How Useful String Theory Is at Describing the Universe?

1. Introduc>on

2. Standard Model

a. Unifica>on of Forces

3. Solu>on Proposed by String Theory

a. Graviton

b. Supersymmetry

4. Unifica>on of Forces in String Theory

5. Unexplained Free Parameters

6. Extra Dimensions

7. Hierarchy Problem

8. Limita>ons

a. The Higgs Mechanism

b. Alterna>ve Theories of Quantum Gravity

c. Complica>ons in Physics

d. Evidence

e. Number of Solu>ons

9. Conclusion

10. Bibliography

Introduc>on

The Universe as we know it is described by the theory of general rela7vity (which is also theory of gravity) at large scale, and quantum theory at microscopic scale. The problem is that these two models cannot be combined into a single theory that would give sensible mathema7cal results. However, when inves7ga7ng events around the event horizon of black holes or understanding laws of physics at the early Universe and how the Universe developed, combina7on of these theories (called quantum gravity) is crucial. One of the aCempts to formulate the theory of quantum gravity is string theory, which could also poten7ally answer more problems in physics, including unifica7on of all known forces. However, its usefulness at describing the Universe has been ques7oned because of extremely complicated mathema7cs involved and never observed phenomena needed for string theory to work and avoid conflict with empirical data.

Standard Model

Based on our current understanding, the Universe can be described by four fundamental forces: weak, strong, electromagne7c and gravita7onal forces. These interac7ons mathema7cally can be described as fields that have different par7cles transmiJng different forces. These par7cles are photons for electromagne7c force, W and Z bosons for weak interac7on, gluons for strong interac7on and gravitons for gravity. There are theories capable of describing the first three interac7ons in quantum level, but aCempts to find the theory of quantum gravity have been unsuccessful. Furthermore, the bosons of the first three forces have all been observed, thus their existence is confirmed, while graviton has never been successfully detected. The theory that is able to describe three forces that are carried by already observed par7cles is called the Standard Model.

Unifica>on of Forces

Figure 1: hCps://www.quantumdiaries.org/wp-content/uploads/2014/03/2000px-Standard_Model_of_Elementary_Par7cles.svg_.jpg

Over the last decades there has been a significant progress at unifying these forces together: electromagne7c and the weak forces have been unified in the Electroweak theory . There have also 1

been some encouraging aCempts to include the strong force into this explana7on (even though this has not been experimentally tested) , but gravity always seems not to fit in such explana7ons, due to 2

the fact that these unified theories are concerned with microscopic distances. The problem is that the par7cle theory only really works if we ignore any influence on par7cles that is caused by gravity (because gravity is much weaker than other interac7ons, it usually does not influence par7cles significantly and therefore can be ignored in most cases). In quantum electrodynamics (QED), quantum chromodynamics (QCD) and quantum electroweak theory the infini7es that arise in calcula7ons can be absorbed into a redefini7on of a small number of parameters in the theory, like the mass and charge of the electron . However, mathema7cal problems concerned with quantum 3

gravity cannot be solved that easily because of quantum foam effects that are significant at microscopic level . 4

While at large scale, gravity is best described by using general theory of rela7vity, it is unable to explain gravity at quantum level. The problem is that according to the general rela7vity gravita7onal force arises from deforma7on of the space-7me, which would be completely smooth if there was no mass or energy affec7ng it. This allows describing how gravita7on affects objects at large scale (e.g. how planets orbit stars, or how galaxies interact in clusters). However, some7mes (e.g. just a_er the Big Bang) descrip7on of how gravity acts at microscopic level is needed. The problem is that at very small scales quantum fluctua7ons that arise from the uncertainty principle allows temporarily providing rela7vity large amount of energy at space 7me. This causes the space 7me to get deformed randomly at microscopic scale. This roughness can be no7ced at 10-32m, but it does not become too problema7c up un7l the Planck-length . It is almost impossible 5

to mathema7cally describe these deforma7ons, as they last for a very short 7me, and they are almost instantly replaced with different random

1. CERN, ‘Unified forces’, CERN, <hCps://home.cern/about/physics/unified-forces> [accessed 1

8 September 2017]

2. Kachru, Shamit, ‘Unit 4: String Theory and Extra Dimensions. Sec7on 1: Introduc7on’, 2

Annenberg Learner, <hCps://www.learner.org/courses/physics/unit/text.html?unit=4&secNum=1> [accessed 11 November 2017]

3. Schwarz, Patricia, ‘Why did Strings Enter the Story’, The Official String Theory Web Site, 3

<www.superstringtheory.com/basics/basic3.html> [accessed 8 September 2017]

4. Neumaier, Arnold, ‘Why Do Gravitons Have Spin 2?’, University of Vienna, <hCp://4

www.mat.univie.ac.at/~neum/physfaq/topics/spin2.html> [accessed 9 September 2017]

5. Review of the Universe, ‘Elementary Par7cles and the World of Planck Scale, Quantum 5

Foam And Loop Quantum Gravity’, Universe Review, <hCps://universe-review.ca/R01-07-quantumfoam.htm> [accessed 14 October 2017]

Figure 2: hCps://universe-review.ca/I01-16-quantumfoam.jpg

space-7me deforma7ons . Since the theory of general rela7vity only works when large, smooth 6

space-7me that is deformed by mass or energy that exist in it, this can be described by Cartesian coordinates. When the space-7me is randomly deformed by ever-changing quantum fluctua7ons, geometry that is used in theory of general rela7vity breaks down , leaving this model not applicable 7

in microscopic distances.

Solu>on Proposed by String Theory

String theory suggests a solu7on. All par7cles have tradi7onally been modelled as point-like par7cles. That means that such par7cles do not have any diameter – they are only zero-dimensional points that exists in a certain place, without any length, width or height.

However, the string theory proposes modelling par7cles as one-dimensional extended objects called strings. This means that such strings would have certain length, but no width or height, and all par7cles are just made of such strings that are oscilla7ng at different paCerns. Providing par7cles with length can solve quantum foam problem.

