How Are General Relativity and Quantum Mechanics Connected?

[San K]

I am new to this area, so pardon me if the below question might seem...

1. What area/subject/sub-topic of physics deals with attempts at bridging GR and QM?

2. What does it say? in layman language

3. What is a quantum field?

4. is there any area of QM where some credible mathematical treatment is used and that arrives at accurate results by "ignoring" time-space?

 

[DennisN]

Hi, San K!

1. E.g. Loop Quantum Gravity (LQG). It's an ongoing work, i.e. attempts.
2. See Wiki: Loop Quantum Gravity. For layman terms, I leave it to other PF members to describe it, as I am definitely a layman in this respect. By the way, LQG often appears as a topic in the subforum Beyond The Standard Model.
3. I pass that question, and hope people who are more aquainted with Quantum Field Theory than me to reply to this .
4. Of course. You don't need to consider space-time in e.g. the double-slit experiment.

EDIT: Concerning LQG, maybe you'll find something in this thread.

 

[Naty1]

Here are some 'survey' sort of comments:

Loop Quantum Gravity
Carlo Rovelli
http://relativity.livingreviews.org/Articles/lrr-2008-5/

The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications.
Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein–Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context.
The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

The paper has some rather advanced mathematics but in the conclusions at page 45 Rovelli notes:

...A key physical result is given by the explicit computation of the eigenvalues of area and volume (see Equation (33)). This result is at the basis of the physical picture of a discrete spacetime.

The theory has numerous physical applications, including quantum cosmology, black hole physics and others....

In my view, loop quantum gravity is the best we can do so far in trying to understand quantum spacetime, from a nonperturbative, background-independent point of view. Theoretically, we have reasons to suspect that this approach could represent a consistent quantum theory with the correct classical limit. The theory yields a definite physical picture of quantum spacetime and definite quantitative predictions, but a systematic way of extracting physical information is still lacking.

Experimentally, there is no support for the theory, neither direct nor indirect. The spectra of area and volume computed within the theory could, or could not, be physically correct. I hope we may find a way to know in the not too distant future.

You should note other theorists have concluded there is no distinction between discrete [quantum] and continuous spacetime...

 

[Naty1]

Here is another set of overview comments from Rovelli:

Unfinished revolution
Introductive chapter of a book on Quantum Gravity, edited by Daniele Oriti,
to appear with Cambridge University Press
Carlo Rovelli
Centre de Physique Th´eorique de Luminy_, case 907, F-13288 Marseille, EU
February 3, 2008

...At the beginning of the XX century, General Relativity (GR) and Quantum Mechanics (QM) once again began reshaping our basic understanding of space and time and, respectively, matter, energy and causality —arguably to a no lesser extent. But we have not been able to combine these new insights into a novel coherent synthesis, yet. The XX century scientific revolution opened by GR and QM is therefore still wide open. We are in the middle of an unfinished scientific revolution. Quantum Gravity is the tentative name we give to the “synthesis to be found”.
In fact, our present understanding of the physical world at the fundamental level is in a state of great confusion. The present knowledge of the elementary dynamical laws of physics is given by the application of QM to fields, namely quantum field theory (QFT), by the particle–physics Standard Model (SM), and by GR. This set of fundamental theories has obtained an empirical success nearly unique in the history of science: so far there isn’t any clear evidence of observed phenomena that clearly escape or contradict this set of theories —or a minor modification of the same, such as a neutrino mass or a cosmological constant.1 But, the theories in this set are based on badly self contradictory assumptions. In GR the gravitational field is assumed to be a classical deterministic dynamical field, identified with the (pseudo) Riemannian metric of spacetime: but with QM we have understood that all dynamical fields have quantum properties. The other way around, conventional QFT relies heavily on global Poincar´e invariance and on the existence of a non–dynamical background spacetime metric: but with GR we have understood that there is no such non–dynamical background spacetime metric in nature.
In spite of their empirical success, GR and QM offer a schizophrenic and confused understanding of the physical world. The conceptual foundations of classical GR are contradicted by QM and the _conceptual foundation of conventional QFT are contradicted by GR. Fundamental physics is today in a peculiar phase of deep conceptual confusion.edit: I saved the following from
Quantum Gravity, Rovelli

http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.1780v2.pdf (6/2010)

because I liked the overview description of the QM/GR 'issues':

"GR was formulated in terms of Riemannian geometry assuming the metric is a smooth and deterministic dynamical field; QM requires any dynamical field to be quantized and at all scales manifests itself as discrete quanta and is governed by probabilistic laws. GR has modified the notions of space and time; QM the notions of causality, matter and measurements. These do not fit together easily and a new coherent picture is not yet available.

