A heavy question about gravity.

[TalonD]

gravity is geometry, curved space time. yes? or so I've read here somewhere. But there is a graviton particle also? So is gravity simply geometry? or is it an energy with a wave particle duality? like a quantum of electromagnetic energy? If there is a graviton then does that mean that space and time itself has a quantum nature, a wave particle duality? is there a quantum of spatial dimension? is there a quantum of time?

 

[marcus]

gravity is geometry, curved space time. yes? or so I've read here somewhere. But there is a graviton particle also? So is gravity simply geometry? or is it an energy with a wave particle duality? like a quantum of electromagnetic energy? If there is a graviton then does that mean that space and time itself has a quantum nature, a wave particle duality? is there a quantum of spatial dimension? is there a quantum of time?

The graviton is a mathematical construct that works well where you assume a flat background geometry and allow small perturbations.
The approaches to QG that I watch closely do not involve gravitons in the general setup.
LQG only introduces gravitons where they are trying to reproduce classic flat-geometry results.
Rovelli, Speziale and others have a bunch of papers about the LQG graviton propagator, n-point functions etc.

In curved space the idea of a particle is problematical---the existence, the number of particles, can depend on the observer, how the system is bounded etc. In curved geometry particles become more a matter of convention, and an excellent, indispensable approximation. Rovelli has a paper about this with a title something like "What is a particle?"

So is gravity simply geometry? ...does that mean that space and time itself has a quantum nature...? is there a quantum of spatial dimension? is there a quantum of time?

Gravity is geometry all right, but it's not all that simple The gravitational field takes care of a lot more than simple Newton gravity. It's what determines what the angles of any given triangle add up to. It determines the relation of linear size to area, and how area relates to volume, for any given figure at any given place on any given day. The gravitational field is geometry.

And moreover it is quantum geometry.

Notice that when something is quantum it doesn't mean that it is divided up into little "quanta". That happens sometimes with some things, but it is not the important thing. What is important is that measurements are quantized. The operation of measuring becomes an operator on the hilbertspace of states. A measurement operator can have a discrete spectrum of values without our having to suppose that what is being measured is itself grainy. There doesn't need to be a little grain of time or a little bitty atom of space.
That could be the wrong way to picture what quantum geometry means.

It means something about the operators representing measurement. (Are you used to the idea of a diagonalizable matrix, a vectorspace with inner product? I don't know how much technical language to use.)

Anyway, quantum geometry is what you really mean when you say "quantized spacetime".
And quantum geometry doesn't mean that space and time are divided into little bits.
The answer to your question

is there a quantum of spatial dimension?

is no.

Not if you mean it naively, like is dimensionality broken up into little bits of dimensionality.

What is true about dimensionality, in the QG context, is that the act of measuring the dimensionality of space at some given place on some given day at some given scale of measurement is a quantum operator---an observable.

Since geometry is dynamic, what you get for an answer can have uncertainty and can change and can even depend on the scale at which you are probing space.

If you want to know more about dimensionality as an observable, check out the Loll SciAm article in my sig.

 

[Pjpic]

gravity is geometry, curved space time. yes? or so I've read here somewhere. But there is a graviton particle also?


I wonder if this has something to do with the mutually exclusive nature of the relationship between quantum mechanics and relativity, that they often speak of. Maybe in one system it is a particle and in the other it's a curve (but I don't really know).

 

[johan01]

Notice that when something is quantum it doesn't mean that it is divided up into little "quanta". That happens sometimes with some things, but it is not the important thing. What is important is that measurements are quantized. The operation of measuring becomes an operator on the hilbertspace of states.

marcus
your statement above has suprised me in my thinking of quantum geometry.

are you saying that the quantum levels of a closed system ,
lets say a simple hydrogen atom , are not fixed.

if one observer measures them , the closed states will be X
if another observer measures them using a different tool he will get Y and a different
"hilbertspace of states"

 

[johan01]

Notice that when something is quantum it doesn't mean that it is divided up into little "quanta". That happens sometimes with some things, but it is not the important thing. What is important is that measurements are quantized. The operation of measuring becomes an operator on the hilbertspace of states.

marcus
your statement above has suprised me in my thinking of quantum geometry.

are you saying that the quantum levels of a closed system ,
lets say a simple hydrogen atom , are not fixed.

if one observer measures them , the closed states will be X
if another observer measures them using a different tool he will get Y and a different
"hilbertspace of states"

 

[my_wan]

marcus
your statement above has suprised me in my thinking of quantum geometry.

I'm not going to pretend my interpretation nessisarily represents marcus's, but I found his answer very satisfactory. I'll give my perspective.

are you saying that the quantum levels of a closed system ,
lets say a simple hydrogen atom , are not fixed.

