Why it is so difficult to quantize spacetime?

[RedShiftam]

Can somebody share an a articles or something related with this topic. I want to understand well the main problem (the root and the details) and why it is so difficult. I've come across many videos and news that give you some kind of metaphorical picture (made for the public), which in some cases is quite misleading. I don't need the approaches (string theory, loop quantum gravity), i need just the problem!

Thank you for your time!

Edited February 3, 2019 by RedShiftam

[studiot]

1 hour ago, RedShiftam said:

Why it is so difficult to quantize spacetime?

 

i need just the problem!

 

The problem is that there is no evidence that Spacetime needs to be quantised.

The quantisation of energy comes quite naturally out of the equations.
That is at least some of solutions to the equations of energy are periodic or quantised.

The equations of Spactime, and in particular Einstein's equations are not, and do not have quantised solutions.
Rather they require a continuous distribution.

[Itoero]

4 hours ago, RedShiftam said:

Can somebody share an a articles or something related with this topic. I want to understand well the main problem (the root and the details) and why it is so difficult. I've come across many videos and news that give you some kind of metaphorical picture (made for the public), which in some cases is quite misleading. I don't need the approaches (string theory, loop quantum gravity), i need just the problem!

Thank you for your time!

This is my oversimplified view/explanation. Spacetime is basically the medium in which quantizable observations do there thing. Spacetime implies a coordinate system to which we attach observations and try to understand/make sense of reality. I  think a quantum gravity model needs to be 'proven' and find its way in the world of  science/technology in order to quantize spacetime.

[Strange]

15 minutes ago, Itoero said:

This is my oversimplified view/explanation. Spacetime is basically the medium in which quantizable observations do there thing. Spacetime implies a coordinate system to which we attach observations and try to understand/make sense of reality. I  think a quantum gravity model needs to be 'proven' and find its way in the world of  science/technology in order to quantize spacetime.

To do that requires creating a quantum theory of gravity (that can be tested). That is the hard part. The question was: why is that hard.

[Itoero]

59 minutes ago, Strange said:

To do that requires creating a quantum theory of gravity (that can be tested). That is the hard part. The question was: why is that hard.

It's hard because only our  logic/intuition tells us it's there, it's a mental construct. 

Gravity is also hard to quantize but that interacts with for example photons so logic dictates there is something physical about gravity.

[Mordred]

The problem in gravity becoming an effective field theory in the quantum regime such as QFT is largely due to the detail that gravity isn't renomalizable. This is a technique that utilizes IR and UV cut-offs to handle infinities. In order to do this one must have invariant quantities that work at thee extremely small and the extremely large scales. In the case of QED etc, these are typically handled by finite quantities of the bosons ie a photon for example. This will correspond to the loop diagrams of the internal and external legs of a Feymann diagram. Now in the other three fields we have effective gauge bosons with an effective coupling constant that provides effective IR and UV cutoffs. However in the case of gravity this would theoretically be the graviton, however gravity is far too weak at the particle scale to quantize the graviton. This prevents us from developing an effective loop integral for number of vertexes etc on Feymann diagrams.

Now one might think this is a huge problem, however our current theories of gravity work just fine at larger scales than the quantum regime and it is simply the quantum regime that gravity becomes an issue ie quantizing a theoretical graviton. (which will be used to prevent infinities) at the upper and lower energy scales. IR being infrared, UV being ultraviolet divergences. In essence it boils down to having effective cut-offs where the same number of parameters work at both scale spectrums. At the Planck mass scale for gravity the number of parameters to absorb the infinity quantities becomes infinite itself in essence (as this is hard to describe without getting too in depth on the mathematical details)

That being said there are other techniques to avoid infinities arising in spacetime, in LQC for example they use Wicks rotation under gauge group to prevent singular conditions. Wicks rotation takes a waveform and uses an inverted mirror image to apply an effective finite portion (where the two waveforms intersect) So in LQC they have no singularity conditions due to infinite quantities by this methodology.

Another proposed technique is one being approached under F(r) gravity which uses a Wilsonian renormalization group. Here is a PDF on this.

http://inspirehep.net/record/1317764/files/Thesis_2010_Machado.pdf

If you read the introductory it will highlight much of what I described in this post. String theory utilizes strings in which the open and closed strings are both finite quantities and have effective cut-offs ( Neumann and Dirichlet boundary conditions) for each string type.

https://math.berkeley.edu/~kwray/papers/string_theory.pdf

Once again the introductory will discuss the renormalization problem.

This is the simplest introductory into renormalization I was able to find hope it helps

https://www.ate.uni-duisburg-essen.de/data/postgraduate_lecture/AJP_2011_Olness.pdf

Edited February 3, 2019 by Mordred

[RedShiftam]

Thanks a lot man!

[Mordred]

Your welcome if anything it will give you the proper direction of research into the issue

[Schmelzer]

On 2/3/2019 at 4:20 PM, RedShiftam said:

Can somebody share an a articles or something related with this topic. I want to understand well the main problem (the root and the details) and why it is so difficult.

The first problem: Quantum theory is incompatible with fundamental relativistic symmetry.  

In quantum theory, you have a configuration q of the system you consider, and the main object is the wave function \(\psi(q)\).  It changes in absolute time \(\psi(q,t)\). The configuration is something global.  For N particles, it consists of the 3N coordinates of these particles. So, this gives a wave function \(\psi(x_1,y_1,z_1, ...,x_N, y_N, z_N, t)\)  There is no natural way to define a Lorentz transformation.  (For special-relativistic field theory, there have been found ways to circumvent this, but an essential part of this is the decision simply not to talk about everything which does not follow relativistic symmetry.  All the conceptual problems, especially those related with the violation of the Bell inequalities, remain problematic in this theory too, but one simply does not argue about it, creating (surprisingly quite successful) that there are no problems with this. 

In GR, this becomes much worse. One cannot really write down a reasonable quantum theory without specifying some time coordinate. In the naive hope, one would like to be able to show that this can be done in a way that does not depend on the choice of the time coordinate.  This fails, and the resulting problem is named "problem of time in QG".

The second problem is that GR is not renormalizable.  This was thought, initially, as being fatal, but today we know that it is not a big problem at all, if one accepts that it is an effective field theory, that means, a theory which is only a large distance approximation of some yet unknown different theory.  Unfortunately, for those who like the spacetime interpretation, this is hard to accept.  To replace GR below some critical distance (say, Planck length) by some different theory without any infinities (this is called regularization) leads to theories which violate relativistic symmetry.  Of course, it would be quite natural to assume that a more fundamental theory has a different symmetry than its large distance approximation.  But for most proponents of fundamental relativity this is simply unacceptable.