This quantum foam effect is really caused by the assump7on that par7cles are point-like. This means that all their interac7ons happen at certain iden7fiable point in space and 7me. However, if we modelled par7cles as strings, which have certain length, this would mean that the point of interac7on between par7cles is extended over a certain space and 7me: there is no single point where all the interac7on happens, and different observers moving at different speeds rela7ve to the string could see interac7on at slightly different places and at slightly different 7mes due to rela7vity of simultaneity as proposed by special theory of rela7vity. This means that the interac7on between par7cles that are modelled as one-dimensional strings is expanded over (s7ll extremely small) area in a space-7me . 8

Strings are expected to have lengths of around 10-33 m , while the Planck length is equal to ≈1.6 x 9

10-35m . The fact that the strings have minimum length that is larger than the Planck length means 10

that effects of quantum foam do not influence par7cles too much, and sensible mathema7cal results can be found (the area of interac7on between strings is large enough to make quantum foam effects

6. NASA, ‘Quantum Foam’, NASA, <hCps://science.nasa.gov/science-news/science-at-nasa/6

2015/31dec_quantumfoam> [accessed 14 October 2017]

7. Review of the Universe, ‘Elementary Par7cles and the World of Planck Scale, Quantum 7

Foam And Loop Quantum Gravity’, Universe Review, <hCps://universe-review.ca/R01-07-quantumfoam.htm> [accessed 14 October 2017]

8. Greene, Brian R., The Elegant Universe: Superstring, Hidden Dimensions and the Quest for 8

the Ul<mate Theory (London: Vintage, 2000), p. 163

9. Djernis Olsen, Lone, ‘Didžioji Fizikų Svajonė: Viena Teorija Apie Viską‘, Iliustruotasis Mokslas, 9

February 2014, pp. 62-65

10. Becker, Katrin, Becker, Melanie and Schwarz, John H., String Theory and M-theory. A 10

Modern Introduc<on, (Cambridge: Cambridge University Press), p.6.

Rela7vity of simultaneity states that different observers moving in rela7ve mo7on will disagree on the 7ming of events at different places

negligible). Therefore, length of strings can be used to escape answers that give result of infinity , 11

which means that renormaliza7on is not needed anymore, as the whole problem was caused just by lack of lower limit on the distances that need to be considered. This allows a consistent theory of quantum gravity that s7ll resembles general rela7vity theory at macroscopic scales, while possessing poten7al to describe other interac7ons, instead of ignoring them.

Graviton

Furthermore, string theory predicts that out of many possible vibra7onal paCerns that string can oscillate, one will always resemble the par7cle that is massless and has spin of 2 . These 12

characteris7cs fit together with the predicted characteris7cs of graviton. Thus, modelling par7cles as one-dimensional strings not just allows escaping problems that are caused by quantum foam effects, but also predicts the existence of par7cle that transmits gravita7onal interac7on.

However, string theory predicts a very wide range of different par7cles to exist. Many of such par7cles have never been observed, but that could be explain by the fact that we lack par7cle accelerators that could reach energies high enough to discover such par7cles (the most powerful par7cle accelerator in the world LHC can only reach the total collision energy of 13TeV , which is far 13

behind the energy needed to observe most of par7cles that string theory predicts to exist).

The problem comes that this string theory (called bosonic string theory) does not incorporate fermion par7cles, but predicts a par7cle, whose mass is an imaginary number (therefore, its mass square is a nega7ve number). Such par7cles (called tachyons) could travel at speed faster than the speed of light, and would gain speed when losing energy . This contradicts the special theory of 14

rela7vity.

Supersymmetry

However, this can be solved by incorpora7ng supersymmetry into string theory. Supersymmetry suggests that each boson par7cle has a superpartner fermion, and that every fermion has a superpartner boson . These superpartners would be significantly heavier than known par7cles 15 16

11. Herdeiro, Carlos, ‘M-theory, the Theory Formerly Known As Strings’, Department of 11

Applied Mathema7cs and Theore7cal Physics, University of Cambridge, <www.damtp.cam.ac.uk/research/gr/public/qg_ss.html> [accessed 9 September 2017]

12. Schwarz, Patricia, ‘Why did Strings Enter the Story’, The Official String Theory Web Site, 12

<www.superstringtheory.com/basics/basic3.html> [accessed 8 September 2017]

13. CERN, ‘Restar7ng the LHC: Why 13 TeV?’, CERN, <hCps://home.cern/about/engineering/13

restar7ng-lhc-why-13-tev> [accessed 12 December 2017]

14. MoCa, Leonardo and Rodrigues Jr., Waldyr A., ‘Tachyon’, Eric Weisstein’s World of Science, 14

<hCp://scienceworld.wolfram.com/physics/Tachyon.html >[accessed 14 October 2017]

15. Strassler, MaC, ‘Supersymmetry – What Is It?’, Of Par7cular Significance. Conversa7ons 15

About Science with Theore7cal Physicist MaC Strassler, <hCps://profmaCstrassler.com/ar7cles-and-posts/some-specula7ve-theore7cal-ideas-for-the-lhc/supersymmetry/supersymmetry-what-is-it/> [accessed 14 October 2017]

16. Djernis Olsen, Lone, ‘Fizikai Ieško Dalelių Dvynių‘, Iliustruotasis Mokslas, January2014, pp. 16

54-57

(some es7mates predicts their masses to be between 100 and 1000GeV ), thus they easily could 17

have remained undetected with accelerators we currently use.

The theory of supersymmetry is not proven – no observa7ons of superpartners have ever been made. Even if such observa7ons would be made, they would not prove that string theory is right, as it has been first developed modelling par7cles as point-like par7cles . 18

However, if incorporated into string theory, supersymmetry solves several major problems: firstly, it makes the vibra7onal paCern of string that predicts existence of tachyon impossible. Secondly, it allows more vibra7onal paCerns of string, and these paCerns result in par7cles, whose proper7es match proper7es of all known fermions. Lastly, it allows unifying coupling constants. Therefore, supersymmetry is a crucial part of string theory, thus if it could be disproven, it would be a good argument against the string theory.