At small scales there should be quanta of space and quanta of time and quantum superposition of space, but what does this mean? GR has modified the notions of space and time; QM the notions of causality, matter and measurements. The novel modified notions do not fit easily together. A new coherent picture is not yet available.

Our present knowledge of the basic structure of the physical universe is summarized by GR, quantum theory and quantum field theory and the particle physics standard model. This set of fundamental theories is inconsistent..."

 

[San K]

Thanks DennisN and Naty1. Lot of good information.

Hi, San K!
4. Of course. You don't need to consider space-time in e.g. the double-slit experiment.

Both the paths have to be same length-time for interference to happen.
A slight difference in length-time will lead to change/shift in interference pattern.

Even the placing/removal of obstacles (in any of the paths) requires consideration of space-time.

Thus space-time need to be considered for this aspect.

Also - does not the evolution of the Schrödinger wave equation depend upon space-time?

In which aspect/facet of the double-slit experiment - do we need not consider time-space?

Are you referring to entangled photons?

 

[Maui]

Both the paths have to be same length-time for interference to happen.
A slight difference in length-time will lead to change/shift in interference pattern.

I am not sure about that - the interference pattern is built up by the accumulation of multiple successive single detection events. At first sight, it looks like the length of the flight path should be irrelevant.

 

[San K]

I am not sure about that - the interference pattern is built up by the accumulation of multiple successive single detection events. At first sight, it looks like the length of the flight path should be irrelevant.

for example in a mach zehnder interferometer the path length-time has to be same for interference to happen.

there would be no interference if the paths were not same length-time

http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer

 

[DennisN]

Both the paths have to be same length-time for interference to happen.
A slight difference in length-time will lead to change/shift in interference pattern.

Even the placing/removal of obstacles (in any of the paths) requires consideration of space-time.

Thus space-time need to be considered for this aspect.

Also - does not the evolution of the Schrödinger wave equation depend upon space-time?

In which aspect/facet of the double-slit experiment - do we need not consider time-space?

Are you referring to entangled photons?

Well, you asked about general relativity in question 1 and talked about spacetime in question 4, so I assumed you meant spacetime in the context of general relativity. General relativity is a theory of gravitation, where gravitation is understood as a geometric curvature of spacetime.

4. is there any area of QM where some credible mathematical treatment is used and that arrives at accurate results by "ignoring" time-space?

So, yes. The Einstein field equations are not needed in e.g. double-slit experiments etc. There is no experimentally validated bridge between QM and GR at the moment. It's research in progress. That's why e.g. Loop Quantum Gravity appears in the subforum Beyond the Standard Model.

 

[San K]

So, yes. The Einstein field equations are not needed in e.g. double-slit experiments etc.

interesting. thanks again DennisN...:)

there is a lot of reading, and thinking, to be done.

btw - what effect does curvature of space-time have on single particle (double-slit or any other) interference?_________________________________________________
Because we are live, and are trapped, in space-time
We might be psychologically biased towards the primacy of Space-Time

 

[Maui]

for example in a mach zehnder interferometer the path length-time has to be same for interference to happen.

there would be no interference if the paths were not same length-time

http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer

Here i am providing the context so that the point i made is more clear:

Hi, San K!
4. Of course. You don't need to consider space-time in e.g. the double-slit experiment.

Both the paths have to be same length-time for interference to happen.
A slight difference in length-time will lead to change/shift in interference pattern.

Whenever you lengthen one of the paths, you are effectively marking it, making the which-path information knowable(both paths must be indistinguishable). It's no surprize you aren't seeing interference pattern. But this doesn't prove that prior to obtaining single measurement results, space and time have the usual form. "What we cannot speak about, we must pass over in silence." L.Wittgenstein