No. This question has some implicit assumptions to articulate. First you speak about an enclosed system. If you observe this system then by definition the enclosed system must include you, as well as how that system relates to you. Fundamentally it is physically pointless to define something that does not interact with the observable universe in any way, irrespective of reality in an absolute sense. In any self referential system there are always parameters that are unmeasurable, complete self-measurement is impossible. Try to get around that is like asking why a meter is exactly one meter. So when you speak of "fixed" quantum levels there is an implicit assumption that "fixed" is absolute. Yet all we can really say is that it is "fixed" with respect to the observer, which is part and parcel to the enclosed system being observed. Yes I am aware that QM separates the measuring device from the system being measured, without actually defining where that separation occurs.

if one observer measures them , the closed states will be X
if another observer measures them using a different tool he will get Y and a different
"hilbertspace of states"

Yes and no. There is a reason for proper mass and such to be defined the way they are. We must restrict the relationship between measuring device and system for proper mass to have meaning. Electric and magnetic forces were once thought to be separate phenomena for the same reason. If we definitionally restrict the relationship between the observer and system then the answer is no. If we generalize for any observer, yes, the Hilbert space of states can appear quiet different (transformed). Electromagnetic fields and the perihelion of Mercery are classic examples. How this might ultimately play out at the quantum level of description and QG remains an open question.

 

[johan01]

https://www.youtube.com/watch?v=No. This question has some implicit assumptions to articulate. First you speak about an enclosed system. If you observe this system then by definition the enclosed system must include you, as well as how that system relates to you. Fundamentally it is physically pointless to define something that does not interact with the observable universe in any way, irrespective of reality in an absolute sense. In any self referential system there are always parameters that are unmeasurable, complete self-measurement is impossible. Try to get around that is like asking why a meter is exactly one meter. So when you speak of "fixed" quantum levels there is an implicit assumption that "fixed" is absolute. Yet all we can really say is that it is "fixed" with respect to the observer, which is part and parcel to the enclosed system being observed. Yes I am aware that QM separates the measuring device from the system being measured, without actually defining where that separation occurs.

this i understand and is well explained by you.


https://www.youtube.com/watch?v=Yes and no. There is a reason for proper mass and such to be defined the way they are. We must restrict the relationship between measuring device and system for proper mass to have meaning. Electric and magnetic forces were once thought to be separate phenomena for the same reason. If we definitionally restrict the relationship between the observer and system then the answer is no. If we generalize for any observer, yes, the Hilbert space of states can appear quiet different (transformed). Electromagnetic fields and the perihelion of Mercery are classic examples. How this might ultimately play out at the quantum level of description and QG remains an open question.


this is still a little open ended

fundamentally , a closed system . Must it include a measurment/observation OR NOT, to be included in its set of equations to describe it completely.

If yes then the notion of proper rest mass , without any external influence , is meaningless, like nothingless , as i imagine it.

If no , well then it exists with proper rest mass , without us knowing , its there but

 

[johan01]

apologies , don't know what happened there, let's try again

No. This question has some implicit assumptions to articulate. First you speak about an enclosed system. If you observe this system then by definition the enclosed system must include you, as well as how that system relates to you. Fundamentally it is physically pointless to define something that does not interact with the observable universe in any way, irrespective of reality in an absolute sense. In any self referential system there are always parameters that are unmeasurable, complete self-measurement is impossible. Try to get around that is like asking why a meter is exactly one meter. So when you speak of "fixed" quantum levels there is an implicit assumption that "fixed" is absolute. Yet all we can really say is that it is "fixed" with respect to the observer, which is part and parcel to the enclosed system being observed. Yes I am aware that QM separates the measuring device from the system being measured, without actually defining where that separation occurs.


this(above) i understand


Yes and no. There is a reason for proper mass and such to be defined the way they are. We must restrict the relationship between measuring device and system for proper mass to have meaning. Electric and magnetic forces were once thought to be separate phenomena for the same reason. If we definitionally restrict the relationship between the observer and system then the answer is no. If we generalize for any observer, yes, the Hilbert space of states can appear quiet different (transformed). Electromagnetic fields and the perihelion of Mercery are classic examples. How this might ultimately play out at the quantum level of description and QG remains an open question.


this(above) is still a little open ended

fundamentally , in a closed system .
Must it include a measurment/observation OR NOT, to be included in its set of equations to describe it completely.

If yes then the notion of proper rest mass , without any external influence , is meaningless, like nothingless , as i imagine it.

If no , well then it exists with proper rest mass , without us knowing , its there but we do not experience it.


which is it to be?? then we can debate the theory to formulate our postulate.

 

[marcus]

are you saying that the quantum levels of a closed system ,
lets say a simple hydrogen atom , are not fixed.

no, that is not what I am saying