Unifica>on of Forces in String Theory

It is experimentally proven that coupling constants of different interac7ons change as the energy of interac7ons is increased. In 1973 it was no7ced that coupling constants would meet together, when the energy of interac7on reaches 1015 GeV (such energy 19

scales have been reached shortly a_er the Big Bang, which suggests that in the very young universe all electromagne7c, strong and weak interac7ons were unified and separated only when the universe cooled down). However, further calcula7ons using more precise values of coupling constants have showed that without superpartners these values would come close to becoming equalling each other, but would not meet . 20

However, if supersymmetry is incorporated in these

17. Preskill, John, ‘Supersymmetry, Supperpartners’, Caltech Par7cle Theory Group, 17

www.theory.caltech.edu/people/jhs/strings/str121.html [accessed 15 October 2017]

18. Woodard, R.P., ‘How Far Are We from the Quantum Theory of Gravity’, Cornell University 18

Library, < hCps://arxiv.org/pdf/0907.4238v1.pdf> [accessed 12 December 2017]

19. Griest, Kim, ‘Mo7va7on for Supersymmetry’, The Net Advance of Physics, <hCp://19

web.mit.edu/redingtn/www/netadv/specr/6/node2.html> [accessed 13 December 2017]

20. ibid20

Figure 3: hCps://www.dreams7me.com/royalty-free-stock-photo-supersymmetry-theory-predicts-partner-par7cle-each-par7cle-standard-model-if-

correct-supersymmetric-image36581835

Figure 4: hCp://blazelabs.com/f-u-const.asp

calcula7ons, the new par7cles would have enough influence on the values of coupling constants, so that they would meet each other at high energies. Thus, superstring theory predicts that all non-gravita7onal interac7ons would become equal at certain energy level, which suggests that supersymmetric string theory could provide a unifying framework for all fundamental interac7ons. However, while this would significantly simplify models of early universe and could help to predict its past, there is no evidence or physical reason for these forces to merge together.

Unexplained Free Parameters

Another major flaw of the Standard Model is that it fails to explain why all par7cles have physical proper7es, like charge or mass that they have . Furthermore, the standard model is completely 21

dependent on about 19 free parameters, which existence cannot be explained by the standard model itself . String theory provides an explana7on for that: if all par7cles are actually just strings, 22

oscilla7ng in different paCerns, then all these parameters and all physical characteris7cs of par7cles are just results of vibra7onal paCerns of iden7cal strings: for example, the energy of par7cle can be determined by the frequency and the amplitude of the vibra7onal paCern of the string. Because energy and mass are related to each other, this energy of the string gives a certain mass for a corresponding par7cle. The only parameter that needs to be predetermined is string tension , which 23

is expected to be equal to approximately 1044 newtons . Thus, the string theory can explain why 24

par7cles have physical proper7es that they have, while standard model just states the experimentally measured values, but does not provide any explana7on on why these proper7es take those certain values.

Extra Dimensions

However, in order for string theory to be mathema7cally consistent, it requires space 7me to have more than 4 dimensions we observe (3 of these being space dimensions and one 7me). In 4 dimensional Universe, the string theory would predict some outcomes to have nega7ve probability of happening . Because all probabili7es should be in range between 0 and 1, it is obvious that 25

predic7on of nega7ve probability is wrong (similarly, all previous aCempts at combining quantum theory with general rela7vity, resulted in predic7ons of infinite probabili7es, which is also outside of the range. Thus, it seemed that with 4 dimensions string theory faces similar problem as all other aCempts to find quantum gravity theory). However, this inconsistency can be solved if the space 7me had more than 4 dimensions that we observe.

Ini7ally, this property of the string theory was seen

21. Mukhi, Sunil, ‘String Theory and the Unifica7on of Forces’, Sunil Mukhi’s Home Page, 21

<hCp://theory.7fr.res.in/~mukhi/Physics/string.html> [accessed 8 September 2017]

22. Toth, Viktor T., ‘The Parameters of the Standard Model’, Spinor.info, <hCps://spinor.info/22

weblog/?p=6355> [accessed 23 September 2017]

23. Mukhi ,Sunil, ‘The Theory of Strings: A Detailed Introduc7on’, Sunil Mukhi’s Home Page, 23

<hCp://theory.7fr.res.in/%7Emukhi/Physics/string2.html> [accessed 21 September 2017]

24. Greene, The Elegant Universe: Superstring, Hidden Dimensions and the Quest for the 24

Ul<mate Theory, p. 148.

25. Schwarz, Patricia, ‘Looking For Extra Dimensions. What Is A Dimension’, The Official String 25

Theory Web Site, <www.superstringtheory.com/experm/exper5.html> [accessed 8 November 2017]

Figure 5: hCp://afriedman.org/AndysWebPage/BSJ/CalabiYauManifold.html

as an argument against it, as the natural ques7on to ask is where these dimensions are and we have not detected them. A possible explana7ons can be that these dimensions are either extremely small, which means that we are not able to no7ce them , and that par7cle accelerators are not powerful 26

enough to observe them. These dimensions should be compac7fied in space called Calabi-Yau manifold . Another explana7on is that our movement is constrained to the 4 dimensional surfaces 27

(called branes) where we can only move in these 4 dimensions, and therefore any other dimensions cannot be no7ced . 28

Hierarchy Problem

Furthermore, later it was realised that extra dimensions needed in string theory can actually be an advantage. The standard model suffers from what is called the ‘Hierarchy problem’. The hierarchy problem asks why there is such a big difference between strengths of different interac7ons (for example, why the weak force is 1024 7mes stronger than gravity ). String theorists suggest that gravity can be ac7ng 29

on more dimensions than the ones we observe. Therefore, the gravita7onal force has a similar magnitude as other fundamental interac7ons, but it is diluted because it acts in more dimensions. Other forces are confined to 3-brane (3-dimensional brane), thus they are not diluted . Thus, the gravity could be weakening at faster rate if there are more dimensions: in this 30

case, the strength of gravita7onal field would be propor7onal to , where r is distance and d is number of spa7al dimensions that gravita7onal field is propaga7ng through . Because there are 31

only 3 visible spa7al dimensions, this would mean that in macroscopic level gravita7onal field would be propor7onal to , which agrees with the inverse square law, but at microscopic level gravita7onal field would be weakening at much faster rate, which means that at this microscopic level gravity could be just as strong as other forces.

