. Hprog.for
compini.f:C beta = 1.D0/1.00001411D0 ! #const "
compini.f: case (4)
compini.f:C fakMeV = 0.05609545 D31 (Sch)
compini.f: eta = pi/Dsqrt(Dsqrt(4.D0+ pi*pi*pi*pi))
compini.f: eq = 3.D0/(4.D0*pi*pi)*Dsqrt(2.D0*theta*hq/Rg)
compini.f: beta = 1.D0/1.00001411D0
compini.f:C eq.4a page 13 ( anno 1985 ? )
compini.f: write(6,101) 'c.f. Anhang B , pg. 54 '
compini.f: goto 400
compini.f:C (4-8) Parametermatrix: entfaellt
compini.f:400 continue
detailini.f: integer*4 jq,jk
detailini.f: do jq = 0,2; n4tab(jk,jq)= -99999.; enddo
detailout.f: integer*4 jq,jk
detailout.f: write(6,*) ' N4(k,q) ,k =', jk, ' q = 0,1,2 :'
detailout.f: write(6,*)( n4tab(jk,jq), jq = 0,2)
etaqk.f:C pi = 3.14159265358979 D0 im Common/CONST/
etaqk.f: integer*4 kq,k
etaqk.f: zw1 = Dsqrt(kq*kq*kq*kq*(4.d0+k)+pi*pi*pi*pi)
fmass.f: Subroutine Fmass(fma,GG4,SS4,FF4,FI4,WN04,sum14,sum24 )
fmass.f:C + , N1,N2,N3,N4,EQK,EQ1,E1K
fmass.f: + ,zw1,zw2,zw3 ,zw4,zw5,AAA ,UU ,sum1,sum2
fmass.f: real*4 fma, WN04,GG4,SS4,FF4,FI4 ,sum14,sum24
fmass.f: integer*4 ibin
fmass.f: zw4 = - zw3*zw1* oc/u
fmass.f:C write(6,*) 'zw5,zw4 =',zw5,zw4
fmass.f: zw4 = zw5 + zw4
fmass.f:C write(6,*) ' ln(0.5*k*N3) = ' ,zw4 , ' q,k=',q,k
fmass.f: N3 = dexp( zw4) * 2.d0/dfloat(k)
fmass.f: N4 = dfloat( 4*( 1 + q*(k-1)) / k )
fmass.f: zw4 = (1.d0 -dsqrt(EQK))/(1.d0+dsqrt(EQK))
fmass.f: zw4 = zw4 * zw4
fmass.f: N5 = AAA*(1.d0+dfloat(k*(k-1)*2**(k*k+3))*AAA*fuNk(k)*zw4)
fmass.f: zw4 = 4.d0*(1.d0 - dsqrt(eta))/(1.d0 + dsqrt(eta))
fmass.f: zw4 = zw4*zw4
fmass.f: zw3 = eta*(1.d0 -alfm/alfp)*zw4*dfloat(qs(k))
fmass.f: N6 = 4.d0*dfloat(k)*
fmass.f: + + dfloat(4*r*BB(k)*(1-QQ)) /dfloat(3-2*q)
fmass.f: + -dfloat((PP-QQ)*(1-q))*4.d0*pi/dsqrt(dsqrt(2.d0)) ) )
fmass.f: fi=N4*dfloat(p*p/(1+p*p))*(dfloat(s+qs(k))/dsqrt(dfloat(1+s*s)))*
fmass.f: + ( dsqrt(dsqrt(2.d0)) -4.d0*UU*dfloat(BB(k))/WN0f )
fmass.f: + + dfloat(p*(p+1))*N3 + dfloat(4*s)
fmass.f: + + dfloat( qp(k)*(1+qp(k)))*N3 + dfloat(4*qs(k))
fmass.f: sum2 = amu* 4.d0* dfloat(q) * alfm
fmass.f:C Fma = mue*((GG + SS + FF + FI)*alfp + 4.*q * alfm )
fmass.f: GG4 = GG ; SS4 = SS; FF4 = FF; FI4 = FIFI
fmass.f: sum14 =sum1; sum24 =sum2 ; Wn04 = Wn0f
fmass.f: n4tab(k,q) = N4 ;n5tab(k,q) = N5 ;n6tab(k,q) = N6
fmass.f: integer*4 k , nk , nkfu
fmass.f: integer*4 function NSk (k) ! eq. 8f1 pg.15
fmass.f: integer*4 k , nk
thetaqk.f: integer*4 q ,k
 
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Vanadium 50

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Your third claim, is completely contrary to the predicted and accepted values that I have seen and I would like to see your source for this info.
Looking at http://www.heim-theory.com/downloads/G_Selected_Results.pdf" [Broken] of heim-theory.com I see the masses of the proton, neutron and electron of

  • proton 938.27959246 MeV
  • neutron 939.57336128 MeV
  • electron 0.51100343 MeV

They give the experimental masses as
  • proton 938.27231±0.00026
  • neutron 939.56563±0.00028
  • electron 0.51099907±0.00000015

Using their own numbers, the measurements are 28, 27 and 29 standard deviations from the prediction.

