A Penrose twistor theory correctly predicts 4 dimensions

1. Nov 7, 2015

kodama

string theory predicts dimensions but predicts 10 dimensions.

Penrose twistor theory correctly predicts 4 dimensions, doesn't this make it more successful?

2. Nov 7, 2015

MathematicalPhysicist

What other predicitions are made in twistor theory?

In the summer I began reading his treatise with Wolfgang Rindler (the green two volumes) there doesn't seem there something groundbreaking (but I only was reading through chapter one and haven't finished yet, I took hiatus from reading the book).

3. Nov 7, 2015

haushofer

Actually, string theory doesn't uniquely give the number of spacetime dimensions; it's also consistent in three spacetime dimensions, as far as i can tell.

4. Nov 7, 2015

MathematicalPhysicist

@haushofer doesn't string theory require extra dimensions?

5. Nov 7, 2015

JorisL

You can find out why string theories we use have extra dimensions in a day or two.(Depending on your level of physics education/knowledge)
I liked the treatment in Becker, Becker and Schwarz's book. But I think you can also find it in Zwiebach as well.

In short they are required to remove the central charge from the virasoro algebra that naturally pops up when you look at strings.

6. Nov 7, 2015

kodama

if there are no extra dimensions, doesn't this falsify string theory as a candidate fundamental theory of nature?

7. Nov 8, 2015

haushofer

In lightcone gauge you need the Lorentz algebra still to be satisfied, which imposes constraints on the mass level parameter a and spacetime dimensions in order to avoid anomalies. But in 2+1 dimensions this anomaly is automatically avoided. I've never understood why people say string theory 'uniquely' predicts the number of spacetime dimensions: it doesn't. It does with the extra assumption that this number shouldn't be less than 4, but that's extra input.

8. Nov 8, 2015

9. Nov 8, 2015

MathematicalPhysicist

Ok, so the extra assumption that the number of dimensions should be greater than 4 is still an extra dimensions requirement of string theory. So is string theory also developped in 3+1 dimensions?

10. Nov 8, 2015

haushofer

I don't think so, because then the anomaly can't be avoided as far as i can tell. I'm not sure about e.g. 2+2 dimensions.

11. Nov 8, 2015

JorisL

If we can prove with 100% certainty that there are no small extra dimensions?

I suppose that would be pretty bad for string theory research. (understatement)

However it wouldn't invalidate all we did so far.
For example AdS/CFT has been succesfully used in analysing heavy-ion collisions.
Even though we believe our universe is de Sitter it improved our understanding of the measurements.

12. Nov 8, 2015

kodama

there's this

Dark Energy, Inflation and Extra Dimensions
Paul J. Steinhardt, Daniel Wesley
(Submitted on 11 Nov 2008 (v1), last revised 7 Dec 2008 (this version, v2))
We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in thecompact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications.
Subjects: High Energy Physics - Theory (hep-th)
Journal reference: Phys.Rev.D79:104026,2009
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1103%2FPhysRevD%252E79%252E104026&v=5096d5ba [Broken]
Report number: DAMTP-2008-104
Cite as: arXiv:0811.1614 [hep-th]

Last edited by a moderator: May 7, 2017
13. Feb 21, 2017

SafetyNow

Hi,
I am just looking into Twistor Theory to include it in my book "The Nuclear Revolution". I am working at the moment from lecture notes by Roger Penrose as these are clearer in establishing the foundations for his theory.
I would say that it is more accurate than String Theory. That's not because there are not more than 4 dimensions but that it keeps the modelling down to four dimensions. I do not think it impossible to extend Twistor Theory into more dimensions and seem to recollect some have actually done this connecting the two theories.
I do not have copyright to use Roger's notes but I hope he would not object. Otherwise I would have to make my own diagrams or leave any diagrams out of the text.
One reservation I have (which applies to all current theories) is that they are strong on effect but weak on causes. When you ask theorists where they can find the cause of their mathematics they will point to other previous worked mathematics.
This would be fine if the previous mathematics was established beyond a shadow of doubt.
For example in this case Twistor Theory agrees with relativity by saying that time and space twist in the same way. This actually goes beyond what Einstein said. Einstein only said that relativistic motion had the effect of slowing time. Quite Different.
The only evidence I can see for twisting space is in rotating black holes. It is actually very difficult to establish the CAUSE of black holes rotating.
I am not suggesting Twistor Theory needs to in order to create a model but it leaves this question in mid-air (pardon the pun). It also opens the question of wether Roger is implying that the relativistics effects seen by Einstein are a result of twisting. If so, he has come to agree with Complex Quantum Mechanics. I suppose even if he doesn't I can put that idea forward for him to shoot down, as he feels the need or not.
Roger got so near ...

14. Feb 22, 2017

MathematicalPhysicist

@Demystifier I see you liked my post; from my memory I do remember that in the first volume of Rindler's and Penrose's book they call the following transformation $M(z) = (az+b)/(cz+d) \ z\in \mathbb{C}$ for $ad-bc=1$, "Spin Transformation", where if I recall correctly from books in pure maths and from courses from the mathematics department it's called "Moebius Transformation".

I wonder why different names to the same thing, I gather mathematical physicists and pure mathematician don't share the same terminology.

15. Feb 22, 2017

Demystifier

I don't know, perhaps only Penrose calls it spin transformation because he likes spinors so much because they are related to his twistors?

16. Feb 22, 2017

weirdoguy

And it will never change because everytime you find a cause it raises a question about causes of that cause. It will never stop, so at one point you have to say "it is the way it is" and move on.

17. Feb 24, 2017

MathematicalPhysicist

Is this anomaly can be refuted by experiments?

I mean there quite a lot of anomalies in nature, isn't "life" such an anomaly?

18. Feb 24, 2017

haushofer

"Anomaly" here means a gauge symmetry which is threatened to be broken by the quantization procedure. That's a problem because in the usual quantization procedure one does not want to change the amount of degrees of freedom. E.g., a classical massless vector field has two polarization states, which one wants to keep upon quantization. This means your quantization shouldn't break the U(1) gauge symmetry.

19. Feb 28, 2017

no-ir

I know things are more complicated than this, but symmetry breaking is not something which is avoided at all costs in other parts of physics. Why would gauge anomalies be undesirable? Perhaps the broken-symmetry theory just is the true quantized theory, or perhaps you started from the wrong assumption of what to quantize to get the desired symmetries in the end, and that's all there is to it? I am sure I am missing something here, though.

20. Feb 28, 2017

haushofer

Well, I see it like this: gauge symmetry is very useful to introduce coupling. But besides that, it's more of a redundancy.

E.g., take the photon. We measure it has two polarizations, and from QFT we think it is massless. So two on-shell degrees of freedom (dof) it is. Next we try to pack these into a representation of the Lorentz group. The smallest possibility is the real vector representation, but this gives us two degrees of freedom too much. This is where gauge symmetry kicks in: it enables us to write down the photon field and its dynamics in a manifestly Lorentz-covariant way.

From that point of view it would be weird (apart from being mathematically inconsistent!) if suddenly, upon quantization, we obtain extra dof's again because the gauge symmetry is lost.

The same goes for the world-sheet of a string. Conformal symmetry is used to rewrite the Nambu-Goto action into the Poyakov action by using Weyl rescalings. If these would be broken by gauge anomalies, that would mean the introduction of an extra dof.