26. Randall, Lisa, ‘Why I Believe In Higher Dimensions’, The Telegraph, <hCp://26

www.telegraph.co.uk/technology/3341260/Why-I-believe-in-higher-dimensions.html> [accessed 11 December 2017]

27. Garisto, Robert, ‘Focus: Curling Up Extra Dimensions in String Theory’, APS Physics, 27

<hCps://physics.aps.org/story/v1/st7> [accessed 11 November 2017]

28. Schwarz, Patricia, ‘Looking For Extra Dimensions. Kaluza-Klein Compac7fica7on’, The 28

Official String Theory Web Site, <www.superstringtheory.com/experm/exper51.html> [accessed 10 November 2017]

29. Gagnon, Pauline, ‘The Standard Model: A Beau7ful But Flawed Theory’, Quantum Diaries, 29

<hCp://www.quantumdiaries.org/2014/03/14/the-standard-model-a-beau7ful-but-flawed-theory/> [accessed 15 October 2017]

30. Kachru, Shamit, ‘Unit 4: String Theory and Extra Dimensions. Sec7on 6: Extra Dimensions 30

And The Hierarchy Problem’, Annenberg Learner, <hCps://www.learner.org/courses/physics/unit/text.html?unit=4&secNum=6> [accessed 11 November 2017]

31. Berman, David, ‘The Ten Dimensions of String Theory’, Plus Magazine, <hCps://31

plus.maths.org/content/10-dimensions-and-more-string-theory> [accessed 11 November 2017]

In string theory, a brane is an object which has certain number of dimensions in which objects inside the brane can interact. This number of dimensions can vary between 1 (a string) and 11 (which is the maximum number of dimensions suggested by most calcula7ons on string theory)

Limita>ons

The original goal of the string theory was to explain how gravity works at quantum scale, and to provide a framework under which all interac7ons of nature could be understood. In doing so, it hoped to explain all free parameters that are not explained by standard model, and use string tension as the only free parameter whose value cannot be explained by the string theory.

One of the advantages of modelling par7cles like strings, as proposed by the string theory, is that it allows to explain why different par7cles have different proper7es (e.g. why top quark has a mass that is over 84,600 7mes larger than the mass of up quark ). Also, as men7oned above, the standard 32

model completely depends on about 19 free parameters, the existence of which cannot be explained by the standard model itself. String theory provides an explana7on how these parameters could be determined by string tension and different vibra7onal paCerns of strings, which would represent par7cles of different physical characteris7cs.

The Higgs Mechanism

While string theory does provide a mathema7cal explana7on for these proper7es, there is another theory that could poten7ally explain 15 of free standard model parameters, and also how par7cles acquire their mass that we observe. This theory is called the Higgs mechanism, and in contrast to the string theory, there is empirical evidence that supports this theory. On 4 July 2012, the par7cle whose mass was consistent with the proposed mass of the Higgs boson was observed for the first 7me . However, even though this suggests that the Higgs mechanism exists in nature, and explains 33

part of the problems that string theory is aCemp7ng to explain, it does not make string theory irrelevant in our understanding of the universe. First of all, the Higgs mechanism s7ll does not explain all 19 free parameters of standard model, and it also does not explain how par7cles acquire other physical characteris7cs, like spin or electric charge. It is also important to no7ce that string theory and the Higgs mechanism can be compa7ble together with each other, and together with supersymmetry. Therefore, it is s7ll completely possible that string theory exists together with the Higgs mechanism . Thus, the Higgs mechanism could explain different masses of par7cles and some 34

free parameters of the standard model, and string theory could fill in the gaps without crea7ng any conflicts with the Higgs mechanism.

Alterna>ve Theories of Quantum Gravity

The Higgs mechanism is s7ll unable to make any explana7on on how gravity acts at microscopic distance. As already men7oned, general rela7vity breaks down at microscopic scales due to quantum foam effects which means that space 7me is not smooth at such scale, thus general rela7vity is not able to make any predic7ons anymore. String theory proposes a way to avoid such problems, by modelling par7cles as one-dimensional strings with certain length, which means that interac7ons are expanded over a certain area of space 7me. However, there have been a number of other proposed

32. Ju, Anne, ‘Masses of Common Quarks Are Revealed’, Phys.org, <hCps://phys.org/news/32

2010-05-masses-common-quarks-revealed.html> [accessed 11 December 2017]

33. CERN, ‘The Higgs Boson’, CERN, <hCps://home.cern/topics/higgs-boson> [accessed 28 33

October 2017]

34. Kane, Gordon, ‘How Does The Higgs Boson Affect String Theory’, Scien7fic American, 34

<hCps://www.scien7ficamerican.com/ar7cle/how-does-the-higgs-boson/> [accessed 29 October 2017]

solu7ons that could solve this problem. None of these theories have any empirical evidence, and none of them have been able to make any verifiable predic7ons; therefore the only way to evaluate them is to compare the complexity of their mathema7cal reasoning and the number of problems it could solve.

