How does quantum mechanics define time

[Chemist@]

How does quantum mechanics define time if there is any definition, or quantum gravity has to be explained first?

 

[naturale]

How does quantum mechanics define time if there is any definition, or quantum gravity has to be explained first?

Quantum mechanics say that every particle is a clock. Its space-time ticks are given by the energy and momentum T=h/E and \lambda = h / p. This set time in physics, as discussed in How a particle tells time (Holger Mueller et al in *Science*) and

On the intrinsically cyclic nature of space-time in elementary particles
http://arxiv.org/pdf/1206.1140.pdf

Example: In relativity the rest energy is the mass E= m c^2. Light has zero mass so the ticks of photons are infinitely long. Light has not time.

These clocks define time in quantum mechanics.

Einstein says that interaction is modulation of clocks. He derived general relativity in this way. Quantum gravity should be explained from these aspects of quantum mechanics and general relativity.

 

[Naty1]

Carlo Rovelli has this to say about that:

http://arxiv.org/abs/gr-qc/0604045
Unfinished revolution

Roughly speaking, we learn from GR that spacetime is a dynamical field and we learn from QM that all dynamical field are quantized. A quantum field has a granular structure, and a probabilistic dynamics, that allows quantum superposition of different states. Therefore at small scales we might expect a “quantum spacetime” formed by “quanta of space” evolving probabilistically, and allowing “quantum superposition of spaces”. The problem of quantum gravity is to give a precise mathematical and physical meaning to this vague notion of “quantum spacetime”.

and

http://arxiv.org/abs/0903.3832
"Forget time"
Authors: Carlo Rovelli...
(Submitted on 23 Mar 2009 (v1), last revised 27 Mar 2009 (this version, v3))

Abstract: Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must "forget time", and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.

[Nobody has figured out how the dynamical spacetime of GR can be incorporated in the Standard Model...quantum gravity theoryies are attempting to reconcile these differences.]

from one of those papers:

The present knowledge of the elementary dynamical laws of physics is given by the application of QM to fields, (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: …..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…

 

[Chemist@]

Thanks, I will examine this.

 

[bohm2]

How does quantum mechanics define time if there is any definition, or quantum gravity has to be explained first?

There was recent article in FQXi Blogs discussing this dichotomy based on some works by Andreas Albrecht. Some interesting quotes relevant to this thread:

Albrecht constructed a simple model to look at how two basic quantum systems interact with each other. It seemed like a simple enough project with nothing too surprising at first, but he immediately ran into a problem when he introduced time into the mix. According to quantum mechanics, time is an external absolute entity that marches to the same beat for everything. Einstein’s classical theory of gravity, general relativity, takes a different view, however. Relativity states that time is not absolute but instead a subjective entity. Observers in different gravitational fields, or in motion relative to each other, for instance, will experience time flowing at different rates... To assert the passage of time in his simple system and construct an evolving story of what happens, Albrecht realized, one must choose a clock. However, that’s easier said than done in an isolated quantum system or for that matter, in the early universe—after all, there are no handy wristwatches floating through space and no daily journey of the sun across the sky to look out for...In the absence of an external clock, Albrecht decided to use the "internal time" concept of general relativity and define time relative to his quantum components...It was entirely up to him to set up these correlations in his simple computer model. Depending on his choice of correlations, he could hypothesise different clocks and radically change the physical behaviour that the quantum system would then follow, all without changing the overall wavefunction...If you choose to measure time using one type of clock in the early universe, the history of the cosmos would pan out very differently, than if you chose another. In other words, when considered at the quantum level, different clocks led to arbitrarily different physical laws.

The Accidental Universe
http://www.fqxi.org/community/articles/display/177

His Perimeter presentation can be found here:

Abstract: The “clock ambiguity” is a general feature of standard formulations of quantum gravity, as well as a much wider class of theoretical frameworks. The clock ambiguity completely undermines any attempt at uniquely specifying laws of physics at the fundamental level. In this talk I explain in simple terms how the clock ambiguity arises. I then present a number of concrete results which suggest that a statistical approach to physical laws could allow sharp predictions to emerge despite the clock ambiguity. Along the way, I get to ask some interesting questions about what we expect of fundamental laws of physics, and give some surprising answers.

The Clock Ambiguity and the Emergence of Physical Laws
http://streamer.perimeterinstitute.ca/mediasite/viewer/NoPopupRedirector.aspx?peid=1a12ed6d-3993-49f7-a9ce-0dd154f38e84&shouldResize=False

 

[Fredrik]

Quantum mechanics doesn't say anything about time. Galilean spacetime and Minkowski spacetime define mathematical frameworks in which both classical and quantum theories of matter can be defined. Time is described by spacetime, not by a theory of matter, at least not by any of these theories of matter.

I think even the GR spacetimes define such frameworks. The problem is just that if we first find a spacetime that satisfies Einstein's equation, and then write down a theory of matter in that spacetime, we are completely ignoring the main lesson of GR, which is that matter should affect spacetime.