Using the most recent CODATA numbers, one gets:

  • proton 938.272013±0.00023
  • neutron 939.565346±0.00028
  • electron 0.510998910±0.000000013

Which are 33, 35 and 347 standard deviations away from the prediction.

Of course, a large source of the uncertainty is in the uncertainty in converting from amu to MeV. So let's look at mass ratios, where this uncertainty cancels. Only two are independent, so I look at the two ratios that are best measured:

[tex]m_p/m_e = 1836.151262118 \; v. \; 1836.15267247 \pm 0.0000008 [/tex]
[tex]m_p/m_n = 0.998623025223 \; v. \; 0.99862347824 \pm 0.0000000046 [/tex]

Which are off by 1764 and 984 standard deviations from the prediction.
 
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Stop harping on with ththe same old rubbish , V: it's been said repeatedly that HT is a work in progress. By it's formulae, proton was 33 standard deviations away from the experimental values, where a standard deviations is 0.00023 MeV. But the much vaunted QCD lattice computations, with many more input parameters, still only gets to within 2% or 81588.87 standard deviations !!!!

That's the real comparison - your rubbish up there is a prime example of 'there are lies, damned lies, and statistics'.

And where is String theory on this? Precisely nowhere!
 

Vanadium 50

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Provocative words like "harping" and "rubbish" don't elevate the level of discourse.

I was told that my claim was "is completely contrary to the predicted and accepted values that I have seen". So I provided the data that I used. That's how science works.

One position would be that Heim's theory should be taken seriously because it makes remarkably accurate predictions of particle masses. Another position is that it's a work in progress so the predictions of particle masses should not be taken so seriously. I have a problem supporting both positions simultaneously.

Logically, string theory and lattice gauge theory could both be wrong and it wouldn't make Heim right.

That said, there is a difference between the lattice gauge calculation of Durr et al. where they claim an accuracy of about 3.5% and calculate the proton mass to within 0.5% and 1.5% (they actually published two calculations) and Heim which claims an accuracy of about a part per trillion (again, from appendix G) and then substantially fails to achieve it.
 
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That said, there is a difference between the lattice gauge calculation of Durr et al. where they claim an accuracy of about 3.5% and calculate the proton mass to within 0.5% and 1.5% (they actually published two calculations) and Heim which claims an accuracy of about a part per trillion (again, from appendix G) and then substantially fails to achieve it.
I can't find any information on the precision of the theoretical values in appendix G. Could you please specify where in the paper an accuracy of ~ 1 per trillion is claimed?
 

Vanadium 50

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I can't find any information on the precision of the theoretical values in appendix G. Could you please specify where in the paper an accuracy of ~ 1 per trillion is claimed?
Look at the number of significant figures on (e.g.) the proton mass.
 
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I doubt these are significant figures, and this is claimed nowhere. On the contrary, in the last part of F ('Concluding remarks') it is stated that

The error Q(N) = Q(0) = Q based on the approximation z = 0 for all of the N only causes an
approximation error less than 0.1 MeV.
This also applys for the ground states N=0. So the accuracy may be around 0.1 MeV, which is still well beyond the 4% precision of QCD.
 

gabbagabbahey

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Provocative words like "harping" and "rubbish" don't elevate the level of discourse.
Agreed. The bolded statements were also unnecessary.

I was told that my claim was "is completely contrary to the predicted and accepted values that I have seen". So I provided the data that I used. That's how science works.
Thank you for providing the data you based your claim on.:smile: I didn't realize that in terms of standard deviations the errors were so large, and though I would say 27,28,29 are on order ~10, I see now that your claim of them being ~100 is not completely contrary to the data.

However, surely you must be at least a little curious as to how Heim theory got values this close (when compared to the QCD lattice calculations)? I know I am; and so far, many attempts to show that the data was simply cooked have come up empty.

One position would be that Heim's theory should be taken seriously because it makes remarkably accurate predictions of particle masses. Another position is that it's a work in progress so the predictions of particle masses should not be taken so seriously. I have a problem supporting both positions simultaneously.
Fair enough.
 

Vanadium 50

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If Heim - or rather, the author of Appendix G - means 123.4 when they write 123.45678901, I guess that's what they mean.

I don't suppose when they say there are 5 neutrinos they might really mean 3? That would solve another problem.
 
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If Heim - or rather, the author of Appendix G - means 123.4 when they write 123.45678901, I guess that's what they mean.

I don't suppose when they say there are 5 neutrinos they might really mean 3? That would solve another problem.
Providing so many insignificant figures seems a bit strange, but on the other hand it makes no sense to assume that by these numbers, the author provides a falsification of the theory he is actually proposing.

Concerning the neutrinos (again taken from F):
The empirical ß-neutrino can be interpreted by n1 and the empirical m-neutrino by n2.
For the time being it cannot be decided whether the rest of the neutrinos also are implemented in
nature or whether it concerns merely logical possibilities.
There appear many resonances in the theory which have not been observed in nature, which is assumed to be due to the present lack of a selection rule for N. This may also be related to the neutrino issue.

Edit: I believe, this has also to do with the mean life, which for many resonances may be very short. Heim spent the rest of his life on calculating the mean lifes in order to find a selection rule.
 
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