There are several alterna7ves to string theory as a theory of quantum gravity (like asympto7cally safe gravity or causal dynamical triangula7on theories), but they suffer from unclear, complicated and loosely defined mathema7cal backgrounds that seem to either be incompa7ble with nature, or 35

unable to make clear predic7ons (similarly to string theory). The most serious alterna7ve theory of quantum gravity is called loop quantum gravity (LQG). This theory avoids quantum foam, by quan7zing space 7me, but s7ll modelling par7cles as point like objects . The biggest advantage of 36

LQG is that instead of mathema7cally extremely complicated geometry that is proposed by string theory, LQG allows this geometry to be well defined, while s7ll keeping it fully general rela7vis7c. It allows gravita7onal fields to be clearly defined and allows presen7ng all dynamics of theory with three equa7ons . This contrasts hugely with string theory, which is so mathema7cally complicated 37

that it lacks any basic equa7ons, which makes it impossible to reach any verifiable physical predic7ons. However, so far LQG has likewise failed to provide any confirmable predic7ons, and also has many unanswered ques7ons surrounding the physics it involves.

Again, it is important to emphasize that LQG does not aCempt to explain so many phenomena by the same mathema7cal framework, as string theory. In my opinion it is also important to highlight that string theory is not finished and is s7ll being developed, therefore it may be unfair to cri7cise unfinished theory, especially as it is s7ll one of the most ac7vely researched areas in physics, and it has seen breakthroughs in its development previously. If string theory could be developed to a stage where it is able to make predic7ons, it would have poten7al to explain more unsolved problems in physics than LQG is even aCemp7ng to.

Complica>ons in Physics

However, LQG can provide mathema7cal framework for quantum gravity that is compa7ble with a descrip7on of the universe that we observe. On the other hand, string theory due to its difficult mathema7cal background, has proposed many unobserved phenomena like extra dimensions or supersymmetry. Richard Feynman has said that each 7me string theorists fail; they just create an explana7on, which is mathema7cally correct, but never observed . This creates several problems for 38

theory that is aCemp7ng to explain all free parameters that exists in the standard model: first of all, because number of extra dimensions is determined only by need to avoid nega7ve probabili7es that arise in string theory calcula7ons when four-dimensional space 7me is used, string theory is unable

35. Siegel, Ethan, ‘What Are Quantum Gravity’s Alterna7ves To String Theory?’, Forbes, 35

<hCps://www.forbes.com/sites/startswithabang/2015/12/17/what-are-quantum-gravitys-alterna7ves-to-string-theory/#33226b917b1b> [accessed 29 October 2017]

36. Max Planck Ins7tute for Gravita7onal Physics, Golm/Potsdam, ‘Loop Quantum Gravity’, 36

Einstein Online, <www.einstein-online.info/elementary/quantum/loops.html> [accessed 29 October 2017]

37. Rovelli, Carlo, ‘A Cri7cal Look at Strings’, Cornell University Library, <hCps://arxiv.org/pdf/37

1108.0868v1.pdf> [accessed 12 December 2017]

38. Krauss, Lawrence M., Quantum Man. Richard Feynman’s Life in Science (New York: W.W. 38

Norton & Company, 2012), p. 254

to explain where this number of dimensions appears. This raises ques7ons about how useful string theory, as a unifying theory of physics, actually is. Its ini7al objec7ve was not just to explain gravity at quantum scale, but also to compute the value of all the free parameters involved in the standard model. However, a_er over 40 years of research in this field, no such explana7on of free parameters was suggested. However, even if string theory will advance enough to explain these problems, it has already raised new and even more complicated ques7ons that it does not seem to be able to explain. On the other hand, I would like to point out that number of new problems that string theory is likely to raise is s7ll significantly smaller than number of problems it could solve. Therefore, from my point of view if string theory will be supported by empirical data, it may not become the ‘theory of everything’, but it would s7ll be a ‘theory of something’, thus it would s7ll provide a useful descrip7on or at least the best available approxima7on of some currently unexplained phenomena. Also, we have to be open to an idea of existence of extra dimensions or supersymmetry as long as they are not proven not to exist, instead of just rejec7ng these ideas because they are unfamiliar and mathema7cally complex.

Similar ques7ons can be raised about supersymmetry. While supersymmetry is needed for string theory to be able to explain all par7cles (as men7oned above, without supersymmetry, string theory is only able to explain bosons, and also suffers from predic7ng tachyon, which clashes with theory of special rela7vity), string theory at its current state of development is unable to make any predic7ons of how massive superpartner par7cles should be. In 1997, string theorist John H. Schwarz said that supersymmetry ‘ought to be discovered before too long’ . 20 years later, no empirical evidence 39

suppor7ng supersymmetry has ever been detected. It is en7rely possible that supersymmetry exists, but the masses of superpartners are simply too large to be detected using contemporary par7cle accelerators. However, even if supersymmetry is discovered, it is by itself not sufficient evidence to prove string theory. As men7oned before, supersymmetry was developed for point like par7cles before string theory was even first formulated, thus discovery of superpartners would not prove string theory.

Evidence

That raises ques7ons on how could string theory be empirically proven. Chances of directly detec7ng strings, extra dimensions, branes, etc. using par7cle accelerators seem to be extremely limited. There has been some hope that extra dimensions may actually be big enough to be discovered using the Large Hadron Collider (LHC), but results obtained from LHC in 2010 suggests that this is not the case . This suggests that we need other methods to try to collect evidence for string theory. 40

One recent proposal is that gravita7onal wave detectors could possibly be able to detect the existence of extra dimensions . In contrast to the discovery of supersymmetry, evidence of extra 41

dimensions would give an extremely solid proof of string theory, as there are no other theories that would predict extra dimensions. Another way to prove string theory could be by finding par7cles

39. Greene, The Elegant Universe: Superstring, Hidden Dimensions and the Quest for the 39

Ul<mate Theory, p. 222

40. Zimmerman Jones, Andrew, ‘Can String Theory Be Tested’, PBS, <www.pbs.org/wgbh/40

nova/blogs/physics/2012/09/can-string-theory-be-tested/> [accessed 29 October 2017]

41. Johnston, Hamish, ‘Evidence For String Theory Could Be Lurking In Gravita7onal Waves’, 41

Physics World, <hCp://physicsworld.com/cws/ar7cle/news/2017/jul/05/evidence-for-string-theory-could-be-lurking-in-gravita7onal-waves> [accessed 14 October 2017]

having charges that were not predicted by standard model , since string theory predicts that some 42

heavy par7cles could be made of strings oscilla7ng in paCerns that would allow these par7cles to acquire electrical charges that have not yet been observed. Also some calcula7ons of string theory suggest that some strings could have acquired enough energy shortly a_er the Big Bang in order to grow to macroscopic size . Observa7on of such strings, could give the most direct evidence of string 43

theory. However, as Roger Penrose have no7ced, if such growth of strings would be possible, strings could have already grew to macroscopic size close to massive objects like planets or black holes, as such objects would have enough energy that could be supplied to strings, in order to increase their sizes, or make extra dimensions visible . On the other hand, it is unclear whether such objects could 44

concentrate this energy needed to expand strings into one point of small enough area to actually act increase the size of the string. However, these examples show that there could be ways to prove string theory in the near future, even with par7cle accelerators unable to reach energies that could allow directly observing extra dimensions or strings themselves.

Nevertheless, there is evidence that clashes with predic7ons made by supersymmetry. Observa7ons of very distant supernovae in distant galaxies suggest that cosmological constant has a non-zero posi7ve value. This data suggests that this value of cosmological constant should be in order of 10-12 eV4. However, the smallest value of cosmological value proposed by supersymmetric theory suggests that this value should be approximately 1044 eV4. This value increases even more if supersymmetric grand unified theories are used . Because supersymmetry is crucial part of string theory, this creates 45

a problem for string theory as well. One of the possible explana7ons is that another undetected feature of string theory could solve this issue. However, a_er more than 20 years of aCemp7ng to find such hidden feature, no explana7on or experimental predic7on has been made in effort to solve this problem.

Number of Solu>ons

However, in my personal opinion, the biggest flaw of string theory is the so called landscape problem. It is concerned with the large number of different eleven dimensional space 7me shapes that are possible under the string theory. Furthermore, each of these shapes is supposed to have a large number of different parameters that determine the size and the shape of these space 7me backgrounds. The string theorists hoped that values of these free parameters can be determined by the string theory itself, and that this could allow making testable predic7ons. The proposed mechanism to achieve this is called KKLT mechanism, but it requires even more complex structure of the space

42. Greene, The Elegant Universe: Superstring, Hidden Dimensions and the Quest for the 42

Ul<mate Theory, p.223

43. Slagter, Reinoud Jan, ‘Evidence of Cosmic Strings by the Observa7on of the Alignment of 43

Quasar Polariza7on Axes on Mpc Scale’, Cornell University Library, <hCps://arxiv.org/pdf/1609.05068.pdf> [accessed December 12 2017]

44. Penrose, Roger, Fashion, Faith and Fantasy in the New Physics of the Universe, Oxford 44

Mathema7cs Public Lectures, October 13, 2016

45. Woit, Peter, Not Even Wrong: The Failure of String Theory and the Con<nuing Challenge to 45

Unify the Laws of Physics (Sydney: Jonathan Cape, 2006), p. 179

KKLT mechanism is a proposed mathema7cal solu7on to help to choose correct free parameters of the string theory without tuning them to every individual situa7on. It involves adding extra layers of structure involving branes and magne7c field flux adjusted to higher dimensions in the Calabi-Yau manifold, which allows to uncover shape duali7es, which allows to decrease the number of possible parameters

7me seJng, meaning that string theory is even more mathema7cally complicated. However, the bigger issue is that KKLT mechanism by lowest es7ma7on proposes around 10500 possible values of these parameters that are equally likely . This enormous number of possible values means that 46

almost any experimental observa7on can be explained by smaller, but s7ll a very large number of these states, which destroys any hope of using the string theory to predict anything , or to create a 47

hypothesis that could be falsifiable, which means that string theory cannot be proved to be wrong. From my viewpoint, this creates a massive ques7on on how useful string theory can be for our understanding of the Universe, as this large number of possible landscapes suggests that even any future breakthroughs will s7ll fail to provide predic7ons.

However, it is important to no7ce that string theorists are s7ll arguing whether the KKLT mechanism is consistent with string theory . If it is not, then it is s7ll possible that real number of these 48

backgrounds is significantly smaller, which could solve the landscape problem and s7ll allow to use string theory to make predic7ons and to falsify it. However, this would mean that the string theory itself is even less developed, thus we are even further from understanding it, despite all the effort invested in trying to understand it.

Even if the KKLT mechanism is correct, some string theorists, like Leonard Susskind, argue that this number of possible landscapes can be an advantage of the string theory . Every solu7on of this very 49

large number of possible solu7ons would have a different value of different parameters, including value of cosmological constant. Thus, there would be nearly con7nuous set of cosmological values that are possible under the string theory, which means that there should be solu7on with the value that corresponds to the observed value . This could make supersymmetry, and thus the string 50

theory compa7ble with experimental data. However, from my point of view, this s7ll struggles to explain why cosmological constant has its measured value; therefore it is another phenomenon that string theory cannot explain. From my perspec7ve, this does not correspond well with the original idea of the string theory, which was aCemp7ng to explain as many free parameters of nature as possible. Some string theorists are arguing that due to extremely complicated mathema7cs involved in some parts of string theory, anthropic principle may be the only way to explain some of these standard model parameters. If it is the case, this compromises string theory because it means it again fails to explain some of the problems that it hoped to solve.

Conclusion

46. Hawking, Stephen and Mlodinow, Leonard, ‘Didysis Projektas’ (Kaunas: Jotema, 2011), p. 46

142

47. Woit, Not Even Wrong: The Failure of String Theory and the Con<nuing Challenge to Unify 47

the Laws of Physics, p. 242

48. ibid48

49. Woit, Peter, ‘KKLT Smackdown’, Not Even Wrong, <www.math.columbia.edu/~woit/49

wordpress/?p=11> [accessed November 1 2017]

50. Ge_er, Amanda, ‘Is String Theory in Trouble’, New Scien7st, <hCps://50

www.newscien7st.com/ar7cle/mg18825305-800-is-string-theory-in-trouble/> [accessed 2 November 2017]

In conclusion, in some cases string theory seems to fall short of its original goals. At its current stage of development, it seems to fail to explain all the free parameters of the standard model, and is unable to make any testable predic7ons. However, it is extremely important to no7ce that string theory is not a completed theory – it is s7ll one of the most ac7vely researched fields in contemporary physics.

Nevertheless, from my point of view, the biggest flaw of string theory is that if KKLT mechanism is correct, then it is very likely that string theory will not be able to make any predic7ons, irrespec7ve of how much it will be developed, which would dras7cally reduce its usefulness. However, if that was the case (which is not certainly proven), it s7ll could provide an explana7on for other currently unexplained problems, for example why gravity is so much weaker than other fundamental interac7ons.

Another weakness of string theory that is o_en pointed out is its dependency on such never observed and seemingly unnecessary concepts like extra dimensions or supersymmetry. While the need for these concepts definitely makes the string theory extremely mathema7cally complicated and ‘clumsy’, I do not personally believe that string theory should be cri7cised just because of that. None of these ideas that are crucial for string theory have been proved to be wrong, and we should not reject string theory just because it is difficult or proposes unfamiliar concepts. We should keep an open mind to the idea that nature may well be mathema7cally difficult to describe and include many unfamiliar concepts.

Indeed, string theory some7mes seems to be too beau7ful to be wrong. It is sugges7ng solu7ons to a larger number of problems than any other theory ever even aCempted to. It is perhaps understandable that this amount of issues cannot be easily described. However, only the possibility of such a wide theory seems to be too aCrac7ve to be rejected. I strongly believe that string theory needs to be developed more – currently it is not very useful at describing the Universe, but it is too promising to be completely rejected. Some cri7cs argue that more than 40 years of development did not give us anything, but some new mathema7cal duali7es, proving that some complex mathema7cal shapes are actually just mirror images of each other, were actually found because of string theory. Thus, while these developments did not allow us to make any predic7ons using string theory, they s7ll benefited another area of science.

With that in mind, I s7ll believe that other theories must be researched alongside string theory. I have focused mostly on comparing string theory with LQG theory, but there are other promising theories of quantum gravity, like asympto7cally safe gravity and causal dynamical triangula7on theories. All these theories s7ll need to be developed further in order to be tested or compared together. However, it is quite jus7fiable that string theory is gaining most aCen7on due to its massive poten7al to solve wide range of issues and all the research that has already been done on it and breakthroughs that have been reached in string theory in the past.

Bibliography

1. Becker, Katrin, Becker, Melanie and Schwarz, John H., String Theory and M-theory. A Modern Introduc<on, (Cambridge: Cambridge University Press), p.6.

2. Berman, David, ‘The Ten Dimensions of String Theory’, Plus Magazine, <hCps://plus.maths.org/content/10-dimensions-and-more-string-theory> [accessed 11 November 2017]

3. CERN, ‘Restar7ng the LHC: Why 13 TeV?’, CERN, <hCps://home.cern/about/engineering/restar7ng-lhc-why-13-tev> [accessed 12 December 2017]

4. __________, ‘The Higgs Boson’, CERN, <hCps://home.cern/topics/higgs-boson> [accessed 28 October 2017]

5. __________, ‘Unified forces’, CERN, <hCps://home.cern/about/physics/unified-forces> [accessed 8 September 2017]

6. Djernis Olsen, Lone, ‘Didžioji Fizikų Svajonė: Viena Teorija Apie Viską‘, Iliustruotasis Mokslas, February 2014, pp. 62-65

7. __________, ‘Fizikai Ieško Dalelių Dvynių‘, Iliustruotasis Mokslas, January2014, pp. 54-57

8. Gagnon, Pauline, ‘The Standard Model: A Beau7ful But Flawed Theory’, Quantum Diaries, <hCp://www.quantumdiaries.org/2014/03/14/the-standard-model-a-beau7ful-but-flawed-theory/> [accessed 15 October 2017]

9. Garisto, Robert, ‘Focus: Curling Up Extra Dimensions in String Theory’, APS Physics, <hCps://physics.aps.org/story/v1/st7> [accessed 11 November 2017]

10. Ge_er, Amanda, ‘Is String Theory in Trouble’, New Scien7st, <hCps://www.newscien7st.com/ar7cle/mg18825305-800-is-string-theory-in-trouble/> [accessed 2 November 2017]

11. Greene, Brian R., The Elegant Universe: Superstring, Hidden Dimensions and the Quest for the Ul<mate Theory (London: Vintage, 2000)

12. Griest, Kim, ‘Mo7va7on for Supersymmetry’, The Net Advance of Physics, <hCp://web.mit.edu/redingtn/www/netadv/specr/6/node2.html> [accessed 13 December 2017]

13. Hawking, Stephen and Mlodinow, Leonard, ‘Didysis Projektas’ (Kaunas: Jotema, 2011), p. 142

14. Herdeiro, Carlos, ‘M-theory, the Theory Formerly Known As Strings’, Department of Applied Mathema7cs and Theore7cal Physics, University of Cambridge, <www.damtp.cam.ac.uk/research/gr/public/qg_ss.html> [accessed 9 September 2017]

15. Johnston, Hamish, ‘Evidence For String Theory Could Be Lurking In Gravita7onal Waves’, Physics World, <hCp://physicsworld.com/cws/ar7cle/news/2017/jul/05/evidence-for-string-theory-could-be-lurking-in-gravita7onal-waves> [accessed 14 October 2017]

16. Ju, Anne, ‘Masses of Common Quarks Are Revealed’, Phys.org, <hCps://phys.org/news/2010-05-masses-common-quarks-revealed.html> [accessed 11 December 2017]

17. Kachru, Shamit, ‘Unit 4: String Theory and Extra Dimensions. Sec7on 1: Introduc7on’, Annenberg Learner, <hCps://www.learner.org/courses/physics/unit/text.html?unit=4&secNum=1> [accessed 11 November 2017]

18. __________, ‘Unit 4: String Theory and Extra Dimensions. Sec7on 6: Extra Dimensions And The Hierarchy Problem’, Annenberg Learner, <hCps://www.learner.org/courses/physics/unit/text.html?unit=4&secNum=6> [accessed 11 November 2017]

19. Kane, Gordon, ‘How Does The Higgs Boson Affect String Theory’, Scien7fic American, <hCps://www.scien7ficamerican.com/ar7cle/how-does-the-higgs-boson/> [accessed 29 October 2017]

20. Krauss, Lawrence M., Quantum Man. Richard Feynman’s Life in Science (New York: W.W. Norton & Company, 2012)

21. Max Planck Ins7tute for Gravita7onal Physics, Golm/Potsdam, ‘Loop Quantum Gravity’, Einstein Online, <www.einstein-online.info/elementary/quantum/loops.html> [accessed 29 October 2017]

22. MoCa, Leonardo and Rodrigues Jr., Waldyr A., ‘Tachyon’, Eric Weisstein’s World of Science, <hCp://scienceworld.wolfram.com/physics/Tachyon.html >[accessed 14 October 2017]

23. Mukhi ,Sunil, ‘The Theory of Strings: A Detailed Introduc7on’, Sunil Mukhi’s Home Page, <hCp://theory.7fr.res.in/%7Emukhi/Physics/string2.html> [accessed 21 September 2017]

24. __________, ‘String Theory and the Unifica7on of Forces’, Sunil Mukhi’s Home Page, <hCp://theory.7fr.res.in/~mukhi/Physics/string.html> [accessed 8 September 2017]

25. NASA, ‘Quantum Foam’, NASA, <hCps://science.nasa.gov/science-news/science-at-nasa/2015/31dec_quantumfoam> [accessed 14 October 2017]

26. Neumaier, Arnold, ‘Why Do Gravitons Have Spin 2?’, University of Vienna, <hCp://www.mat.univie.ac.at/~neum/physfaq/topics/spin2.html> [accessed 9 September 2017]

27. Penrose, Roger, Fashion, Faith and Fantasy in the New Physics of the Universe, Oxford Mathema7cs Public Lectures, October 13, 2016

28. Preskill, John, ‘Supersymmetry, Supperpartners’, Caltech Par7cle Theory Group, www.theory.caltech.edu/people/jhs/strings/str121.html [accessed 15 October 2017]

29. Randall, Lisa, ‘Why I Believe In Higher Dimensions’, The Telegraph, <hCp://www.telegraph.co.uk/technology/3341260/Why-I-believe-in-higher-dimensions.html> [accessed 11 December 2017]

30. Review of the Universe, ‘Elementary Par7cles and the World of Planck Scale, Quantum Foam And Loop Quantum Gravity’, Universe Review, <hCps://universe-review.ca/R01-07-quantumfoam.htm> [accessed 14 October 2017]

31. Rovelli, Carlo, ‘A Cri7cal Look at Strings’, Cornell University Library, <hCps://arxiv.org/pdf/1108.0868v1.pdf> [accessed 12 December 2017]

32. Schwarz, Patricia, ‘Looking For Extra Dimensions. Kaluza-Klein Compac7fica7on’, The Official String Theory Web Site, <www.superstringtheory.com/experm/exper51.html> [accessed 10 November 2017]

33. __________, ‘Looking For Extra Dimensions. What Is A Dimension’, The Official String Theory Web Site, <www.superstringtheory.com/experm/exper5.html> [accessed 8 November 2017]

34. __________, ‘Why did Strings Enter the Story’, The Official String Theory Web Site, <www.superstringtheory.com/basics/basic3.html> [accessed 8 September 2017]

35. Siegel, Ethan, ‘What Are Quantum Gravity’s Alterna7ves To String Theory?’, Forbes, <hCps://www.forbes.com/sites/startswithabang/2015/12/17/what-are-quantum-gravitys-alterna7ves-to-string-theory/#33226b917b1b> [accessed 29 October 2017]

36. Slagter, Reinoud Jan, ‘Evidence of Cosmic Strings by the Observa7on of the Alignment of Quasar Polariza7on Axes on Mpc Scale’, Cornell University Library, <hCps://arxiv.org/pdf/1609.05068.pdf> [accessed December 12 2017]

37. Strassler, MaC, ‘Supersymmetry – What Is It?’, Of Par7cular Significance. Conversa7ons About Science with Theore7cal Physicist MaC Strassler, <hCps://profmaCstrassler.com/ar7cles-and-posts/some-specula7ve-theore7cal-ideas-for-the-lhc/supersymmetry/supersymmetry-what-is-it/> [accessed 14 October 2017]

38. Toth, Viktor T., ‘The Parameters of the Standard Model’, Spinor.info, <hCps://spinor.info/weblog/?p=6355> [accessed 23 September 2017]

39. Woit, Peter, ‘KKLT Smackdown’, Not Even Wrong, <www.math.columbia.edu/~woit/wordpress/?p=11> [accessed November 1 2017]

40. __________, Not Even Wrong: The Failure of String Theory and the Con<nuing Challenge to Unify the Laws of Physics (Sydney: Jonathan Cape, 2006)

41. Woodard, R.P., ‘How Far Are We from the Quantum Theory of Gravity’, Cornell University Library, < hCps://arxiv.org/pdf/0907.4238v1.pdf> [accessed 12 December 2017]

42. Zimmerman Jones, Andrew, ‘Can String Theory Be Tested’, PBS, <www.pbs.org/wgbh/nova/blogs/physics/2012/09/can-string-theory-be-tested/> [accessed 29 October 2017]